Analysis of photonic crystal double heterostructure resonant cavities

Two-dimensional photonic crystals represent a versatile technology platform for constructing photonic integrated circuits. Low-loss and small footprint waveguides and cavities can be combined to make delay lines, modulators, filters and lasers for efficient optical signal processing. However, this diverse functionality comes at the expense of higher complexity in both the fabrication and themodeling of these devices. This Thesis discusses the finite-difference time-domain numerical modeling of large quality factor photonic crystal cavities for chip-scale laser applications.;In Chapter 2 the role of the quality factor in estimating laser threshold is derived starting from Maxwell's equations. Expressions for modal loss and gain are derived. Chapter 3 discusses methods for extracting the quality factor from finite-difference time-domain simulations. Even with large-scale parallel computing, only a short record of the time evolution of the fields can be recorded. To get around this issue, Pade functions are fitted to the available data in the frequency domain.;Once the analysis tools have been described and demonstrated, they are applied to the photonic crystal double heterostructure cavity which has been shown to have quality factors in excess of one million and mode volumes on the order of a cubic wavelength. A detailed description of the spectral and modal properties of heterostructure cavities is presented, and a method for mode discrimination is discussed.;The effect of heat sinking dielectric lower substrates on the optical loss of the heterostructure cavity is investigated, and it is seen that the quality factor is significantly reduced as the index of the lower substrate is increased. A modified heterostructure cavity with glide plane symmetry is shown to have significantly reduced out-of-plane leakage. An optimized design is proposed for continuous wave edge-emitting laser operation.;Finally, a novel approach for laser simulation is introduced in which a material gain model is included in the finite-difference time-domain simulation. The effects of spatially varying gain distributions are investigated and agree well with the modal gain derivation in Chapter 2.