Parameter control of optical soliton in one‐dimensional photonic crystal

Abstract The paper deals with finding of soliton solution for Schrodinger equation with periodic linear and nonlinear properties of medium in 1D case. Such structure is named as photonic crystal. To find soliton solution the corresponding problem for finding of eigenfunctions and eigenvalues is formulated. Iterative process is proposed for solution of this problem. Using the technique of continuation on parameter we investigate a dependence of soliton location on its maximum intensity, on ratio between light frequency and frequency of structure, on ratio between dielectric permittivity of alternating linear and nonlinear layers and on position between centre of initial distribution of eigenfunction and center of considered photonic structure area. The results of this paper confirm the features of soliton self‐formation investigated early in our papers [37, 38, 39, 40, 41, 42], in which one considered a propagation of femtosecond laser pulse through nonlinear layered structure.

[1]  A. Martinez,et al.  Design of Silicon-Based Slot Waveguide Configurations for Optimum Nonlinear Performance , 2007, Journal of Lightwave Technology.

[2]  Vyacheslav A. Trofimov,et al.  Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity , 2008 .

[3]  James Demmel,et al.  Applied Numerical Linear Algebra , 1997 .

[4]  Svetlana A. Varentsova,et al.  Computational Method for Finding of Soliton Solutions of a Nonlinear Shrödinger Equation , 2004, NAA.

[5]  S. Turitsyn,et al.  Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion. , 1998, Optics letters.

[6]  F. M. Knox,et al.  Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion , 1997 .

[7]  P. Sheng,et al.  Introduction to Wave Scattering, Localization and Mesoscopic Phenomena. Second edition , 1995 .

[8]  Vyacheslav A. Trofimov,et al.  Stop of light in nonlinear photonic crystal , 2005, Saratov Fall Meeting.

[9]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[10]  Vyacheslav A. Trofimov,et al.  Localization of the femtosecond pulse train energy in a one-dimensional nonlinear photonic crystal , 2004 .

[11]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[12]  Adrian Ankiewicz,et al.  Solitons : nonlinear pulses and beams , 1997 .

[13]  Vyacheslav A. Trofimov,et al.  Localization of light energy of a femtosecond laser pulse upon generation of the second harmonic in a one-dimensional nonlinear photonic crystal with alternating nonlinear response , 2008 .

[14]  B A Malomed,et al.  Mismatch management for optical and matter-wave quadratic solitons. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Vyacheslav A. Trofimov,et al.  Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity , 2008 .

[16]  Boris A. Malomed,et al.  Soliton Management in Periodic Systems , 2006 .

[17]  Christophe Besse,et al.  A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations , 2008 .

[18]  Víctor M. Pérez-García,et al.  Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers , 2003, nlin/0305030.

[19]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[20]  A. Hasegawa,et al.  Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion , 2002 .

[21]  A. Booth Numerical Methods , 1957, Nature.

[22]  Vassilios Yannopapas,et al.  Anderson localization of light in inverted opals , 2003 .

[23]  Víctor M. Pérez-García,et al.  Numerical studies of stabilized Townes solitons , 2003, Math. Comput. Simul..

[24]  Vyacheslav A. Trofimov,et al.  Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a nonlinear photonic crystal with nonreflecting boundary conditions , 2006 .

[25]  B. Malomed,et al.  Conditions for stationary pulse propagation in the strong dispersion management regime , 1998, Nonlinear Guided Waves and Their Applications.

[26]  Mindaugas Radziunas,et al.  Numerical Algorithms for Schrödinger Equation with Artificial Boundary Conditions , 2009 .

[27]  Yuri S. Kivshar,et al.  Nonlinear localized modes in waveguide bends , 2003 .

[28]  D Mihalache,et al.  Stable three-dimensional optical solitons supported by competing quadratic and self-focusing cubic nonlinearities. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  B. A. Malomed,et al.  Multidimensional solitons in periodic potentials , 2003 .

[30]  L. M. Kovachev,et al.  Vortex solitons in dispersive nonlinear Kerr type media , 2005, SPIE Optics + Optoelectronics.

[31]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[32]  Philip Holmes,et al.  Strong NLS Soliton-Defect Interactions , 2002, nlin/0203057.

[33]  Bowden,et al.  Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials. , 1994, Physical review letters.

[34]  Joseph W. Haus,et al.  Photonic Band Gap Structures , 2004 .

[35]  Mindaugas Radziunas,et al.  Numerical algorithms for simulation of multisection lasers by using traveling wave model , 2008 .

[36]  Vyacheslav A. Trofimov New approach to numerical simulation of femtosecond pulse propagation in photonic crystals , 2000, Saratov Fall Meeting.

[37]  Gene H. Golub,et al.  Matrix computations , 1983 .

[38]  Vyacheslav A. Trofimov,et al.  Soliton self-formation in nonlinear photonic crystal , 2006, International Conference on Coherent and Nonlinear Optics.

[39]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[40]  Vyacheslav A. Trofimov,et al.  Soliton-like propagation of light pulses in a nonlinear photonic crystal , 2004 .

[41]  Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity , 2006 .

[42]  Boris A. Malomed,et al.  Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity , 2002 .

[43]  John,et al.  Strong localization of photons in certain disordered dielectric superlattices. , 1987, Physical review letters.

[44]  E. Yablonovitch,et al.  Inhibited spontaneous emission in solid-state physics and electronics. , 1987, Physical review letters.

[45]  Wolfgang Freude,et al.  Highly-Nonlinear Silicon Photonics Slot Waveguide , 2008 .

[46]  U. Al Khawaja,et al.  Integrability of a general Gross-Pitaevskii equation and exact solitonic solutions of a Bose-Einstein condensate in a periodic potential , 2009 .