## Abstract

We present a numerical study of a two dimensional all-optical switching device
which consists of two crossed waveguides and a nonlinear photonic band-gap
structure in the center. The switching mechanism is based on a dynamic shift of
the photonic band edge by means of a strong pump pulse and is modeled on the
basis of a two dimensional finite volume time domain method. With our
arrangement we find a pronounced optical switching effect in which due to the
cross-waveguide geometry the overlay of the probe beam by a pump pulse is
significantly reduced.

©1998 Optical Society of America

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### Equations (11)

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(1)
$$\frac{1}{c}\frac{\partial}{\partial t}{D}_{z}=\frac{\partial}{\partial x}{H}_{y}-\frac{\partial}{\partial y}{H}_{x}$$
(2)
$$\frac{1}{c}\frac{\partial}{\partial t}{B}_{x}=-\frac{\partial}{\partial y}{E}_{z}$$
(3)
$$\frac{1}{c}\frac{\partial}{\partial t}{B}_{y}=\frac{\partial}{\partial x}{E}_{z}$$
(4)
$$\frac{\partial}{\partial x}{B}_{x}+\frac{\partial}{\partial y}{B}_{y}=0,$$
(5)
$${D}_{z}=\u03f5\xb7{E}_{z}+{\chi}_{3}\xb7{E}_{z}^{3}={\u03f5}_{\mathit{nl}}\xb7{E}_{z}.$$
(6)
$$w=\frac{1}{2}\left({E}_{z}{D}_{z}+{B}_{x}^{2}+{B}_{y}^{2}\right).$$
(7)
$$\frac{\partial}{\partial t}\overrightarrow{V}+\frac{\partial}{\partial x}{\overrightarrow{F}}_{x}+\frac{\partial}{\partial y}{\overrightarrow{F}}_{y}=0$$
(8)
$${\int}_{G}{\overrightarrow{V}}_{n+1}\mathit{dv}={\int}_{G}{\overrightarrow{V}}_{n}\mathit{dv}-{\int}_{{t}_{n}}^{{t}_{n+1}}{\int}_{O\left(G\right)}\overrightarrow{F}\xb7\overrightarrow{\mathit{d}}o,$$
(9)
$${D}_{z}=-A\xb7\mathrm{sin}\left({k}_{y}y\right)\xb7\mathrm{sin}\left({k}_{x}x-\mathit{\omega t}+{\varphi}_{x}\right)$$
(9)
$${B}_{x}=A\xb7\frac{{k}_{y}c}{\omega}\xb7\mathrm{cos}\left({k}_{y}y\right)\xb7\mathrm{cos}\left({k}_{x}x\xb7\mathit{\omega t}+{\varphi}_{x}\right)$$
(9)
$${B}_{y}=A\xb7\frac{{k}_{x}c}{\omega}\xb7\mathrm{sin}\left({k}_{y}y\right)\xb7\mathrm{sin}\left({k}_{x}x\xb7\mathit{\omega t}+{\varphi}_{x}\right),$$