This talk focuses on a universal unitary architecture based on layers of diagonal matrices and specific interlacing unitary matrices. Numerical evidence shows that such an interlacing matrix can have a random pattern as long as it fulfills the required density properties. In this regard, Haar-generated random matrices are suitable candidates that lead to suitable interlacing matrices. The efficacy of such random matrices is classified by a density criterion, which provides a priori conditions to ensure the validity of the interlacing matrix in question, reducing the computational workload due to heavy numerical optimization. This approach allows for more possibilities for further interlacing matrices beyond particular waveguide arrays. Also, the random nature of the interlacing matrix provides resilience due to manufacturing defects. These results are illustrated through some full-wave simulations.
This talk discusses a new photonic implementation to perform general discrete linear operations. This is achieved by properly factorizing any arbitrary NxN complex matrix in terms of a prefixed unitary discrete fractional Fourier transform (DFrFT) matrix and complex diagonal matrices. This approach is handy as it allows for an all-optical implementation using N+1 amplitude and N+1 phase modulation layers, interlaced with fixed DFrFT layers implemented via a coupled waveguide array. Numerical optimizations show that target matrices can indeed be represented through this approach by accordingly tunning the phase and amplitude layers. The proposed architecture enables the development of novel families of programmable lossy and lossless photonic circuits for on-chip analog information processing.
This talk introduces an on-chip realization of the discrete fractional Fourier transform (DFrFT), proposed and experimentally implemented in the microwave domain utilizing a passive metamaterial coupled lines network (MCLN). This renders a lensless device capable of performing the DFrFT in real-time. The MCLN comprises N microstrip transmission lines coupled to their nearest neighbors through an array of interdigital capacitors composed of interlaced microstrip fingers. In the latter, the dimension and number of fingers allow for controlled and enhanced coupling terms that render the required DFrFT couplings highly accurate.
The MCLN is exploited to design a new compact planar electromagnetic lensless solution that enables a beam steering operation through the focal plane array concept. The latter is performed by independently exciting the input ports of the MCLN through a switch tree, while the output ports are connected to an antenna array to realize a focal plane array system. Contrary to other approaches, this device does not require any external phase element, reducing the overall power consumption.
This talk introduces the design and analysis of a passive and fully optical on-chip direction-finding architecture, which can operate effectively in broad or narrow detection scenarios. The proposed system is based on an equally spaced linear array of M grating couplers that steer incoming waves toward a passive and non-unitary photonic processor. This performs a processing operation from which the incident angles of the incoming waves are discretely determined at the N outputs of the photonic processor. The detection functionalities are enhanced by introducing some tracking functions implemented in a post-processing stage at the photonic unit output. The benefits and disadvantages of each tracking function are illustrated. Lastly, an approximation to reduce the photonic unit to a unitary one is discussed, rendering a compact device that operates only on a narrow detection range.
Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Here, we present a novel architecture for efficient integrated photonic implementation of arbitrary matrix operations. The proposed architecture is built on interlacing discrete fractional Fourier transform layers with programmable phase shifter arrays. This circuit is resilient to defects in the phase shifters and perturbations in the intervening Fourier operators. We delve into the core attributes of this architectural design and explore its practical applications in the realm of analog information processing.
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 of different lengths that perform DFrDT operations of complementary orders. Numerical simulations show that smoothing and edge detection tasks are indeed performed even for noisy input signals. A design recipe based on the standard silicon-on-insulator fabrication technology is provided. The scaling properties of the proposed architecture are discussed. Finally, the use of the proposed photonic convolutional accelerator for chip-scale photonic AI systems is discussed.
We propose utilizing coherently coupled laser networks for neural computing. The proposed scheme is built on harnessing the collective behavior of laser networks for storing phase patterns as stable fixed points of the governing dynamical equations and retrieving such patterns through proper excitation conditions, thus exhibiting an associative memory property. We further show that limitations on the number of images can be overcome by using nonreciprocal coupling between lasers, thus allowing for utilizing the large storage capacity inherent to the laser network. This work opens new possibilities for neural computation with coherent laser networks as a novel physical analog processor.
Here we present an innovative free-space optical (FSO) communication system which is capable of training database in real-time and demultiplex multiplexed spatial structured laser beams such as orbital angular momentum (OAM) beams under varying atmospheric turbulent conditions. The core part of our detection system is heterogeneous convolutional neural network includes an optical 4f system using first Fourier convolution neural network layer driven by kilohertz-fast reprogrammable high-resolution digital micromirror devices (DMDs). This optical-filtering-based convolutional neural network is utilized to realize the training and demultiplexing 4-bit OAM-coded beams under simulated turbulent condition using modified von K´arm´an atmospheric model. The current implementation shows classification accuracy of 89.35% (under weak turbulence) and 38.26% (under strong turbulence).
This Conference Presentation, “Self-induced vortex and anti-vortex singularities in laser arrays,” was recorded at SPIE Optics + Photonics 2021 held in San Diego, California, United States.
It is shown that the onset of signal oscillations in the parametric nonlinear process of three-photon down-conversion is analogous with a first-order phase transition. Such an oscillator exhibits phase tristability, such that by reaching above the oscillation threshold it can take three different states with uniform phase contrasts. An analytically solvable second-order oscillator model is derived and the stability of the trinary phase states is proven through a Lyapunov function. The phase tristability of a three-photon down-conversion oscillator intrinsically emulates a classical trinary digit (trit). Such a trinary digit can be utilized for applications in unconventional computing.
Dissipative interaction facilitates the global phase locking of a network of lasers with generally complex graph topologies. Recently, we showed that the equilibrium states of such laser networks are optimal solutions of governing cost functions that are of non-convex quadratic form. This realization allows for mapping a large class of non-convex optimization problems onto laser networks, which provides a promising route for optically solving such computationally-hard problems. Here, by numerical simulation of the underlying dynamical equations, we investigate the accuracy of the solutions obtained for well-known non-convex problems and discuss the role of parameter tuning for escaping the local minima.
This Conference Presentation, "Fundamental limitations for phase-locking of integrated laser arrays," was recorded at Photonics West 2020 held in San Francisco, California, United States.
Parity time (PT) symmetric systems are known to exhibit two distinct phases: those associated with an unbroken and broken symmetry. In the domain of optics, PT-symmetry can be established by incorporating a balanced distribution of gain and loss in a system. Under linear conditions, in a coupled dimer, composed of two cavities or waveguides, if the gain-loss contrast increases beyond a critical value with respect to the coupling constant, a transition is expected from the unbroken symmetry to the broken symmetry regime. However, in the presence of nonlinearity, this transition behavior can be drastically modified. We here study a system of two coupled semiconductor-based resonators that are lasing around an exceptional point. The quantum wells in such structures not only provide gain but also lead to strong levels of saturable loss in the absence of any optical pumping. Interestingly, in sharp contrast with linear PT-symmetric configurations, such nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. If the ratio of the net loss to coupling is less than unity in one of the cavities, as the pumping level in the other resonator is increased, the nonlinear eigenmodes move from an unbroken symmetric state to a broken one. Moreover, in this nonlinear domain, the structural form of the resulting solutions are isomorphic to the corresponding linear eigenvectors expected above and below the phase transition point. Experimental results are in good agreement with these predictions.
KEYWORDS: Photonics, Diffraction, Active optics, Near field optics, Digital video recorders, Video, Current controlled current source, Light scattering, Scattering, Diffraction gratings
Parity-time (PT) symmetric complex structures can exhibit peculiar properties which are otherwise unattainable in traditional Hermitian systems. This is achieved by judiciously involving balanced regions of gain and loss. Here we investigate the scattering properties of PT-symmetric diffraction gratings. The presence of the imaginary potential can modify the light transport properties in their far field. This is an outcome of a local power flow taking place between the gain and loss regions in the near field. We show that for a certain gain/loss contrast, all the negative diffraction orders can be eliminated while the positive diffraction orders can be amplified.
In recent years, the ever-increasing demand for high-capacity transmission systems has driven remarkable advances in technologies that encode information on an optical signal. Mode-division multiplexing makes use of individual modes supported by an optical waveguide as mutually orthogonal channels. The key requirement in this approach is the capability to selectively populate and extract specific modes. Optical supersymmetry (SUSY) has recently been proposed as a particularly elegant way to resolve this design challenge in a manner that is inherently scalable, and at the same time maintains compatibility with existing multiplexing strategies.
Supersymmetric partners of multimode waveguides are characterized by the fact that they share all of their effective indices with the original waveguide. The crucial exception is the fundamental mode, which is absent from the spectrum of the partner waveguide. Here, we demonstrate experimentally how this global phase-matching property can be exploited for efficient mode conversion. Multimode structures and their superpartners are experimentally realized in coupled networks of femtosecond laser-written waveguides, and the corresponding light dynamics are directly observed by means of fluorescence microscopy. We show that SUSY transformations can readily facilitate the removal of the fundamental mode from multimode optical structures. In turn, hierarchical sequences of such SUSY partners naturally implement the conversion between modes of adjacent order. Our experiments illustrate just one of the many possibilities of how SUSY may serve as a building block for integrated mode-division multiplexing arrangements. Supersymmetric notions may enrich and expand integrated photonics by versatile optical components and desirable, yet previously unattainable, functionalities.
PT-symmetric optical structures represent a new generation of artificial optical systems which utilize gain and loss in a balanced fashion in order to perform a desired task. Such non-Hemitian arrangements exhibit interesting properties which are otherwise unattainable in passive Hermitian systems. As a result, since the first experimental demonstration of PT-symmetry in coupled optical configurations, there has been a flurry of activities in understanding and utilizing PT-symmetric processes in optics. Here we review recent developments in the newly emerging field of PT-symmetric optics.
We experimentally demonstrate single longitudinal mode operation in microring laser using the concept of PT symmetry.
A PT-symmetric coupled resonator arrangement can considerably enhance the maximum achievable gain of single mode
microring cavity. The method is broadband thus work well for inhomogenously broadened gain mediums. It doesn’t rely
on any additional component to ensure its mode selective performance, and it is robust with respect to fabrication
inaccuracies. This result may pave the way for a novel way of designing integrated laser sources based on PT symmetry.
We show that the concept of supersymmetry (SUSY) can be utilized as a versatile tool to design integrated optical
structures with desirable eigenmode spectra. Our approach relies on the intriguing ability of SUSY transformations
to systematically construct a “superpartner” structure that shares all of its propagation constants with the original
waveguide. This approach can be employed to any given one-dimensional refractive index landscapes and
establishes perfect global phase matching condition between an, in principle, arbitrarily large number of guided
modes, while separating the fundamental mode of the original waveguide. In doing so, SUSY transformations also
relate the field distributions of the paired modes, in turn allowing for mode conversion with unity efficiency. Here,
the concept of supersymmetry is illustrated through several examples of one-dimensional waveguides. These include
the step-index (slab) waveguide as well as parabolic and exponential index profiles. In all cases the superpartner can
be obtained analytically. The unique properties of coupled superpartner arrangements make them an ideal platform
for integrated mode filtering and multiplexing applications. The key idea behind this is that global phase matching
allows each mode from the original waveguide to interact freely with the neighboring guides, while the fundamental
mode remains isolated. Here, this whole set of modes can be simultaneously manipulated, attenuated/amplified, or
passed through to higher-order SUSY arrangements.
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