Narrowband optical parametric amplification measurements in Ga0.5In0.5P photonic crystal waveguides.

We report the first demonstration of narrowband parametric amplification in a chip scale semiconductor waveguide. A dispersion engineered, Ga0.5In0.5P photonic crystal waveguide with a dispersion function that exhibits two zero crossings was used with a pulsed pump placed in the normal dispersion regime while a tunable probe was scanned on either side of the pump. A peak conversion efficiency of -10 dB was obtained with a peak pump power of only 650 mW. The narrowband nature of the gain spectrum was clearly demonstrated.

Dual-pump parametric amplification in dispersion engineered photonic crystal waveguides.

This paper describes a numerical simulation of narrow band parametric amplification in dispersion engineered photonic crystal waveguides. The waveguides we analyze exhibit group velocity dispersion functions which cross zero twice thereby enabling many interesting pumping schemes. We analyze the case of two pulsed pumps each placed near one of the zero dispersion wavelengths. These configurations are compared to conventional single pump schemes. The two pumps may induce phase matching conditions in the same spectral location enabling to control the gain spectrum. This is used to study the gain and fidelity of 40 G bps NRZ data signals.

Parametric gain in dispersion engineered photonic crystal waveguides.

We present a numerical simulation of parametric gain properties in GaInP PhC dispersion engineered waveguides in which the group velocity dispersion crosses zero twice and where the pump and the signal are 100 ps pulses. The simulations use the M-SSFT algorithm which incorporates dispersive nonlinear coefficients and losses. We concentrate on narrow band parametric gain which occurs for pump wavelengths in the normal group velocity dispersion regime. The effects of structural details, of pump wavelength and of losses are carefully analyzed.

Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides.

We predict narrowband parametric amplification in dispersion-tailored photonic crystal waveguides made of gallium indium phosphide. We use a full-vectorial model including the dispersive nature both of the nonlinear response and of the propagation losses. An analytical formula for the gain is also derived.

Dynamic Brillouin gratings permanently sustained by chaotic lasers.

A method to induce only one permanent and localized dynamic Brillouin grating in polarization maintaining optical fibers is introduced. The generation of the grating exploits the thumbtack correlation of the chaotic laser signals. A numerical calculation, corroborated by a theoretical analysis, is performed and the grating properties, length, and reflectance determined.

Theory of slow light enhanced four-wave mixing in photonic crystal waveguides.

The equations for Four-Wave-Mixing in a Photonic Crystal waveguide are derived accurately. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences with simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, unoptimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.

Highly efficient four wave mixing in GaInP photonic crystal waveguides.

We report highly efficient four wave mixing in a GaInP photonic crystal waveguide. Owing to its large bandgap, the ultrafast Kerr nonlinearity of GaInP is not diminished by two photon absorption and related carrier effects for photons in the 1550 nm range. A four-wave-mixing efficiency of -49 dB was demonstrated for cw pump and probe signals in the milliwatt range, while for pulsed pumps with a peak power of 25 mW the conversion efficiency increased to -36 dB. Measured conversion efficiency dependencies on pump probe detuning and on pump power are in excellent agreement with a simple analytical model from which the nonlinear parameter gamma is extracted. Gamma scales approximately with the square of the slow down factor and varies from 800 W(-1) m(-1) at a pump wavelength lambda(p)=1532 nm to 2900 W(-1) m(-1) at lambda(p)=1550 nm. These values are consistent with those obtained from self phase modulation experiments in similar devices.

Polarization patterns and vectorial defects in type-II optical parametric oscillators.

Previous studies of lasers and nonlinear resonators have revealed that the polarization degree of freedom allows for the formation of polarization patterns and novel localized structures, such as vectorial defects. Type- II optical parametric oscillators are characterized by the fact that the down-converted beams are emitted in orthogonal polarizations. In this paper we show the results of the study of pattern and defect formation and dynamics in a type-II degenerate optical parametric oscillator, for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations that appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.

Phase-locked spatial domains and Bloch domain walls in type-II optical parametric oscillators.

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II optical parametric oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is observed numerically and the dynamics and chiral properties of the fronts are investigated. Bloch walls connect homogeneous regions of self-phase-locked solutions by means of a polarization transformation. The parameter range for phase locking is found analytically. The polarization properties and the dynamics of walls in one and two transverse spatial dimensions are explained. The transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. The wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.

Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

Degenerate optical parametric oscillators can exhibit both uniformly translating fronts and nonuniformly translating envelope fronts under the walk-off effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main characteristics of the walk-off effect on pattern selection. The predictions of the selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equations describing the optical parametric oscillator.

Bloch domain walls in type II optical parametric oscillators.

Evidence of Bloch domain walls in nonlinear optical systems is given. These walls are found in the transverse fields of optical parametric oscillators when the polarization degree of freedom, the cavity birefringence, and (or) dichroism are taken into account. These domain walls arise spontaneously and exhibit defects where Bloch walls of different chirality join together. Two dynamic regimes are found:In the first one the vector field approaches a final homogeneous state, and in the other the walls are continually generated and annihilated. This dynamic behavior is caused by the fact that walls of opposite chirality move spontaneously with opposite velocity.

Walk-off and pattern selection in optical parametric oscillators.

The effect of walk-off in pattern selection in optical parametric oscillators is theoretically examined. We show that a dynamic mechanism also allows us to observe the formation of structures for positive signal detunings. In this regime the pattern that is generated is a periodic array of kinks that separate regions in which one of two stable steady states is alternately selected. This structure can be regarded as a train of dark soliton stripes because the two solutions have opposite signs. The wavelength of the selected pattern is theoretically predicted, and the prediction agrees with the results of the numerical solutions of the equations governing the device.

Growth dynamics of noise-sustained structures in nonlinear optical resonators.

The existence of macroscopic noise-sustained structures in nonlinear optics is theoretically predicted and numerically observed, in the regime of convective instability. The advection-like term, necessary to turn the instability to convective for the parameter region where advection overwhelms the growth, can stem from pump beam tilting or birefringence induced walk-off. The growth dynamics of both noise-sustained and deterministic patterns is exemplified by means of movies. This allows to observe the process of formation of these structures and to confirm the analytical predictions. The amplification of quantum noise by several orders of magnitude is predicted. The qualitative analysis of the near- and far-field is given. It suffices to distinguish noise-sustained from deterministic structures; quantitative informations can be obtained in terms of the statistical properties of the spectra.

Induced modulational instability in high-birefringence fibers: the strong conversion regime.

We show that modulational instability pumped by a mixed mode beam propagating in a high-birefringence fiber is driven in the regime of strong conversion by a four-wave-mixing interaction. This allows one to predict new period-doubling instabilities as well as the optimum conditions for frequency conversion.

Higher-order effects in bandwidth-limited soliton propagation in optical fibers.

By means of numerical studies and soliton perturbation theory we examine the effects of higher-order linear and nonlinear terms in bandwidth-limited amplified soliton propagation. We show that these effects are responsible for strong reductions of soliton-soliton interaction in such systems.