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Conference on Lasers and Electro-Optics

Reciprocity and constants of integration in photorefractive wave mixing

Claire Gu, Pochi Yeh

Published May 12, 1991• 0 citations
OpenAlex

Abstract

Reciprocity is a fundamental law in both quantum physics1 and classical physics.2 For electromagnetic scattering by a static dielectric medium, the reciprocity relationship is written as S(k,k′) = S(-k′,-k), where S(k,k′) is the amplitude-scattering coefficient for incident plane wave with wave vector k and scattered plane wave with wave vector k'. Notice that (-k',-k) is the reversed scattering process of the direct scattering (k,k′), and the reciprocity relationship stated above is valid even when the medium has absorption loss.

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Reciprocity is a fundamental law in both quantum physics1 and classical physics.2 For electromagnetic scattering by a static dielectric medium, the reciprocity relationship is written as S(k,k′) = S(-k′,-k), where S(k,k′) is the amplitude-scattering coefficient for incident plane wave with wave vector k and scattered plane wave with wave vector k'. Notice that (-k',-k) is the reversed scattering process of the direct scattering (k,k′), and the reciprocity relationship stated above is valid even when the medium has absorption loss.
Abstract Three linear equations are proposed as quantum-mechanical equations for the free propagating photons. The solution of these equations is the vector potential of the electromagnetic field and it is a product of the Gaussian functions for the transverse coordinates and the eigenfunction of the harmonic oscillator for the longitudinal coordinate. This solutions is used to describe the reflection and refraction of photons on the boundary between two dielectrics. The amplitude of the reflected field coincides with the Fresnel formulae for the plane waves, but the amplitude of the refracted field is different. These amplitudes are the probability’s amplitudes of reflection and refraction of photons—like in the quantum mechanics. The photons propagated from the first into the second medium increase (decrease) their transverse size in the plane of incidence, if the refraction index of the second medium is greater (smaller) than in the first medium. The increasing or decreasing grow when increasing the angle of incidence. The difference between the quantum mechanics of the particles with a mass and the photons, as well as the interpretation of the wave function of photons, is discussed.
We derive general relationships of the S matrix of fields containing evanescent components. Our formalism covers time-independent quantum scattering as well as scattering of classical scalar waves. We show that reciprocity, energy (or probability) conservation, and time-reversal symmetry in the presence of evanescent waves lead to relationships that extend the well-known relations previously derived in asymptotic scattering. On this basis, we discuss the link between reciprocity and time-reversal symmetry. We also address the experimental feasibility of time reversal of a field containing evanescent components.
We study the behavior of light waves at an interface between linear and photorefractive media, where the incident wave propagates from the linear side. We find bistable behavior of the reflection coefficient as a function of the incident angle at incident wave directions in the vicinity of the critical angle for total internal reflection. The analysis is based on approximations in the photorefractive-process equations, for which an analytical plane-wave solution for the boundary problem is found. In this regime an exponentially decaying evanescent field induces a uniform change of the refractive index. The limitation of this solution is also studied by a numerical analysis.
Since in quantum optics light is represented in terms of photons, light propagation through a linear medium is discussed quantum mechanically in this paper by following the multiple-scattering process of one incident photon from the medium. To treat the photon and the medium on the same quantum footing, the medium is assumed to be an ensemble of uniformly distributed identical two-level atoms. It is found that inside the medium the incident photon follows the same propagation rules as a plane wave does in the classical domain, and has a possibility to become entangled with the atoms. It is also found that when interacting with a two-level test atom outside the medium, the output photon appears to be formally in a single mode identical to that of the incident photon.