Sensitivity analysis of photonic crystal fiber.

Photonic crystal fibers are well-known to offer a number of unusual properties, including supercontinuum generation, large mode-areas and controllable dispersion behavior. Their manufacturability would be enhanced by a more detailed understanding of how small perturbations in the fiber's geometric structure cause variations in the fiber's fundamental modes. In this paper, we demonstrate that such sensitivity analysis is feasible using highly accurate boundary integral techniques.

Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: Theory.

We present a new integral equation method for calculating the electromagnetic modes of photonic crystal fiber (PCF) waveguides. Our formulation can easily handle PCFs with arbitrary hole geometries and irregular hole distributions, enabling optical component manufacturers to optimize hole designs as well as assess the effect of manufacturing defects. The method produces accurate results for both the real and imaginary parts of the propagation constants, which we validated through extensive convergence analysis and by comparison with previously published results.

The thermal explosion revisited.

The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction alpha of its wall is ideally thermally conducting while the remaining fraction 1-alpha is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive alpha and isolated 1-alpha parts of the boundary occupy together the segments 2pi/N (N is the number of segments) of the boundary.