60 research outputs found
Complete photonic bandgaps in supercell photonic crystals
We develop a class of supercell photonic crystals supporting complete
photonic bandgaps based on breaking spatial symmetries of the underlying
primitive photonic crystal. One member of this class based on a two-dimensional
honeycomb structure supports a complete bandgap for an index-contrast ratio as
low as , making this the first such 2D photonic crystal
to support a complete bandgap in lossless materials at visible frequencies. The
complete bandgaps found in such supercell photonic crystals do not necessarily
monotonically increase as the index-contrast in the system is increased,
disproving a long-held conjecture of complete bandgaps in photonic crystals.Comment: 5 pages, 4 figure
Ab-initio theory of quantum fluctuations and relaxation oscillations in multimode lasers
We present an \emph{ab-initio} semi-analytical solution for the noise
spectrum of complex-cavity micro-structured lasers, including central
Lorentzian peaks at the multimode lasing frequencies and additional sidepeaks
due to relaxation-oscillation (RO) dynamics. In~Ref.~1, we computed the
central-peak linewidths by solving generalized laser rate equations, which we
derived from the Maxwell--Bloch equations by invoking the
fluctuation--dissipation theorem to relate the noise correlations to the
steady-state lasing properties; Here, we generalize this approach and obtain
the entire laser spectrum, focusing on the RO sidepeaks. Our formulation treats
inhomogeneity, cavity openness, nonlinearity, and multimode effects accurately.
We find a number of new effects, including new multimode RO sidepeaks and three
generalized factors. Last, we apply our formulas to compute the noise
spectrum of single- and multimode photonic-crystal lasers.Comment: 27 pages, 3 figure
Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
We provide a systematic study of non-Hermitian topologically charged systems.
Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary
topological charge, adding a non-Hermitian perturbation transforms the Weyl
points to one-dimensional exceptional contours. We analytical prove that the
topological charge is preserved on the exceptional contours. In contrast to
Hermitian systems, the addition of gain and loss allows for a new class of
topological phase transition: when two oppositely charged exceptional contours
touch, the topological charge can dissipate without opening a gap. These
effects can be demonstrated in realistic photonics and acoustics systems.Comment: 11 pages, 9 figure
Even spheres as joint spectra of matrix models
The Clifford spectrum is a form of joint spectrum for noncommuting matrices.
This theory has been applied in photonics, condensed matter and string theory.
In applications, the Clifford spectrum can be efficiently approximated using
numerical methods, but this only is possible in low dimensional example. Here
we examine the higher-dimensional spheres that can arise from theoretical
examples. We also describe a constuctive method to generate five real symmetric
almost commuting matrices that have a -theoretical obstruction to being
close to commuting matrices. For this, we look to matrix models of topological
electric circuits.Comment: 19 pages, 4 figure
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