252 research outputs found
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
Quantitative test of general theories of the intrinsic laser linewidth
We perform a first-principles calculation of the quantum-limited laser
linewidth, testing the predictions of recently developed theories of the laser
linewidth based on fluctuations about the known steady-state laser solutions
against traditional forms of the Schawlow-Townes linewidth. The numerical study
is based on finite-difference time-domain simulations of the semiclassical
Maxwell-Bloch lasing equations, augmented with Langevin force terms, and thus
includes the effects of dispersion, losses due to the open boundary of the
laser cavity, and non-linear coupling between the amplitude and phase
fluctuations ( factor). We find quantitative agreement between the
numerical results and the predictions of the noisy steady-state ab initio laser
theory (N-SALT), both in the variation of the linewidth with output power, as
well as the emergence of side-peaks due to relaxation oscillations.Comment: 24 pages, 10 figure
Local invariants identify topology in metals and gapless systems
Although topological band theory has been used to discover and classify a
wide array of novel topological phases in insulating and semi-metal systems, it
is not well-suited to identifying topological phenomena in metallic or gapless
systems. Here, we develop a theory of topological metals based on the system's
spectral localizer and associated Clifford pseudospectrum, which can both
determine whether a system exhibits boundary-localized states despite the
presence of degenerate bulk bands and provide a measure of these states'
topological protection even in the absence of a bulk band gap. We demonstrate
the generality of this method across symmetry classes in two lattice systems, a
Chern metal and a higher-order topological metal, and prove the topology of
these systems is robust to relatively strong perturbations. The ability to
define invariants for metallic and gapless systems allows for the possibility
of finding topological phenomena in a broad range of natural, photonic, and
other artificial materials that could not be previously explored.Comment: 10 pages, 4 figure
An operator-based approach to topological photonics
Recently, the study of topological structures in photonics has garnered
significant interest, as these systems can realize robust, non-reciprocal
chiral edge states and cavity-like confined states that have applications in
both linear and non-linear devices. However, current band theoretic approaches
to understanding topology in photonic systems yield fundamental limitations on
the classes of structures that can be studied. Here, we develop a theoretical
framework for assessing a photonic structure's topology directly from its
effective Hamiltonian and position operators, as expressed in real space, and
without the need to calculate the system's Bloch eigenstates or band structure.
Using this framework, we show that non-trivial topology, and associated
boundary-localized chiral resonances, can manifest in photonic crystals with
broken time-reversal symmetry that lack a complete band gap, a result which may
have implications for new topological laser designs. Finally, we use our
operator-based framework to develop a novel class of invariants for topology
stemming from a system's crystalline symmetries, which allows for the
prediction of robust localized states for creating waveguides and cavities.Comment: 12 pages, 3 figures, 2 pages of supplemental materia
Generating and processing optical waveforms using spectral singularities
We show that a laser at threshold can be utilized to generate the class of
dispersionless waveforms
at optical frequencies.We derive these properties analytically and demonstrate
them in semiclassical time-domain laser simulations. We then utilize these
waveforms to expand other waveforms with high modulation frequencies and
demonstrate theoretically the feasibility of complex-frequency
coherent-absorption at optical frequencies, with efficient energy transduction
and cavity loading. This approach has potential applications in quantum
computing, photonic circuits, and biomedicine
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