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

Polarization proximity effect in isolator crystal pairs

We experimentally studied the polarization dynamics (orientation and ellipticity) of near infrared light transmitted through magnetooptic Yttrium Iron Garnet crystal pairs using a modified balanced detection scheme. When the pair separation is in the sub-millimeter range, we observed a proximity effect in which the saturation field is reduced by up to 20%. 1D magnetostatic calculations suggest that the proximity effect originates from magnetostatic interactions between the dipole moments of the isolator crystals. This substantial reduction of the saturation field is potentially useful for the realization of low-power integrated magneto-optical devices.Comment: submitted to Optics Letter

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

Transmission of Slow Light through Photonic Crystal Waveguide Bends

The spectral dependence of a bending loss of cascaded 60-degree bends in photonic crystal (PhC) waveguides is explored in a slab-type silicon-on-insulator system. Ultra-low bending loss of (0.05+/-0.03)dB/bend is measured at wavelengths corresponding to the nearly dispersionless transmission regime. In contrast, the PhC bend is found to become completely opaque for wavelengths range corresponding to the slow light regime. A general strategy is presented and experimentally verified to optimize the bend design for improved slow light transmission.Comment: 4 pages, 3 figures; submitted to Optics Letter

Waveguiding properties of surface states in photonic crystals

We propose and analyze novel surface-state-based waveguides in bandgap photonic crystals. We discuss surface mode band structure, field localization and effect of imperfections on the waveguiding properties of the surface modes. We demonstrate that surface-state-based waveguides can be used to achieve directional emission out of the waveguide. We also discuss the application of the surface-state waveguides as efficient light couplers for conventional photonic crystal waveguides.Comment: 4 pages 5 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

Quantum localization in rough billiards

We study the level spacing statistics p(s) and eigenfunction properties in a billiard with a rough boundary. Quantum effects lead to localization of classical diffusion in the angular momentum space and the Shnirelman peak in p(s) at small s. The ergodic regime with Wigner-Dyson statistics is identified as a function of roughness. Applications for the Q-spoiling in optical resonators are also discussed.Comment: revtex, 4 pages, 5 figure

Kink propagation in a two-dimensional curved Josephson junction

We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to assume a homogeneous kink solution. Using a simple collective variable approach based on the kink coordinate, we show that curved regions act as potential barriers for the wave and determine the threshold velocity for the kink to cross. The analysis is confirmed by numerical solution of the 2D sine-Gordon equation.Comment: 8 pages, 4 figures (2 in color

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