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American Journal of Physics

Energy balance in the superposition of light waves with lossless beam splitters

Francese Pi, Gaspar T. Orriols

Published Jul 1, 1985• 11 citations
Publisher

Abstract

The energy balance in the superposition of light waves with a lossless beam splitter is analyzed along with its connection with some general relations between the parameters describing beam-splitter effects on the two incoming waves. These general relations are derived either from the electromagnetic theory or from energy conservation considerations. The apparent paradox of a symmetric beam splitter producing complementary outputs is explained.

DOI
10.1119/1.14282

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The energy balance in the superposition of light waves with a lossless beam splitter is analyzed along with its connection with some general relations between the parameters describing beam-splitter effects on the two incoming waves. These general relations are derived either from the electromagnetic theory or from energy conservation considerations. The apparent paradox of a symmetric beam splitter producing complementary outputs is explained.
The lossless beam splitter is classically well understood. The purpose of this work is to enable one to describe the action of a lossless plane-parallel beam splitter on an incident light beam in purely quantum-mechanical terms. Such a description may be obtained in terms of a unitary transformation that connects the incoming radiation-field operator to the outgoing one. This transformation, which we shall derive and discuss here, provides an elegant means to address issues and concepts that are intrinsically quantum-mechanical.
The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.
Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including “which-way” determination or the EPR paradox and their measurement apparatus. Although they look as common optical components at first glance, their behaviour remains somewhat mysterious since they apparently exhibit stand-alone particle-like features, and then wave-like characteristics when inserted into a Mach-Zehnder interferometer. In this communication are examined and discussed some basic properties of these beamssplitters, both from a classical optics and quantum physics point of view. Herein the most evident convergences and contradictions are highlighted, and the results of a few emblematic experiments demonstrating photon existence are discussed. Alternative empirical models are also proposed in order to shed light on some remaining issues.