264 research outputs found
Supersymmetry-generated complex optical potentials with real spectra
We show that the formalism of supersymmetry (SUSY), when applied to
parity-time (PT) symmetric optical potentials, can give rise to novel
refractive index landscapes with altogether non-trivial properties. In
particular, we find that the presence of gain and loss allows for arbitrarily
removing bound states from the spectrum of a structure. This is in stark
contrast to the Hermitian case, where the SUSY formalism can only address the
fundamental mode of a potential. Subsequently we investigate isospectral
families of complex potentials that exhibit entirely real spectra, despite the
fact that their shapes violate PT-symmetry. Finally, the role of SUSY
transformations in the regime of spontaneously broken PT symmetry is
investigated.Comment: 6 pages, 4 figure
Universal Unitary Photonic Circuits by Interlacing Discrete Fractional Fourier Transform and Phase Modulation
We introduce a novel parameterization of complex unitary matrices, which
allows for the efficient photonic implementation of arbitrary linear discrete
unitary operators. The proposed architecture is built on factorizing an unitary matrix into interlaced discrete fractional Fourier transforms
and -parameter diagonal phase shifts. We show that such a configuration can
represent arbitrary unitary operators with phase layers. We discuss a
gradient-based algorithm for finding the optimal phase parameters for
implementing a given unitary matrix. By increasing the number of phase layers
beyond the critical value of , the optimization consistently converges
faster as the system becomes over-determined. We propose an integrated photonic
circuit realization of this architecture with coupled waveguide arrays and
reconfigurable phase modulators. The proposed architecture can pave the way for
developing novel families of programmable photonic circuits for optical
classical and quantum information processing.Comment: Under review since January 15, 202
Integrated Photonic Fractional Convolution Accelerator
An integrated photonic circuit architecture to perform a modified-convolution
operation based on the Discrete Fractional Fourier Transform (DFrFT) is
introduced. This is accomplished by utilizing two nonuniformly-coupled
waveguide lattices with equally-spaced eigenmode spectra and with different
lengths that perform DFrDT operations of complementary orders sandwiching a
modulator array. Numerical simulations show that smoothing and edge detection
tasks are indeed performed even for noisy input signals
Parity-time and supersymmetry in optics
Symmetry plays a crucial role in exploring the laws of nature. By exploiting some of the underlying analogies between the mathematical formalism of quantum mechanics and that of electrodynamics, in this dissertation we show that optics can provide a fertile ground for studying, observing, and utilizing some of the peculiar symmetries that are currently out of reach in other areas of physics. In particular, in this work, we investigate two important classes of symmetries, parity-time symmetry (PT) and supersymmetry (SUSY), within the context of classical optics. The presence of PT symmetry can lead to entirely real spectra in non-Hermitian systems. In optics, PT-symmetric structures involving balanced regions of gain and loss exhibit intriguing properties which are otherwise unattainable in traditional Hermitian systems. We show that selective PT symmetry breaking offers a new method for achieving single mode operation in laser cavities. Other interesting phenomena also arise in connection with PT periodic structures. Along these lines, we introduce a new class of optical lattices, the so called mesh lattices. Such arrays provide an ideal platform for observing a range of PT-related phenomena. We show that defect sates and solitons exist in such periodic environments exhibiting unusual behavior. We also investigate the scattering properties of PT-symmetric particles and we show that such structures can deflect light in a controllable manner. In the second part of this dissertation, we introduce the concept of supersymmetric optics. In this regard, we show that any optical structure can be paired with a superpartner with similar guided wave and scattering properties. As a result, the guided mode spectra of these optical waveguide systems can be judiciously engineered so as to realize new families of mode filters and mode division multiplexers and demultiplexers. We also present the first experimental demonstration of light dynamics in SUSY ladders of photonic lattices. In addition a new type of transformation optics based on supersymmetry is also explored. Finally, using the SUSY formalism in non-Hermitian settings, we identify more general families of complex optical potentials with real spectra
Auto-calibrating Universal Programmable Photonic Circuits: Hardware Error-Correction and Defect Resilience
It is recently shown that discrete linear unitary operators can
be represented by interlacing phase shift layers with a fixed intervening
operator such as Discrete Fractional Fourier Transform (DFrFT). Here, we show
that introducing perturbations to the intervening operations does not
compromise the universality of this architecture. Furthermore, we show that
this architecture is resilient to defects in the phase shifters as long as no
more than one faulty phase shifter is present in each layer. These properties
enable post-fabrication auto-calibration of such universal photonic circuits,
effectively compensating for fabrication errors and defects in phase
components
Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators
A system of two coupled semiconductor-based resonators is studied when lasing
around an exceptional point. We show that the presence of nonlinear saturation
effects can have important ramifications on the transition behavior of this
system. In sharp contrast with linear PT-symmetric configurations, nonlinear
processes are capable of reversing the order in which the symmetry breaking
occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states
still retain the structural form of the corresponding linear eigenvectors
expected above and below the phase transition point. The conclusions of our
analysis are in agreement with experimental data.Comment: 9 pages, 8 figure
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