Dedicated to the 50th anniversary of the laser 80th anniversary of Kharkov National University of Radio Electronics 205th anniversary of V. N. Karazin Kharkov National University bicentenary of Mexican independence

PROCEEDINGS

10th International Conference on Laser and Fiber-Optical Networks Modeling

LFNM*2010

2nd IEEE International Workshop On THz Radiation: Basic Research and Applications

TERA*2010

Kharkov National University of Radio Electronics

V. N. Karazin Kharkov National University

Taurida National V. I. Vernadsky University

Sevastopol, Ukraine

12-14 September 2010

I

LFNM*2010 program committee I. A.Sukhoivanov LFNM PC Co-Chair, University of Guanajuato, Mexico

National University of Radio Electronics, Kharkiv, Ukraine W. Freude LFNM PC Co-Chair, University of Karlsruhe, Germany L. A. Ageev V. N. Karazin National University, Kharkov, Ukraine L. A. Angelsky Chernivtsi State University, Chernivtsi, Ukraine S. S. Anufrik State University, Grodno, Belarus G. Belenky State University of New York, USA P. Chamorro-Posada Universidad de Valladolid, Valladolid, Spain N. Dogru University of Gaziantep, Gaziantep, Turkey S. F. Dyubko V. N. Karazin National University, Kharkov, Ukraine M. I. Dzubenko Institute Radiophys and Electronics of National Academy of Sciences of Ukraine, Kharkov, Ukraine N. N. Elkin State R&D Center TRINITI, Troitsk, Russia S. O. Iakushev National University of Radio Electronics, Kharkov, Ukraine V. K. Kononenko Institute of Physics, Minsk, Belarus M. Marciniak National Institute of Telecommunications, Poland V. K. Miloslavsky V. N. Karazin National University, Kharkiv, Ukraine A. I. Nosich Institute Radiophys and Electronics of National Academy of Sciences of Ukraine, Kharkov, Ukraine S. Ponomarenko Dalhousie University, Halifax, Canada V. E. Privalov BSTU, St. Petersburg, Russia Yu. S. Shmaly University of Guanajuato, Mexico M. O. Szymanski Institute of Electron Technology, Warsaw, Poland J. Tervo University of Joensuu, Finland R. Vlokh Institute of Physical Optics, Ukraine V. G. Volostnikov Samara branch of P. N. Lebedev Physical Institure of RAS

TERA*2010 program committee I. A. Sukhoivanov Workshop and PC Co-Chair, University of Guanajuato, Mexico

National University of Radio Electronics, Kharkiv, Ukraine M. F. Pereira Workshop Co-Chair, Sheffild Halam University, UK M. Marciniak PC Co-Chair, Nat. Institute of Telecommunications, Warsaw, Poland V. A. Svich PC Co-Chair, V. N. Karazin National University, Kharkiv, Ukraine D. Mittleman Rice Univ. ECE Dept., Houston, USA S. I. Petrov National University of Radio Electronics, Kharkiv, Ukraine O. V. Shulika National University of Radio Electronics, Kharkiv, Ukraine S. I. Tarapov Institute Radiophys and Electronics of National Academy of Sciences of Ukraine, Kharkov, Ukraine LFNM/TERA*2010 organizing committee I. A. Sukhoivanov General Chair, University of Guanajuato, Mexico J. A. Andrade-Lucio University of Guanajuato, Mexico V. N. Berzhansky Local Organization, Taurida National V.I.Vernadsky University, Simferopol, Ukraine I. V. Dzedolik Local Chair, Taurida National V. I. Vernadsky University, Simferopol, Crimea, Ukraine A. V. Degtyarev Local Organization, V. N. Karazin National University, Kharkiv, Ukraine E. Eres'ko Taurida National V.I.Vernadsky University, Simferopol, Ukraine V. I. Fesenko Local Organization, National University of Radio Electronics, Kharkiv, Ukraine A. I. Filipenko National University of Radio Electronics, Kharkiv, Ukraine T. B. Gryschenko National University of Radio Electronics, Kharkiv, Ukraine O. V. Gurin Local Organization, V. N. Karazin National University, Kharkiv, Ukraine I. V. Guryev National University of Radio Electronics, Kharkiv, Ukraine O. Ibarra-Manzano University of Guanajuato, Mexico S. O. Iakushev National University of Radio Electronics, Kharkiv, Ukraine A. V. Kublik Coordinator, Registration, National University of Radio Electronics, Kharkiv, Ukraine M. V. Klymenko National University of Radio Electronics, Kharkiv, Ukraine A. Levchenko V. N. Karazin National University, Kharkiv, Ukraine V. A. Maslov Co-chair, Local Management, V. N. Karazin National University, Kharkiv, Ukraine Y. P. Machekhin National University of Radio Electronics, Kharkiv, Ukraine J. Mikulska Local Organization, Taurida National V.I.Vernadsky University, Simferopol, Ukraine S. I. Petrov Co-chair, National University of Radio Electronics, Kharkiv, Ukraine T. F. Ruban V. N. Karazin National University, Kharkiv, Ukraine A. Rubass Local Organization, Taurida National V. I. Vernadsky University, Simferopol, Crimea, I. M. Safonov National University of Radio Electronics, Kharkiv, Ukraine A. N. Shaposhnikov Local Organization, Taurida National V. I. Vernadsky University, Simferopol, Ukraine O. V. Shulika Coordinator, Publication Chair, Web-designer, National University of Radio Electronics, Kharkiv, Ukraine A. N. Topkov V. N. Karazin National University, Kharkiv, Ukraine A. V. Vasyanovich National University of Radio Electronics, Kharkiv, Ukraine

II

Contents Semiconductor Lasers and Structures Band Structure of InGaN/GaN Quantum Wells Under Influence of Internal Fields and Indium Surface Segregation M.V.Klynemko, O. V. Shulika ...........................................................................................................................................................................................1 In-Doped ZnO Single Crystals as a Novel Laser Material L.E. Li , L.N. Demyanets ...................................................................................................................................................................................................5 Optimization of CdxHg1 – xTe Laser Structures and Stimulated Emission at Room Temperature under Optical Excitation A. A. Andronov, Yu. N. Nozdrin, A. V. Okomel’kov, N. N. Mikhailov, G. Yu. Sidorov, V. S. Varavin .............................................................7 Novel High-Power Superluminescent Diodes with Wide Active Channels Yu. O. Kostin, A. A. Lobintsov, S. D. Yakubovich ..................................................................................................................................................... 10 Femtosecond Laser-Induced Self-Ordered Nanostructures in Semiconducting 4H-SiC V.S. Makin, R.S. Makin, I.A. Silantyeva ........................................................................................................................................................................ 13 Stimulated Emission and Amplification Coefficient for Quantum Dots Arrays under Optical Pumping A. A. Andronov, Yu. N. Nozdrin, A. V. Okomel’kov, A. P. Vasiljev, A. E. Zhukov, V. M. Ustinov ................................................................ 16 On a Possibility to Reduce the Electron Beam Energy Used for Pumping of ZnSe-Based Green Semiconductor Laser Heterostructures M. M. Zverev, N. A. Gamov, E. V. Zdanova, V. B. Studionov, D. V. Peregoudov, S. V. Ivanov, I. V. Sedova, S. V. Sorokin, S. V. Gronin, P. S. Kop’ev ........................................................................................................................ 19 Calculation of Energy Characteristics of Si1−xGex–Si Quantum-Well Heterostructures Using k·p Method D. V. Ushakov, V. K. Kononenko ................................................................................................................................................................................. 23 Band Engineering of Complex Asymmetric Multiple Quantum Wells for Optically Pumped Semiconductor Disk Lasers O. V. Shulika, I. A. Sukhoivanov, M. V. Klymenko, I. M. Safonov, J. A. Andrade-Lucio, A. Garcia-Perez, R. Rojas-Laguna ........................................................................................................................................... 26 Nanophotonics, Metamaterials, Photonics Crystals Near-field resonances in diagnostics of multilayered media K. P. Gaikovich, P. K. Gaikovich ................................................................................................................................................................................... 30 Light Propagation Characteristics in Metal-Dielectric Optical Nanocables O. N. Kozina, L. A. Melnikov, I.S. Nefedov ................................................................................................................................................................. 32 Thermal Tuning of the Free-Standing Mesoporous Microcavity Infiltrated with Liquid Crystal G. V. Tkachenko, O. V. Shulika ..................................................................................................................................................................................... 34 Plasmon Resonances in the H-wave Scattering by a Nanosize Thin Flat Silver Strip O. V.Shapoval, R. Sauleau, A. I.Nosich ........................................................................................................................................................................ 37 Spontaneous Emission in 1D Band Gap Structure A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov .................................................................................................................................................. 40 Enhancement of Plasmon Resonances in the Wave Scattering by Finite Grids of Circular Silver Wires D. M. Natarov, T.M. Benson, A. Altintas, R. Sauleau, A. I. Nosich ......................................................................................................................... 42 Thermal Sensors based on Ytterbium-Erbium Doped Nano-Glassceramics V. Aseev, A. Abdrshin, E. Kolobkova, R. Nuryev, K. Moskaleva, N. Nikonorov ................................................................................................. 45 Properties of BaTiO3 Confined in Opal Matrices - Lattice Packings of Nanospheres Silica Dioxide D. Nuzhnyy, P. Vanek, J. Petzelt, V. Bovtun, M. Kempa, I. Gregora, M. Savinov, R. Krupkova, V. Studnicka, M.I. Samоylovich, A.B. Rinkevich, A.F. Belyanin, S.M. Klescheva ....................................................................... 47 Acoustooptic Bragg Interaction in 2D Photonic Crystals D. A. Parhomenko, S. A. Kolenov ................................................................................................................................................................................ 50 Design of All-Optical XOR and AND Logic Gates Based on Multi-Mode Interference Devices Y. Ishizaka, Y. Kawaguchi, K. Saitoh, M. Koshiba ..................................................................................................................................................... 53 The ε" < 0 Approximation vs Semi-Classical Approach to Active Media A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. P. Vinogradov ................................................................................................................. 56

III

Criterion for the Appearance of Negative Dielectric Areas in Crystals S. G. Felinskyi, G. S. Felinskyi ........................................................................................................................................................................................ 58 The Temperature- and Thickness-Dependence of the Photonic Band Gap Spectra of the One-Dimensional Photonic Crystal with a Superconducting Defect Layer N.N. Dadoenkova, A.E. Zabolotin, I.L. Lyubchanskii, Y.P. Lee, Th. Rasing .......................................................................................................... 60 Surface Plasmon-Polaritons and Waveguide Modes in Prismatic Structures I.Ya.Yaremchuk, V.M. Fitio, Ya.V. Bobitski ................................................................................................................................................................. 63 Nonlinear Optical Response of Smectic Structure Glasses Based on Cobalt Alkanoates G. V. Klimusheva, Yu. A. Garbovskiy, A. V. Gridyakina, A. S. Tolochko, D. A. Melnik, T. A. Mirnaya .......................................................... 66 A New Optical Polymer Nanocomposite Antireflection Medium for Optical Devices N. M. Ushakov, O. N. Gadomsky, I. D. Kosobudskii, V. Ya. Podvigalkin, P.A. Muzalev, D.M. Kulbatskii .................................................... 69 One-Dimensional Magnetophotonic Crystals Based on Double-Layer Bi-substituted Iron Garnet Films V. N. Berzhansky, A. V. Karavainikov, A. R. Prokopov, A. N. Shaposhnikov, M. I. Sharipova, T. V. Dolgova, A. A. Fedyanin .................................................................................................................... 71 Scattering of the Polarized Gaussian Beam on the Metamaterial Slab E. N. Odarenko, A. A. Shmat’ko, A. S. Naklutskiy .................................................................................................................................................... 74 The Evolution of Pressed Wave Fields Excited by Grating Coupler V.S. Makin, V.V. Trubaev ............................................................................................................................................................................................... 76 Dispersive Media, Light Propagation, Nonlinearities in Active and Passive Media CzechLight Family of Optical Networking Equipment K. Slavicek, J. Vojtech ..................................................................................................................................................................................................... 79 Broadband Aperiodic Multilayer Mirrors for Supercontinuum Reflection S.O. Iakushev, I.A.Sukhoivanov, E. Alvarado-Mendez, M. Trejo-Duran, J.A.Andrade-Lucio, R.Rojas-Laguna, O. Ibarra-Manzano .......................................................................................................... 84 Performance Comparison of OOC Codes at Various Receivers for OCDMA System R. Khurana, G. Kaur ...................................................................................................................................................................................................... 87 The Reflection Profile Engineering Approach to Optimize VIPA Demultiplexer for UWB-Over-Fiber Systems A. Mokhtari, M. Akbari .................................................................................................................................................................................................. 90 General Noise Considerations of Amplified Photons in Lightwave Systems with Optically Bistable Elements H. Abediasl, A. Naqavi, K. Mehrany, S. M. Mousavi, J. Aliakbar, S. M. Mousavi ............................................................................................... 93 Interplay of Non-Linearity and Dispersion in Chalcogenide Glass E. A. Romanova, A. I. Konyukhov, Yu.S.Chaikina, V.S. Shiryaev ........................................................................................................................... 96 Effect of Stimulated Raman Scattering on the Fission of High-Order Solitons in the Fiber with Periodically Modulated Core Diameter A. Konyukhov, A. Sysoliatin, V. Stasuyk, L. Melnikov ............................................................................................................................................. 98 Classification of Binary Acentric Tellurides V. V. Atuchin, B. I. Kidyarov ........................................................................................................................................................................................ 101 Fused Silica As a Composite Nanostructured Material E. D. Makovetsky, V. K. Miloslavsky, L. A. Ageev, K. S. Beloshenko ................................................................................................................... 104 Optical Bistability Involving Planar Metamaterial with a Broken Structural Symmetry V. Tuz, S. Prosvirnin, L. Kochetova ............................................................................................................................................................................ 107 Time-Domain BPM for Modeling Ultrashort Pulsed Optical Beams in Dispersive Medium M. Shahed Akond, H. M. Masoudi, M. A. Alsunaidi ............................................................................................................................................... 110 Localized Modes Configuration of a Cantor-like Chiral Photonic Structure V. Tuz, O. Batrakov ........................................................................................................................................................................................................ 113 Evolution of Waves after Plasma Ignition in a Sphere T. Ye. Remayeva, A. G. Nerukh, N. K. Sakhnenko ................................................................................................................................................... 116 Determination of Atmospheric Transmission Media Properties in Optical Spectrum by Analysis of Optical Beam Profile L. Dordova, O. Wilfert ................................................................................................................................................................................................... 119

IV

Optical Formation of Stable Polymeric Units for Fiber-Optics S. N. Mensov, Yu. V. Polushtaytsev ............................................................................................................................................................................ 122 Computer Simulation and Experimental Investigation of Non-Uniform Polymeric Structures Optical Formation for Fibers Interconnecting S. N. Mensov, Yu. V. Polushtaytsev ............................................................................................................................................................................ 125 Design and Optimization of Concave Diffraction Grating for WDM Multi/Demultiplexer L. V. Bartkiv, Ya. V. Bobitski ........................................................................................................................................................................................ 128 Theoretical and Experimental Optical Properties in Three Ionic Liquids of [BMIM] Family M. Trejo-Durán, E. Alvarado-Méndez, J. A. Andrade-Lucio, K. A. Barrera-Rivera, J.M. Estudillo-Ayala, I. A. Sukhoivanov .............................................................................................................................. 131 Pulsewidth Evolution and Blending Rate of Strongly DM Interacting Solitons F. J. Diaz-Otero, P. Chamorro-Posada ........................................................................................................................................................................ 133 Electrical dc conductivity and laser damage threshold of pure and urea-doped KDP single crystals A. N. Levchenko, I. M. Pritula, A. V. Kosinova, M. I. Kolybayeva, V. B. Tyutyunnik, A. V. Krivtsov, A. I. Starikov, A. P. Gavrik ............................................................................................................................... 136 Analysis of the Dynamics Shaping Microstructured Optical Fiber During Drawing Process A. I. Filipenko, A. V. Ponomaryova ............................................................................................................................................................................ 139 Research of Autoconvolution Method Efficiency under Control of Photonic Crystal Fibers Positioning A.I. Filipenko, O.V. Sychova ........................................................................................................................................................................................ 143 Interrelationship “Structure – Nonlinear Optical Properties” for Acentric Chlorides V. V. Atuchin, B. I. Kidyarov ........................................................................................................................................................................................ 146 Reflection Grating Theory at Fulfillment of the Second and Third Orders Bragg Conditions V. M. Fitio, Y. V. Bobitski .............................................................................................................................................................................................. 149 Novel Temperature/Humidity-Sensitive Multilayer Thick-Film Structures for Integrated Sensors Application H. I. Klym, I. V. Hadzaman, O. I. Shpotyuk .............................................................................................................................................................. 152 Localization and Polarization Transformation of Waves by an Asymmetrical Modified Fibonacci Chiral Multilayer V. Tuz, O. Batrakov ........................................................................................................................................................................................................ 155 Design of Faraday Rotator for the Optical Switch G. D. Basiladze, V. N. Berzhansky, A. I. Dolgov ....................................................................................................................................................... 158 Refraction of Power-Law Spatial Solitons – the Helmholtz-Snell Law J. M. Christian, J. Sánchez-Curto, P. Chamorro-Posada, G. S. McDonald, E. A. McCoy ................................................................................... 161 Passive Polarization Converter Based on the Bragg Reflector with Multiple Defects V. I. Fesenko .................................................................................................................................................................................................................... 164 Induced Refraction Rings from Cumarine Materials E. Alvarado-Méndez, M. Trejo-Durán, J. A. Andrade-Lucio, J. M. Estudillo-Ayala, M. de la L. Sánchez-Estrada, M. A. Vázquez-Guevara, Y. Alcaraz-Contreras, I. Sukhoivanov ...................................................................... 165 Focused Femtosecond Vortex Laser Pulse V. G. Shvedov, C. Hnatovsky, W. Krolikowski, A. V. Rode ................................................................................................................................... 167 Optical Spectral-Selective Elements, Using Effect of the Light Scattering V.A. Manko, A.A. Manko ............................................................................................................................................................................................. 170 Application Efficiency Increasing of LiNbO3:MgO and GaP Crystals for Acoustooptical High-Frequency Control of Powerful Laser Irradiation A. S. Andrushchak, M. V. Kaidan, Ye. M. Chernyhivskiy, O. V. Yurkevych, T. A. Maksymyuk, B. G. Mytsyk, A. V. Kityk ............................................................................................................................ 172 Optical Wave Breaking Cancelation and Formation of Quasi-Parabolic Ultrashort Pulses S. O. Iakushev, O. V Shulika, J. Juan Rosales Garcia ................................................................................................................................................ 176 Laser Modeling Superradiation in the Course of the Electron Scattering by Ions in a Light Field S. P. Roshchupkin, V. A. Tsybul'nik .......................................................................................................................................................................... 180

V

Polariton Mode Lasing in Quantum-Well Traps for Bose-Condensation of Dipolar Excitons P. A. Kalinin, V. V. Kocharovsky, V. V. Kocharovsky ............................................................................................................................................ 183 Conservative Finite-Difference Scheme for a Two-Dimensional Problem of Plasma Generation in a Semiconductor Under a Laser Pulse Action V.A. Trofimov, M.M. Loginova .................................................................................................................................................................................. 186 Microscopic Statistical Theory of Inhomogeneous Broadening in InGaN/GaN Quantum Wells M. V.Klymenko, O. V. Shulika .................................................................................................................................................................................... 189 Resonant Over-Barrier Hole States in Multiple Quantum Wells A. F. Polupanov, A. N. Kruglov ................................................................................................................................................................................. 192 About Phase Components of Differential-Phase LBIC from p-n Junction Transversal Plane Scanning L. N. Ilchenko, S. O. Kolenov, S.V. Litvinenko, P. V. Molochko ........................................................................................................................... 195 Selection of Electrodes Profile for Excimer Lasers S. S. Anufrik, A. P. Volodenkov, K. F. Znosko ......................................................................................................................................................... 198 Dynamic Regimes of a Dual-Wavelength Vertical External Cavity Surface-Emitting Laser Yu. A. Morozov, M. Yu. Morozov, V. V. Popov ....................................................................................................................................................... 201 Influence of the Spectral Tuning on Modulation Response of Dynamic Single-Mode Heterolasers (1.5 μm-Diapason) B. F. Kuntsevich, V. K. Kononenko ............................................................................................................................................................................. 203 Super-Radiance in Radiation Spectrum of Four Electrons Moving in Spiral in Transparent Medium A. V. Konstantinovich, I. A. Konstantinovich ........................................................................................................................................................... 206 Diffusive Random Lasing Modeling Yashchuk V. P., Zhuravsky M. V., Prigodyuk O. A. ................................................................................................................................................ 209 Quantum Fields Theory in Laser Physics Nonresonant Scattering of a Photon by an Electron in the Pulsed Electromagnetic Field V. N. Nedoreshta, S. P. Roshchupkin, A. I. Voroshilo ............................................................................................................................................. 211 Resonant Scattering of a Lepton by a Lepton in the Pulsed Electromagnetic Field E. A. Padusenko, S. P. Roshchupkin ........................................................................................................................................................................... 214 Resonant Bremsstrahlung of an Electron Scattered by an Ion in a Pulsed Light Field A. A. Lebed', S. P. Roshchupkin .................................................................................................................................................................................. 217 Resonance Two-Photon Annihilation of an Electron-Positron Pair in the Light Wave Field O. I. Denisenko, S. P. Roshchupkin ............................................................................................................................................................................. 220 The Uranium Nuclei Attraction Effect in the Pulsed Field of two Counter-Propagating Laser Waves S. S. Starodub, S. P. Roshchupkin ................................................................................................................................................................................ 223 Resonance of Direct Amplitude of Process of Scattering of a Photon by an Electron in the Pulsed Laser Field A. I. Voroshilo, S. P. Roshchupkin, V. N. Nedoreshta ............................................................................................................................................. 226 Nonresonant Photoproduction of an Electron-positron Pair with Radiation of a Photon P. I. Fomin, R. I. Kholodov ............................................................................................................................................................................................ 229 Spin-polarization Effects in QED-Processes in a Pulsar Magnetosphere O. P. Novak, R. I. Kholodov ......................................................................................................................................................................................... 232 TERA Workshop (Invited) 21st Century Optical Engineering: Manipulating Nonequilibrium Many Body Effects to Create new TERA-MIR Sources M. F. Pereira ................................................................................................................................................................................................................... 235 (Invited) Plasmonic Microdevices for Terahertz Frequencies V. V. Popov .................................................................................................................................................................................................................... 237 THz Emission Efficiency of Grating-Outcoupled Nonlinear-Mixing Heterolasers A. V. Andrianov, A. A. Belyanin, V. V. Kocharovsky, V. V. Kocharovsky .......................................................................................................... 242 Using Terahertz Cascade Lasers for Determination of Optical Losses in Active Medium of Silicon Intracenter Lasers S. G. Pavlov, R. Eichholz, N.V. Abrosimov, H. Riemann, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. T. Grahn, A. Tredicucci, H.E. Beere, D.A. Ritchie and H.-W. Hübers ............................................................................................... 245

VI

(Invited) Application of High Power Terahertz Sources to Nonlinear Spectroscopy of Direct Bandgap Semiconductors R. Morandotti, L. Razzari, F. Blancharda, F. H. Suc, G. Sharmaa, A. Ayesheshimc, T. L. Cocker, L. V. Titova, H-C Bandulet, J-C Kieffer, T. Ozaki, M. Reid, F. A. Hegmann .............................................................................................................................. 248 A compact THz Source for Imaging and Spectroscopy H. Richter, M. Greiner-Bär, S. G. Pavlov, A. D. Semenov, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. Grahn, H.-W. Hübers ................................................................................................................................... 251 Optically Driven Tuning of Gain Spectra in Quantum Cascade Lasers M.V.Klymenko, O. V. Shulika , S. I. Petrov ............................................................................................................................................................... 253 The Ability of CW Operation of THz Lasing from Group-V Donors in Silicon V. N. Shastin, R. Kh. Zhukavin, K. A. Kovalevsky, V. V. Tsyplenkov, S. G. Pavlov, H.-W. Hübers ............................................................... 256 Technique of Measuring the Effective Constitutive Parameters of Metamaterials S. I. Tarapov, D.P. Belozorov, M.K. Khodzitsky, S.V. Nedukh .............................................................................................................................. 259 Proteins Vibrations in THz Frequency Domain M. Mernea, O. Calborean, L. Petrescu, M. P. Dinca, A. Leca, D. Apostol, T. Dascalu, D. Mihailescu ............................................................. 261 Terahertz Properties and the Negative Dielectric Regions in Boron Nitride S. G. Felinskyi, P. A. Korotkov, G. S. Felinskyi ......................................................................................................................................................... 265 (Invited) THz Multifunctional Quasi-Optical Measuring System for Education and Science V.K. Kiseliov, Ye.M. Kuleshov , M.S. Yanovsky ...................................................................................................................................................... 267 Asymptotic Analysis of the Far Field of the Terahertz Antenna E. A. Gorodnitskiy, N. S. Averkiev, A. M. Monakhov, M. V. Perel ....................................................................................................................... 272 Thermopile as THz Detector B. Szentpáli, P. Basa, P. Fürjes, G. Battistig, I. Bársony ............................................................................................................................................ 275 Absorbtion and Quantum Efficiency Calculation for Quantum Cascade Photodetector S. Gryshchenko, M. Klymenko, O. Shulika, V. Lysak ............................................................................................................................................. 278 The Resulted Impedance of the Cylinder Covered with a Thin Dielectric Layer V. I. Vyunnik, A. A. Zvyagintsev ............................................................................................................................................................................... 280 Novel Double-Mode O-type Source of Coherent Subterahertz Radiation E. N. Odarenko, А. A. Shmat’ko, P.V.Yudintcev, V. M. Vasilenko ....................................................................................................................... 283 Periodic Nano- and Microstructures for Reception and Transmission of Information of the Terahertz Range A. K. Esman, V. K. Kuleshov, G. L. Zykov, V. B. Zalesski, V. M. Kravchenko .................................................................................................... 285 Polariton Spectrum Control in Dielectric Medium I. V. Dzedolik, J. P. Mikulska ........................................................................................................................................................................................ 288 (Invited) Methods of Microwave Physics in Developing THz Frequency Range V. L. Vaks ......................................................................................................................................................................................................................... 291

Optical Wave Breaking Cancelation and Formationof Quasi-Parabolic Ultrashort Pulses

S. O. Iakushev1, Student Member, IEEE, O. V Shulika1, Member, IEEE,, J. Juan Rosales Gacia2,1Kharkov National University of Radio Electronics, Ukraine

2University of Guanajuato, Mexico

Abstract—We consider formation of ultrashort quasi-parabolicpulses in conventional silica fibers both in the near and farfields of dispersion. Through solution of nonlinear Schrodingerequation we show that in case of high soliton order N the opticalwave breaking effect, occurring in optical fibers during ultrashortpulse propagation, is canceled in the far field of dispersion.This is accompanied by nonlinear pulse reshaping from initialGaussian shape towards nearly parabolic pulse with almost linearchirp. We suppose that this process is associated with relaxingconditions required for optical shock formation. Divergence ofthe resulted pulse shape from the parabolic one is quantitativelyexamined. Optimal conditions for soliton order and fiber lengthrequired for nearly parabolic shape formation is given for caseof low N .

Index Terms—Optical wave breaking, quasi-parabolic pulses,parabolic pulses, ultrashort pulses, nonlinear pulse reshaping.

I. INTRODUCTION

LAST years intensive efforts were devoted to the theoret-ical and experimental investigations of parabolic pulses

formed in fiber amplifiers [1]. These pulses called similaritonshold their temporal and spectral shape with a scale factorduring propagation over the nonlinear fiber with gain in thenormal dispersive regime. Moreover these pulses hold a linearchirp. Similaritons are attractive for such implementationsas pulse amplification, pulse compression, pulse synthesis.However, for many applications, parabolic pulse generationschemes based on passive fiber components are preferable.Therefore, applications of dispersion decreasing fibers [2]and fiber Bragg gratings [3] to obtain parabolic pulses areproposed. But the simplest way was found based on passivenonlinear pulse reshaping in a normally dispersive fiber [4].The last one was investigated in the near field of dispersion(propagation distance doesn’t exceed the dispersion length). Itturns out that some optimal combination of the initial pulsepower and fiber length according to the initial pulse shape canprovide a parabolic pulse at the system output.

Recently was experimentally demonstrated that it is possibleto obtain parabolic pulses in the far field of dispersion inpassive nonlinear fiber under low soliton order [5]. However,there is no quantitative estimation to the divergence of thereal pulse shape from the parabolic one, which is importantfor practical applications. Moreover, perhaps more interestingand important question is what the conditions and materialparameters are to obtain parabolic pulses in conventionalfibers. Here we address those questions and discuss propertiesof parabolic pulses in the far field of dispersion and comparethem to parabolic pulses obtained in the near field.

II. QUASI-PARABOLIC PULSES IN THE NEAR AND FARFIELDS OF DISPERSION

We base our analysis on the nonlinear Schrodinger equationwhich govern evolution of the ultrashort pulse during itspropagation in a fiber with dispersion and Kerr nonlinearity

i∂A

∂z=β22

2

∂2A

∂T 2− γ|A|2A (1)

where A(z, T ) is the slowly varying complex envelope ofthe pulse; β2 is the second order dispersion; γ is the nonlinearcoefficient; T is the time in a copropagating time-frame;z is thepropagation distance. We neglect loss and high-order effectsin Eq.1 and analyze here only interplay between normal-dispersion (β2) and self-phase modulation (γ).

It is convenient to use following notations for the disper-sion length LD, nonlinear length LNL, soliton order N andnormalized length ξ:

LD =

(T0β2

)2

, LNL = (γP0)−1 (2)

N =

(LD

LNL

)1/2

, ξ =z

LD, (3)

here P0 is the peak power of the initial pulse, T0 is theinitial pulse width, β2 is the second order dispersion, γ is thenonlinear coefficient.

A. Low soliton order (↓ N )

The optical wave breaking appears (OWB) when N > 1,such that the effects of self-phase modulation (SPM) shoulddominate over those of normal group velocity dispersion(GVD), at least during the initial stages of the pulse evolution[1]. However, OWB is very weak and in fact is not observablein case of ↓ N . Here we address particular case of weak OWB,1 ≤ N ≤ 8. Under this conditions pulse evolution Gaussian→ parabolic runs relatively smoothly, Fig.1.

To characterize divergence between the shape of the realpulses and parabolic one we use the misfit parameter M[4] which collects in a single value difference between thepulse intensity profile |A(T )|2 and a parabolic fit |Ap(T )|2of the same energy. Smaller value of M shows better fit tothe parabolic shape. The misfit parameter M is calculated asa function of the soliton order N and normalized length ξand is shown on Fig.1(a). This allows to understand influenceof the initial pulse parameters P0 and T0 (relative to the

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(a)

(b)

(c)

(d)

Fig. 1. Normalized temporal intensities of pulses in the near (a) and far (b)fields of dispersion at different propagation distances ξ, and their normalizedspectral intensities (c) and (d). Soliton order N = 4.

fiber parameters β2 and γ) on the pulse reshaping. We havefound that quasi-parabolic pulses in the far field of dispersionare formed after the overcome of the optical wave breakingboundary.

On Fig.2(a) three specific areas are denoted by numerals.Numeral 1 indicates narrow and dip vertical valley in thenear dispersion field (ξ < 1). The terms ”vertical” and”horizontal” we use to emphasize the relation between rangesof propagation distance ξ and soliton order N . Vertical valleyrefers to ∆N � ∆ξ, and horizontal one refers to ∆N � ∆ξ.Area 1 has been extensively investigated by Finot et al. [4].A suitable M is achieved only over the narrow propagationdistance band, but it has been overcame using additional pieceof fiber [4]. Next we should point out adjacent wider verticalvalley (Numeral 2). Here the required propagation distance israther small (0.8 < ξ < 2) and misfit parameter M is closeto that one in the first area. Thus, this second area can beused in a similar way as the first one to obtain quasi-parabolicpulses. After the second valley (ξ > 2) M increases untilsome maximum is achieved as shown in Fig.2(b), and then Mreduces very slowly. We can see from Fig.2(b) that pulse shapetends to parabolic one with increasing of propagation distance.But actually this tendency becomes weaker with propagationdistance and increasing of N . Our calculations show thatM = 0.06 can be achieved only at ξ > 100 (N = 2).

The value of N strongly affects on the misfit parameter,M increases with increasing of N over the whole propagationdistance (ξ > 2). On Fig.2(a) we can point out the horizontalvalley 1.5 < N < 2.5, where misfit parameter achievessmaller value as compared to the outside value of N . MoreoverM reduces faster with propagation distance in this valley asFig.2(b) shows.

It is important to note the parabolic shape fit is worse in the

(a)

(b)

Fig. 2. (a) Evolution of the misfit parameter M versus soliton order Nand normalized length ξ. Numerals at the figure denote three specific areasdescribed in the text. The white solid line shows the wave-breaking condition[?]. (b) Evolution of the misfit parameter versus ξ for certain values of N .

far dispersion field as compared to parabolic pulse obtained inthe near field of dispersion for optimal conditions. The valueof misfit parameter in the near field of dispersion (for optimalparameter ξ = 0.2, N = 4) is M = 0.04 and in the far field ofdispersion (ξ = 8, N = 4) M = 0.09. However, as comparedto the quasi-parabolic pulses formed in the near field, in thefar field of dispersion there is no restriction of the specificshort propagation distance. It is possible to obtain similar pulsecharacteristics over the wide range of fiber lengths within thesuitable parameter ranges 1.5 < N < 2.5 and ξ = 8. Thefound conditions for nearly parabolic pulse formation in the farfield of dispersion can be released in the conventional siliconfiber within the positive dispersion region (β2 ≈ 0.03 ps2/m,γ ≈ 2 W−1km−1 at λ0 = 800 nm) using state-of-the-artTi:Sapphire or fiber lasers (P0 ∼ 9 kW, T0 ∼ 60 fs), so thatN ≈ 1.5 and LD ≈ 0.12 m. Thus, it can be possible toobtain nearly parabolic pulse (M ≈ 0.07) at ≈ 1 m of thefiber length and even less with decreasing of the initial pulseduration. Moreover, owing to the well defined spectral phaseit will be possible to provide appropriate chirp compensationusing some of the dispersive elements, like chirped mirrors forexample [6]–[9].

B. High soliton order (N ↑): Optical wave breaking cancela-tion

OWB becomes strong approximately for N > 15, whereassmaller N leads to the much lower pulse distortions associatedwith OWB. Here we start our consideration of the pulse evo-lution from the OWB stage occurred during initial unchirpedGaussian pulse in optical fiber when N = 30, Fig.3.

For the first time a pulse evolution resulted in the establish-ing of optical wave breaking was investigated by Lassen et al.[10] and Tomlinson et al. [11]. The optical wave breaking (seestage ξ = 0.065 at Fig.3) comprises following features. Pulsebecomes nearly rectangular with relatively sharp leading andtrailing edges. The instantaneous frequency function showsthat there is a nearly linear frequency chirp over most of thepulse width, and that steep transition regions have developedat the leading and trailing edges. The explanation of the opticalwave breaking establishment can be found elsewhere [11],[12], [13]. The key feature includes an optical shock formationand subsequent optical wave breaking [12]. Now let us look to

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Fig. 3. Evolution of the Gaussian pulse in a fiber showing optical wavebreaking cancelation (N = 30). First row comprises pulse temporal intensityover the increasing length ξ; second row - instantaneous frequency (chirp);third row - pulse spectrum. All quantities are normalized to their maxima;time and frequency are normalized to the initial pulse width.

the pulse evolution after the OWB stage is achieved. One cansee from Fig. 3 (ξ = 0.1 and ξ = 0.25 ) that oscillations ofthe chirp function decay at the pulse edges such that remainonly two bends around the pulse center. The magnitudes ofthese bends decrease with distance, thus actually instantaneousfrequency tends to flattening. At the same time oscillations ofthe pulse intensity envelope decay as well and we can seealso two symmetrical bends on the pulse intensity profile.These bends becomes weaker and moves to center of the pulsewith propagation distance. A quite long propagation distanceis required to complete this process. Only at ξ = 22 there areno any bends in the pulse intensity profile with the exceptionof bends at the foot of the pulse. The same behavior onecan observe in the pulse spectrum, i.e. the bends indicatingspectral sidelobes moves to the center of the spectrum and theirmagnitude decreases. In addition the oscillations in the top ofthe spectrum decay and SPM-induced spectrum broadeningstops. At the last stage (ξ = 22) pulse spectrum is smooth andit actually repeats temporal intensity profile.

Thus, evolutions of the pulse temporal intensity and pulsespectrum are quite similar, although optical wave breaking fea-tures at the pulse intensity profile disappear faster as comparedto the pulse spectrum. Symmetrical bends in the edges of thepulse temporal intensity and the spectrum indicate actually aboundary between low-intensity wings and old pulse edges.These low-intensity wings have a distinguished curvature ascompared to the old edges. Owing to the expansion of thesewings to the pulse center the new pulse edges distinguishedfrom the initial one are formed.

C. Analysis of OWB cancelation

Thus we can point out that initial unchirped Gaussianpulse evolves to the optical wave breaking but OWB is notmaintained with propagation distance. At some distance OWBactually canceled and we get fully smooth pulse with linearchirp. We explain these transformations by the followingway. It is clear that the mentioned above picture of OWB

Fig. 4. Pulse intensity - (a), chirp - (b) and spectrum - (c) at the distancesξ = 0.1 and ξ = 0.25. Dashed lines show the position of symmetricalbends. Pulse temporal intensity and spectrum are normalized to its maxima atξ = 0.1; time, frequency and chirp are normalized to the initial pulse width.

onset doesn’t freeze with propagation distance. Owing to thenormal dispersion a frequency-shifted light should overtakethe unshifted light in the pulse edges more and more withpropagation distance. When this frequency-shifted light com-pletely overtakes the unshifted light it forms new smooth pulsewings. Simultaneously because frequency-shifted light leavesthe zone of overtaking (maximum shifted light the fastest)one can expect flattening of the chirp function and weakeningof the shock. Respectively the oscillations associated withOWB should decay. Due to the flattening of the chirp in turnSPM induces spectral oscillation should decay and spectrumbroadening stops as well.

Owing to all these transformations we can see from Fig. 3 (ξ = 0.1 and ξ = 0.25) only weak symmetrical bends at pulsecharacteristics eventually. But another important feature is thatthis bends moves to the pulse center its magnitude decreasesand this is associated with expanding of novel temporal andspectral wings. Fig. 4 shows this process more in details.

One can see that there is an explicit relation between theposition of bends at the pulse intensity figure, chirp figure andspectrum figure. It can be explained in the following way: themaximum frequency-shifted light overtakes unshifted light thefastest but at the same time this light leaves an overtaken zoneat first and forms low intensity wings. However, it is naturalto expect that less frequency-shifted light will overtake theunshifted light further due to the action of normal dispersion.Owing to less frequency-shifted light is located closer to thepulse center we can observe the movement of symmetricalbends with propagation distance indicating the movement ofovertaken zone. At the same time the low-intensity pulse wingsexpand comprising a new frequency-shifted light. Becausethe difference between frequency-shifted light and unshiftedlight becomes lower approaching the pulse center, the bendsmagnitude decreases with propagation distance and breakingoscillations no longer appear.

Thus, from the shown pulse evolution we can point outthe main trend: GVD tends to flatten SPM induced nonlineardouble-peak chirp pattern with propagation distance. At firstit leads to the steepening of the chirp function, the steeptransition regions have developed at the leading and trailingedges. The difference between maximum frequency shiftedlight and unshifted light is the highest at first and strongshock is formed accompanied by breaking oscillations (OWBonset). But then the maximum frequency shifted light over-takes completely an unshifted light and forms new smooth

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pulse wings. Simultaneously chirp nonlinear pattern tends tofattening. This process continues with propagation distancesuch that less frequency shifted light is able to overtake anunshifted light however the steep transition becomes weakermore and more. This is accompanied by expanding of newpulse wings resulted in the new smooth pulse profile. Thus wesee actually the cancelation of OWB with propagation distanceand formation of smooth pulse with linear chirp whose shapeis different as compared to the initial Gaussian.

III. CONCLUSION

We have analyzed through numerical modeling features ofthe quasi-parabolic pulses obtained due to nonlinear reshapingin the near and far fields of dispersion of a passive opticalfiber. In case of high soliton order N we have found thatquasi-parabolic pulses in the far field of dispersion are formedafter the overcome of the optical wave breaking boundary. Theshape of the quasi-parabolic pulses tends to parabolic limitwith propagation distance but this tendency decays sufficiently.In case of low soliton order N its value strongly affects onthe misfit parameter M . We found that the misfit parameterM achieves the least value within 1.5 < N < 2.5 and pulseshape moves away from the parabolic with increasing of N .The misfit parameter M in the case of optimal N is almosttwo times larger as compared to the parabolic pulse in thenear field of dispersion (for the optimal conditions). The nearlyparabolic pulse (M ≈ 0.07) in the far field of dispersion canbe obtained using ≈ 1 m of the conventional silicon fiber underthe realistic initial pulse and fiber parameters.

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[3] F. Parmigiani, et al., “Ultra-flat SPM-broadened spectra in a highlynonlinear fiber using parabolic pulses formed in a fiber Bragg grating,”Opt. Express, vol.14, pp.7617–7622, 2006.

[4] C. Finot, et al., “Parabolic pulse generation through passive nonlinearpulse reshaping in a normally dispersive two segment fiber device,” Opt.Express, vol.15, pp.852–864, 2007.

[5] A. Zeytunyan, et al., “Spectrotemporal similarity and self-imaging ofnonlinear-dispersive similariton,” Proc. Int. Conf. Advan. Optoel. Lasers,CAOL 2008, Alushta, Crimea, Ukraine, p.131–133, 2008.

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[9] I.V. Guryev, O. V. Shulika, I.A. Sukhoivanov,et al., ”Improvement ofcharacterization accuracy of the nonlinear photonic crystals using finiteelements iterative method”, App. Phys. B, vol. 84, No 1-2, pp. 83-87,July 2006.

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[11] W. J. Tomlinson, R. H. Stolen, A. M. Johnson, ”Optical wave breakingof pulses in nonlinear optical fibers,” Opt. Lett., vol.10, pp.457–459, 1985.

[12] J. E. Rothenberg, ”Femtosecond optical shocks and wave breaking infiber propagation,” J. Opt. Soc. Am. B, vol.6, pp.2392–2401, 1989.

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