Optical parametric amplifiers using chirped quasi-phase-matching (QPM) gratings offer the possibility of engineering the gain and group delay spectra. We give practical formulas for the design of such amplifiers. We consider linearly chirped QPM gratings providing constant gain over a broad bandwidth, sinusoidally modulated profiles for selective frequency amplification and a pair of QPM gratings working in tandem to ensure constant gain and constant group delay at the same time across the spectrum. The analysis is carried out in the frequency domain using Wentzel-Kramers-Brillouin analysis.

We present a broadband optical parametric amplifier design using tapered gain and tandem chirped quasi-phase-matching gratings to obtain flat gain and group-delay spectra suitable for applications such as ultrashort-pulse amplification and fiber-optic communication systems. Although a tapered-gain amplifier consisting of a single chirped grating can provide constant gain over a wide frequency range, it cannot be used to control the group delay across the spectrum. We propose controlling both the gain and the group delay profiles using a two-stage amplifier configuration, in which the idler of the first is used as the input signal of the second.

Chirped quasi-phase-matched optical parametric amplifiers (chirped QPM OPAs) are investigated experimentally. The measured collinear gain is constant over a broad bandwidth, which makes these devices attractive candidates for use in femtosecond amplifier systems. The experiment also shows that chirped QPM OPAs support noncollinear gain-guided modes. These modes can dominate the desired collinear gain and generate intense parametric fluorescence. Design guidelines to mitigate these parasitic processes are discussed.

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.

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.