Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable orbit modes

By combining detailed imaging measurements at different tilt angles with simulations of ray emission from prolate deformed lasing micro-droplets, we conclude that the probability density for the lasing modes in a three-dimensional dielectric microcavity must reside in the chaotic region of the ray phase space. In particular, maximum emission from such chaotic lasing modes is not from tangent rays emerging from the highest curvature part of the rim. The laser emission is observed and calculated to be non-tangent and displaced from the highest curvature due to the presence of stable orbits. In this Letter we present the first experimental evidence for this phenomenon of ``dynamical eclipsing''.Comment: 4 figure

Curvature-induced radiation of surface plasmon polaritons propagating around bends

We present a theoretical study of the curvature-induced radiation of surface plasmon polaritons (SPPs) propagating around bends at metal-dielectric interfaces. We explain qualitatively how the curvature leads to distortion of the phase front, causing the fields to radiate energy away from the metal-dielectric interface. We then quantify, both analytically and numerically, radiation losses and energy transmission efficiencies of SPPs propagating around bends with varying radii- as well as sign-of-curvature.Comment: 9 pages, 8 figures, submitted to Physical Review

Methods for 3-D vector microcavity problems involving a planar dielectric mirror

We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to their tight focusing of light onto the flat surface. The first method uses the Bessel wave basis. From this method evolves a two-basis method, which ultimately uses a multipole basis. Each method is developed for both the scalar field and the electromagnetic vector field and explicit ``end user'' formulas are given. All of these methods characterize the arbitrary dielectric stack mirror entirely by its 2\times2 transfer matrices for s- and p-polarization. We explain both theoretical and practical limitations to our method. Non-trivial demonstrations are given, including one of a stack-induced effect (the mixing of near-degenerate Laguerre-Gaussian modes) that may persist arbitrarily far into the paraxial limit. Cavities as large as 50 \lambda are treated, far exceeding any vectorial solutions previously reported.Comment: For high-quality figures, visit http://darkwing.uoregon.edu/~noeckel/papers.ph

Bragg-induced orbital angular-momentum mixing in paraxial high-finesse cavities

Numerical calculation of vector electromagnetic modes of plano-concave microcavities reveals that the polarization-dependent reflectivity of a flat Bragg mirror can lead to unexpected cavity field distributions for nominally paraxial modes. Even in a rotationally symmetric resonator, certain pairs of orbital angular momenta are necessarily mixed in an excitation-independent way to form doublets. A characteristic mixing angle is identified, which even in the paraxial limit can be designed to have large values. This correction to Gaussian theory is zeroth-order in deviations from paraxiality. We discuss the resulting nonuniform polarization fields. Observation will require small cavities with sufficiently high Q. Possible applications are proposed.Comment: Corrected typos in Fig. 2 and text. Added Journal Ref. For higher-quality figures, see http://darkwing.uoregon.edu/~noeckel/papers.php#xref3

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

Goos-Haenchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Haenchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its "V". A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.Comment: 4 pages, 4 figure