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Laser Physics

Reflection of light from amplifying medium

R. V. Karapetyan

Published Aug 1, 2007• 5 citations
Publisher

Abstract

The existing linear theory of the reflection of light waves from an amplifying medium is debated. The exiting data are often contradictory, a reflection coefficient of amplifying medium of greater than unity is discussed, an upper bound of 5.82 is imposed on this quantity, significant corrections of prelaser concepts regarding the reflection and refraction of light in such media are proposed, etc. This stimulates reconsideration of the existing results. Evidently, the corresponding analysis must be based on the data obtained with a commonly accepted and, preferably, simplest approach. In our opinion, such an approach represents an analytical continuation of the known prelaser achievements (the Airy formulas for the reflection and transmission of light in a transparent medium proposed in 1833) to the domain of the amplifying media. The results presented can improve the basis of a linear theory for the interaction of light with amplifying media.

DOI
10.1134/s1054660x07080051

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The existing linear theory of the reflection of light waves from an amplifying medium is debated. The exiting data are often contradictory, a reflection coefficient of amplifying medium of greater than unity is discussed, an upper bound of 5.82 is imposed on this quantity, significant corrections of prelaser concepts regarding the reflection and refraction of light in such media are proposed, etc. This stimulates reconsideration of the existing results. Evidently, the corresponding analysis must be based on the data obtained with a commonly accepted and, preferably, simplest approach. In our opinion, such an approach represents an analytical continuation of the known prelaser achievements (the Airy formulas for the reflection and transmission of light in a transparent medium proposed in 1833) to the domain of the amplifying media. The results presented can improve the basis of a linear theory for the interaction of light with amplifying media.
We investigate the reflection of plane waves of s and p polarization from the interface between a homogeneous transparent medium and an amplifying medium with a gain profile decreasing exponentially with depth of penetration. For angles of incidence less than critical angle, the reflectance curves are essentially the same as those deduced from the usual Fresnel formulas for two transparent media. In the vicinity of critical angle, the reflection coefficients are virtually the same for both polarizations and are greater than unity. Beyond critical angle, the reflectances fall toward unity as grazing incidence is approached. Both the reflectance and the far-field transmittance peak in the immediate vicinity of critical angle. For angles less than critical angle, the transmittance can be 2 orders of magnitude greater than the reflectance. Certain values of gain parameters and incident angle lead to singularities in the theoretical reflectance. At these points the usual neglect of the effect of the transmitted wave on the population inversion is no longer valid.
A study is made of the problem of transmission of light pulses by a boundary of a nonlinear medium under conditions of coherent interaction with matter. It is shown that in the case of a semiinfinite nonlinear medium the reflection coefficient is governed by the linear characteristics of the media in contact so that the boundary-value problem reduces to the Cauchy problem. In another case, when a nonlinear medium is a thin film at the interface between two linear media, it is found that such a film is an almost perfect mirror reflecting weak pulses but it becomes transparent to pulses of sufficiently high intensity and the mirror then modulates the amplitude of such pulses.
We analyse in detail the necessary conditions to obtain amplified reflection (AR) in isotropic interfaces when a plane wave propagates from a transparent medium towards an active one. First, we demonstrate analytically that AR is not possible if a single interface is involved. Then, we study the conditions for AR in a very simple configuration: normal incidence on an active slab immersed in transparent media. Finally, we develop an analysis in the complex plane in order to establish a geometrical method that not only describes the behaviour of active slabs but also helps to simplify the calculus.
Enhancing light transmission through scattering media is of much interest in many fields. Here, numerical simulations are performed to study the impact of gain on the value of reflection of the minimum reflection channel in a random medium. Surprisingly, in some random configurations, the reflection falls when gain is added even through the intensity inside the medium presumably increases once gain is introduced. This unexpected behavior is explained based on a decomposition of quasinormal modes.
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.