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Highly efficient second-harmonic generation can be achieved by harnessing resonance effects in microring resonator structures. We propose an angular quasi-phase-matching scheme based on the position dependence of polarization inside the ring resonator.
We consider finite-size effects in coupled cavity structures. Starting with microring resonator structures well described by transfer matrices, we obtain conditions that lead to the minimization of finite-size effects. Our approach does not require numerical optimization and requires only slight modification of design parameters guided by closed-form… (More)
We analyze the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry–Perot resonator arrays. We develop a transfer matrix method to calculate the amplitude and phase responses of the arrays. We also discuss the inclusion of optical gain in the system to compensate for losses in these structures. Owing… (More)
We present a Hamiltonian formulation of coupled mode theory for scenarios in which the coupled modes are associated with different "parent structures," such as two nearby waveguides. The relativistic nature of the photon leads to the complication that not any set of orthonormal modes can be used as a basis if the associated amplitudes are to satisfy… (More)
We introduce an effective field theory for the nonlinear optics of photonic crystals of arbitrary dimensionality. Based on a canonical Hamiltonian formulation of Maxwell's equations, canonical effective fields are introduced to describe the electromagnetic field. Conserved quantities are easily constructed and their physical significance identified; the… (More)
Planar broad-area single-mode lasers, with modal widths of the order of tens of microns, are technologically important for high-power applications and improved coupling efficiency into optical fibers. They may also find new areas of applications in on-chip integration with devices that are of similar size scales, such as for spectroscopy in microfluidic… (More)
We analyze side-coupled standing-wave cavity structures consisting of Fabry-Perot and photonic crystal resonators coupled to two waveguides. We show that optical bright and dark states, analogous to those observed in coherent light-matter interactions, can exist in these systems. These structures may be useful for variable, switchable delay lines.
We numerically demonstrate the feasibility of constructing an all-optical AND gate by using a microresonator structure with Kerr nonlinearity. The gate is much smaller than similar AND gates based on Bragg gratings and has lower power requirements.
We show theoretically that it is possible to trap light in a microresonator structure by use of four-wave mixing. The efficiency of the parametric process is substantially increased by the high group delay of light inside the structure. The energy that is trapped has a half-life of approximately 500 ps in the presence of both linear and nonlinear loss in… (More)
We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of N particles coupled to lineal gravity and can be considered as a model of N relativistically interacting sheets of uniform mass. The partition function and one-particle distribution functions are computed to leading order in 1/c… (More)