Photonic crystal heterostructures, like their semiconductor quantum electronic counterparts, generate complex function from simple, well-understood building blocks. They have led to compact photonic crystal-based waveguides and record-quality-factor resonant cavities. Here the progress on the experimental realization of photonic crystal heterostructure devices, and on the development of convenient, intuitive, and computationally efficient models of devices that unite multiple finite-sized photonic crystal media to engineer photon localization and guidance is summarized.

We report transient absorption saturation measurements on lead sulfide colloidal nanocrystals at the first and second exciton energies and fit the results to a model incorporating intraband and interband relaxation processes. We study in detail the Auger recombination from the first excited state, which takes place when more than one electron-hole pair is excited in a dot. We find an Auger coefficient of 4.5 x 10(-30) cm6/s for dots of 5.5 nm diameter, and observe saturation of the absorption bleaching when the (8-fold degenerate) first level is filled. We develop a model for the absorption dynamics using Poisson statistics and find a good fit with our experimental measurements.

We present an envelope approximation formalism to study three-dimensional photonic crystal heterostructures which only requires knowledge of the bulk crystal band structure and heterostructure design. Applying this method to photonic crystal waveguides, we predict within 1% accuracy the frequencies of guided modes and obtain the correct waveguided mode shapes. We show that guided modes are allowed for wave vectors where the curvature of a band in a direction perpendicular to the plane of the waveguide has the same sign as the refractive index contrast between the core and the cladding. We show that elementary waveguide theory can be employed to compute mode shapes and dispersion relations.

Band structures and Bloch modes give a generalized description of light in infinite photonic crystals. We show that the band structure and Bloch modes also contain the information necessary to find the amplitude and phase of light reflected and transmitted from interfaces in systems made using finite and semi-infinite photonic crystals. We obtain the equivalent of the Fresnel coefficients for photonic crystals. We use these coefficients to derive the reflection of light from a photonic crystal of finite size and the resonant modes of photonic crystal cavities and line defects. Results are given for ideal two-dimensional crystals, as well as crystals etched in semiconductor slab waveguides.

We develop an envelope function formalism to describe the behavior of light inside a structure assembled out of dissimilar photonic band-gap materials. These photonic heterostructures are the optical analogs of quantum electronic heterostructures that make up resonant tunneling diodes and superlattices. We show that the behavior of these media is readily quantified and explained by reducing each constituent photonic band-gap material to a set of parameters related to the photonic crystals' dispersion relation, which are then used as inputs to an envelope equation. We also prove the validity of the approximation by comparison to full numerical simulations.