Diffraction effects on diffusive bistable optical arrays and optical memory

Research output: Contribution to journalArticle

Abstract

Bistable responses of Fabry-Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, with strong diffusion and weak diffraction, behaves very differently than dispersive bistability with Kerr nonlinearity. Nevertheless, focusing nonlinearity can improve its response characteristics significantly. For example, it is found that hysteresis loops are much wider when nonlinearity is self-focusing than when nonlinearity is self-defocusing. For self-defocusing nonlinearity, strong diffraction can close a hysteresis loop completely. Because of strong diffusion, refractive index distributions are smoothed versions of intensity distributions. This weakens the nonlinear behavior of the system. By approximating the refractive index by a constant, the model is reduced to a discrete map. This reduction incorporates diffraction into a nonlinear response function, allowing diffractive effects to be studied analytically, and shown to agree well with more extensive numerical simulations. Optical arrays are also studied numerically. Because of weaker diffractive crosstalk and a wider "operation gap" between "on" bits and "off" bits, an array with focusing nonlinearity allows finer packing than with self-defocusing nonlinearity. Using the reduced map, optimal packing densities of optical arrays are estimated.

Original languageEnglish (US)
Pages (from-to)163-195
Number of pages33
JournalPhysica D: Nonlinear Phenomena
Volume138
Issue number1-2
StatePublished - Apr 1 2000

Fingerprint

Optical data storage
Diffraction
nonlinearity
Nonlinearity
Hysteresis loops
diffraction
defocusing
Refractive index
Hysteresis Loop
Refractive Index
Packing
Crosstalk
Nonlinear equations
Nonlinear systems
hysteresis
refractivity
Self-focusing
Bistable System
Bistability
Nonlinear Response

Keywords

  • Bistable optical array
  • Diffraction effect

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Diffraction effects on diffusive bistable optical arrays and optical memory. / Chen, Yuchi; McLaughlin, David W.

In: Physica D: Nonlinear Phenomena, Vol. 138, No. 1-2, 01.04.2000, p. 163-195.

Research output: Contribution to journalArticle

@article{4c81859a25104fc586db563417411240,
title = "Diffraction effects on diffusive bistable optical arrays and optical memory",
abstract = "Bistable responses of Fabry-P{\'e}rot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schr{\"o}dinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, with strong diffusion and weak diffraction, behaves very differently than dispersive bistability with Kerr nonlinearity. Nevertheless, focusing nonlinearity can improve its response characteristics significantly. For example, it is found that hysteresis loops are much wider when nonlinearity is self-focusing than when nonlinearity is self-defocusing. For self-defocusing nonlinearity, strong diffraction can close a hysteresis loop completely. Because of strong diffusion, refractive index distributions are smoothed versions of intensity distributions. This weakens the nonlinear behavior of the system. By approximating the refractive index by a constant, the model is reduced to a discrete map. This reduction incorporates diffraction into a nonlinear response function, allowing diffractive effects to be studied analytically, and shown to agree well with more extensive numerical simulations. Optical arrays are also studied numerically. Because of weaker diffractive crosstalk and a wider {"}operation gap{"} between {"}on{"} bits and {"}off{"} bits, an array with focusing nonlinearity allows finer packing than with self-defocusing nonlinearity. Using the reduced map, optimal packing densities of optical arrays are estimated.",
keywords = "Bistable optical array, Diffraction effect",
author = "Yuchi Chen and McLaughlin, {David W.}",
year = "2000",
month = "4",
day = "1",
language = "English (US)",
volume = "138",
pages = "163--195",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Diffraction effects on diffusive bistable optical arrays and optical memory

AU - Chen, Yuchi

AU - McLaughlin, David W.

PY - 2000/4/1

Y1 - 2000/4/1

N2 - Bistable responses of Fabry-Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, with strong diffusion and weak diffraction, behaves very differently than dispersive bistability with Kerr nonlinearity. Nevertheless, focusing nonlinearity can improve its response characteristics significantly. For example, it is found that hysteresis loops are much wider when nonlinearity is self-focusing than when nonlinearity is self-defocusing. For self-defocusing nonlinearity, strong diffraction can close a hysteresis loop completely. Because of strong diffusion, refractive index distributions are smoothed versions of intensity distributions. This weakens the nonlinear behavior of the system. By approximating the refractive index by a constant, the model is reduced to a discrete map. This reduction incorporates diffraction into a nonlinear response function, allowing diffractive effects to be studied analytically, and shown to agree well with more extensive numerical simulations. Optical arrays are also studied numerically. Because of weaker diffractive crosstalk and a wider "operation gap" between "on" bits and "off" bits, an array with focusing nonlinearity allows finer packing than with self-defocusing nonlinearity. Using the reduced map, optimal packing densities of optical arrays are estimated.

AB - Bistable responses of Fabry-Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, with strong diffusion and weak diffraction, behaves very differently than dispersive bistability with Kerr nonlinearity. Nevertheless, focusing nonlinearity can improve its response characteristics significantly. For example, it is found that hysteresis loops are much wider when nonlinearity is self-focusing than when nonlinearity is self-defocusing. For self-defocusing nonlinearity, strong diffraction can close a hysteresis loop completely. Because of strong diffusion, refractive index distributions are smoothed versions of intensity distributions. This weakens the nonlinear behavior of the system. By approximating the refractive index by a constant, the model is reduced to a discrete map. This reduction incorporates diffraction into a nonlinear response function, allowing diffractive effects to be studied analytically, and shown to agree well with more extensive numerical simulations. Optical arrays are also studied numerically. Because of weaker diffractive crosstalk and a wider "operation gap" between "on" bits and "off" bits, an array with focusing nonlinearity allows finer packing than with self-defocusing nonlinearity. Using the reduced map, optimal packing densities of optical arrays are estimated.

KW - Bistable optical array

KW - Diffraction effect

UR - http://www.scopus.com/inward/record.url?scp=0347316224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347316224&partnerID=8YFLogxK

M3 - Article

VL - 138

SP - 163

EP - 195

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -