Waveguiding power of photonic crystal slabs

We consider the waveguiding by thin patterned slabs embedded in a homogeneous medium. In the longwave limit, the wave spectra of slabs are found to be well described by a single frequency-independent parameter, which we call the "guiding power". The guiding power can be evaluated in an effective medium approximation, similar to the Maxwell Garnett theory, but modified for the local field corrections specific to the two-dimensional geometry. The guiding power is different for the transverse magnetic (TM) and transverse electric (TE) polarizations. We show that the confinement factor of TM waves in a porous layer with high index ratio can exceed that for a homogeneous layer. Similarly enhanced confinement of TM waves is demonstrated for a layer of elongated cylinders or elliptic inclusion with a high axis length ratio. The effect originates from the suppression of local field effects and the increasing internal field in the inclusion. It may be useful in the design of far-infrared or THz quantum cascade lasers.Comment: 15 pages, 5 figure

Modal control in semiconductor optical waveguides with uniaxially patterned layers

Uniaxially patterned dielectric layers have an optical anisotropy that can be externally controlled. We study the effects of patterning the cladding or the core layer of a 3-layer optical waveguide on the polarization properties of propagating radiation. Particular attention is paid to the case when the core material is a semiconductor with optical gain. We discuss a number of devices based on incorporating an uniaxially patterned layer in the structure design, such as a polarization-insensitive amplifier, a polarizer, an optically-controlled polarization switch, and an optically controlled modal coupler.Comment: 9 pages 7 figure

Fluctuations of the partial filling factors in competitive RSA from binary mixtures

Competitive random sequential adsorption on a line from a binary mix of incident particles is studied using both an analytic recursive approach and Monte Carlo simulations. We find a strong correlation between the small and the large particle distributions so that while both partial contributions to the fill factor fluctuate widely, the variance of the total fill factor remains relatively small. The variances of partial contributions themselves are quite different between the smaller and the larger particles, with the larger particle distribution being more correlated. The disparity in fluctuations of partial fill factors increases with the particle size ratio. The additional variance in the partial contribution of smaller particle originates from the fluctuations in the size of gaps between larger particles. We discuss the implications of our results to semiconductor high-energy gamma detectors where the detector energy resolution is controlled by correlations in the cascade energy branching process.Comment: 19 pages, 8 figure

Random sequential adsorption of shrinking or spreading particles

We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a function of the size change are obtained. Results are compared with approximate analytical solutions.Comment: 9 pages, 8 figure

Correlation effects in sequential energy branching: an exact model of the Fano statistics

Correlation effects in in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state "shot-glass" model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable -- especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission.Comment: 11 pages, 4 figures. Submitted to Physical Review