Time-domain green's function-based parametric sensitivity analysis of multiconductor transmission lines

We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines. This technique can handle multiple design parameters, such as substrate or geometrical layout features, and provide time-domain sensitivity information for voltages and currents at the ports of the lines. It is derived from the dyadic Green's function of the 1-D wave propagation problem. The rational nature of the Green's function permits the generation of a time-domain macromodel for the computation of transient voltage and current sensitivities with respect to both electrical and physical parameters, completely avoiding similarity transformation, and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels that provide sensitivity information are well suited for design space exploration, design optimization, and crosstalk analysis. Two numerical examples validate the proposed approach in both frequency and time-domain

Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation

Impact of slow-light enhancement on optical propagation in active semiconductor photonic crystal waveguides

We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, which is interpreted as distributed feedback effects or reflection at passive-active interfaces, depending on the approach taken. For very large material gain values, the band structure of the waveguide is perturbed, and deviations from the simple coupled Bloch wave model are found.Comment: 8 pages, 5 figure

A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic non- linear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits.An efficient scheme to buildtheJacobian matrix with exact partial derivatives with respect to the oscillation period and with re- spect to the samples of the unknowns is described. Without any modifica- tion in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.Peer ReviewedPostprint (published version