9 research outputs found
Negative refraction and spatial echo in optical waveguide arrays
The special symmetry properties of the discrete nonlinear Schrodinger
equation allow a complete revival of the initial wavefunction. That is employed
in the context of stationary propagation of light in a waveguide array. As an
inverting system we propose a short array of almost isolated waveguides which
cause a relative pi phase shift in the neighboring waveguides. By means of
numerical simulations of the model equations we demonstrate a novel mechanism
for the negative refraction of spatial solitons.Comment: 3 pages, 2 figure
Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity
We extend a recently developed Hamiltonian formalism for nonlinear wave
interaction processes in spatially periodic dielectric structures to the
far-off-resonant regime, and investigate numerically the three-wave resonance
conditions in a one-dimensional optical medium with nonlinearity.
In particular, we demonstrate that the cascading of nonresonant wave
interaction processes generates an effective nonlinear response in
these systems. We obtain the corresponding coupling coefficients through
appropriate normal form transformations that formally lead to the Zakharov
equation for spatially periodic optical media.Comment: 14 pages, 4 figure
Nonlinear Wave Interaction In Photonic Band Gap Materials
We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose-Einstein condensates in optical lattices. © 2006
Justification Of The Nonlinear Schrödinger Equation In Spatially Periodic Media
The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media can approximately be described by solutions of a Nonlinear Schrödinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall\u27s inequality. © Birkhäuser Verlag, Basel 2006
All-Optical Diode In An Asymmetrically Apodized Kerr Nonlinear Microresonator System
We show numerically that a Kerr nonlinear system composed of two channel waveguides coupled periodically by circular microresonators can be used as an all optical diode. The diode has low intensity requirements ( ∼ 50 MW/cm2) and compact dimensions (∼ 100 μm). © 2004 Elsevier B.V. All rights reserved