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.

Far field of polarization gratings.

In a recent Letter [Opt. Lett. 24, 584 (1999)], Gori analyzed polarization gratings and proposed using them as a tool to measure Stokes parameters. Most of his analysis dealt with the near field, but practical exploitation of his approach relies on the far field. A discussion focusing on the far field is presented, and recipes are suggested for actual implementations of such devices.

Theory of linearly birefringent fibers: an alternative approach.

We tackle the theory of linearly birefringent single-mode dielectric fibers in terms of magnetic fields, instead of the usual electric fields. The new approach simplifies the analysis of the minor field component as a function of the radial coordinate. Several previous results are reconfirmed and unified. New closed-form expressions are found for the field in a fiber in which the physical index seen by the minor component matches, in a part of the cross section, the guided-mode equivalent index.

Experimental investigation of linear polarization in high-birefringence single-mode fibers.

We report on measurements of linear polarization ratio in high-birefringence fibers as a function of wavelength. Comparison with standard step-index and with dispersion-shifted fibers reconfirms that the modes of polarization-maintaining fibers are not linearly polarized.

Second-order perturbation theory of rectangular waveguides and directional couplers.

Perturbation theory is applied to rectangular-core coupled waveguides, whose cladding can be homogeneous or not. Second-order corrections are evaluated for the phase constants of the guided modes and for the coupling coefficient. This requires the full spectrum of radiation modes, which are found within the same approximation as Marcatili's guided modes. It is found that the second-order terms are negligible in most cases of practical interest. However, there are cases for which these terms are so large that the usual first-order theory collapses.

Antiresonant decoupling of parallel dielectric waveguides.

Two open waveguides with finite spacing can be decoupled, if the index between them is a suitable function of the transverse coordinates. An analytical proof is provided that makes use of vector properties of electromagnetic waves. On the contrary, decoupling is shown to be impossible for scalar waves and thus incompatible with the weakly guiding assumption. Decoupling can be interpreted as a distributed antiresonance in the region between the waveguides.