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arXiv:1508.04792 · Physical Review B

Minimum reflection channel in amplifying random media

Seng Fatt Liew, Hui W. Cao

Published Dec 29, 2015• 5 citations
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Abstract

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.

DOI
10.1103/physrevb.92.224202

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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.
The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.
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.
We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble-averaged correlation functions due to the existence of lasing realizations. We introduce a conditional average for correlation functions by omitting the divergent realizations. Our numerical simulation reveals that amplification does not affect local spatial correlation. The nonlocal intensity correlations are strongly magnified due to selective enhancement of the contributions from long propagation paths. We also show that by increasing gain, the average mode linewidth can be made comparable to the average mode spacing. This implies that light transport through a diffusive random system with gain may exhibit some similarities with that through a localized passive system.
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.