Quasi-Phase Matching Effective in Microring Resonator

Breck Hitz

Quasi-phase-matched second-harmonic generation in crystals has evolved into a successful technique of avoiding the beam walk-off and degradation of beam quality associated with angular phase matching. Moreover, quasi-phase matching provides a technique of phase matching nonlinear materials for which conventional birefringent phase matching is not possible.

In crystals, quasi-phase matching typically entails periodically flipping the phase between the fundamental and harmonic fields so that the phase mismatch between the two that accumulates as a result of dispersion is compensated. A report published in Photonics Spectra last month (see “Phase-Matching Technique for High-Harmonic Generation,” page 91) describes an alternative approach to quasi-phase matching in which no phase flipping occurs; rather, the (high-order) harmonic generated from the out-of-phase regions is suppressed, so only the in-phase harmonic field contributes to the output.

The scientists analyzed an AlGaAs microring resonator in which both the fundamental and second harmonic were resonant. Reprinted with permission of Optics Letters.

Recently, scientists at the University of Toronto and at the University of Iowa in Iowa City calculated that a similar approach to quasi-phase matching could be effective for enhancing second-harmonic generation in microring resonators.

They analyzed an AlGaAs microring resonator in which both the fundamental and second harmonic were resonant (see figure). They considered the case where the fundamental is polarized in the plane of the figure and the second harmonic is perpendicular to the plane. Quasi-phase matching occurs because, although the orientation of the crystal axes is independent of angular position in the ring (θ), the polarization fields vary with angular position. Thus, the effective nonlinear susceptibility depends on the angular location in the ring.

By designing the microring judiciously, the scientists arranged for effective harmonic generation to occur only in those regions of the ring from which an in-phase signal was generated.

Invoking a numerical analysis of their theoretical model, they predicted that, ideally, 100 percent of the single-frequency fundamental wave could be converted to the second harmonic. Even with a pulsed input, if the spectrum were essentially transform-limited, 92 percent of the incoming fundamental energy could be converted to the second harmonic. These calculated results assume lossless propagation and no fabrication errors in the ring, but even folding these factors into account, the scientists believe that at least half the incoming energy could be converted to the second harmonic with this technique.

Optics Letters, April 1, 2007, pp. 826-828.