Defining cylindrical space optical resonators through supported mode properties: inverse numerical process.

Faraday's and Ampere's laws are converted to matrix operator form and rearranged such that the unknown relative permittivity and relative permeability tensors can be determined. The material and geometry of cylindrically symmetric optical resonator structures are determined through the electric and magnetic field component profiles and complex angular frequency of a proposed localized state. This differs from the usual utilization of the electromagnetic wave equations, solving for states given the material properties and geometry. Thus the technique presented here is an inverse numerical process. The theoretical expressions are provided based on a Fourier-Bessel numerical approach which is highly suitable for cylindrical geometry resonators. Without loss of the generality of the technique, examples of resonant structure determination are presented for non-magnetic and diagonal relative permittivity tensor. Axial field propagation is included to demonstrate the design capabilities related to optical fiber and photonic crystal fiber structures.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Dielectric profile segmentation used to reduce computation effort of the Fourier-Bessel mode solving technique.

The Fourier-Bessel space conversion of Maxwell's wave equations into an eigenvalue formulation is a useful numerical tool for computing the steady states of cylindrically symmetric dielectric structures. The relative dielectric profile, inverse (1/εr) present in wave equations, is split into a constant offset and corresponding spatially dependent residue and greatly reduces the matrix building time (and thus computation time) when alternate dielectric configurations are considered with identical spatial distributions. Such a process significantly speeds up the theoretical analysis of numerous optical designs, such as index of refraction sensors, hole infiltration sensors and resonator tuning. The theoretical steps involved are presented along with examples of the technique applied to the well-known Bragg resonator and central defect containing hexagonal array.

Fourier-Bessel analysis of localized states and photonic bandgaps in 12-fold photonic quasi-crystals.

A Fourier-Bessel (FB) basis is used to solve two-dimensional (2D) cylindrical Maxwell's equations for localized states within dielectric structures that possess rotational symmetry. The technique is used to determine the wavelengths and profiles of the stationary states supported by the structure and identify the bandgaps. 12-fold quasi-crystals for the TE and TM polarizations are analyzed. Since the FB approach with 2D photonic crystals in this fashion is new, the accuracy of the results is confirmed using finite-difference time-domain simulations.

Modal analysis and device considerations of thin high index dielectric overlay slab waveguides.

The effect of adding a thin high index dielectric overlay layer onto a 3-layer slab waveguide demonstrates several interesting features that can be exploited in integrated optical device configurations. A simple modal analysis is employed to examine the behavior of guided light launched from a 3-layer waveguide structure then coupled and propagated in the 4-layer overlay region. Modal properties typically overlooked in conventional slab waveguides are made use of in the design and theoretical analysis of an MMI device and optical index of refraction sensor. The optical structure presented here can form the backdrop waveguide design for more complex and active devices.

Mode localization and band-gap formation in defect-free photonic quasicrystals.

Defects in photonic crystals are local regions in which the translational symmetry is broken. The same definition can be applied to photonic quasicrystals except in this case the symmetry is the 2pi/n rotational symmetry, where n is the rotational fold number. In this context, if no such defects are present, the structure is called "defect-free". Even though photonic quasicrystal patterns can be defect-free, localized modes can still exist in such structures. These modes resemble those of a central potential that suggests that localization in photonic quasicrystals are actually "extended" modes of the rotational symmetry. A possible connection is suggested between these localized modes and short-range dependence of the photonic band gap (PBG). Such a connection implies a tight-binding description of PBG formation of photonic quasicrystals - making them more similar to electronic semiconductors than regular photonic crystals.

Self-centering of a ball lens by laser trapping: fiber-ball-fiber coupling analysis.

Fiber-to-fiber coupling through use of a laser-trapped microball lens is examined. A model based on radiation pressure predicts that the ball lens will align axially between the fiber endfaces. Laser manipulation of the ball lens axial position results in a configuration in which the ball lens optically bridges the gap between the fibers. Experimental results are presented for several fiber endface separations, and it is found that the presence of the microball lens can increase the coupling by a factor of 2 above the level expected by direct fiber-to-fiber coupling for the same fiber endface separation.

Laser-trapping properties of dual-component spheres.

The optical trapping properties of dual-component spheres consisting of a cocentered outer transparent dielectric spherical shell and internal solid sphere are examined on the basis of the enhanced ray optics model. It is shown that stable trapping can occur on axis, off axis, or at multiple axial positions and depends on the dual-sphere and laser beam parameters. Computation results are also presented for an internal reflecting sphere surrounded by an outer dielectric spherical shell.

Activation of microcomponents with light for micro-electro-mechanical systems and micro-optical-electro-mechanical systems applications.

We examine the light-activation properties of micrometer-sized gear structures fabricated with polysilicon surface micromachining techniques. The gears are held in place on a substrate through a capped anchor post and are free to rotate about the post. The light-activation technique is modeled on photon radiation pressure, and the equation of motion of the gear is solved for this activation technique. Experimental measurements of torque and damping are found to be consistent with expected results for micrometer-scale devices. Design optimization for optically actuated microstructures is discussed.