Four-wave mixing in slow light photonic crystal waveguides with very high group index

Soliton Pulse Propagation in the Presence of Disorder-Induced Multiple Scattering in Photonic Crystal Waveguides

We introduce a new coupled mode theory to model nonlinear Schrödinger equations for counterpropagating Bloch modes that include disorder-induced multiple scattering effects on nonlinear soliton propagation in photonic crystal waveguides. We also derive subunit-cell coupling coefficients and use these to introduce a generalized length scale associated with each coupling effect. In particular, we define a multiple-scattering length scale that quantifies the spatial extent of a disorder-induced cavity mode. Our numerical simulations of nonlinear pulse propagation are in excellent qualitative agreement with recent experiments and provide insight into how structural disorder inhibits soliton propagation and other nonlinear propagation effects in photonic crystal waveguides.

Effect of loss on slow-light-enhanced second-harmonic generation in periodic nanostructures

We theoretically analyze the dependence of second-harmonic generation efficiency on the group index in periodic optical waveguides with loss. We investigate different possible scenarios of using slow light to enhance the efficiency of this process and show that in some cases there exists a maximally achievable efficiency reached for finite values of the group index at the point of phase-matching. Furthermore, we identify situations for which slow light, surprisingly, does not enhance the second-harmonic generation efficiency. Our results are corroborated by rigorous nonlinear simulations of second-harmonic generation in periodic nanobeam waveguides with loss.

Comparative analysis of four-wave mixing of optical pulses in slow- and fast-light regimes of a silicon photonic crystal waveguide

We present an in-depth study of four-wave mixing (FWM) of optical pulses in silicon photonic crystal waveguides. Our analysis is based on a rigorous model that includes all relevant linear and nonlinear optical effects and their dependence on the group velocity, as well as the influence of free carriers on pulse dynamics. In particular, we reveal key differences between FWM in the slow- and fast-light regimes and how they are related to the physical parameters of the pulses and waveguide. Finally, we illustrate how these results can be used to design waveguides with optimized FWM conversion efficiency.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Designing photonic crystal waveguides for broadband four-wave mixing applications

We present photonic crystal waveguide designs which exhibit large four-wave mixing efficiencies over a wide wavelength region. These designs are identified using an optimization process taking into account sophisticated figure-of-merits that depend on the pump bandwidth and the signal/pump tunability. The obtained designs achieve up to -18.9  dB conversion efficiency, tunable over a 10 nm tunability range. We also present alternative designs that are less efficient but have smaller power requirements and are far more compact.

Extraction of group index of lossy photonic crystal waveguides

We present a numerical approach to extract group index in photonic crystal (PhC) waveguides using two- and three-dimensional finite-difference time-domain methods and make a quantitative study of the effects of loss on slow light propagation in PhC waveguides. PhC waveguides are simulated with varying material loss and varying PhC waveguide length. Finally, we validate our method by comparing three-dimensional simulation results with experimental results.

Designing slow-light photonic crystal waveguides for four-wave mixing applications

We discuss the optimization of photonic crystal waveguides for four-wave mixing (FWM) applications, taking into account linear loss and free-carrier effects. Suitable figures of merit are introduced in order to guide us through the choice of practical, high-efficiency designs requiring relatively low pump power and small waveguide length. In order to realistically perform the waveguide optimization process, we propose and validate an approximate expression for the FWM efficiency, which significantly alleviates our numerical calculations. Promising waveguide designs are identified by means of an exhaustive search, altering some structural parameters. Our approach aims to optimize the waveguides for nonlinear signal-processing applications based on the FWM.

Enhanced four-wave-mixing effects by large group indices of one-dimensional silicon photonic crystal waveguides

Enhanced four-wave-mixing (FWM) effects have been observed with the help of large group-indices near the band edges in one-dimensional (1-D) silicon photonic crystal waveguides (Si PhCWs). A significant increase of the FWM conversion efficiency of about 17 dB was measured near the transmission band edge of the 1-D PhCW through an approximate 3.2 times increase of the group index from 8 to 24 with respect to the central transmission band region despite a large group-velocity dispersion. Numerical analyses based on the coupled-mode equations for the degenerated FWM process describe the experimentally measured results well. Our results indicate that the 1-D PhCWs are good candidates for large group-index enhanced nonlinearity devices even without having any special dispersion engineering.

Reducing disorder-induced losses for slow light photonic crystal waveguides through Bloch mode engineering

We present theory and measurements of disorder-induced losses for low loss 1.5 mm long slow light photonic crystal waveguides. A recent class of dispersion engineered waveguides increases the bandwidth of slow light and shows lower propagation losses for the same group index. Our theory and experiments explain how Bloch mode engineering can substantially reduce scattering losses for the same slow light group velocity regime.