Attila Mekis

Molding the flow of light

A new class of materials, called photonic crystals, affects a photons properties in much the some way that a semiconductor affects an electrons properties. The ability to mold and guide light leads naturally to novel applications in several fields, including optoelectronics and telecommunications. The authors present an introductory survey of the basic concepts and ideas, including results for never before possible photon phenomena. The paper considers how computer calculations and design play particularly important and complementary roles in experimental investigations of photonic crystals.

Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides

We design tapered waveguide junctions for coupling between photonic crystal and traditional dielectric waveguides and evaluate their transmission efficiency. While the transmission efficiency is less than 60% using no taper, the tapered couplers have over 90% power transmission. We show that different types of couplers are needed for efficient coupling into and out of photonic crystal waveguides.

Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap

We describe and demonstrate a new mechanism for low radiation losses in structures lacking a complete band gap, and show how resonant cavities with Q>103 can be achieved without sacrificing strong localization in 3d. This involves a forced cancellation in the lowest-order term(s) of the multipole far-field radiation expansion. We focus on the system of photonic-crystal slabs, one- to two-dimensionally periodic dielectric structures of finite height with vertical index guiding. Simulations and analytical results in 2d and 3d are presented.

Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides

We present a novel numerical scheme for the reduction of spurious reflections in simulations of electromagnetic wave propagation in photonic crystal waveguides. We use a distributed Bragg reflector waveguide termination to reduce reflection from photonic crystal waveguide ends by improving k-matching for photonic crystal waveguided modes. We describe computational procedures and show that a significant reduction in reflection amplitude can be achieved across a large part of the guided mode spectrum. This method enables one to reduce simply and effectively the computational requirements in photonic crystal waveguide simulations.

Two-dimensional photonic crystal couplers for unidirectional light output

We investigate the use of two-dimensional photonic crystal slabs to improve the directionality of output coupling from planar waveguides and distributed-feedback lasers. We present the theory underlying the operation of such structures and design criteria for emission in desired directions. As an example, we demonstrate a vertical coupler that is integrated with an organic distributed-feedback laser, use computer simulations to find its coupling constant and efficiency, and then discuss its feasibility.

Manipulating light with photonic crystals

Within the past several years “photonic crystals” have emerged as a new class of materials providing new possibilities for the control and manipulation of light. These materials are viewed ideally as a composite of a periodic array of macroscopic dielectric or metallic scatterers in a homogeneous dielectric matrix. A photonic crystal affects the properties of a photon in much the same way that a semiconductor affects the properties of an electron. Consequently, photons in photonic crystals can have band structures, localized defect modes, surface modes, etc. This new ability to mold and guide light leads naturally to many novel phenomena associated with light.

Novelties of Light with Photonic Crystals

Within the past several years “photonic crystals” have emerged as a new class of materials providing capabilities along new dimensions for the control and manipulation of light. These materials are viewed ideally as a composite of a periodic array of macroscopic dielectric or metallic scatterers in a homogeneous dielectric matrix. A photonic crystal affects the properties of a photon in much the same way that a semiconductor affects the properties of an electron. Consequently, photons in photonic crystals can have band structures, localized defect modes, surface modes, etc. This new ability to mold and guide light leads naturally to many novel phenomena associated with light — phenomena that have not been possible with traditional materials.

Finite differencing of periodic structures

Finite difference time domain is a powerful numerical method. We review our modeling and design of optical gratings and 2D photonic crystals, aided by the recently developed quartic perfectly matched layer boundary condition. For optical gratings with a quarter wave phase shift, we show that light can be confined in an air bridge micro-cavity. Such devices exhibit sharp transmission resonances in the stop bands. Photonic crystals also demonstrate strong localization of light so waveguides of air can be formed. In addition, even when the bending radius is zero, the transmission exceeds 0.95 percent.