A new high order finite difference modal method (FDMM) is developed for analyzing diffraction gratings in conical and classical mountings. The difference scheme is constructed by enforcing the internal interface conditions in each grating layer to high order derivatives, and it gives a high order of accuracy for computing the eigenmodes of the grating layer. Between different layers, the interf...

The theory of dynamical networks is concerned with systems of dynamical units coupled according to an underlying graph structure. It therefore investigates the interplay between dynamics and structure, between the temporal processes going on at the individual units and the static spatial structure linking them. In order to analyse that spatial structure, formalized as a graph, we discuss an ess...

The excitation of forward and backward, Electromagnetic (EM) modes and fields in an anisotropic, parallel plate waveguide (meeting Dirichlet and Neumann boundary conditions), is studied, using a modified coordinate transformation which reduces Maxwell’s equations to the form of a Helmholtz wave equation satisfying Dirichlet and mixed-partial derivative boundary conditions. The EM modes and fiel...

What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this problem taking a whole-versus-parts perspective, wherein one explicitly computes the amount of information generated by a network as a whole over and above tha...

Analysis of integrated optical cylindrical microresonators involves the coupling between a straight waveguide and a bent waveguide. Our (2D) variant of coupled mode theory is based on analytically represented mode profiles. With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way and solved by numerical integration. Proper manipulation of ...

Low-mass disks orbiting a massive body can support " slow " normal modes, in which the eigenfrequency is much less than the orbital frequency. Slow modes are lopsided, i.e., the azimuthal wavenumber m = 1. We investigate the properties of slow modes, using softened self-gravity as a simple model for collective effects in the disk. We employ both the WKB approximation and numerical solutions of ...

The NORmal-To-Anything (NORTA) algorithm requires a correlation matrix of multivariate normal variables to convert a multivariate normal vector to any other distribution. This paper presents a new simulation method that works in combination with the NORTA algorithm yet avoids having to solve some complicated equations which need to be solved to achieve this matrix. The performance of the propos...