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|Title:||Propagation of Gaussian beams in the presence of gain and loss|
|Keywords:||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;quant-ph;physics.optics;Optoelectronics & Photonics;0205 Optical Physics;0906 Electrical And Electronic Engineering;0206 Quantum Physics|
|Publisher:||Institute of Electrical and Electronics Engineers (IEEE)|
|Description:||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.|
|Type Of Material:||OTHER|
|Appears in Collections:||Mathematics|
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