Time Dependent Theory for Random Lasers

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate $P_{r}^{c}$ exists for the appearance of the lasing peaks. The number of lasing modes increase with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length $\xi$ and average mode length $L_m$.Comment: 8 pages. Send to PR

Super-reflection of light from a random amplifying medium with disorder in the complex refractive index : Statistics of fluctuations

The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is derived using the method of invariant imbedding. The statistics of fluctuations have been obtained for both the correlated telegraph noise and the Gaussian white-noise models for the disorder. In both cases, an enhanced backscattering (super-reflection with reflection coefficient greater than unity) results because of coherent feedback due to Anderson localization and coherent amplification in the medium. The results show that the effect of randomness in the imaginary part of the refractive index on localization and super-reflection is qualitatively different.Comment: RevTex 6 pages, 3 figures in ps file

Study of transmission and reflection from a disordered lasing medium

A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in the site energies in the disordered segment of the single-band tight binding model. It is shown that $t$ is a non-self-averaging quantity. The cross-over length scale above which the amplification suppresses the transmittance is studied as a function of amplification strength. A new cross-over length scale is introduced in the regime of strong disorder and weak amplification. The stationary distribution of the backscattered reflection coefficient is shown to differ qualitatively from the earlier analytical results obtained within the random phase approximation.Comment: 5 pages RevTex (twocolumn format), 5 EPS figures, considerably modifie

Propagation inhibition and wave localization in a 2D random liquid medium

Acoustic propagation and scattering in water containing many parallel air-filled cylinders is studied. Two situations are considered and compared: (1) wave propagating through the array of cylinders, imitating a traditional experimental setup, and (2) wave transmitted from a source located inside the ensemble. We show that waves can be blocked from propagation by disorders in the first scenario, but the inhibition does not necessarily imply wave localization. Furthermore, the results reveal the phenomenon of wave localization in a range of frequencies.Comment: Typos in Fiures are correcte

Engineering disorder in three-dimensional photonic crystals

We demonstrate the effect of introducing controlled disorder in self-assembled three-dimensional photonic crystals. Disorders are induced through controlling the self-assembling process using an electrolyte of specific concentrations. Structural characterization reveals increase in disorder with increase in concentrations of the electrolyte. Reflectivity and transmittance spectra are measured to probe the photonic stop gap at different levels of disorder. With increase in disorder the stop gap is vanished and that results in a fully random photonic nanostructure where the diffuse scattered intensity reaches up to 100%. Our random photonic nanostructure is unique in which all scatters have the same size and shape. We also observe the resonant characteristics in the multiple scattering of light.Comment: 13 pages, 3 figure

Localization of Light: Dual Symmetry between Absorption and Amplification

We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $\epsilon$, and show that dual systems, which differ only in the sign of the imaginary part of $\epsilon$, have the same localization length. Paradoxically, absorption and stimulated emission of radiation suppress the transmittance of the waveguide in the same way.Comment: Added a reference to the paper by Z.Q. Zhang, Phys.Rev.B. 52, 7960 (1995

Symmetry between absorption and amplification in disordered media

We address the issue of whether amplification, like absorption, suppresses wave transmission at large gain, as has been claimed in previous studies of wave propagation in active random media. A closer examination reveals that the paradoxical symmetry between absorption and amplification is an artifact of unphysical solutions from the time-independent wave equation. Solutions from the time-dependent equation demonstrate clearly that when gain is above the threshold, the amplitude of both the transmitted and the reflected wave actually increases with time, apparently without bound. The implications of the current finding is discusse

Manifestation of photonic band structure in small clusters of spherical particles

We study the formation of the photonic band structure in small clusters of dielectric spheres. The first signs of the band structure, an attribute of an infinite crystal, can appear for clusters of 5 particles. Density of resonant states of a cluster of 32 spheres may exhibit a well defined structure similar to the density of electromagnetic states of the infinite photonic crystal. The resonant mode structure of finite-size aggregates is shown to be insensitive to random displacements of particles off the perfect lattice positions as large as half-radius of the particle. The results were obtained by an efficient numerical method, which relates the density of resonant states to the the scattering coefficients of the electromagnetic scattering problem. Generalized multisphere Mie (GMM) solution was used to obtain scattering matrix elements. These results are important to miniature photonic crystal design as well as understanding of light localization in dense random media.Comment: 4 pages, 2 figure

Wave localization at the boundary of disordered photonic lattices

We report on the experimental observation of reduced light energy transport and disorder-induced localization close to a boundary of a truncated one-dimensional (1D) disordered photonic lattice. Our observations uncover that near the boundary a higher level of disorder is required to obtain similar localization than in the bulk.Comment: 13 pages, 5 figures, to appear in Optics Letter