Hsi-Chun Liu

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.

Abstract 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.

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.

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.

We present a design of “ideal” optical delay lines (ie, constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs.

Slow light has been an inter-disciplinary topic and a rapidly growing area, especially over the last decade with the improvement of fabrication technology. The ability to slow down and control the group velocity of light may find applications such as optical buffers, optical delay lines, and enhanced light-matter interaction in optical modulator, amplifier, detectors, lasers, and nonlinear optics. The spirit of slow light is to replace a bulky device with a much shorter, compact structure.