Immittance Matching for Multi-dimensional Open-system Photonic Crystals

An electromagnetic (EM) Bloch wave propagating in a photonic crystal (PC) is characterized by the immittance (impedance and admittance) of the wave. The immittance is used to investigate transmission and reflection at a surface or an interface of the PC. In particular, the general properties of immittance are useful for clarifying the wave propagation characteristics. We give a general proof that the immittance of EM Bloch waves on a plane in infinite one- and two-dimensional (2D) PCs is real when the plane is a reflection plane of the PC and the Bloch wavevector is perpendicular to the plane. We also show that the pure-real feature of immittance on a reflection plane for an infinite three-dimensional PC is good approximation based on the numerical calculations. The analytical proof indicates that the method used for immittance matching is extremely simplified since only the real part of the immittance function is needed for analysis without numerical verification. As an application of the proof, we describe a method based on immittance matching for qualitatively evaluating the reflection at the surface of a semi-infinite 2D PC, at the interface between a semi-infinite slab waveguide (WG) and a semi-infinite 2D PC line-defect WG, and at the interface between a semi-infinite channel WG and a semi-infinite 2D PC slab line-defect WG.Comment: 8 pages, 6 figure

Ray and wave chaos in asymmetric resonant optical cavities

Optical resonators are essential components of lasers and other wavelength-sensitive optical devices. A resonator is characterized by a set of modes, each with a resonant frequency omega and resonance width Delta omega=1/tau, where tau is the lifetime of a photon in the mode. In a cylindrical or spherical dielectric resonator, extremely long-lived resonances are due to `whispering gallery' modes in which light circulates around the perimeter trapped by total internal reflection. These resonators emit light isotropically. Recently, a new category of asymmetric resonant cavities (ARCs) has been proposed in which substantial shape deformation leads to partially chaotic ray dynamics. This has been predicted to give rise to a universal, frequency-independent broadening of the whispering-gallery resonances, and highly anisotropic emission. Here we present solutions of the wave equation for ARCs which confirm many aspects of the earlier ray-optics model, but also reveal interesting frequency-dependent effects characteristic of quantum chaos. For small deformations the lifetime is controlled by evanescent leakage, the optical analogue of quantum tunneling. We find that the lifetime is much shortened by a process known as `chaos-assisted tunneling'. In contrast, for large deformations (~10%) some resonances are found to have longer lifetimes than predicted by the ray chaos model due to `dynamical localization'.Comment: 4 pages RevTeX with 7 Postscript figure

Semiclassical theory of the emission properties of wave-chaotic resonant cavities

We develop a perturbation theory for the lifetime and emission intensity for isolated resonances in asymmetric resonant cavities. The inverse lifetime $\Gamma$ and the emission intensity $I(\theta)$ in the open system are expressed in terms of matrix elements of operators evaluated with eigenmodes of the closed resonator. These matrix elements are calculated in a semiclassical approximation which allows us to represent $\Gamma$ and $I(\theta)$ as sums over the contributions of rays which escape the resonator by refraction.Comment: 4 pages, 2 color figure

Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators

We study lasing emission from asymmetric resonant cavity (ARC) GaN micro-lasers. By comparing far-field intensity patterns with images of the micro-laser we find that the lasing modes are concentrated on three-bounce unstable periodic ray orbits, i.e. the modes are scarred. The high-intensity emission directions of these scarred modes are completely different from those predicted by applying Snell's law to the ray orbit. This effect is due to the process of ``Fresnel filtering'' which occurs when a beam of finite angular spread is incident at the critical angle for total internal reflection.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, submitted to Phys. Rev. Lett; corrected a minor (transcription) erro

Semiconductor Surface Studies

Contains an introduction, reports on two research projects and a list of publications.Joint Services Electronics Program Grant DAAH04-95-1-003

Emergence of Quantum Ergodicity in Rough Billiards

By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked structure. The results of numerical simulations and implications for level statistics are also discussed.Comment: revtex, 4 pages, 4 figure

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.Comment: 5 pages, 5 figure

Testing and development of transfer functions for weighing precipitation gauges in WMO-SPICE

Weighing precipitation gauges are used widely for the measurement of all forms of precipitation, and are typically more accurate than tipping-bucket precipitation gauges. This is especially true for the measurement of solid precipitation; however, weighing precipitation gauge measurements must still be adjusted for undercatch in snowy, windy conditions. In WMO-SPICE (World Meteorological Organization Solid Precipitation InterComparison Experiment), different types of weighing precipitation gauges and shields were compared, and adjustments were determined for the undercatch of solid precipitation caused by wind. For the various combinations of gauges and shields, adjustments using both new and previously existing transfer functions were evaluated. For most of the gauge and shield combinations, previously derived transfer functions were found to perform as well as those more recently derived. This indicates that wind shield type (or lack thereof) is more important in determining the magnitude of wind-induced undercatch than the type of weighing precipitation gauge. It also demonstrates the potential for widespread use of the previously developed transfer functions. Another overarching result was that, in general, the more effective shields, which were associated with smaller unadjusted errors, also produced more accurate measurements after adjustment. This indicates that although transfer functions can effectively reduce measurement biases, effective wind shielding is still required for the most accurate measurement of solid precipitation

Dynamical Tunneling in Mixed Systems

We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. We show that tunneling transport is dominated by chaos-assisted paths that tunnel into and out of the chaotic layer via the ``beach'' regions sandwiched between the regular islands and the chaotic sea. Level splittings are shown to fluctuate on two scales as functions of energy or an external parameter: they display a dense sequence of peaks due to resonances with states supported by the chaotic sea, overlaid on top of slow modulations arising from resonances with states supported by the ``beaches''. We obtain analytic expressions which enable us to assess the relative importance of tunneling amplitudes into the chaotic sea vs. its internal transport properties. Finally, we average over the statistics of the chaotic region, and derive the asymptotic tail of the splitting distribution function under rather general assumptions concerning the fluctuation properties of chaotic states.Comment: 28 pages, Latex, 16 EPS figure