Marin Soljacic

Coupling, scattering, and perturbation theory: Semi-analytical analyses of photonic-crystal waveguides

Although brute-force simulations of Maxwells equations, such as FDTD methods, have enjoyed wide success in modelling photonic-crystal systems, they are not ideally suited for the study of weak perturbations, such as surface roughness or gradual waveguide transitions, where a high resolution and/or large computational cells are required. Instead, we suggest that these important problems are ideally suited for semi-analytical methods, which employ perturbative corrections (typically only needing the lowest order) to the exactly understood perfect waveguide. However, semi-analytical methods developed for the study of conventional waveguides require modification for high index-contrast, strongly periodic photonic crystals, and we have developed corrected forms of coupled-wave theory, perturbation theory, and the volume-current method for this situation. In this paper, we survey these new developments and describe the most significant results for adiabatic waveguide transitions and disorder losses. We present design rules and scaling laws for adiabatic transitions. In the case of disorder, we show both analytically and numerically that photonic crystals can suppress radiation loss without any corresponding increase in reflection, compared to a conventional strip waveguide with the same modal area, group velocity, and disorder strength.

Prediction of Coherent Optical Radiation from Shock Waves in Polarizable Crystals

We predict that coherent electromagnetic radiation in the 1-100 THz frequency range can be generated in crystalline materials when subject to a shock wave or soliton-like propagating excitation. To our knowledge, this phenomenon represents a fundamentally new form of coherent optical radiation source that is distinct from lasers and free-electron lasers. General analytical theory and molecular dynamics simulations demonstrate coherence lengths on the order of mm (around 20 THz) and potentially greater. The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material.

Collisions between 2+1D Composite Solitons: DelayedAction Interaction and SpinOrbit Coupling

We report on new fundamental phenomena in soliton interactions: delayed- action interaction and spin-orbit coupling upon collision between two-dimensional composite solitons.

Modulation instability and pattern formation of incoherent light

Modulation instability and pattern formation in spatially incoherent light beams is experimentally demonstrated, and we show that patterns, such as 2D self-ordered arrays of light spots, can form spontaneously from noise. This is a universal phenomena that relates to other nonlinear systems of weakly-correlated particles, such as Bose-Einstein condensates and semiconductors near the quantum Hall regime.