Photonic crystal circuits: A theory for two- and three-dimensional networks

Abstract

A discussion is given of waveguides in photonic crystals and branching network geometries of waveguides formed by joining several waveguide channels into conducting circuits for the transmission of light in photonic crystals. We shall refer to these structures in general as photonic crystal circuits. These conducting networks, which transport light, are an optical analogy to electrical circuits, which transport electrons through electrical networks. Photonic crystal circuits, however, unlike most electrical circuits, exhibit a variety of interference effects in their transport properties. The interference effects are related to the nondiffusive nature of the optical transport. The transport properties of light in a variety of circuit geometries are studied. Emphasis is placed on network geometries, which include barriers formed by the addition of dielectric materials to waveguide channels, bends in waveguide channels, closed loops, and interconnecting branched networks. Results for the transmission and reflection properties of photonic circuit modes are presented as functions of the mode frequencies and the dielectric constants of the materials forming the waveguide channels. A comparison is made of the properties of photonic crystal circuits with those of layered optical systems.

Photon, electron, magnon, phonon and plasmon mono-mode circuits

“…By photonic crystal we mean a crystal build out of a periodic arrangement of inclusions of one material inside another one. Since the first proposals [1,2] of photonic crystals for inhibited spontaneous light emission and localization of photons [3,4], there was an explosion of investigations for such novel materials (see, for example, [5][6][7], see also [8]) and in particular for their utilization in the fabrication of micro-photonic wave-guides (see, for example, [9][10][11][12]). Other surface techniques enable also to manufacture micro-photon circuits.…”

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

“…25 Still other larger scale applications deal with ILMs in Josephson arrays, 26,27 E&M ILMs in optical switches, 28 and in nonlinear photonic crystal wave guides. 29,30 The largest scale application has to do with localized multibunch modes in accelerators. 31 Thus from condensed matter physics to arrays used in high technology, one sees a new class of problems emerging, which share a common denominator.…”

Multi-channel waveguides based on two dimensional phononic crystals

“…Here, the radius of water cylinders in the perfect material (r 0 ) is 0.31a and the corresponding volume fraction f=0. 3. When in the perfect system (r d = r 0 ), from the normalized frequency 0.305 to 0.801, in unit of ωa/2πC l , where a is the lattice constant and C l is the longitudinal velocity in mercury, it exhibits a big complete band gap.…”

“…The studies have been concerned with manipulating the propagation of light through channels (or waveguides) created inside the photonic crystal that can be considered as photonic circuits [3]. In recent years, a great deal of attention has extended to the phononic crystals, the counterpart of photonic crystals, for which acoustic waves (AC) and/or elastic waves (EL) are considered [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”