Designing coupled-resonator optical waveguides based on high-Q tapered grating-defect resonators.

We present a systematic design of coupled-resonator optical waveguides (CROWs) based on high-Q tapered grating-defect resonators. The formalism is based on coupled-mode theory where forward and backward waveguide modes are coupled by the grating. Although applied to strong gratings (periodic air holes in single-mode silicon-on-insulator waveguides), coupled-mode theory is shown to be valid, since the spatial Fourier transform of the resonant mode is engineered to minimize the coupling to radiation modes and thus the propagation loss.

Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs).

We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators.

Grating induced transparency (GIT) and the dark mode in optical waveguides.

We propose and describe a new class of optical modes consisting of superposition of three waveguide modes which can be supported by a few-mode waveguide spatially modulated by two co-spatial gratings. These supermodes bear a close, but not exact, formal analogy to the three-level quantum states involved in EIT and its attendant slow light propagation characteristics. Of particular interest is the supermode which we call the dark mode in which, in analogy with the dark state of EIT, one of the three uncoupled waveguide modes is not excited.

Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system.

By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates epsilon, the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2/piepsilon1/2 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well.

Substantial gain enhancement for optical parametric amplification and oscillation in two-dimensional chi(2) nonlinear photonic crystals.

We have analyzed optical parametric interaction in a 2D NPC. While in general the nonlinear coefficient is small compared to a 1D NPC, we show that at numerous orientations a multitude of reciprocal vectors contribute additively to enhance the gain in optical parametric amplification and oscillation in a 2D patterned crystal. In particular, we have derived the effective nonlinear coefficients for common-signal amplification and common-idler amplification for a tetragonal inverted domain pattern.