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Frontiers in Optics

Squeezed states of the parabolic index fiber

Shaine Joseph, Vasudevan Lakshminarayanan

Published Jan 1, 2003• 0 citations
Publisher

Abstract

We define the squeezed states of a parabolic index fiber by analogy with the Schrodinger equation for the harmonic oscillator. The expectation values of x for a squeezed and coherent state shows that in paraxial approximation, both the squeezed states and the coherent states represent the rays.
DOI
10.1364/fio.2003.mt11

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The purpose of this work is to introduce, in a simple, intuitive way, the coherent and squeezed states of the quantum harmonic oscillator (QHO), through a series of exercises, which are solved in detail. Starting from the application of a spatial translation to the ground state of the QHO, we introduce the spatial and momentum translations, focusing on their application to the QHO, which leads us to the displacement operator. Next, we introduce the coherent states and examine their basic aspects. We then proceed to give a simple and purely intuitive introduction to the squeezed states and we conclude by identifying the coherent states as states of minimum energy expectation value compared to the respective squeezed states. The reader is assumed to have a basic knowledge of the postulates and the mathematical formalism of quantum mechanics, including the Dirac notation and the ladder operator method of the QHO.
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The authors discuss the harmonic oscillator problem in the domains of classical mechanics and the parabolic index optical waveguide problem in the domains of ray optics. While discussing the classical mechanics and the ray optics of the two problems the authors have used the Lagrangian formalism which allows them to see the close relationship between the two problems. In part II of the paper the authors study the corresponding quantum mechanical and wave optical problems. In particular whilst looking at the time evolution of a coherent state the authors demonstrate that it has a close relationship to the propagation of a Gaussian beam in a parabolic index optical waveguide.