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Discrete Fractional Fourier Transforms (DFrFT) are universal mathematical tools in signal processing, communications and microwave sensing. Despite the excessive applications of DFrFT, implementation of corresponding fractional orders in the baseband signal often leads to bulky, power-hungry, and high-latency systems. In this paper, we present a passive metamaterial coupled lines network (MCLN) that performs the analog DFrFT in real-time at microwave frequencies. The proposed MCLN consists of M parallel microstrip transmission lines (TLs) in which adjacent TLs are loaded with interdigital capacitors to enhance the coupling level. We show that with proper design of the coupling coefficients between adjacent channels, the MCLN can perform an M-point DFrFT of an arbitrary fractional order that can be designed through the length of the network. In the context of real-time signal processing for realization of DFrFT, we design, model, simulate and implement a 16x16 MCLN and experimentally demonstrate the performance of the proposed structure. The proposed innovative approach is versatile and is capable to be used in various applications where DFrFT is an essential tool. The proposed design scheme based on MCLN is scalable across the frequency spectrum and can be applied to millimeter and submillimeter wave systems.

Modern quantum technologies using matter are designed as closed quantum systems to isolate them from interactions with the environment. This design paradigm greatly constrains the scalability and limits practical implementation of such systems. Here, we introduce a novel computing paradigm, entropy computing, that works by conditioning a quantum reservoir thereby enabling the stabilization of a ground state. In this work, we experimentally demonstrate the feasibility of entropy computing by building a hybrid photonic-electronic computer that uses measurement-based feedback to solve non-convex optimization problems. The system functions by using temporal photonic modes to create qudits in order to encode probability amplitudes in the time-frequency degree of freedom of a photon. This scheme, when coupled with electronic interconnects, allows us to encode an arbitrary Hamiltonian into the system and solve non-convex continuous variables and combinatorial optimization problems. We show that the proposed entropy computing paradigm can act as a scalable and versatile platform for tackling a large range of NP-hard optimization problems.

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. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary $N \times N$ unitary operators with $N+1$ phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.

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. Considering their wide range of applications as one of the most fundamental mathematical operations there has been a particular interest in programmable photonic circuits that perform matrix-vector multiplication. In this regard, there has been great interest in developing novel circuit architectures for performing matrix operations that are compatible with the existing photonic integrated circuit technology which can thus be reliably implemented. Recently, it has been shown that discrete linear unitary operations can be parameterized through diagonal phase parameters interlaced with a fixed operator that enables efficient photonic realization of unitary operations by cascading phase shifter arrays interlaced with a multiport component. Here, we show that such a decomposition is only a special case of a much broader class of factorizations that allow for parametrizing arbitrary complex matrices in terms of diagonal matrices alternating with a fixed unitary matrix. Thus, we introduce a novel architecture for physically implementing discrete linear operations. The proposed architecture is built on representing an $N \times N$ matrix operator in terms of $N+1$ amplitude-and-phase modulation layers interlaced with a fixed unitary layer that could be implemented via a coupled waveguide array. The proposed architecture enables the development of novel families of programmable photonic circuits for on-chip analog information processing.

It is recently shown that discrete $N\times N$ linear unitary operators can be represented by interlacing $N+1$ 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.

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.

Network synchronization of lasers is critical for reaching high-power levels and for effective optical computing. Yet, the role of network topology for the frequency synchronization of lasers is not well understood. Here, we report our significant progress toward solving this critical problem for networks of heterogeneous laser model oscillators with repulsive coupling. We discover a general approximate principle for predicting the onset of frequency synchronization from the spectral knowledge of a complex matrix representing a combination of the signless Laplacian induced by repulsive coupling and a matrix associated with intrinsic frequency detuning. We show that the gap between the two smallest eigenvalues of the complex matrix generally controls the coupling threshold for frequency synchronization. In stark contrast with Laplacian networks, we demonstrate that local rings and all-to-all networks prevent frequency synchronization, whereas full bipartite networks have optimal synchronization properties. Beyond laser models, we show that, with a few exceptions, the spectral principle can be applied to repulsive Kuramoto networks. Our results may provide guidelines for optimal designs of scalable laser networks capable of achieving reliable synchronization.

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 $N \times N$ unitary matrix into interlaced discrete fractional Fourier transforms and $N$-parameter diagonal phase shifts. We show that such a configuration can represent arbitrary unitary operators with $N+1$ 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 $N+1$, 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, 2023

Recent years have seen great advancements in the development of deep learning models for histopathology image analysis in digital pathology applications, evidenced by the increasingly common deployment of these models in both research and clinical settings. Although such models have shown unprecedented performance in solving fundamental computational tasks in DP applications, they suffer from catastrophic forgetting when adapted to unseen data with transfer learning. With an increasing need for deep learning models to handle ever changing data distributions, including evolving patient population and new diagnosis assays, continual learning models that alleviate model forgetting need to be introduced in DP based analysis. However, to our best knowledge, there is no systematic study of such models for DP-specific applications. Here, we propose CL scenarios in DP settings, where histopathology image data from different sources/distributions arrive sequentially, the knowledge of which is integrated into a single model without training all the data from scratch. We then established an augmented dataset for colorectal cancer H&E classification to simulate shifts of image appearance and evaluated CL model performance in the proposed CL scenarios. We leveraged a breast tumor H&E dataset along with the colorectal cancer to evaluate CL from different tumor types. In addition, we evaluated CL methods in an online few-shot setting under the constraints of annotation and computational resources. We revealed promising results of CL in DP applications, potentially paving the way for application of these methods in clinical practice., Comment: Accepted by MOVI, a MICCAI2022 workshop: https://sites.google.com/view/movi2022

We show that a coherent network of lasers exhibits emergent neural computing capabilities. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of 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. The associative memory functionality is first discussed in the strong pumping regime of a network of passive dissipatively coupled lasers which simulate the classical XY model. It is discussed that despite the large storage capacity of the network, the large overlap between fixed-point patterns effectively limits pattern retrieval to only two images. Next, we show that this restriction can be uplifted by using nonreciprocal coupling between lasers and this allows for utilizing a large storage capacity. This work opens new possibilities for neural computation with coherent laser networks as novel analog processors. In addition, the underlying dynamical model discussed here suggests a novel energy-based recurrent neural network that handles continuous data as opposed to Hopfield networks and Boltzmann machines which are intrinsically binary systems.

It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a photonic lattice with diagonal disorder, which turns out to be a random complex Gaussian matrix. Thus, by collecting the output light from a subset of the waveguide channels, one can perform an embedding from a higher-dimension to a lower-dimension space that respects the Johnson-Lindenstrauss lemma and nearly preserves the Euclidean distances. It is discussed that distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive spreading of light from a single channel excitation, as opposed to strong disorder which initiates the localization regime. The proposed scheme can be utilized as a simple and powerful integrated dimension reduction stage that can greatly reduce the burden of a subsequent neural computing stage.

Recently it is shown that dissipatively coupled laser arrays simulate the classical XY model. We show that phase-locking of laser arrays can give rise to the spontaneous formation of vortex and antivortex phase patterns that are analogous to topological defects of the XY model. These patterns are stable although their formation is less likely in comparison to the ground state lasing mode. In addition, we show that small ratios of photon-to-gain lifetime destabilizes vortex and antivortex phase patterns. These findings are important for studying topological effects in optics as well as for designing laser array devices.

Patch antennas are among the most popular radiating elements, yet their quasi-2-D structure reduces the degrees of freedom available to tailor their radiation pattern. To overcome this limitation, a possible solution consists in etching on a grounded substrate two concentric radiating elements and combining two modes (one for each element) with proper amplitude/phase relations. Although this technique leads, in principle, to an infinite number of possible configurations (i.e., each patch element can support an infinite number of modes), the theoretical and experimental verifications available in the literature are limited to the first two radiating modes (TM 11 and TM 21 ) of a circular patch antenna. Recently, we have shown that the design of this circular patch can be effectively performed by exploiting the topological properties of vortex fields and, in particular, by controlling the phase singularity exhibited by the higher order right-handed circularly polarized (RHCP) TM 21 mode of the circular patch. Since the number of RHCP higher order modes of a circular patch is infinite, we can in principle deal with an arbitrary number of phase singularity points, whose combined control leads to unprecedented possibilities to shape the radiation pattern of a circular patch. In this article, we present a complete design tool to determine the number and position of phase singularity points arising when combining the RHCP modes of a circular patch antenna and, eventually, manipulate them to synthesize the required radiation pattern. As a realistic application example, we show how the proposed tool can be used to effectively design a single antenna whose radiation pattern can be properly tailored to switch between two different states, i.e., a sector and a saddle shape, widely used in base stations for mobile and satellite communications, respectively.

Engineered non-Hermitian systems featuring exceptional points can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce and present non-Hermitian dynamics of coupled optical parametric oscillators (OPOs) arising from phase-sensitive amplification and de-amplification, and show their distinct advantages over conventional non-Hermitian systems relying on laser gain and loss. OPO-based non-Hermitian systems can benefit from the instantaneous nature of the parametric gain, noiseless phase-sensitive amplification, and rich quantum and classical nonlinear dynamics. We show that two coupled OPOs can exhibit spectral anti-PT symmetry and an exceptional point between its degenerate and non-degenerate operation regimes. To demonstrate the distinct potentials of the coupled OPO system compared to conventional non-Hermitian systems, we present higher-order exceptional points with two OPOs, tunable Floquet exceptional points in a reconfigurable dynamic non-Hermitian system, and generation of squeezed vacuum around exceptional points, all of which are not easy to realize in other non-Hermitian platforms. Our results show that coupled OPOs are an outstanding non-Hermitian setting with unprecedented opportunities in realizing nonlinear dynamical systems for enhanced sensing and quantum information processing.

In recent years there has been a growing interest in the physical implementation of classical spin models through networks of optical oscillators. However, a key missing step in this mapping is to formally prove that the dynamics of such a nonlinear dynamical system is toward minimizing a global cost function which is equivalent with the spin model Hamiltonian. Here, we introduce a minimal dynamical model for a network of dissipatively coupled optical oscillators and prove that the dynamics of such a system is governed by a Lyapunov function that serves as a cost function for the system. This cost function is in general a function of both phases and intensities of the oscillators and depends strongly on the pump parameter. In case of bipartite network topologies, the amplitudes of the oscillators become identical in the steady state and the cost function reduces to the XY Hamiltonian. In the general case for non-trivial network topologies, however, the cost function approaches the XY Hamiltonian only in the strong pump limit. We show that by adiabatically tuning the pump parameter, the network can largely avoid trapping into the local minima of the governing cost function and stabilize into the ground state of the associated XY Hamiltonian. These results show the great potential of laser networks for unconventional computing.

Hetero-epitaxial crystalline films underlie many electronic and optical technologies but are prone to forming defects at their hetero-interfaces. Atomic-scale defects such as threading dislocations that propagate into a film impede the flow of charge carriers and light degrading electrical-optical performance of devices. Diagnosis of subsurface defects traditionally requires time consuming invasive techniques such as cross sectional transmission electron microscopy. Using III-V films grown on Si, we have demonstrated noninvasive, bench-top diagnosis of sub-surface defects by optical second-harmonic scanning probe microscope. We observed a high-contrast pattern of sub-wavelength hot spots caused by scattering and localization of fundamental light by defect scattering sites. Size of these observed hotspots are strongly correlated to the density of dislocation defects. Our results not only demonstrate a global and versatile method for diagnosing sub-surface scattering sites but uniquely elucidate optical properties of disordered media. An extension to third harmonics would enable irregularities detection in non-X(2) materials making the technique universally applicable., Comment: 23 pages-4 figures-5 Supplementary figures

Scattering of electromagnetic waves lies at the heart of most experimental techniques over nearly the entire electromagnetic spectrum, ranging from radio waves to optics and X-rays. Hence, deep insight into the basics of scattering theory and understanding the peculiar features of electromagnetic scattering is necessary for the correct interpretation of experimental data and an understanding of the underlying physics. Recently, a broad spectrum of exceptional scattering phenomena attainable in suitably engineered structures has been predicted and demonstrated. Examples include bound states in the continuum, exceptional points in PT-symmetrical non-Hermitian systems, coherent perfect absorption, virtual perfect absorption, nontrivial lasing, non-radiating sources, and others. In this paper, we establish a unified description of such exotic scattering phenomena and show that the origin of all these effects can be traced back to the properties of poles and zeros of the underlying scattering matrix. We provide insights on how managing these special points in the complex frequency plane provides a powerful approach to tailor unusual scattering regimes.

Optical circulators are important components of modern day communication technology. With their ability to route photons directionally, these nonreciprocal elements provide useful functionality in photonic circuits and offer prospects for fundamental research on information processing. Developing highly efficient optical circulators thus presents an important challenge, in particular to realize compact reconfigurable implementations that do not rely on a magnetic field bias to break reciprocity. We demonstrate optical circulation based on radiation pressure interactions in an on-chip multimode optomechanical system. We show that mechanically-mediated optical mode conversion in a silica microtoroid provides a synthetic gauge bias for light, which enables a 4-port circulator by exploiting tailored interference between appropriate light paths. We identify two sideband conditions under which ideal circulation is approached. This allows to experimentally demonstrate $\sim$10 dB isolation and $<$ 3 dB insertion loss in all relevant channels. We show the possibility of actively controlling the bandwidth, isolation ratio, noise performance and circulation direction, enabling ideal opportunities for reconfigurable integrated nanophotonic circuits.

We explore the dynamics of spontaneous breakdown of mirror symmetry in a pair of identical optomechanical cavities symmetrically coupled to a waveguide. Large optical intensities enable optomechanically-induced nonlinear detuning of the optical resonators, resulting in a pitchfork bifurcation. We investigate the stability of this regime and explore the possibility of inducing multistability. By injecting proper trigger pulses, the proposed structure can toggle between two asymmetric stable states, thus serving as a low-noise nanophotonic all-optical switch or memory element., Comment: 19 pages, 6 figures

Optical isolation, non-reciprocal phase transmission and topological phases for light based on synthetic gauge fields have been raising significant interest in the recent literature. Cavity-optomechanical systems that involve two optical modes coupled to a common mechanical mode form an ideal platform to realize these effects, providing the basis for various recent demonstrations of optomechanically induced non-reciprocal light transmission. Here, we establish a unifying theoretical framework to analyze optical non-reciprocity and breaking of time-reversal symmetry in multimode optomechanical systems. We highlight two general scenarios to achieve isolation, relying on either optical or mechanical losses. Depending on the loss mechanism, our theory defines the ultimate requirements for optimal isolation and the available operational bandwidth in these systems. We also analyze the effect of sideband resolution on the performance of optomechanical isolators, highlighting the fact that non-reciprocity can be preserved even in the unresolved sideband regime. Our results provide general insights into a broad class of parametrically modulated non-reciprocal devices, paving the way towards optimal non-reciprocal systems for low-noise integrated nanophotonics., Comment: 42 pages, 15 figures