Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal.

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO(3) and LiTaO(3) .

Two-dimensional local density of states in two-dimensional photonic crystals.

We calculate the two-dimensional local density of states (LDOS) for two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length. The LDOS determines the dynamics of radiation sources embedded in a photonic crystal. We show that the LDOS decreases exponentially inside the crystal for frequencies within a photonic band gap of the associated infinite array and demonstrate that there exist ;;hot' and ;;cold' spots inside the cluster even for wavelengths inside a gap, and also for wavelengths corresponding to pass bands. For long wavelengths the LDOS exhibits oscillatory behavior in which the local density of states can be more than 30 times higher than the vacuum level.

Propagation through apodized gratings.

It is shown that light propagation in an apodized fiber Bragg grating with a Kerr nonlinearity approximately obeys a nonlinear Schr"odinger-like equation, but with extra terms because the eigenstates of the grating vary with position. It is shown that propagation through such a grating leads to field enhancement, and to a nontrivial phase shift; an approximate expression for the reflectivity is also found.

Nonlinear pulse reflections from chirped fiber gratings.

We study the nonlinear evolution of optical pulses reflected from a chirped fiber grating experimentally and with numerical simulations. Over a broad range of grating parameters the nonlinearly reflected pulse splits into a pair of pulses in the range of incident pulse intensities where the transmitted pulse is a single narrowed pulse evolving into a fundamental soliton.