Ildar R Gabitov

Interests

Teaching

Complex variables, PDEs and ODEs, Mathematical modeling, Applied mathematics, dynamical systems, nonlinear waves.

Research

Mathematical and theoretical physics, nonlinear optics, nonlinear waves and their applications, theory of integrability, nonlinear PDEs, optical fiber communications, nonlinear waves, multiscale phenomena and nanomaterials, nanophotonics and nanoplasmonics.

Courses

Scholarly Contributions

Chapters

• Gabitov, I. R., & Turitsyn, S. K. (1996). Breathing Soliton in Cascaded Transmission System with Passive Dispersion Compensation. In Physics and Applications of Optical Solitons in Fibres ’95. Solid-State Science and Technology Library, vol 3. Springer, Dordrecht.. Springer, Dordrecht. doi:10.1007/978-94-009-1736-1_27
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  A theory of optical pulse propagation in cascaded transmission systems which are based on dispersion-compensating fiber technique is developed. The existence of two scales associated with fiber dispersion and system residual dispersion leads to a simple model for the averaged pulse dynamics. In the particular case of practical importance, the averaged pulse dynamics is governed by the nonlinear Schrodinger equation. The pulse transmission stability is examined.

Journals/Publications

• Gabitov, I. R., Drachev, V., Levchenko, S., & Pogodaeva, M. (2021). Dielectric function of six elemental metals Pogodaeva, Maria K ; Levchenko, Sergey V ; Drachev, Vladimir P ; Gabitov, Ildar R. Journal of physics. Conference series, Vol.1890(1), p.12008.
• Gabitov, I. R., Drachev, V. P., Levchenko, S. V., & Pogodaeva, M. K. (2021). Dielectric function of six elemental metals. Journal of physics. doi:10.1088/1742-6596/1890/1/012008
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021). Pulse interactions in weakly nonlinear coherent optical communication links. Journal of physics. Conference series, Vol.1890 ,(1), p.12006.
• Gabitov, I. R., Onishchenko, D. A., Grekhov, L., & Zhao, J. (2021). Methods for calculating fuel heating in electrically controlled injectors of Common Rail diesel systems. Fuel. doi:10.1016/j.fuel.2021.121526
• Gabitov, I. R., Abdulagatov, I. M., Gumerov, F. M., Minkin, V. I., Sal’manov, R. S., Alyaev, V., Fomina, M., Khairutdinov, V. F., & Sagdeev, D. I. (2020). New Design of the Falling-Body Rheoviscometer for High and Extra-High Viscous Liquid Measurements. Viscosity of Vacuum Oils. Journal of Chemical & Engineering Data. doi:10.1021/acs.jced.9b01071
• Biondini, G., Biondini, G., Kovacic, G., Kovacic, G., Li, S., & Li, S. (2019). Inverse scattering transform for two-level systems with nonzero background. Journal of Mathematical Physics, 60(073510), 49. doi:doi.org/10.1063/1.5084720
• Gabitov, I., Biondini, G., Kovačič, G., & Li, S. (2019). Inverse scattering transform for two-level systems with nonzero background. Journal of Mathematical Physics, 60(7), 073510. doi:10.1063/1.5084720
• , A. O., , K. E., , G. K., , V. R., , A. I., , I. R., & , .. (2018). Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index.
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  We study numerically the propagation of two-color light pulses through ametamaterial doped with active atoms such that the carrier frequencies of thepulses are in resonance with two atomic transitions in the $\Lambda$configuration and that one color propagates in the regime of positiverefraction and the other in the regime of negative refraction. In such ametamaterial, one resonant color of light propagates with positive and theother with negative group velocity. We investigate nonlinear interaction ofthese forward- and backward-propagating waves, and find self-trapped waves,counter-propagating radiation waves, and hot spots of medium excitation.[Journal_ref: ]
• , E. P., , P. R., , G. K., & , I. R. (2018). Stochastic Pulse Switching in a Degenerate Resonant Optical Medium.
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  Using the idealized integrable Maxwell-Bloch model, we describe randomoptical-pulse polarization switching along an active optical medium in theLambda-configuration with disordered occupation numbers of its lower energysub-level pair. The description combines complete integrability and stochasticdynamics. For the single-soliton pulse, we derive the statistics of theelectric-field polarization ellipse at a given point along the medium in closedform. If the average initial population difference of the two lower sub-levelsvanishes, we show that the pulse polarization will switch intermittentlybetween the two circular polarizations as it travels along the medium. If thisdifference does not vanish, the pulse will eventually forever remain in thecircular polarization determined by which sub-level is more occupied onaverage. We also derive the exact expressions for the statistics of thepolarization-switching dynamics, such as the probability distribution of thedistance between two consecutive switches and the percentage of the distancealong the medium the pulse spends in the elliptical polarization of a givenorientation in the case of vanishing average initial population difference. Wefind that the latter distribution is given in terms of the well-known arcsinelaw.[Journal_ref: ]
• , H. P., , M. E., & , I. G. (2018). On the stability of a space vehicle riding on an intense laser beam.
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  The Breakthrough Starshot Initiative is suggested to develop the concept ofpropelling a nano-scale spacecraft by the radiation pressure of an intenselaser beam. If such a nanocraft could be accelerated to 20 percent of lightspeed, it could reach the vicinity of our nearest potentially habitableexoplanet within our life time and capture its images and obtain otherscientific data. In this project the nanocraft is a gram-scale roboticspacecraft comprising two main parts: StarChip and Lightsail. To achieve the goal of the project it is necessary to solve a number ofoutstanding scientific problems. One of these tasks is to make sure that thenanocraft position and orientation inside the intense laser beam column isstable. The nanocraft driven by intense laser beam pressure acting on itsLightsail is sensitive to the torques and lateral forces reacting on thesurface of the sail. These forces influence the orientation and lateraldisplacement of the spacecraft, thus affecting its dynamics. If unstable thenanocraft might be expelled from the area of laser beam. In choosing the modelsfor nanocraft stability studies we are using several assumptions: 1.configuration of nanocraft is treated as rigid body (applicability of Eulerequations); 2. flat or concave shape of circular sail; 3. mirror reflection oflaser beam from surface of the Lightsail. We found conditions of positionstability for spherical and conical shape of the sail. The simplest stableconfigurations require the StarChip to be removed from the sail to make thedistance to the center of mass of nanocraft bigger than curvature radius of thesail. Stability criteria do not require the spinning of the nanocraft. A flatsail is never stable (even with spinning).[Journal_ref: ]
• , J. -., , I. G., & , A. I. (2018). Electrodynamics of a split-ring Josephson resonator in a microwave line.
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  We consider the coupling of an electromagnetic wave to a split-ring Josephsonoscillator or radio-frequency SQUID in the hysteretic regime. This device issimilar to an atomic system in that it has a number of steady states. We showthat one can switch between these with a suitable short external microwavepulse. The steady states can be characterized by their resonant lines which areof the Fano type. Using a static magnetic field, we can shift these spectrallines and lift their degeneracy.[Journal_ref: ]
• , J. -., , I. G., & , A. I. (2018). Polarization rotation by an rf-SQUID metasurface.
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  We study the transmission and reflection of a plane electromagnetic wavethrough a two dimensional array of rf-SQUIDs. The basic equations describingthe amplitudes of the magnetic field and current in the split-ring resonatorsare developed. These yield in the linear approximation the reflection andtransmission coefficients. The polarization of the reflected wave isindependent of the frequency of the incident wave and of its polarization; itis defined only by the orientation of the split-ring. The reflection andtransmission coefficients have a strong resonance that is determined by theparameters of the rf-SQUID; its strength depends essentially on the incidentangle.[Journal_ref: ]
• , Z. K., , I. G., & , A. M. (2018). The effect of phase mismatch on second harmonic generation in negative index materials.
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  Second harmonic generation in negative index metamaterials is considered.Theoretical analysis of the corresponding model demonstrated significantdifference of this phenomenon in conventional and negative index materials. Incontrast to conceptional materials there is nonzero critical phase mismatch.The behavior of interacting weaves is dramatically different when phasemismatch is smaller or greater than critical value.[Journal_ref: ]
• Kovavis, G., & Newhall, K. A. (2018). Polarization dynamics in a resonant optical medium with initial coherence between degenerate states,. Discrete Contin. Dyn. Syst. Ser. S, 5. doi:10.3934/dcdss.2020189
• Li, S., Biondini, G., & Kovacic, G. (2018). Resonant optical pulses on a continuous-wave background in two-level active media. EPL (Europhysics Letters), 121(2), 20001-p1 -- 20001-p7. doi:10.1209/0295-5075/121/20001
• Neskorenyuk, V., Lukashchuk, A., Chipouline, A., Malekizandi, M., Kueppers, F., & Ovchinnikov, G. (2018). Nonlinear Pulses in Dispersion-Managed Fiber-Optic Systems in Presence of High Losses. Journal of Physics: Conference Series, 1124(051011), 5. doi::10.1088/1742-6596/1124/5/051011
• Bhatta, H., Aliev, A., Gabitov, I. R., & Drachev, V. P. (2016). Magnetic Platform for UV Surface-Enhanced Resonance Raman and Fluorescence. 2016 INTERNATIONAL CONFERENCE LASER OPTICS (LO).
• Gabitov, I. R., & Negovora, A. V. (2016). Ensuring operability of fuel-delivery systems of diesels by individual adjustment of basic characteristics of fuel feed control. Russian Agricultural Sciences. doi:10.3103/s1068367416050062
• Mukhametkarimov, Y. S., Kudyshev, Z. A., Kissan, A., & Gabitov, I. R. (2016). Hyperbolic metamaterials based on graphene sheets with different values of chemical potentials. Physical Sciences and Technology, 3(2), 4-11. doi:10.26577/phst-2016-2-100
• Gabitov, I. R., & Maĭmistov, A. I. (2015). Anomalous refraction of an ultrashort light pulse at a nonlinear interface of dielectric media. Journal of Optical Technology, 82(11), 727-733.
• Gabitov, I. R., Caputo, J., & aimistov, A. (2015). Polarization rotation by an rf-SQUID metasurface. Phys. Rev. B,, 91(11), 115430.
• Gabitov, I. R., Maimistov, A. I., Kupaev, T., Kudyshev, Z. A., & Сaputo, J. (2015). Electromagnetic Field Scattering on rf-SQUID Based Metasurfaces. Epj Web of Conferences. doi:10.1051/epjconf/201510301004
• Gabitov, I. R., Turitsyn, S. K., Blow, K. J., Derevyanko, S. A., & Prilepsky, J. E. (2014). Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels. Physical Review Letters. doi:10.1103/physrevlett.113.013901
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  We scrutinize the concept of integrable nonlinear communication channels, resurrecting and extending the idea of eigenvalue communications in a novel context of nonsoliton coherent optical communications. Using the integrable nonlinear Schrödinger equation as a channel model, we introduce a new approach-the nonlinear inverse synthesis method-for digital signal processing based on encoding the information directly onto the nonlinear signal spectrum. The latter evolves trivially and linearly along the transmission line, thus, providing an effective eigenvalue division multiplexing with no nonlinear channel cross talk. The general approach is illustrated with a coherent optical orthogonal frequency division multiplexing transmission format. We show how the strategy based upon the inverse scattering transform method can be geared for the creation of new efficient coding and modulation standards for the nonlinear channel.
• Maimistov, A. I., Kazantseva, E. V., & Gabitov, I. R. (2014). The positive-negative index coupled waveguide systems: couplers, arrays and bundles. 2014 INTERNATIONAL CONFERENCE LASER OPTICS.
• Korotkevich, A. O., Rasmussen, K. E., Kovačič, G., Roytburd, V., Maimistov, A. I., & Gabitov, I. R. (2013). Optical pulse dynamics in active metamaterials with positive and negative refractive index. Journal of the Optical Society of America B: Optical Physics, 30(4), 1077-1084.
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  Abstract: We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the Λ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves and find selftrapped waves, counterpropagating radiation waves, and hot spots of medium excitation. © 2013 Optical Society of America.
• Kudyshev, Z. A., Gabitov, I. R., Maimistov, A. I., & Litchinitser, N. M. (2013). Second Harmonic Generation in Transition Metamaterials. 2013 CONFERENCE ON LASERS AND ELECTRO-OPTICS (CLEO).
• Kudyshev, Z. A., Gabitov, I. R., Maimistov, A. I., & Litchinitser, N. M. (2013). Second harmonic generation in transition metamaterials. CLEO: QELS_Fundamental Science, CLEO:QELS FS 2013, QM1A.3.
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  Abstract: We show that resonant field enhancement of obliquely incident light in a quadratically nonlinear metamaterial with refractive index gradually changing from positive to negative values enables efficient second harmonic generation at significantly reduced input intensities. © OSA 2013.
• Kudyshev, Z., Gabitov, I., & Maimistov, A. (2013). Effect of phase mismatch on second-harmonic generation in negative-index materials. Physical Review A - Atomic, Molecular, and Optical Physics, 87(6).
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  Abstract: Second-harmonic generation in negative-index metamaterials is considered. Theoretical analysis of the corresponding model demonstrates a significant difference of this phenomenon in conventional and negative-index materials. For example, and in contrast to conventional materials, there is nonzero critical phase mismatch. The behavior of interacting waves is dramatically different when phase mismatch is smaller or greater than a critical value. © 2013 American Physical Society.
• Newhall, K. A., Atkins, E. P., Kramer, P. R., Kovačič, G., & Gabitov, I. R. (2013). Random polarization dynamics in a resonant optical medium. Optics Letters, 38(6), 893-895.
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  PMID: 23503251;Abstract: Random optical-pulse polarization switching along an active optical medium in the Λ configuration with spatially disordered occupation numbers of its lower energy sublevel pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte Carlo numerical simulations. © 2013 Optical Society of America.
• Atkins, E. P., Kramer, P. R., Kovačič, G., & Gabitov, I. R. (2012). Stochastic pulse switching in a degenerate resonant optical medium. Physical Review A - Atomic, Molecular, and Optical Physics, 85(4).
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  Abstract: Using the idealized integrable Maxwell-Bloch model, we describe random optical-pulse polarization switching along an active optical medium in the Λ configuration with disordered occupation numbers of its lower-energy sublevel pair. The description combines complete integrability and stochastic dynamics. For the single-soliton pulse, we derive the statistics of the electric-field polarization ellipse at a given point along the medium in closed form. If the average initial population difference of the two lower sublevels vanishes, we show that the pulse polarization will switch intermittently between the two circular polarizations as it travels along the medium. If this difference does not vanish, the pulse will eventually forever remain in the circular polarization determined by which sublevel is more occupied on average. We also derive the exact expressions for the statistics of the polarization-switching dynamics, such as the probability distribution of the distance between two consecutive switches and the percentage of the distance along the medium the pulse spends in the elliptical polarization of a given orientation in the case of vanishing average initial population difference. We find that the latter distribution is given in terms of the well-known arc sine law. © 2012 American Physical Society.
• Gibson, E. A., Gabitov, I. R., Maimistov, A. I., & Litchinitser, N. M. (2011). Transition metamaterials with spatially separated zeros. Optics Letters, 36(18), 3624-3626.
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  PMID: 21931412;Abstract: We report analytical and numerical studies of the effect of the separation distance between zeros of dielectric permittivity and magnetic permeability on the phenomena of resonant absorption and anomalous field enhancement in transition metamaterials. Our studies indicate that these phenomena are robust and strongly polarization-dependent in the presence of the spatial shift between these points. These results are likely to be important for future fundamental and applied studies in the areas of transformation, polarization, and nonlinear optics in metamaterials. © 2011 Optical Society of America.
• Gibson, E. A., Pennybacker, M., Maimistov, A. I., Gabitov, I. R., & Litchinitser, N. M. (2011). Resonant absorption in transition metamaterials: Parametric study. Journal of Optics, 13(2).
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  Abstract: We perform a detailed study of the phenomenon of resonant absorption that occurs at an oblique incidence in the vicinity of the zero refractive index transition in graded index metamaterials with the refractive index changing from positive to negative values. We compare the results of numerical simulations with analytical predictions for the case of the linear gradient index profile. Furthermore, we numerically study the transition phenomena in graded index layers with more complex index profiles. A detailed understanding of the phenomenon of resonant absorption may be of considerable importance in the context of transformation optics as it strongly modifies the field distribution near the zero index transition. © 2011 IOP Publishing Ltd.
• Becker, W., Gabitov, I., Stepanov, M., Kois, J., Smidt, A., & Becker, B. E. (2010). Minimally invasive treatment for papillae deficiencies in the esthetic zone: A pilot study. Clinical Implant Dentistry and Related Research, 12(1), 1-8.
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  PMID: 19843105;Abstract: Background: The presence of papillary deficiencies adjacent to dental implants or teeth presents an esthetic concern for the dental team and patients. Purpose: The aim of this pilot project is to evaluate a new method for reducing or eliminating small papillary deficiencies. The use of a commercially available gel was evaluated as a possible method for enhancing deficient papillae. Materials and Methods: Eleven patients, seven females and four males, with an average age of 55.8 years (ranging from 25 to 75 years) with 14 treated sites are included in this pilot study. Patients had a minimum of one papillary deficiency in the esthetic zone. Prior to treatment photographs were either taken at a 1:1 ratio or converted to a 1:1 ratio using a commercially available program. A standardization photographic device was not used. After administration of a local anesthetic, a 23-gauge needle was used to inject less than 0.2 mL of a commercially available and Food and Drug Administration-approved gel of hyaluronic acid 2-3 mm apical to the coronal tip of the involved papillae. Patients were seen every three weeks and treatment was repeated up to three times. Patients were followed from 6 to 25 months after initial gel application. A computer program measured changes in pixels between initial and final treatments. A formula was derived to determine percentage change in the negative space between initial and final examinations. Results: Each site was individually evaluated. Three implant sites and one site adjacent to a tooth had 100% improvement between treatment examinations. Seven sites improved from 94 to 97%, three sites improved from 76 to 88%, and one site adjacent to an implant had 57% improvement. Conclusion: Results from this pilot study are encouraging and present evidence that small papillary deficiencies between implants and teeth can be enhanced by injection of a hyaluronic gel. Improvements were maintained for a range of 6 to 25 months. © 2009, Copyright the Authors. Journal Compilation © 2009, Wiley Periodicals, Inc.
• Elyutin, S. O., Maimistov, A. I., & Gabitov, I. R. (2010). On the third harmonic generation in a medium with negative pump wave refraction. Journal of Experimental and Theoretical Physics, 111(1), 157-169.
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  Abstract: The propagation of the pump and its third harmonic pulses in a cubically nonlinear medium is considered theoretically, provided that the linear properties of the medium are characterized by a negative refractive index at the pump frequency and a positive refractive index at the harmonic frequency. For low-intensity interacting waves, the pump and third harmonic pulses propagate in opposite directions, but sufficiently intense pulses can produce a simulton-a solitary two-frequency wave that propagates in a certain direction as a single whole. The system of equations is investigated numerically for a model that, apart from the harmonic generation, includes the second-order group velocity dispersion and the nonlinear self- and cross-phase modulations of the interacting waves. The separation of the pump and harmonic pulses due to the difference in the directions of their group velocities and peculiarities of the Manley-Rowe relation for parametric processes in metamedia are discussed. © 2010 Pleiades Publishing, Inc.
• Gabitov, I. R., Kennedy, B., & Maimistov, A. I. (2010). Coherent amplification of optical pulses in metamaterials. IEEE Journal on Selected Topics in Quantum Electronics, 16(2), 401-409.
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  Abstract: In this paper, we theoretically study propagation of steady-state ultrashort pulse in dissipative medium. We considered two cases: 1) medium consisting of lossy metallic nanostructures embedded into a gain material and 2) the gain material is embedded directly into the nanostructures. We found the shape and the velocity of an optical pulse coupled with the polarization wave. © 2006 IEEE.
• Gabitov, I. R., Maimistov, A. I., & Kennedy, B. (2010). Coherent Amplification of Optical Pulses in Metamaterials. IEEE Journal of Selected Topics in Quantum Electronics. doi:10.1109/jstqe.2009.2032667
• Gibson, T., Pennybacker, M., Mozjerin, I., Gabitov, I. R., Shalaev, V. M., & Litchinitser, N. M. (2010). Design optimization of transition metamaterials. Optics InfoBase Conference Papers.
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  Abstract: We report a detailed study of the effect of the graded index transition metamaterials design parameters on the resonant absorption of the obliquely incident electromagnetic wave in the vicinity of the zero index transition point(s). © 2010 Optical Society of America.
• Maimistov, A. I., & Gabitov, I. R. (2010). Nonlinear response of a thin metamaterial film containing Josephson junctions. Optics Communications, 283(8), 1633-1639.
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  Abstract: An interaction of electromagnetic field with metamaterial thin film containing split-ring resonators with Josephson junctions is considered. It is shown that dynamical self-inductance in a split-rings results in reduction of magnetic flux through a ring and this reduction is proportional to a time derivative of split-ring magnetization. Evolution of thin film magnetization taking into account dynamical self-inductance is studied. New mechanism for excitation of waves in one dimensional array of split-ring resonators with Josephson junctions is proposed. Nonlinear magnetic susceptibility of such thin films is obtained in the weak amplitude approximation. © 2009 Elsevier B.V. All rights reserved.
• Mozjerin, I., Gibson, E. A., Furlani, E. P., Gabitov, I. R., & Litchinitser, N. M. (2010). Electromagnetic enhancement in lossy optical transition metamaterials. Optics Letters, 35(19), 3240-3242.
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  PMID: 20890346;Abstract: We investigate the effect of anomalous field enhancement in metamaterials (MMs) where the effective refractive index gradually changes from positive to negative values, i.e., transition MMs. We demonstrate that considerable field enhancement can be achieved in lossy optical transition MMs that have electromagnetic material properties obtained from experimental data. The field enhancement factor is found to be polarization dependent and largely determined by the material parameters and the width of the transition layer. © 2010 Optical Society of America.
• Mozjerin, I., Gibson, T., Furlani, E. P., Gabitov, I. R., & Litchinitser, N. M. (2010). Electromagnetic Field Enhancement in Realistic Transition Metamaterials. 2010 CONFERENCE ON LASERS AND ELECTRO-OPTICS (CLEO) AND QUANTUM ELECTRONICS AND LASER SCIENCE CONFERENCE (QELS).
• Mozjerin, I., Gibson, T., Furlani, E. P., Gabitov, I. R., & Litchinitser, N. M. (2010). Electromagnetic field enhancement in realistic transition metamaterials. Optics InfoBase Conference Papers.
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  Abstract: We investigate the effect of anomalous field enhancement in lossy optical transition metamaterials and provide guidelines for optimizing the profile of the transition layer for maximum enhancement in these structures. © 2010 Optical Society of America.
• Gabitov, I. R., & Lushnikov, P. M. (2009). Symposium: Nonlinear waves and singularities in optics, hydrodynamics and plasmas. AIP Conference Proceedings, 1168, 1217-1218.
• Gabitov, I., Kennedy, B., Maimistov, A., & Roytburd, V. (2009). Near field amplification in metamaterials. AIP Conference Proceedings, 1168, 1224-.
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  Abstract: We presented comparative analysis of the far and near field amplification techniques for loss compensation in metamaterials using solitary pulse dynamics as an example. In both cases we found the spatial period of pulse oscillations, as well as the velocity and shape of these pulses. The analytic results were verified against the direct numerical simulations. © 2009 American Institute of Physics.
• Litchinitser, N. M., Gibson, T., Gabitov, I. R., Maimistov, A. I., & Shalaev, V. M. (2009). Inhomogeneous and guided-wave metamaterials: Linear and nonlinear optics. AIP Conference Proceedings, 1168, 1233-1234.
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  Abstract: Abstract: We discuss our recent results on linear and nonlinear phenomena taking place in inhomogeneous and guidedwave metamaterial structures with positive, negative and near-zero refractive index. We perform a detailed study of the effect of resonant field enhancement and absorption taking place near zero index transition point, new regimes of optical bistability, modulational instability, and gap solitons, and their potential applications. © 2009 American Institute of Physics.
• Gabitov, I. R., Korotkevich, A. O., Maimistov, A. I., & Mcmahon, J. B. (2008). Coherent optical pulse dynamics in nano-composite plasmonic Bragg gratings. Lecture Notes in Physics, 751, 337-360.
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  Abstract: The propagation of solitary waves in a Bragg grating formed by an array of thin nanostructured dielectric films is considered. A system of equations of Maxwell-Duffing type, describing forward- and backward-propagating waves in such a grating, is derived. Exact solitary wave solutions are found, analyzed, and compared with the results of direct numerical simulations. © 2008 Springer-Verlag Berlin Heidelberg.
• Litchinitser, N. M., Maimistov, A. I., Gabitov, I. R., & Shalaev, V. M. (2008). From Positive- to Negative-Index Materials: Transitional Phenomena. 2008 CONFERENCE ON LASERS AND ELECTRO-OPTICS & QUANTUM ELECTRONICS AND LASER SCIENCE CONFERENCE, VOLS 1-9, 3195-+.
• Litchinitser, N. M., Maimistov, A. I., Gabitov, I. R., & Shalaev, V. M. (2008). From positive- To negative-index materials: transitional phenomena. Conference on Quantum Electronics and Laser Science (QELS) - Technical Digest Series.
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  Abstract: We investigate light propagation through a transition layer between the positive- and negative-index materials with linearly changing material parameters. Strong enhancement of TE-and TM-wave components near the point of zero refractive index is predicted. ©2008 Optical Society of America.
• Litchinitser, N. M., Maimistov, A. I., Gabitov, I. R., Sagdeev, R. Z., & Shalaev, V. M. (2008). Metamaterials: Electromagnetic enhancement at zero-index transition. Optics Letters, 33(20), 2350-2352.
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  PMID: 18923619;Abstract: Resonant enhancement of electromagnetic waves propagating at oblique incidence in metamaterials, with dielectric permittivity and magnetic permeability linearly changing from positive to negative values, has been predicted and theoretically studied. This effect occurs for both TE and TM polarizations near the point where a refractive index changes its sign. Our model elucidates the unique features of the resonant enhancement in "positive-to-negative transition" metamaterials for a broad frequency range from microwaves to optics. © 2008 Optical Society of America.
• Maimistov, A. I., & Gabitov, I. R. (2008). Nonlinear optical effects in media with a positive-negative refractive index. Bulletin of the Russian Academy of Sciences: Physics, 72(5), 704-707.
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  Abstract: The nonlinear phenomena in media whose linear refractive index changes its magnitude and sign with a change in the wave carrier frequency or spatial coordinate, are considered. The results of theoretical investigations of the generation of harmonics in a homogeneous medium, optical bistability, and propagation of stationary solitary waves in a two-channel waveguide are discussed. © Allerton Press, Inc. 2008.
• Maǐmistov, A., Gabitov, I. R., & Litchinitser, N. M. (2008). Solitary waves in a nonlinear oppositely directed coupler. Optics and Spectroscopy (English translation of Optika i Spektroskopiya), 104(2), 253-257.
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  Abstract: The propagation of pulses in the system of two tunnel-coupled optical waveguides from optically nonlinear materials one of which has a negative refractive index, while the other one, positive, is investigated theoretically. The propagation of nonlinear waves in this structure is studied based on the model of coupled modes. For linear waves, this pair of coupled waveguides behaves as a mirror resulting in the change of direction of the energy flow upon penetration of radiation from one waveguide to the other. The solutions to the system of nonlinear equations describing the stationary propagation of the solitary wave, the gap soliton, in a particular direction are found. This soliton is formed by the coupled pair of wave packets each localized in the corresponding waveguide. © 2008 Pleiades Publishing, Ltd.
• Shalaev, V. M., Maimistov, A. I., Litchinitser, N. M., & Gabitov, I. R. (2008). Chapter 1 Negative refractive index metamaterials in optics. Progress in Optics, 51, 1-67. doi:10.1016/s0079-6638(07)51001-2
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  Publisher Summary Recent advances in nanofabrication have led to the demonstration of a novel class of optical materials—metamaterials—that are artificially engineered structures with electromagnetic properties unattainable in nature. One of the most fascinating examples of such structures is negative-index metamaterials (NIMs). The emergence of optical metamaterials opens up fundamentally new regimes of light–matter interaction and prompts unique opportunities for manipulating light and has given rise to numerous unusual linear and nonlinear optical phenomena that cannot be realized in conventional materials. The constituent components of these materials, meta-atoms, can be designed to empower optical magnetic activity, to enable fundamentally new regimes of linear and nonlinear light–matter interaction, and even to manipulate an object's degree of visibility at optical frequencies. The ultimate goal from the experimental viewpoint is the fabrication of three-dimensional, low-loss, tunable and broadband NIMs. Owing to the complexity of NIMs, theoretical predictions and numerical analysis are the essential components of NIM research. The demonstration of NIMs and magnetic activity at optical frequencies has motivated re-consideration of almost all well-established linear and nonlinear optical phenomena that reveal themselves in unusual and often counter-intuitive ways in NIMs. Optical metamaterials, without doubt, constitute one of the most exciting areas of research in modern optics that is likely to result in discoveries of new phenomena and the development of novel device applications for nanophotonics.
• Gabitov, I. R., Korotkevich, A. O., & Maimistov, A. I. (2007). Coherent propagation of an optical pulse in a Bragg plasmon grating. Quantum Electronics. doi:10.1070/qe2007v037n06abeh013468
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  The propagation of ultrashort pulses in a dielectric medium with periodically arranged metal nanoparticles is considered theoretically. Plasmon oscillations in these particles are described by the model of an anharmonic oscillator with the driving force proportional to the electric-field strength of an electromagnetic pulse. A system of equations determining the behaviour of electromagnetic waves is obtained in the approximation of slowly varying envelopes of ultrashort pulses and medium polarisation. Under the assumption that the frequencies of the carrier wave and oscillators coincide and the Bragg resonance condition is fulfilled, the solution of the obtained equations is found, which corresponds to the solitary wave of the ultrashort-pulse field and the medium polarisation (Bragg soliton). The numerical simulation shows the formation of a Bragg soliton (from the initial Gaussian pulse of the sufficient energy) and a nonstationary solitary wave with the vanishing group velocity.
• Gabitov, I. R., Korotkevich, A. O., Maimistov, A. I., & McMahon, J. B. (2007). Solitary waves in plasmonic Bragg gratings. Applied Physics A: Materials Science and Processing, 89(2), 277-281.
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  Abstract: Light propagation in a Bragg periodic structure containing thin films with metallic nanoparticles is studied. The plasmonic resonance frequency, Bragg frequency, and the light carrier frequency are assumed to be close. Exact solutions describing solitary gap-waves are found, and a light arrest phenomenon due to the nonlinearity of plasmonic oscillations is studied. © 2007 Springer-Verlag.
• Indik, R., Lushnikov, P., Mollenauer, L., & Shkarayev, M. (2007). Twin Families of Bisolitons in Dispersion Managed Systems. Optics Letters, 32(6), 605-607. doi:10.1364/ol.32.000605
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  We calculate bisoliton solutions using a slowly varying stroboscopicequation. The system is characterized in terms of a single dimensionlessparameter. We find two branches of solutions and describe the structure of thetails for the lower branch solutions.[Journal_ref: ]
• Litchinitser, N. M., Gabitov, I. R., & Maimistov, A. I. (2007). Optical bistability in a nonlinear optical coupler with a negative index channel. Physical Review Letters, 99(11).
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  Abstract: We discuss a novel kind of nonlinear coupler with one channel filled with a negative index metamaterial. The opposite directionality of the phase velocity and the energy flow in the negative index metamaterial channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation. © 2007 The American Physical Society.
• Litchinitser, N. M., Gabitov, I. R., Maimistov, A. I., & Shalaev, V. M. (2007). Chapter 1 Negative refractive index metamaterials in optics. Progress in Optics, 51, 1-67.
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  Abstract: The emergence of optical metamaterials, and NIMs in particular, has given rise to numerous unusual linear and nonlinear optical phenomena that cannot be realized in conventional materials. The constituent components of these materials, meta-atoms, can be designed to empower optical magnetic activity, to enable fundamentally new regimes of linear and nonlinear light-matter interaction, and even to manipulate an object's degree of visibility at optical frequencies. The fabrication of optical NIMs is quite challenging and requires approaches going beyond a straightforward scaling of meta-atom sizes from microwave to near-infrared and visible frequencies. Several proof-of-principle experiments reported over the last two years form the basis for building functional NIMs and the realization of new photonic devices. Nevertheless, there is a lot of room for improvement and, therefore, for both experimental and theoretical fundamental and applied studies. The ultimate goal from the experimental viewpoint is the fabrication of three-dimensional, low-loss, tunable and broadband NIMs. Owing to the complexity of NIMs, theoretical predictions and numerical analysis are the essential components of NIM research. The demonstration of NIMs and magnetic activity at optical frequencies has motivated re-consideration of almost all well-established linear and nonlinear optical phenomena that reveal themselves in unusual and often counter-intuitive ways in NIMs. Optical metamaterials, without doubt, constitute one of the most exciting areas of research in modern optics, that is likely to result in discoveries of new phenomena and the development of novel device applications for nanophotonics. © 2008 Elsevier B.V. All rights reserved.
• Litchinitser, N. M., Gabitov, I. R., Maimistov, A. I., & Shalaev, V. M. (2007). Effect of an optical negative index thin film on optical bistability. Optics Letters, 32(2), 151-153.
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  PMID: 17186047;Abstract: We investigate nonlinear transmission in a layered structure consisting of a slab of positive index material with Kerr-type nonlinearity and a subwavelength layer of linear negative index material (NIM) sandwiched between semi-infinite linear dielectrics. We find that a thin layer of NIM leads to significant changes in the hysteresis width when the nonlinear slab is illuminated at an angle near that of total internal reflection. Unidirectional diodelike transmission with enhanced operational range is demonstrated. These results may be useful for NIMs characterization and for designing novel NIMs-based devices. © 2006 Optical Society of America.
• Maimistov, A. I., & Gabitov, I. R. (2007). Nonlinear optical effects in artificial materials. European Physical Journal: Special Topics, 147(1), 265-286.
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  Abstract: We consider some nonlinear phenomena in metamaterials with negative refractive index properties. Our consideration includes a survey of previously known results as well as identification of the phenomena that are important for applicationsof this new field. We focus on optical behavior of thin films aswell as multi-wave interactions. © EDP Sciences/Societé Italiana di Fisica/Springer-Verlag 2007.
• Maimistov, A. I., Gabitov, I. R., & Kazantseva, E. V. (2007). Three wave interaction in negative refractive index materials with quadratic nonlinearity. Conference on Quantum Electronics and Laser Science (QELS) - Technical Digest Series.
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  Abstract: We examine waves propagation in negative refractive index materials with quadratic nonlinearity. We analyze the modulational instability of the wave with constant background. The solitary wave solutions binding pump and second harmonic waves are found. ©2006 Optical Society of America.
• Maimistov, A. I., Gabitov, I. R., & Korotkevich, A. O. (2007). Coherent propagation of an optical pulse in a Bragg plasmon grating. Quantum Electronics, 37(6), 549-553.
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  Abstract: The propagation of ultrashort pulses in a dielectric medium with periodically arranged metal nanoparticles is considered theoretically. Plasmon oscillations in these particles are described by the model of an anharmonic oscillator with the driving force proportional to the electric-field strength of an electromagnetic pulse. A system of equations determining the behaviour of electromagnetic waves is obtained in the approximation of slowly varying envelopes of ultrashort pulses and medium polarisation. Under the assumption that the frequencies of the carrier wave and oscillators coincide and the Bragg resonance condition is fulfilled, the solution of the obtained equations is found, which corresponds to the solitary wave of the ultrashort-pulse field and the medium polarisation (Bragg soliton). The numerical simulation shows the formation of a Bragg soliton (from the initial Gaussian pulse of the sufficient energy) and a nonstationary solitary wave with the vanishing group velocity.
• Maǐmistov, A., Gabitov, I. R., & Kazantseva, E. V. (2007). Quadratic solitons in media with negative refractive index. Optics and Spectroscopy (English translation of Optika i Spektroskopiya), 102(1), 90-97.
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  Abstract: The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton-a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave. © Nauka/Interperiodica 2007.
• Gabitov, I. R. (2006). Multi-Wave Interaction in Nanostructured Materials. Frontiers in Optics. doi:10.1364/fio.2006.ftub1
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  We investigated parametric amplification and second-harmonic generation arising from three-wave interaction in nanocomposite materials with negative refractive index. The sign of the refractive index is assumed to change with the frequencies of the interacting waves.
• Gabitov, I. R., & Maimistov, A. I. (2006). Double resonance in nanostructured optical materials and negative refractive index properties. Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference, CLEO/QELS 2006.
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  Abstract: Equations modeling resonance interaction of electromagnetic waves with a nanocomposite material containing metallic LC- nanocircuits are derived. Solitary pulse solutions are discovered and analyzed. © 2006 Optical Society of America.
• Gabitov, I. R., Litchinitser, N. M., & Maimistov, A. I. (2006). Nonlinear surface waves in negative refractive index thin films. Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference, CLEO/QELS 2006.
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  Abstract: The effects of a sub-wavelength transition layer of negative index material on surface wave propagation are investigated. Dispersion relations at interfaces of linear and nonlinear dielectrics separated by this transition layer are derived and analyzed. © 2006 Optical Society of America.
• Soneson, J. E., Shalaev, V. M., Maimistov, A. I., Litchinitser, N. M., Indik, R. A., & Gabitov, I. R. (2006). Double-resonant optical materials with embedded metal nanostructures. Journal of The Optical Society of America B-optical Physics, 23(3), 535-542. doi:10.1364/josab.23.000535
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  We derive equations modeling the resonant interaction of electric and magnetic components of light fields with metal nanostructures. This paired resonance was recently shown to produce negative refractive index. The model equations are a generalization of the well-known Maxwell-Lorentz model. We demonstrate that in the case of nonlinear polarization and linear magnetization, these equations are equivalent to a system of equations describing the resonant interaction of light with plasmonic oscillations in metal nanospheres. A family of solitary wave solutions is found that is similar to pulses associated with self-induced transparency in the framework of the Maxwell-Bloch model. The evolution of incident optical pulses is studied numerically, as are the collision dynamics of the solitary waves. These simulations reveal that the collision dynamics vary from near perfectly elastic to highly radiative, depending on the relative phase of the initial pulses.
• Wabnitz, S., Tonello, A., Indik, R. A., & Gabitov, I. R. (2006). Analyse statistique de la phase des solitons optiques. Journal De Physique Iv, 135(1), 287-288. doi:10.1051/jp4:2006135092
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  On analyse numeriquement la statistique de la phase des solitons optiques et on arrive a determiner la fonction de densite de probabilite. Nos resultats sont en accord avec les theories existantes, qui sont basees sur les proprietes des solitons.
• Wabnitz, S., Tonello, A., Indik, R. A., & Gabitov, I. R. (2006). Importance sampling of Gordon-Mollenauer soliton phase noise in optical fibers. IEEE Photonics Technology Letters, 18(7), 886-888. doi:10.1109/lpt.2006.871817
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  We develop an importance sampling method to perform the direct numerical computation of the probability density function of the random optical soliton phase under the influence of both amplifier spontaneous emission noise and nonlinear conversion of amplitude to phase fluctuations owing to the Kerr effect, or nonlinear phase noise.
• Vasic, B., Vasic, B., Ivkovic, M., Gabitov, I. R., & Djordjevic, I. B. (2005). Achievable information rates for high-speed long-haul optical transmission. Journal of Lightwave Technology, 23(11), 3755-3763. doi:10.1109/jlt.2005.857751
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  There have been numerous attempts to determine the channel capacity of a nonlinear fiber-optic communication channel. The main approach was to consider amplified spontaneous emission (ASE) noise as a predominant effect and to observe the fiber nonlinearities as the perturbation of a linear case or as the multiplicative noise. In this paper, the achievable information rates for high-speed optical transmission (40 Gb/s and above) are calculated using the finite-state-machine approach. In calculations, the combined effect of ASE noise, Kerr nonlinearity [self-phase modulation (SPM), intrachannel four-wave mixing (IFWM), intrachannel cross-phase modulation (IXPM)], stimulated Raman scattering (SRS), chromatic dispersion, and (optical/electrical) filtering is taken into account.
• Chernyak, V., Chertkov, M., Gabitov, I., Kolokolov, I., & Lebedev, V. (2004). PMD-induced fluctuations of bit-error rate in optical fiber systems. Journal of Lightwave Technology, 22(4), 1155-1168.
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  Abstract: This paper presents a method that allows evaluating the performance of an optical fiber system where bit errors result from a complex interplay of spontaneous noise generated in optical amplifiers and birefringent disorder of the transmission fiber. We demonstrate that in the presence of temporal fluctuations of birefringence characteristics, the bit-error rate (BER) itself is insufficient for characterizing system performance. Adequate characterization requires introducing the probability distribution function (PDF) of the BER obtained by averaging over many realizations of birefringent disorder. Our theoretical analysis shows that this PDF has an extended tail indicating the importance of anomalously large values of BER. We present the results of comprehensive analysis of the following issues: 1) The dependence of the PDF tail shape on detection details, such as filtering and regular temporal shift adjustment; 2) the changes in the PDF of BER that occur when the first- or higher order polarization mode dispersion (PMD) compensation techniques are applied; 3) an alternative PMD compensation method capable of providing more efficient suppression of extreme outages.
• Chertkov, M., Gabitov, I., Kolokolov, I., & Schäfer, T. (2004). Periodic compensation of polarization mode dispersion. Journal of the Optical Society of America B: Optical Physics, 21(3), 486-498.
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  Abstract: Polarization mode dispersion is the effect of signal broadening in a fiber with birefringent disorder. The disorder, frozen into the fiber, is characterized by the so-called vector of birefringence (VB). In a linear medium a pulse broadens as the two principal states of polarization split. It is well-known that, under the action of short-correlated disorder, naturally present in fibers, the dispersion vector (DV), characterizing the split, performs a Brownian random walk. We discuss a strategy of passive (i.e., pulse-independent) control of the DV broadening. The suggestion is to pin (compensate) periodically or quasi-periodically the integral of VB to zero. As a result of the influence of pinning, the probability distribution function of the DV becomes statistically steady in the linear case. Moreover, pinning improves confinement of the pulse in the weakly nonlinear case. The theoretical findings are confirmed by numerical analysis. © 2004 Optical Society of America.
• Peleg, A., Chertkov, M., & Gabitov, I. (2004). Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion. Journal of the Optical Society of America B: Optical Physics, 21(1), 18-23.
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  Abstract: We study the effect of third-order dispersion on the interaction between two solitons from different frequency channels in an optical fiber. The interaction may be viewed as an inelastic collision in which energy is lost to continuous radiation owing to nonzero third-order dispersion. We develop a perturbation theory with two small parameters: the third-order dispersion coefficient d3 and the reciprocal of the interchannel frequency difference 1/Ω. In the leading order the amplitude of the emitted radiation is proportional to d3/Ω2, and the source term for this radiation is identical to the one produced by perturbation of the second-order dispersion coefficient. The only other effects up to the third order are shifts in the soliton's phase and position. Our results show that the statistical description of soliton propagation in a given channel influenced by interaction with a quasi-random sequence of solitons from other channels is similar to the description of soliton propagation in fibers with weak disorder in the second-order dispersion coefficient.
• Vasic, B., Vasic, B., Rao, V. S., Kostuk, R. K., Gabitov, I. R., & Djordjevic, I. B. (2004). Ghost-pulse reduction in 40-Gb/s systems using line coding. IEEE Photonics Technology Letters, 16(7), 1784-1786. doi:10.1109/lpt.2004.828844
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  At high bit rates, four-wave mixing and nonlinearities in the optical channel give rise to ghost pulses. In this letter, we propose the application of modulation codes to tackle this effect.
• Byrne, J. A., Gabitov, I. R., & Kovačič, G. (2003). Polarization switching of light interacting with a degenerate two-level optical medium. Physica D: Nonlinear Phenomena, 186(1-2), 69-92.
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  Abstract: Polarization switching of light in a degenerate two-level medium, known as the Λ-configuration, is described. The polarization dynamics of light pulses is investigated by means of the inverse-scattering transform. The mathematical formalism of the inverse-scattering transform that takes into account the initial fluctuations of the medium polarization components corresponding to atomic transitions between the excited state and the two degenerate ground sub-levels in Λ-configuration atomic system is formulated. The characteristic switching length is evaluated via the physical parameters of the prepared medium and the optical pulse. © 2003 Elsevier B.V. All rights reserved.
• Chertkov, M., Chung, Y., Dyachenko, A., Gabitov, I., Kolokolov, I., & Lebedev, V. (2003). Shedding and interaction of solitons in weakly disordered optical fibers. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 67(3 2), 036615/1-036615/21.
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  Abstract: Structural disorder is built in the fiber. The effect of this disorder on the propagation, i.e., the longer some pulse travels along the fiber the more strongly disorder affects it. Even weak disorder may cause essential damage to pulse integrity. This paper describes a strong effect of weak disorder in the fiber dispersion coefficient on the shedding and interaction of pulses, a problem which is crucial for progress in modern nonlinear fiber optics and related communication technology.
• Peleg, A., Chertkov, M., & Gabitov, I. (2003). Interchannel interaction of optical solitons. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 68(2 2), 026605/1-026605/15.
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  Abstract: The interaction between two solitons from different frequency channels propagating in an optical fiber was studied. The spectrum and intensity of the radiation emitted in the frequency channels of the colliding solitons as a result of the collision were calculated. Collision induced change in the soliton parameters was also calculated. The resultant data were analyzed in detail.
• Soneson, J., Khanov, I., Indik, R. A., & Gabitov, I. R. (2003). Non-Gaussianity of amplitude jitter in DM fiber links with DPSK coding. Frontiers in Optics. doi:10.1364/fio.2003.tuh4
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  Amplitude jitter due to nonlinear intra-channel pulse interaction is investigated in dispersion managed optical fiber links with Differential Phase Shift Keying. It is shown that as in the case of amplitude modulation, nonlinear effects lead to errors. The probability distribution function is characterized for the energy of the output pulses.
• Chertkov, M., Gabitov, I., Lushnikov, P. M., Moeser, J., & Toroczkai, Z. (2002). Pinning method of pulse confinement in optical fiber with random dispersion. Journal of the Optical Society of America B: Optical Physics, 19(11), 2538-2550.
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  Abstract: Pulse propagation in optical fiber links with randomness in the dispersion is investigated theoretically and numerically for systems with and without dispersion management. The main effects of locally correlated noise are inevitable pulse destruction and statistical broadening. However, periodic/quasi-periodic management of fiber randomness, achieved by setting the accumulated dispersion to its nominal value (pinning), essentially decreases pulse broadening. If the pinning period is short enough, we observe a statistical state that is numerically indistinguishable from the steady state in the dispersion-managed case. © 2002 Optical Society of America.
• Gabitov, I. R., & Lushnikov, P. M. (2002). Nonlinearity management in a dispersion-managed system. Optics Letters, 27(2), 113-115.
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  PMID: 18007729;Abstract: We propose using a nonlinear phase-shift interferometric converter (NPSIC), a new device, for lumped compensation for nonlinearity in optical fibers. The NPSIC is a nonlinear analog of the Mach-Zehnder interferometer and provides a way to control the sign of the nonlinear phase shift. We investigate a potential use of the NPSIC for compensation for nonlinearity to develop a dispersion-managed system that is closer to an ideal linear system. More importantly, the NPSIC can be used to essentially improve single-channel capacity in the nonlinear regime.
• Gabitov, I. R., & Lushnikov, P. M. (2002). Nonlinearity management in a dispersion-managed system. Optics Letters. doi:10.1364/ol.27.000113
• Moeser, J., Gabitov, I., & Jones, C. K. (2002). Pulse stabilization by high-order dispersion management. Optics Letters, 27(24), 2206-2208.
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  PMID: 18033484;Abstract: The stabilizing effects of dispersion management (DM) at second and third order are studied for both single-channel and wavelength-division multiplexed (WDM) systems. We first derive a model for the slow evolution of a pulse in an optical fiber with high-order dispersion management (HODM). For single-channel systems, in contrast with conventional DM with constant third-order dispersion, this equation possesses a stable solution, the ground state for its associated Hamiltonian, which propagates nearly periodically under direct numerical simulation. Improved performance for WDM systems is also observed, as complicated pulse interactions, which can lead to undesirable effects such as frequency shift, are prevented by HODM. © 2002 Optical Society of America.
• Omenetto, F. G., Chung, Y., Yarotski, D., Schaefer, T., Gabitov, I., & Taylor, A. J. (2002). Phase analysis of nonlinear femtosecond pulse propagation and self-frequency shift in optical fibers. Optics Communications, 208(1-3), 191-196.
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  Abstract: Phase sensitive analysis of femtosecond pulse propagation in optical fibers employing frequency resolved optical gating (FROG) is presented and compared to numerical simulations employing a modified cubic nonlinear Schrödinger equation (NLSE). Phase information obtained from deconvolution of the experimental traces allows the observation and characterization of specific pulse propagation features as a function of energy and distance. The experimental observation of the phase signature of a soliton during propagation and the phase properties of the soliton self-frequency shift are described and are found to be in remarkable agreement with the simulations. © 2002 Elsevier Science B.V. All Rights Reserved.
• Chertkov, M., Gabitov, I., Kolokolov, I., & Lebedev, V. (2001). Shedding and interaction of solitons in imperfect medium. JETP Letters, 74(7), 357-361.
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  Abstract: The propagation of a soliton pattern through one-dimensional medium with weakly disordered dispersion is considered. Solitons, perturbed by this disorder, radiate. The emergence of a long-range interaction between the solitons, mediated by the radiation, is reported. Basic soliton patterns are analyzed. The interaction is triple and is extremely sensitive to the phase mismatch and relative spatial separations within the pattern. This phenomenon is a generic feature of any problem explaining adiabatic evolution of solitons through a medium with frozen disorder. © 2001 MAIK "Nauka/Interperiodica".
• Chertkov, M., Gabitov, I., Kolokolov, I., & Lebedev, V. (2001). Solitons in a disordered anisotropic optical medium. JETP Letters, 74(11), 535-538.
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  Abstract: The radiation-mediated interaction of solitons in a one-dimensional nonlinear medium (optical fiber) with birefringent disorder is shown to be independent of the separation between solitons. The effect produces a potentially dangerous contribution to the signal lost. © 2001 MAIK "Nauka/Interperiodica".
• Chertkovt, M., Gabitov, I., & Moeser, J. (2001). Pulse confinement in optical fibers with random dispersion. Proceedings of the National Academy of Sciences of the United States of America, 98(25), 14208-14211.
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  PMID: 11717397;PMCID: PMC64660;Abstract: Short-range correlated uniform noise in the dispersion coefficient, inherent in many types of optical fibers, broadens and eventually destroys all initially ultra-short pulses. However, under the constraint that the integral of the random component of the dispersion coefficient is set to zero (pinned), periodically or quasiperiodically along the fiber, the dynamics of the pulse propagation changes dramatically. For the case that randomness is present in addition to constant positive dispersion, the pinning restriction significantly reduces average pulse broadening. If the randomness is present in addition to piece-wise constant periodic dispersion with positive residual value, the pinning may even provide probability distributions of pulse parameters that are numerically indistinguishable from the statistically steady case. The pinning method can be used to both manufacture better fibers and upgrade existing fiber links.
• Gabitov, I. R., Phillips, A., & Kiselev, S. (2000). Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles. Physics Letters. doi:10.1016/s0375-9601(00)00415-1
• Gabitov, I. R., Turitsyn, S. K., & Schafer, T. (2000). Lie-transform averaging in nonlinear optical transmission systems with strong and rapid periodic dispersion variations. Physics Letters. doi:10.1016/s0375-9601(99)00901-9
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  Abstract Using Lie-transform techniques, we derive higher-order corrections to the path-averaged model governing evolution of dispersion-managed solitons in the spectral domain. The result holds in the case of arbitrary (including moderate and strong) dispersion. The general theory is illustrated by deriving the exact formulas + for a specific symmetric dispersion map.
• Gabitov, I., Schäfer, T., & Turitsyn, S. K. (2000). Lie-transform averaging in nonlinear optical transmission systems with strong and rapid periodic dispersion variations. Physics Letters, Section A: General, Atomic and Solid State Physics, 265(4), 274-281.
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  Abstract: Using Lie-transform techniques, we derive higher-order corrections to the path-averaged model governing evolution of dispersion-managed solitons in the spectral domain. The result holds in the case of arbitrary (including moderate and strong) dispersion. The general theory is illustrated by deriving the exact formulas + for a specific symmetric dispersion map. (C) 2000 Published by Elsevier Science B.V.
• Kiselev, S., Phillips, A., & Gabitov, I. (2000). Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles. Physics Letters, Section A: General, Atomic and Solid State Physics, 272(1-2), 130-142.
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  Abstract: This Letter investigates the stochastic dynamics of a simplified agent-based microscopic model describing stock market evolution. Our mathematical model includes a stochastic market and a sealed-bid double auction. The dynamics of the model are determined by the game of two types of traders: (i) 'intelligent' traders whose strategy is based on nonlinear technical data analysis1 and (ii) 'random' traders that act without a consistent strategy. We demonstrate the effect of time-scale separations on the market dynamics. We study the characteristics of the market relaxation in response to perturbations caused by large cash flows generated between these two groups of traders. We also demonstrate that our model exhibits the formation of a price bubble2 and the subsequent transition to a bear market. (C) 2000 Elsevier Science B.V.
• Shaulov, G., Gabitov, I., & Haus, J. W. (1999). Pulse dynamics in absorber dominated optical cavities. Optics Communications, 164(1), 39-45.
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  Abstract: We investigate optical field dynamics in lasers cavities dominated by a saturable absorber. We found that for a specific parameter range the solitary wave-type solutions exist and can be expressed in analytic form, including a new gray-pulse solution. Stability of these solitary waves is discussed and numerically examined.
• Gabitov, I., & Marshall, I. (1998). Removing the time dependence in a rapidly oscillating Hamiltonian. Nonlinearity, 11(4), 845-857.
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  Abstract: Hamiltonian systems with rapidly oscillating explicit dependence on time are considered. The wavelength of this oscillation is treated as a small parameter and it is shown how to remove the time dependence up to some order in the small parameter by means of a canonical transformation presented in the form of an asymptotic series. The result has applications for the study of pulse propagation for high bit-rate transmission in optical fibres.
• Gabitov, I., Hein, B., Kuppers, F., Muller, M., & Weiershausen, W. (1998). Experimental and numerical investigation of ps-pulse transmission in presence of PMD. Conference on Optical Fiber Communication, Technical Digest Series, 342-343.
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  Abstract: Theoretical aspects and measurement techniques of polarization-mode dispersion (PMD) and its influence on picosecond-pulse transmission are discussed. A numerical model is developed from the linear fiber birefringence with randomly varying orientation along the fiber. The fiber is considered as a sequence of segment where the birefringence orientation is fixed and randomly varying from segment to segment as well as segment length. The standard system of coupled nonlinear Schrodinger equations for polarization mode is used to simulate pulse propagation within each segment. A mode-locked Er-doped fiber ring laser is used in investigating the different effects of PDM.
• Matera, F., Mecozzi, A., Settembre, M., Gabitov, I., Turitsyn, S., & Haunstein, H. (1998). Theoretical evaluation of the noise growth and of the system performance for a link constituted by a chain of N optical amplifiers with in-line filters. Conference on Optical Fiber Communication, Technical Digest Series, 202-204.
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  Abstract: The amplified spontaneous emission (ASE) noise growth in a chain of N amplifiers in the presence of in-line filters is analyzed including the semiconductor optical amplifiers (SOA) where the noise growth are combined with fast saturation of the amplifier gain. The peak power of the noise and the Q factor of the system are determined using erbium optical amplifiers, and by computer simulation using split-step method. The results indicate that the dynamics of SOA gives a qualitative agreement between theory and simulation.
• Turitsyn, S. K., Gabitov, I., Laedke, E. W., Mezentsev, V. K., Musher, S. L., Shapiro, E. G., Schäfer, T., & Spatschek, K. H. (1998). Variational approach to optical pulse propagation in dispersion compensated transmission systems. Optics Communications, 151(1-3), 117-135.
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  Abstract: Within the area of optical pulse propagation in long-haul transmission systems various designs for dispersion compensation are investigated. On the basis of variational procedures with collective coordinates, a very effective method is presented which allows to determine quite accurately the possible operation points. We have obtained an analytical formula for the soliton power enhancement. This analytical expression is in good agreement with numerical results, in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. The procedure is suitable to analyze the proper design of dispersion compensating elements. The results allow also to describe the shape of the dispersion-managed soliton. We discuss also a qualitative physical explanation of the possibility to transmit a soliton at zero or normal average dispersion. Analytical predictions are confirmed by direct numerical simulations. © 1998 Elsevier Science B.V. All rights reserved.
• Breuer, D., Jürgensen, K., Küppers, F., Mattheus, A., Gabitov, I., & Turitsyn, S. K. (1997). Optimal schemes for dispersion compensation of standard monomode fiber based links. Optics Communications, 140(1-3), 15-18.
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  Abstract: Different schemes of dispersion management for cascaded transmission systems composed of standard monomode fibers (SMFs) and dispersion compensating fibers have been studied considering the most essential boundary conditions for practical network design. Alternating ordering of the compensation sections is found to improve considerably the eye opening penalty for high amplifier spacings of 120 km. © 1997 Elsevier Science B.V.
• Breuer, D., Küppers, F., Mattheus, A., Shapiro, E. G., Gabitov, I., & Turitsyn, S. K. (1997). Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifier spacing. Optics Letters, 22(13), 982-984.
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  PMID: 18185726;Abstract: Optical 10-Gbit/s return-to-zero pulse transmission in cascaded communication systems using dispersion compensation of the standard monomode fiber with large amplifier spacing is examined. It is shown that pulse distortions that are due to Kerr nonlinearity are significantly diminished by symmetrical ordering of the compensation sections when the total number of precompensation and postcompensation sections is equal. Repositioning of these sections is not critical. © 1997 Optical Society of America.
• Chernikov, S. V., Taylor, J. R., Platonov, N. S., Gapontsev, V. P., Kuppers, F., Mattheus, A., & Gabitov, I. (1997). High-power, compact, high-efficiency, fiber laser source around 1.24 μm for pumping Raman amplifiers. Conference on Optical Fiber Communication, Technical Digest Series, 345-.
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  Abstract: The application of a high-power, compact, high-efficiency, fiber laser source for pumping fiber Raman amplifiers at 1.3 μm to distributed Raman amplification over a 35 km length of standard telecommunications fiber was investigated. Transparency over this length was observed for a launched pump power of 600 mW and low noise figures were measured under these conditions. Initial investigations to wavelength-division multiplexed applications employing two signal channels separated by approximately 2 nm showed no crosstalk effect and equal, mutually independent gains were measured for both channels. Short pulse amplification and transmission were measured and distortion-free transmission of 18-ps soliton pulses at 10-GHz repetition rate over 37.8 km STF were observed.
• Gabitov, I. R., Turitsyn, S. K., Zengerle, R., Mattheus, A., & Hagele, V. (1997). Analysis of ≥ 10 Gbit/s 1.3 μm RZ Transmission through 500 km of Standard Monomode Fiber with In-line Semiconductor Optical Amplifiers. Journal of optical communications. doi:10.1515/joc.1997.18.6.213
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  Article Analysis of ≥ 10 Gbit/s 1.3 μm RZ Transmission through 500 km of Standard Monomode Fiber with In-line Semiconductor Optical Amplifiers was published on December 1, 1997 in the journal Journal of Optical Communications (volume 18, issue 6).
• Gabitov, I., Holm, D. D., & Luce, B. P. (1997). Low-noise picosecond soliton transmission by use of concatenated nonlinear amplifying loop mirrors. Journal of the Optical Society of America B: Optical Physics, 14(7), 1850-1855.
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  Abstract: We compare two systems that are specially configured with loop mirrors to provide stable picosecond soliton transmission. One configuration, created by Smith and Doran [J. Opt. Soc. Am. B 12, 1117 (1995)], uses nonlinear optical loop mirrors. This configuration is compared with another that uses nonlinear amplifying loop mirrors, the configuration of which we systematically determine from the amplitude and the pulse-width switching characteristics of the nonlinear optical loop mirror. It is found that the nonlinear optical loop mirror configuration allows stable pulse transmission with much less dispersive background waves than does the nonlinear optical loop mirror configuration. This clean performance is obtained at the cost of slightly lessening the parameter region of global stability of pulses. A technique for accurately estimating the region of global stability for amplitude and pulse-width perturbations of the stable pulse is also given. © 1997 Optical Society of America.
• Gabitov, I., Shapiro, E. G., & Turitsyn, S. K. (1997). Asymptotic breathing pulse in optical transmission systems with dispersion compensation. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 55(3 SUPPL. B), 3624-3633.
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  Abstract: We study a nonlinear process of the formation of a breathing solitary wave in the optical transmission systems with periodic amplification and dispersion compensation. Results of our numerical simulations demonstrate remarkably stable asymptotic propagation of such breathing pulse over long distances. We have derived approximate equations describing pulse amplitude and width oscillations and found that results obtained by this approach are in good agreement with the results of direct numerical modeling on the short and middle distances. It is shown that asymptotic averaged pulses have a form typically close to a Gaussian shape. We have found numerically that an input pulse evolves asymptotically into a stable breathing structure. After the first stage of propagation, the input pulse emits radiation that spreads due to dispersion. The asymptotic structure that is formed realizes a balance between the main pulse and the radiative tail.
• Gabitov, I., Shapiro, E. G., & Turitsyn, S. K. (1997). Optical pulse dynamics in fiber links with dispersion compensation. Optics Communications, 134(1-6), 317-329.
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  Abstract: We examine optical pulse propagation in a transmission system with periodical pulse amplification and dispersion compensation both numerically and by a variational method. We confirm by direct numerical simulations the validity of the concept of a "breathing" soliton, which we previously proposed. We demonstrate that the sign of the residual dispersion is responsible for the stability of the pulse stream.
• Hãgele, V., Mattheus, A., Zengerie, R., Gabitov, I., & Turitsyn, S. K. (1997). Analysis of ≥ 10 Gbit/s 1.3 μm RZ transmission through 500 km of standard monomode fiber with in-line semiconductor optical amplifiers. Journal of Optical Communications, 18(6), 213-221.
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  Abstract: Optical transmission systems based on standard monomode fibers (SMF) and periodic amplification by means of semiconductor optical amplifiers (SOA) are examined taking into account practical boundary conditions of installed core networks, such as amplifier spacing, fiber attenuation and chromatic dispersion. The performance of ≥10 Gbit/s solution transmission in the second optical window (around λo = 1300 nm) has been investigated numerically. The results show the feasibility of transmission over at least 500 km SMF, even for a system design without signal filtering after the amplification Optimization of the laser transmitter parameters in terms of initial peak power. relative optical phase of neighbouring pulses and mark-to-space ratio leads to a significant improvement of the system capacity and bit error rate and allows a stable operation up to 23 Gbit/s. The capacity and Q-factor can be effectively upgraded using optical bandpass filters.
• Settembre, M., Matera, F., Hägele, V., Gabitov, I., Mattheus, A. W., & Turitsyn, S. K. (1997). Cascaded optical communication systems with in-line semiconductor optical amplifiers. Journal of Lightwave Technology, 15(6), 962-966.
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  Abstract: The optimization of the performance of installed standard-monomode fibers based optical transmission systems with in-line semiconductor optical amplifiers (SOA's) is reported in this paper. Both solitons and nonreturn-to-zero (NRZ) signals are studied and their capacities are compared. This investigation is based on numerical simulations by solving the nonlinear Schrödinger equations with the split-step method while the SOA is simulated with two different models that we show to be in a good agreement. Transmissions over distances of the order of several hundreds of kilometers are shown to be possible, and very long distances can be reached expecially if in-line sliding filters are used.
• Settembre, M., Tamburrini, M., Matera, F., Haunstein, H., Teichmann, B., Gabitov, I., Laedke, E., Spatschek, K., Turitsyn, S. K., & Reid, J. J. (1997). Evaluation of 10 Gbit/s1.3 μm signal transmission in fiber link using semiconductor optical amplifiers. IEE Conference Publication, 75-78.
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  Abstract: The implementation of optical systems operating in the 1.3 μm optical window with in-line semiconductor optical amplifiers (SOAs) is analyzed. The model was verified by experiment using the laboratory prototype of the link between Kassel and Hannover (KH). As an example the performance of the fibre line between Madrid and Lisbon (ML) is examined showing the importance of the noise suppression for 10 Gbit/s RZ data transmission.
• Gabitov, I. R., & Turitsyn, S. K. (1996). Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation. Optics Letters, 21(5), 327-329.
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  PMID: 19865394;Abstract: A theory of optical pulse propagation in cascaded transmission systems that are based on the dispersion-compensating fiber technique is developed. The existence of two scales associated with fiber dispersion and system residual dispersion leads to a simple model for the averaged pulse dynamics. In the particular case of practical importance, the averaged pulse dynamics is governed by the nonlinear Schrödinger equation. The pulse transmission stability is examined. © 1996 Optical Society of America.
• Gabitov, I., & Turitsyn, S. K. (1996). Breathing solitons in optical fiber links. JETP Letters, 63(10), 861-866.
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  Abstract: We introduce the concept of "breathing" solitons to describe the dynamics of optical pulses in transmission lines with passive compensation of fiber chromatic dispersion. The "breathing" pulse can be used as the information carrier. The theory presented is complimentary to the concept of the guiding-center soliton. It is shown that an average bright soliton can propagate in a system with large variations of the dispersion, including segments with high normal dispersion. © 1996 Ameri-can Institute of Physics.
• Baker, V. R., Gabitov, I. R., Finn, V. S., Dyachenko, A., Dolginov, A. Z., & Baker, V. R. (1995). Large-scale spatial patterns in topography at Alpha Regio, Venus. Geophysical Research Letters, 22(14), 1901-1904. doi:10.1029/95gl00908
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  Hypsometric topographic analysis of Magellan altimetry data at Alpha Regio results in a multimodal distribution. Planimetric display of the spatial distribution for altitudes close to each mode reveals large-scale ring-like and crescentic patterns. The latter result from the intersection of horizontal altitude ranges with sloping patterns that are quasi-circular in shape. The spatial patterns of topographic features near Alpha Regio have the following attributes: (1) quasi-circular shapes of individual elements; (2) a hierarchy of distinctive sizes for those elements, with diameters of various elements at approximately 2800, 1500, 500–700, and 200 km; and (3) a large-scale arrangement or pattern in which the 1500-km highland plateau of Alpha Regio is surrounded by a ring of 500-km structures, all of which constitute a 2800-km megastructure. We hypothesize that the intricate patterns of hierarchical scaling for large-scale spatial elements of Venusian topography result from corresponding complexity in Venusian mantle convection.
• Gabitov, I., Holm, D. D., Luce, B. P., & Mattheus, A. (1995). Recovery of solitons with nonlinear amplifying loop mirrors. Optics Letters, 20(24), 2490-2492.
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  Abstract: This work examines the operation of nonlinear amplifying loop mirror (NALM) introduced by Fermann et al. (1993) as an alternative to the oversoliton method to recuperate the soliton profile of nonadiabatically disfigured pulses in the standard monomode fiber networks. Fixed-point solitons of the pulse mapping, generated by propagation in lossy fibers followed by a NALM plus some additional linear amplification, can be approximated very well with particular soliton input pulses for a wide range of amplifier spacings and fiber losses.
• Burtsev, S. P., & Gabitov, I. R. (1994). Alternative integrable equations of nonlinear optics. Physical Review A - Atomic, Molecular, and Optical Physics, 49(3), 2065-2070.
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  Abstract: The paper describes the different theory of nonlinear optics equations interpreted by inverse scattering transform with a variable spectral parameter. Mathematical techniques such as the Maxwell-Bloch system (a complex generalization of the sine-Gordon equation), the three wave resonant interaction system were integrated into the inverse scattering transform (IST), with a nonlinear Schrodinger-Bloch equation are presented and discussed in details.
• Liedenbaum, C. T., Reid, J. J., Tiemeijer, L. F., Boot, A. J., Kuindersma, P. I., Gabitov, I., & Mattheus, A. (1994). Experimental long haul 1300 nm soliton transmission on standard single mode fibres using quantum well laser amplifiers. European Conference on Optical Communication, ECOC, 233-236.
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  Abstract: We report the first successful use of quantum well laser amplifiers in the transmission, at 1300 nm, of a 6.5 Gbit/s soliton signal over 250 km of standard single mode optical fibre with a repeater spacing of 50 km. The amplifiers exhibit a small signal, fibre to fibre, gain of 25 dB (saturation power: 15 dBm). Stable transmission performance is demonstrated and we relate these results to the theory of the propagation of guiding-centre solitons. We show that this system can be readily expanded to transmission over a thousand kilometres.
• Mattheus, A., Gabitov, I., Boot, A. J., Liedenbaum, C. T., Reid, J. J., & Tiemeijer, L. F. (1994). Analysis of periodically amplified soliton propagation on long-haul standard-monomode fiber systems at 1300 nm wavelength. European Conference on Optical Communication, ECOC, 491-494.
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  Abstract: Optical soliton transmission on standard monomode fibers is analyzed in their low dispersion regime around 1300 nm wavelength where the guiding center soliton concept can be applied. The feasibility for ≥ 10 Gbit/s and ≥ 1000 km data transmission on the existing national fiber optical networks is shown considering all relevant practical constraints. We show that a first experimental realization supports this concept.
• Gabitov, I. R., Romagnoli, M., & Wabnitz, S. (1991). Femtosecond soliton collapse and coherent pulse train generation in erbium-doped fiber amplifiers. Applied Physics Letters, 59(15), 1811-1813.
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  Abstract: The study of the interplay of coherent and Raman effects on femtosecond soliton collapse and pulse train generation in erbium-doped fiber amplifiers is examined.
• Zakharov, V. E., Mikhailov, A. V., & Gabitov, I. R. (1985). Maxwell-Bloch equation and the inverse scattering method. Theoretical and Mathematical Physics, 63(1), 328-343. doi:10.1007/bf01017833
• Gabitov, I. R., & Manakov, S. V. (1983). Propagation of ultrashort optical pulses in degenerate laser amplifiers. Physical Review Letters, 50(7), 495-498.
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  Abstract: The shape and area of the output from physically realizable amplifiers of inverted Q(2)-degenerate two-level atoms are calculated analytically. The (4π-δ)- or δ-pulse output is made up from a sequence of ±4π double-humped pulses followed by ±(4π-2δ) pulses, where δ=2invcos(-14). © 1983 The American Physical Society.

Proceedings Publications

• Gabitov, I. R., Drachev, V. P., Bhatta, H., & Aliev, A. E. (2016). Magnetic platform for UV surface-enhanced resonance Raman and fluorescence. In 2016 International Conference Laser Optics (LO).
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  Cobalt nanoparticles with high quality crystal structure and spin polarization support an excellent plasmon resonance at about 275 nm, which is comparable with gold nanoparticles. The quality of plasmon resonance is highly correlated with the superparamagnetic response of the isolated nanoparticles and disappeared in the aggregates. The fluorescence enhancement of about 3×103 for surfactant molecules is demonstrated.
• Gabitov, I. R., Kudyshev, Z. A., Maimistov, A. I., & Kupaev, T. R. (2015, Jan 1 2015). Electromagnetic Field Scattering on rf-SQUID Based Metasurfaces. In Journal: EPJ Web of conferences, 103, 01004.
• Shalaev, V. M., Pennybacker, M., Mozjerin, I., Litchinitser, N. M., Gibson, T., & Gabitov, I. R. (2010). Design Optimization of Transition Metamaterials. In Imaging and Applied Optics Congress.
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  We report a detailed study of the effect of the graded index transition metamaterials design parameters on the resonant absorption of the obliquely incident electromagnetic wave in the vicinity of the zero index transition point(s).
• Gabitov, I. R., Shalaev, V. M., Sagdeev, R. Z., Maimistov, A. I., & Litchinitser, N. M. (2007). From Positive- to Negative-Index Materials: Transitional Phenomena. In Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies OSA Technical Digest (CD) (Optica Publishing Group, 2008), paper QMG5.
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  Electromagnetic field propagation through a transition layer between the positive-index and negative-index materials with linearly changing dielectric permittivity and magnetic permeability was investigated. It is shown that at oblique incidence, the components of both TE- and TM-waves exhibit singular behavior in the vicinity of the point where both dielectric permittivity and magnetic permeability are equal to zero. In this case, finite dissipation of electromagnetic field energy takes place even at infinitesimally small values of losses. These results are applicable to a broader class of inhomogeneous metamaterials and may provide a new platform for the realization of low intensity nonlinear optics in metamaterials.
• Maimistov, A. I., Litchinitser, N. M., & Gabitov, I. R. (2007). Negative Index Waveguide Arrays. In Photonic Metamaterials: From Random to Periodic.
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  We investigate linear and nonlinear transmission properties of photonic lattices, or waveguide arrays, composed of waveguides filled with negative index material separated by positive index material layers. A wide range of initial conditions is investigated.
• Vasic, B. V., Vasic, B. V., Ivkovic, M., Gabitov, I. R., & Djordjevic, I. B. (2005). Achievable information rates for high-speed long-haul optical transmission. In 2005 Quantum Electronics and Laser Science Conference, 3, 1711-1713.
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  Achievable information rates for high-speed optical transmission (40 Gb/s and above) are calculated using finite-state machine approach with combined effect of ASE noise, Kerr nonlinearity (SPM, intrachannel FWM, intrachannel XPM), SRS, chromatic dispersion, and (optical/electrical) filtering.
• Wabnitz, S., Wabnitz, S., Tonello, A., Indik, R. A., & Gabitov, I. R. (2005). Importance sampling of optical soliton phase. In CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005., 224-224.
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  We obtain by the importance sampling method a direct numerical estimation of the probability density function of the optical soliton phase in a periodically amplified fiber optics link.
• Mattheus, A., Luce, B. P., Holm, D. D., & Gabitov, I. R. (1995). Nonlinear Amplification of Solitons in High Dispersion Fiber Transmission Systems. In Fluctuation Phenomena: Disorder and Nonlinearity, 378-384.

Presentations

• Gabitov, I. R. (2023, march). Nonlinear optics of advanced materils. colloquium at Gebze Technical University. Gebze, Istanbul, Turkey: Gebze Technical University.
• Gabitov, I. R. (2023, may). Nonlinear optics of nanostructured materials. Colloquium at UNAM. Mexico City: UNAM.
• Gibney, J., & Kuk, I. (2023, May). Invited talk:  Random four-wave interactions in optical fiber communications. Conference on Lasers and Electro-Optics (CLEO). San Jose, California: Optica (former OSA).
• Gabitov, I. R. (2021, May). Light and Technology. Special lecture as part of the activities of the Scientific and Educational Center of the Republic of Bashkortostan. Ufa, Russia (online).
• Gabitov, I. R. (2022, November). Nonlinear Electrodynamics of Nanostructured Materials. Physics Session, RASA XIII International Conference November 19-20, 2022. University of La Verne, La Verne, CA: Richard Lounsbery Foundation, UNC at Chapel Hill, University of Laverne.
• Gabitov, I. R., Gibney, J., & Ilya, K. (2022, January). Machine learning and optical fiber  coherent systems with nonlinearity. XI International Conference on Photonics and Information Optics. Moscow Engineering Physics Institute, Moscow.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021, July). Riemann-Hilbert Problem and High Speed Communications. SIAM Dynamical Systems 2021. Online: SIAM.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021, October). Linear Mappings for Solving the Strongly Nonlinear Schrödinger Equation: An Application in High-Speed ​​Telecommunications. XXV INTERNATIONAL CONFEENCE "COHERENT OPTICS AND OPTICAL SPECTROSCOPY". Kazan: Russian Ministry of Sciences and Education, Russian Academy of Sciences.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2022, August 30 - September 2). Nonlinearity and optical fiber communications: new aspects of an old problem. Conference on Nonlinear Waves and Coherent Structures (NWCS22) 1. University of Bremen, Bremen Germany: SIAM.
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  In the early 2000s, due to advances in the technology of telecommunications system components and the principles of information transmission in optical fibers, there was a significant progress in the field of high-speed telecommunications. Coherent information transmission systems have been developed and implemented that allow transmitting 100 gigabits per second in a single frequency channel. A distinctive feature of such systems is their linear nature. However, as the transmission length or system performance increases, limitations inevitably arise due to the non-linearity of the optical fiber. For this reason, extending the principles of coherent communication to the non-linear case is one of the most important challenges of high-speed communication. The presentation will provide an overview of the principal approaches to address this problem.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2022, July 4). Nonlinearity and high-speed communications: new view on the old problem. ONL2022: Nonlinear Waves and Networks. Rouen, Normandy, France: CNRS, LMRS.
• Gibney, J., & Kuk, I. (2022, July).

  1.     Invited talk:  Nonlinearity and high-speed communications: new view on the old problem

  . ONL2022: Nonlinear Waves and Networks. Rouen, Normandy, France.
• Gabitov, I. R., & Kovacic et al., G. (2021, July). Chasing Dispersive Waves. SIAM Dynamical Systems 2021SIAM.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021, January). OPTICAL COMMUNICATIONS IN PRESENCE OF DISPERSIVE BROADENED PULSE OVERLAPPING AND FOUR WAVE MIXING. X International Conference Photonics and Information Optics. Moscow: Russian Academy of Sciences.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021, July). Pulse Overlap and Nonlinear Intrachannel Interactions in Coherent Telecommunication Lines. 2021 SIAM Annual Meeting. Online: SIAM.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2021, October). Intra-Channel Interactions in Optical Fiber lines: New Approaches to a Known Problem. Conference on fiber optics. Perm, Russia: Russian Ministry of Science and Education.
• Gabitov, I. R. (2020, August). Stochastic phenomena in high speed optical fiber communication systems: theory and applications. St. Petersburg Seminar on computational and theoretical acoustics of the scientific council on acoustics of the Russian Academy of Sciences. St. Petersburg, Russia.
• Gabitov, I. R. (2020, July). Integrability and high-speed optical fiber communications. St. Petersburg Seminar on computational and theoretical acoustics of the scientific council on acoustics of the Russian Academy of Sciences. St Petersburg, Russia.
• Gabitov, I. R. (2020, November). Brain-Eye connectivity: How to add experimental results to developed model?. Seminar of Roald Sagdeev University of Maryland. online: University of Maryland.
• Gabitov, I. R. (2020, October). Brain – eye connectivity. Seminar of Roald Sagdeev at the University of Maryland. Online: University of Maryland.
• Gabitov, I. R. (2020, October). Integrable equations of nonlinear optics. XVIII International Conference Optical Technologies in Telecommunications-2020. Ufa, Russia: Russian Ministry of Sciences and Education, Russian Academy of Sciences.
• Gabitov, I. R., Gibney, J., & KUK, I. (2020, October). Riemann-Hilbert Problem and nonlinearity “compensation” in coherent optical communication systems. International conference "Basic Problems of Optics" BPO'2020. St. Petersburg, Russia: OpticalSociety of America (OSA), Society of Photo-optical Instrumentation Engineers (SPIE) , Institute of Electrical and Electronics Engineers (IEEE).
• Gabitov, I. R., Gibney, J., & Kuk, I. (2020, December). Intrachannel pulse interaction in optical fiber communication systems. XXIV International conference Coherent optics and optical spectroscopy. Kazan, RUSSIA: Ministry of Science and Education of the Russian Federation.
• Gabitov, I. R., Gibney, J., & Kuk, I. (2020, December). Nonlinearity in coherent communication systems: the return of a forgotten problem. XXIX Scientific Session of the Council on Nonlinear Dynamics, Russian Academy of Sciences. Moscow, Russia (online): Russian Academy of Scinces.
• Gibney, J. (2019, August). Negative Impact of Nonlinearity on High Speed Optical Fiber Communications. International School on Nonlinear Photonics. Skoltech, Moscow: Skolkovo Institute of Science and Technology, Novosibirsk State University, and Russian Science Foundation.
• Gibney, J. (2019, July 15-19). Negative Impact of Nonlinearity on High Speed Optical Fiber Communications: New Approach to Address Old Challenge. 9th International Congress on Industrial and Applied Mathematics 2019. Valencia.
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  ICIAM2019 PROGRAM & ABSTRACTS BOOK, page 120
• Gabitov, I. R. (2018, Feb). Nonlinear phenomena in structured materials. 3-rd International Conference "February Readings". Baku, Azerbaijan: National Aviation Academy.
• Gabitov, I. R. (2018, Feb). Photonics for life. 3rd International Conference "February Readings". Baku, Azerbaijan: National Aviation Academy.
• Gabitov, I. R. (2018, Nov). Surface Waves on the Interface Between Hyperbolic Matter and Topological Insulator. Nanophotonics Session Russian Academy of Sciences. Moscow: Russian Academy of Sciences.
• Gabitov, I. R. (2018, Sep). Bounded optical pulses in dispersion managed systems. 17th International Conference on Laser Physics. Akademgorodok, Russia: Siberian Branch of the Russian Academy of Sciences.

Others

• Gabitov, I. R., Maimistov, A. I., & Lyashko, E. (2017, 19 Jun 2017). Surface Waves on the Interface Between Hyperbolic Material and Topological Insulator. 1. arXiv:1706.05951 [physics.optics]. https://arxiv.org/abs/1706.05951