41,021 research outputs found
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
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