The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it applies to analyze the Floquet-modes of photonic crystal waveguides. This paper shows that the Floquet-mode calculation with large truncation order is limited and explains the reason. Furthermore, two techniques of the formulation are presented to relieve this limitatio...

Previous studies dealing with Floquet secondary stability analysis of the wakes of circular and square cross-section cylinders have shown that there are two synchronous instability modes, with long ~mode A! and short ~mode B! spanwise wavelengths. At intermediate wavelengths another mode arises, which reaches criticality at Reynolds numbers higher than modes A or B. Here we concentrate on these...

The exchange of power between two identical coupled waveguides with embedded periodic structure along the z direction is studied in the framework of Floquet–Bloch theory. A one-period propagator is calculated and a spectrum of its eigenvalues (eigenphases) is studied. We show that due to special symmetry properties of the Floquet–Bloch operator, a strong enhancement or a total suppression of po...

Dynamical tunneling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunneling process is governed by nonlinear resonances that manifest within the regular phase-space islands on which the stable modes are localized. By means of a quantitative numerical study of the corresponding Floquet problem, we identify the trace of s...

| The exchange of power between two identical coupled waveguides with embedded periodic structure along z-direction is studied in the framework of Floquet-Bloch theory. A one-period propagator is calculated and a spectrum of its eigenvalues (eigenphases) is studied. We show that due to special symmetry properties of the Floquet-Bloch operator , a strong enhancement or a total suppression of pow...

Aims. We apply Floquet analysis to study the dynamical stability of two-dimensional axisymmetric Keplerian flows distorted by an m = 2 epicyclic periodic forcing term, representing a tidal perturbation in a thin accretion disk (AD) of a cataclysmic variable (CV). This tidal mode is responsible for the disk truncation mechanism. Methods. Floquet analysis reveals, with a positive Floquet exponent...

Explosive particle production due to parametric resonance is a crucial feature of reheating in inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter and gravitational fluctuations and often induce a parametric resonance instability. In a previous paper (hep-ph/9709273) it was shown that homogeneous (i.e. space...

We calculate exactly the two bound Floquet modes of a periodic linear waveguide induced in a medium by a second-order soliton of the nonlinear Schrödinger equation. The modes are degenerate at the writing frequency, having the same quasi-propagation constant, which suggests applications of our method to spectral filtering.

We propose a Y-junction device for splitting the two Floquet modes of a periodic waveguide. Although the junction is a passive, linear device, it is designed using nonlinear techniques. It acts as a standard modal splitter in a multimode slab waveguide, but in this case the input modes are degenerate.