Stable Magnetostatic Solitons in Yttrium Iron Garnet Film Waveguides for Tilted in-Plane Magnetic Fields

The possibility of nonlinear pulses generation in Yttrium Iron Garnet thin films for arbitrary direction between waveguide and applied static in-plane magnetic field is considered. Up to now only the cases of in-plane magnetic fields either perpendicular or parallel to waveguide direction have been studied both experimentally and theoretically. In the present paper it is shown that also for other angles (besides 0 or 90 degrees) between a waveguide and static in-plane magnetic field the stable bright or dark (depending on magnitude of magnetic field) solitons could be created.Comment: Phys. Rev. B (accepted, April 1, 2002

On occurrence of spectral edges for periodic operators inside the Brillouin zone

The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the (reduced) Brillouin zone only, rather than the whole zone? Or, do the edges of the spectrum occur necessarily at the set of ``corner'' high symmetry points? This is known to be true in 1D, while no apparent reasons exist for this to be happening in higher dimensions. In many practical cases, though, this appears to be correct, which sometimes leads to the claims that this is always true. There seems to be no definite answer in the literature, and one encounters different opinions about this problem in the community. In this paper, starting with simple discrete graph operators, we construct a variety of convincing multiply-periodic examples showing that the spectral edges might occur deeply inside the Brillouin zone. On the other hand, it is also shown that in a ``generic'' case, the situation of spectral edges appearing at high symmetry points is stable under small perturbations. This explains to some degree why in many (maybe even most) practical cases the statement still holds.Comment: 25 pages, 10 EPS figures. Typos corrected and a reference added in the new versio

Nonlinear Three-Wave Interaction In Photonic Crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals. © Springer-Verlag 2005

General theory of nonresonant wave interaction: Giant soliton shift in photonic band gap materials

The nonresonant interaction of nonlinear waves in one-dimensional photonic band gap materials is investigated analytically and numerically. We derive highly accurate analytical formulae that determine the phase shift experienced by nonlinear waves during nonresonant interaction. The case of nonresonant interaction of Bragg and gap solitons is considered in detail. We show that the phase shift of the interacting solitons should be experimentally observable, and can be used as a probe to determine the existence and the parameters of a gap soliton

Testing Random Numbers With Periodic Structures

We investigate the effect of random and nonrandom disorder on the properties of periodic media. Specifically, we show that the complex transmission is particularly sensitive to whether the disorder is truly random or not. We exploit this effect as a flexible and efficient test to detect subtle biases in sequences of random numbers. Based on this approach, we suggest the implementation of a simple physical device requiring single-frequency analysis. © EDP Sciences

Testing random numbers with periodic structures

We investigate the effect of random and nonrandom disorder on the properties of periodic media. Specifically, we show that the complex transmission is particularly sensitive to whether the disorder is truly random or not. We exploit this effect as a flexible and efficient test to detect subtle biases in sequences of random numbers. Based on this approach, we suggest the implementation of a simple physical device requiring single-frequency analysis