Design of broad-band PMD compensation filters

We describe a new design approach for broad-band polarization-mode dispersion (PMD) compensation filters. An efficient algorithm for minimization of the maximum differential group delay within a given frequency band is described

Measurement of high-order polarization mode dispersion

We demonstrate a new method to measure high-order polarization mode dispersion (PMD) using the Jones matrix exponential expansion. High-order PMD is characterized by measuring a series of characteristic matrices, which are convenient quantities for analyzing PMD effects in the time-domain. An experimental method is developed to estimate the validity range of the exponential expansion

Representation of second-order polarisation mode dispersion

A new expansion for the Jones matrix of a transmission medium is used to describe high-order polarisation dispersion. Each term in the expansion is characterised by a pair of principal states and the corresponding dispersion parameters. With these descriptors, a new expression for pulse deformation is derived and confirmed by simulation

Programming of inhomogeneous resonant guided wave networks

Photonic functions are programmed by designing the interference of local waves in inhomogeneous resonant guided wave networks composed of power-splitting elements arranged at the nodes of a nonuniform waveguide network. Using a compact, yet comprehensive, scattering matrix representation of the network, the desired photonic function is designed by fitting structural parameters according to an optimization procedure. This design scheme is demonstrated for plasmonic dichroic and trichroic routers in the infrared frequency range

Probing Supersymmetric Flavor Models with ϵ′/ϵ\epsilon'/\epsilon

We discuss the supersymmetric contribution to $\epsilon'/\epsilon$ in various supersymmetric flavor models. We find that in alignment models the supersymmetric contribution could be significant while in heavy squark models it is expected to be small. The situation is particularly interesting in models that solve the flavor problems by either of the above mechanisms and the remaining CP problems by means of approximate CP, that is, all CP violating phases are small. In such models, the standard model contributions cannot account for $\epsilon'/\epsilon$ and a failure of the supersymmetric contributions to do so would exclude the model. In models of alignment and approximate CP, the supersymmetric contributions can account for $\epsilon'/\epsilon$ only if both the supersymmetric model parameters and the hadronic parameters assume rather extreme values. Such models are then strongly disfavored by the $\epsilon'/\epsilon$ measurements. Models of heavy squarks and approximate CP are excluded.Comment: 16 pages, harvmac. v2: We added a discussion of the intriguing implications that would follow if a recent lattice result is confirme

Statistical determination of the length dependence of high-order polarization mode dispersion

We describe a method of characterizing high-order polarization mode dispersion (PMD).Using a new expansion to approximate the Jones matrix of a polarization-dispersive medium, we study the length dependence of high-order PMD to the fourth order. A simple rule for the asymptotic behavior of PMD for short and long fibers is found. It is also shown that, in long fibers (~1000 km), at 40 Gbits/s the third- and fourth-order PMD may become comparable to the second-order PMD

Contractions of Degenerate Quadratic Algebras, Abstract and Geometric

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by B\^ocher contractions of the conformal Lie algebra $\mathfrak{so}(4,\mathbb {C})$ to itself. In 2 dimensions there are two kinds of quadratic algebras, nondegenerate and degenerate. In the geometric case these correspond to 3 parameter and 1 parameter potentials, respectively. In a previous paper we classified all abstract parameter-free nondegenerate quadratic algebras in terms of canonical forms and determined which of these can be realized as quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces, and studied the relationship between B\^ocher contractions of these systems and abstract contractions of the free quadratic algebras. Here we carry out an analogous study of abstract parameter-free degenerate quadratic algebras and their possible geometric realizations. We show that the only free degenerate quadratic algebras that can be constructed in phase space are those that arise from superintegrability. We classify all B\^ocher contractions relating degenerate superintegrable systems and, separately, all abstract contractions relating free degenerate quadratic algebras. We point out the few exceptions where abstract contractions cannot be realized by the geometric B\^ocher contractions

Polarization mode dispersion in radio-frequency interferometric embedded fiber-optic sensors

The effect of fiber birefringence on the propagation delay in an embedded fiber-optic strain sensor is studied. The polarization characteristics of the sensor are described in terms of polarization mode dispersion through the principal states of polarization and their differential group delay. Using these descriptors, an analytical expression for the response of the sensor for an arbitrary input state of polarization is given and experimentally verified. It is found that the differential group delay, as well as the input and output principal states of polarization, vary when the embedded fiber is strained, leading to fluctuations in the sensor output. The use of high birefringence fibers and different embedding geometries is examined as a means for reducing the polarization dependency of the sensor

Intrinsic localized modes in parametrically driven arrays of nonlinear resonators

We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory