期刊
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS
卷 22, 期 5, 页码 -出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JSTQE.2016.2555800
关键词
Schrodinger equation; geometric optics; nonlinear dynamical systems
资金
- Royal Society via a University Research Fellowship [UF130339]
- L'Oreal-UNESCO for Women in Science U.K.
- Ireland Fellowship
- Engineering and Physical Sciences Research Council [EP/K502856/1]
- Engineering and Physical Sciences Research Council [1231392] Funding Source: researchfish
We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schrodinger 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.
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