Relation between Transmission and Energy Stored in Random Media with Gain

In this work, we investigate a possibility of using the ratio between optical transmission, T, and energy stored inside the system, E, as a quantitative measure of the enhanced mesoscopic corrections to diffusive transport of light through a random medium with gain. We obtain an expression for T/E as a function of amplification strength in the diffusive approximation and show that it does not a have tendency to diverge when the threshold for random lasing is approached, as both T and E do. Furthermore, we find that a change in T/E signifies a change in the electric field distribution inside the random medium. In the localization regime, we also investigate the correlations between transmission and energy stored in the medium with and without amplification. Our results suggest that T/E is a promising parameter which can help characterize the nature of wave transport in random medium with gain

Marginally Unstable Periodic Orbits in Semiclassical Mushroom Billiards

Optical mushroom shaped billiards offer a unique opportunity to isolate and study non-dispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external fields presents unanticipated consequences for the far-field distribution, including directional emission. This is mediated by interactions of marginally unstable periodic orbits with chaotic modes and is potentially relevant for the design of microcavity lasers. We also show that such orbits are robust against perturbations to the shape of the cavity, despite the non-generic character of the classical counterpart and the lack of structural stability of the corresponding classical orbits.Comment: 10 pages, 6 figure

Modes of Random Lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, ... In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. In this paper, we review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. We will discuss in particular the link between random laser modes near threshold (TLM) and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime where differences between quasi-bound states and lasing modes were measured. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the TLM are better described in terms of the so-called constant-flux states.Comment: Review paper submitted to Advances in Optics and Photonic

Effects of Spatially Nonuniform Gain on Lasing Modes in Weakly Scattering Random Systems

A study on the effects of optical gain nonuniformly distributed in one-dimensional random systems is presented. It is demonstrated numerically that even without gain saturation and mode competition, the spatial nonuniformity of gain can cause dramatic and complicated changes to lasing modes. Lasing modes are decomposed in terms of the quasi modes of the passive system to monitor the changes. As the gain distribution changes gradually from uniform to nonuniform, the amount of mode mixing increases. Furthermore, we investigate new lasing modes created by nonuniform gain distributions. We find that new lasing modes may disappear together with existing lasing modes, thereby causing fluctuations in the local density of lasing states.Comment: 26 pages, 10 figures (quality reduced for arXiv

Nonlinear effects in random lasers

Recent numerical and theoretical studies have demonstrated that the modes at threshold of a random laser are in direct correspondence with the resonances of the same system without gain, a feature which is well known in a conventional laser but which was not known until recently for a random laser. This paper presents numerical results, which extend such studies to the multimode regime that takes place when the pumping rate is progressively increased above threshold. Behavior that is already known in standard lasers, such as mode competition and nonlinear wave-mixing, are shown to also take place in random lasers thus reinforcing their recent modal description. However, due to the complexity of the laser modes and to the openness of such lasers, which requires large external pumping to compensate for strong loss, one observes that these effects are more pronounced than in a conventional laser