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Journal of the Optical Society of America B

Photon density wave resonances of amplifying inhomogeneities in a random medium

Lalruatfela Renthlei, S. Anantha Ramakrishna, Harshawardhan Wanare

Published Jun 8, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1364/josab.34.001386

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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.
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.
We investigated several types of random lasing modes against frequency and the excitation of active medium. Random lasing occurring from multiple light scatterings and the interference effect of the scattered light has various complex lasing states in disordered structures, in which light waves are localized in various forms. Modes of random lasing are generally classified into localized, extended and transition modes based on their localization types. Numerical methods are used for analysing such complex phenomena. In this paper, a finite-element method is used to investigate the relationship among lasing modes, frequency and population inversion density of active medium for random lasing. Light amplification defined as the ratio of radiative powers between excited and non-excited states of the active medium is computed by changing both the frequency and the population inversion density of the active medium, which is modelled by the negative imaginary part of relative permittivity. The distributions of random lasing modes is strongly influenced by the lasing frequency. We also found that the localized modes that are strongly confined lasing modes in disordered structures do not appear in the frequency ranges in which mean free paths are approximately equal to the half-wavelength.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.
We study the dynamics of lasing from photonic paints excited by short, localized, optical pulses, using a time-dependent diffusion model for light propagating in the medium containing active atoms. The full time-dependent, nonadiabatic nonlinear response of the atomic system to the local optical field intensity is described using the Einstein rate equations for absorption and emission of light. Solving the time-dependent diffusion equation for the light intensity in the medium with nonlinear gain and loss, we derive detailed information on the spectral, spatial, and temporal properties of the emitted laser light. Our model recaptures the effects of scatterers to narrow the emission spectral linewidth and to narrow the emitted pulse duration, at a specific threshold pump intensity. Our model also describes how this threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results.
We investigate diffusive propagation of light and consequent random lasing in a medium comprising resonant spherical scatterers. A Monte‐Carlo calculation based on photon propagation via three‐dimensional random walks is employed to obtain the dwell‐times of light in the system. We compare the inter‐scatterer and intra‐scatterer dwell‐times for representative resonant and non‐resonant wavelengths. Our results show that more efficient random lasing, with intense coherent modes, is obtained when the gain is present inside the scatterers. Further, a larger reduction in frequency fluctuations is achieved by the system with intra‐scatterer gain.