Optical bright and dark states in side-coupled resonator structures.

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.

Enhanced second-harmonic generation in AlGaAs microring resonators.

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.

Hamiltonian formulation of coupled-mode theory in waveguiding structures.

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 canonical commutation relations. This difficulty is circumvented by the introduction of "dressed parent modes," which are in fact seen to be the "coupled modes" of the system. While an exact solution of the linear problem within the restricted basis of interest formally must be found before these modes can be constructed, in practice they can be constructed directly from the modes of the parent structures. The approach can be applied to periodic parent structures, such as photonic crystal waveguiding structures, as well as to simpler waveguides. We illustrate the accuracy of the various approximations employed by studying two sample systems in detail. We derive the linear coupled mode equations, and show how the approach can be immediately generalized from the linear regime to treat problems in nonlinear quantum optics.

Electrically-pumped, broad-area, single-mode photonic crystal lasers.

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 chambers or optical signal processing with micro-electromechanical systems. An outstanding challenge is that broad-area lasers often require external means of control, such as injection-locking or a frequency/spatial filter to obtain single-mode operation. In this paper, we propose and demonstrate effective index-guided, large-area, edge-emitting photonic crystal lasers driven by pulsed electrical current injection at the optical telecommunication wavelength of 1550 nm. By suitable design of the photonic crystal lattice, our lasers operate in a single mode with a 1/e(2) modal width of 25 microm and a length of 600 microm.

Minimizing finite-size effects in artificial resonance tunneling structures.

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 analytical expressions. Using a Breit-Wigner scattering formalism, we demonstrate that the scheme can be used to minimize finite-size effects in a general class of coupled cavity structures. The strength of the present technique lies in its simplicity and its applicability to a wide variety of structures described by tight-binding formalisms.

Effective field theory for the nonlinear optical properties of photonic crystals.

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 formalism can be easily quantized. We illustrate the approach by considering a periodic Kerr medium, and show how the nonlinear coupled mode and nonlinear Schrödinger equations emerge. We extend the latter to treat optical shock effects, and compare our canonical formulation with earlier treatments.

Depositing light in a photonic stop gap by use of Kerr nonlinear microresonators.

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 the channel waveguides and resonators. We also demonstrate that the energy can be extracted from the cavity with a similar process.

All-optical AND gate by use of a Kerr nonlinear microresonator structure.

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.