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arXiv:1311.5985 · Physical Review A

Enhanced propagation of photon density waves in random amplifying media

Lalruatfela Renthlei, Harshawardhan Wanare, S. Anantha Ramakrishna

Published Apr 15, 2015• 6 citations
arXivHTMLPDF

Abstract

We demonstrate enhanced wavelike character of diffuse photon density waves (DPDW) in an amplifying random medium. The amplifying nature makes it necessary to choose the wave solution that grows inside the amplifying medium, and has a propagation vector pointing opposite to the growth direction. This results in negative refraction of the DPDW at an absorbing-amplifying random medium interface as well as the possibility of supporting ``anti''-surface-like modes at the interface. A slab of an amplifying random medium sandwiched between two absorbing random media supports waveguide resonances that can be utilized to extend the imaging capabilities of DPDW.

DOI
10.1103/physreva.91.043825

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We demonstrate enhanced wavelike character of diffuse photon density waves (DPDW) in an amplifying random medium. The amplifying nature makes it necessary to choose the wave solution that grows inside the amplifying medium, and has a propagation vector pointing opposite to the growth direction. This results in negative refraction of the DPDW at an absorbing-amplifying random medium interface as well as the possibility of supporting ``anti''-surface-like modes at the interface. A slab of an amplifying random medium sandwiched between two absorbing random media supports waveguide resonances that can be utilized to extend the imaging capabilities of DPDW.
Amplification in random media is investigated from the perspective of diffuse photon density waves (DPDWs). These exponentially decaying waves, typical in absorbing media, exhibit significantly enhanced propagation characteristics in random amplifying media. Consequently, finite amplifying regions, embedded in an absorbing random medium, exhibit specific resonant features governed by the geometry of the amplifying region. For a spheroidal amplifying region, the scattered waves are dominated by the characteristic multipolar resonances, and the monopolar as well as the dipolar resonances are closely related to random lasing thresholds. The levels of amplification at which the resonance (or lasing) occurs can be used to identify the size, shape, and orientation of the amplifying region. These resonant modes are quite robust and survive, even as the modulation frequency of the DPDW is varied from about 100 MHz to zero, thereby indicating a deeper connection between random lasing path distributions and the appropriate gain profiles resulting in the associated intensity distribution of the DPDW 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.
The analysis of the phenomenon of refraction of electromagnetic waves at the interface between two media suggests that their velocity when passing from one medium to another changes. This chapter describes the basic principles of amplification and discusses the main features of wave propagation in amplifying media. Amplification occurs due to the induced coherent emission by excited atoms under the influence of the field of the electromagnetic wave. The chapter illustrates the attenuation of waves in an absorbing medium by using the Bouguer’s law. Bouguer’s law holds for a wide range of electromagnetic radiation—from radio waves to X-rays and gamma rays. The chapter discusses the main features of the different types of lasers such as solid-state lasers, gas lasers, dye lasers, and semiconductor lasers. It also includes some exercise problems related to the propagation of electromagnetic waves in amplifying media.
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.
By utilizing the interference between an absorptive resonance and an amplifying resonance, one can achieve an enhanced refractive index without an increase in absorption to the beam. We analyze noise added to the beam due to spontaneous emission while propagating through such an index enhanced medium. We find that, for a medium with a refractive index of nnn and of length LLL, $\ensuremath{\approx}(n\ensuremath{-}1)(2\ensuremath{\pi}∕{\ensuremath{\lambda}}_{0})L$ noise photons are added to the beam.