This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorith...

We present a powerful sensitivity analysis method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for finding eigenvalue and transmission gradients with respect to the perturbation. The method permits fast analysis of a large number of dielectric perturbation situations for multiple devices in a photonic crystal....

We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at lo...

The solution to the problem of optical or electromagnetic-wave scattering from perfectly conducting rough surfaces modeled by a multiscale fractal function is generalized to the case of relative uniform translating motion with respect to the observer. The presence of motion can be treated by the relativistic frame hopping method by means of plane-wave simplification techniques, since the soluti...

We characterize the dispersion relation for electromagnetic-wave propagation in two-dimensional dielectric arrays, using the coherent microwave transient spectroscopy technique. Results of measurements along various symmetry directions of square and triangular lattices are presented. The experimental results are in excellent agreement with theoretical calculations made by using the plane-wave e...

The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed...

The method based on fast Fourier transforms proposed by G. Román-Pérez and J. M. Soler [Phys. Rev. Lett. 103, 096102 (2009)], which allows for a computationally fast implementation of the nonlocal van der Waals (vdW) functionals, has significantly contributed to making the vdW functionals popular in solid-state physics. However, the Román-Pérez-Soler method relies on a plane-wave expansion of t...