Propagation of Gaussian beams in the presence of gain and loss
File(s)
Accepted version
Author(s)
Graefe, E-M
Rush, A
Schubert, R
Type
Journal Article
Abstract
We consider the propagation of Gaussian beams in a waveguide with gain and
loss in the paraxial approximation governed by the Schr\"odinger equation. We
derive equations of motion for the beam in the semiclassical limit that are
valid when the waveguide profile is locally well approximated by quadratic
functions. For Hermitian systems, without any loss or gain, these dynamics are
given by Hamilton's equations for the center of the beam and its conjugate
momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian
component, causing the width of the Gaussian beam to play an important role in
its propagation. Here we show how the width affects the motion of the beam and
how this may be used to filter Gaussian beams located at the same initial
position based on their width.
loss in the paraxial approximation governed by the Schr\"odinger equation. We
derive equations of motion for the beam in the semiclassical limit that are
valid when the waveguide profile is locally well approximated by quadratic
functions. For Hermitian systems, without any loss or gain, these dynamics are
given by Hamilton's equations for the center of the beam and its conjugate
momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian
component, causing the width of the Gaussian beam to play an important role in
its propagation. Here we show how the width affects the motion of the beam and
how this may be used to filter Gaussian beams located at the same initial
position based on their width.
Date Issued
2016-06-30
Date Acceptance
2016-04-14
Citation
IEEE Journal of Selected Topics in Quantum Electronics, 2016, 22 (5)
ISSN
1558-4542
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Journal / Book Title
IEEE Journal of Selected Topics in Quantum Electronics
Volume
22
Issue
5
Copyright Statement
© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
The Royal Society
Identifier
http://arxiv.org/abs/1601.07802v1
Grant Number
UF130339
Subjects
Science & Technology
Technology
Physical Sciences
Engineering, Electrical & Electronic
Optics
Physics, Applied
Engineering
Physics
Schrodinger equation
geometric optics
nonlinear dynamical systems
QUANTUM-MECHANICS
HYBRID MECHANICS
DYNAMICS
quant-ph
physics.optics
Optoelectronics & Photonics
0205 Optical Physics
0906 Electrical And Electronic Engineering
0206 Quantum Physics
Publication Status
Published
Article Number
5000906