The Goldilocks principle of learning unitaries by interlacing fixed operators with programmable phase shifters on a photonic chip.

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 × 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.

Auto-calibrating universal programmable photonic circuits: hardware error-correction and defect resilience.

It is recently shown that discrete N × 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.

Inverse design of omnidirectional coherent absorbers for optical power beaming applications.

An efficient photovoltaic power converter is a critical element in laser power beaming systems for maximizing the end-to-end power transfer efficiency while minimizing beam reflections from the receiver for safety considerations. We designed a multilayer absorber that can efficiently trap monochromatic light from broad incident angles. The proposed design is built on the concept of a one-way coherent absorber with inverse-designed aperiodic multilayer front- and back-reflectors that enable maximal optical absorption in a thin-film photovoltaic material for broad angles. We argue that the broad bandwidth is achieved through an optimization search process that automatically engineers the modal content of the cavity to create multiple overlapping resonant modes at the desired angle or frequency range. A realistic design is provided based on GaAs thin films with inverse-designed multilayer binary AlAs/AlGaAs mirrors. The proposed device can pave the way for efficient optical power beaming systems.

On-Chip Microwave Frequency Combs in a Superconducting Nanoelectromechanical Device.

Nanomechanical resonances coupled to microwave cavities can be excited, measured, and controlled simultaneously using electromechanical back-action phenomena. Examples of these effects include sideband cooling and amplification, which are commonly described through linear equations of motion governed by an effective optomechanical Hamiltonian. However, this linear approximation is invalid when the pump-induced cavity microwave field is large enough to trigger optomechanical nonlinearities, resulting in phenomena like frequency combs. Here, we employ a niobium-based superconducting electromechanical device to explore the generation of microwave frequency combs. We observe the formation of combs around a microwave resonant frequency (3.78 GHz) with 8-MHz frequency spacing, equal to the mechanical resonant frequency. We investigate their dynamics for different optomechanical parameters, including detuning, pump powers, and cavity decay rates. Our experimental results show excellent agreement with numerical modeling. These electromechanical frequency combs can be beneficial in nanomechanical sensing applications that require precise electrical tracking of mechanical resonant frequencies.

Integrated random projection and dimensionality reduction by propagating light in photonic lattices.

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 random subset of the waveguide channels, one can perform an embedding from a higher- to a lower-dimensional space that respects the Johnson-Lindenstrauss lemma and nearly preserves the Euclidean distances. The distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive propagation of light. 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 computation stage.

Phase tristability in parametric three-photon down-conversion.

This Letter shows that the parametric processes of spontaneous three-photon down-conversion is accompanied by phase tristability of the sub-harmonic signal. The oscillations of the signal in a resonant cavity are modeled through an analytically solvable second-order nonlinear oscillator. Self-sustained oscillations of the signal at a finite amplitude are found to be equally probable in three states with uniform phase contrasts. The onset of oscillations is a case of bifurcation from infinity. The stability of the ternary states is proven through an energy landscape function that identifies the attractor basins of the three states. An analogy is drawn between the oscillation threshold of a three-photon down-conversion oscillator and a first-order phase transition. The investigated phase-tristable oscillator can serve as a classical ternary bit for unconventional computing applications.

Study of the effectiveness of comprehensive, timely, and family-oriented interventions in reducing the symptoms of autism in children.

BACKGROUND AND OBJECTIVES: The onset of rehabilitation interventions in children with autism spectrum disorder below 5 years old has been associated with the reduction of autism symptoms in all developmental domains. The present study aimed to illustrate the importance of early family-oriented interventions in the reduction of the problems and symptoms of children with autism spectrum disorder. METHODOLOGY: This study was a pretest-posttest clinical trial without a control group. Fifty patients were selected using a convenience sampling method, of which forty patients were male and 10 females with a mean age of 3.2 ± 1.4. The efficacy assessment was evaluated using the Autism Behavior Checklist (ABC) and the Autism Treatment Evaluation Checklist (ATEC) as pretest and posttest. Data were analyzed by independent T-test using SPSS software. RESULTS: The difference between pretest and posttest was significant in all aspects of the ATEC test (communication, health, sensory and cognitive awareness, socialization) at the level of P < 0.001. Moreover, the difference between pretest and posttest was significant at P < 0.001 for the aspects of speech, social and communication, and general performance, and at P < 0.002 for the sensory processing. CONCLUSION: Timely interventions under 6 years old with an emphasis on family-oriented and growth aspects over one year can help autistic children in the aspects of speech, social and communication, sensory processing, and sensory and cognitive awareness.

Momentum-Topology-Induced Optical Pulling Force.

We report an ingenious mechanism to obtain robust optical pulling force by a single plane wave via engineering the topology of light momentum in the background. The underlying physics is found to be the topological transition of the light momentum from a usual convex shape to a starlike concave shape in the carefully designed background, such as a photonic crystal structure. The principle and results reported here shed insightful concepts concerning optical pulling, and pave the way for a new class of advanced optical manipulation technique, with potential applications of drug delivery and cell sorting.

Mode discrimination in dissipatively coupled laser arrays.

We show that dissipative coupling between an array of passive optical resonators creates a ladder of decay rates in the complex eigenfrequencies. This effect promotes mode discrimination in laser arrays, while the lowest-order and highest-order modes exhibit the highest and lowest lasing thresholds, respectively. The array supermodes and their corresponding eigenfrequencies are calculated analytically through a tight-binding model, and the single-mode operation range is derived. The results are exemplified through the finite element simulation of an array of transversely coupled semiconductor laser cavities.

Anomalous optical forces in PT-symmetric waveguides.

Evanescently coupled passive waveguides experience optical forces of attractive or repulsive nature, depending on the mode of operation. Here we explore the optical forces between parity-time-symmetric coupled waveguides, with balanced levels of gain and loss. We find that, besides the diagonal stress components that result in a pressure normal to the surface of the waveguides, this system exhibits an off-diagonal stress component that creates a shear along the propagation direction. In addition, for a critical value of balanced gain and loss, the normal pressure can be reduced to zero. These anomalous optical forces are related to the unusual power flow in coupled active-passive channels, and open interesting opportunities for microfluidics and micro-optomechanical systems.

Anti-parity-time symmetry in diffusive systems.

Various concepts related to parity-time symmetry, including anti-parity-time symmetry, have found broad applications in wave physics. Wave systems are fundamentally described by Hermitian operators, whereas their unusual properties are introduced by incorporation of gain and loss. We propose that the related physics need not be restricted to wave dynamics, and we consider systems described by diffusive dynamics. We study the heat transfer in two countermoving media and show that this system exhibits anti-parity-time symmetry. The spontaneous symmetry breaking results in a phase transition from motionless temperature profiles, despite the mechanical motion of the background, to moving temperature profiles. Our results extend the concepts of parity-time symmetry beyond wave physics and may offer opportunities to manipulate heat and mass transport.

Exceptional points in optics and photonics.

Exceptional points are branch point singularities in the parameter space of a system at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become degenerate. Such peculiar degeneracies are distinct features of non-Hermitian systems, which do not obey conservation laws because they exchange energy with the surrounding environment. Non-Hermiticity has been of great interest in recent years, particularly in connection with the quantum mechanical notion of parity-time symmetry, after the realization that Hamiltonians satisfying this special symmetry can exhibit entirely real spectra. These concepts have become of particular interest in photonics because optical gain and loss can be integrated and controlled with high resolution in nanoscale structures, realizing an ideal playground for non-Hermitian physics, parity-time symmetry, and exceptional points. As we control dissipation and amplification in a nanophotonic system, the emergence of exceptional point singularities dramatically alters their overall response, leading to a range of exotic optical functionalities associated with abrupt phase transitions in the eigenvalue spectrum. These concepts enable ultrasensitive measurements, superior manipulation of the modal content of multimode lasers, and adiabatic control of topological energy transfer for mode and polarization conversion. Non-Hermitian degeneracies have also been exploited in exotic laser systems, new nonlinear optics schemes, and exotic scattering features in open systems. Here we review the opportunities offered by exceptional point physics in photonics, discuss recent developments in theoretical and experimental research based on photonic exceptional points, and examine future opportunities in this area from basic science to applied technology.

Optical gradient forces between evanescently coupled waveguides.

Evanescently coupled dielectric waveguides exert optical forces on each other, which may be attractive or repulsive as a function of the excited optical mode. Through energy conservation considerations, it is possible to show that the optical force between two waveguides is proportional to the derivative of the effective propagation index with respect to the separation between waveguides. Here, we prove analytically that the lateral force calculated from the spatial derivative of the propagation index is equivalent to the one obtained from a formal calculation based on the Maxwell's stress tensor. Interestingly, this latter approach reveals that the sign and magnitude of the force depend only on the field intensity at the channel interfaces. In addition, our derivation provides insights into the design of the waveguide profile in order to increase or decrease the optical forces between coupled channels.

Optical circulation in a multimode optomechanical resonator.

Breaking the symmetry of electromagnetic wave propagation enables important technological functionality. In particular, circulators are nonreciprocal components that can route photons directionally in classical or quantum photonic circuits and offer prospects for fundamental research on electromagnetic transport. Developing highly efficient circulators thus presents an important challenge, especially to realise compact reconfigurable implementations that do not rely on magnetic fields to break reciprocity. We demonstrate optical circulation utilising radiation pressure interactions in an on-chip multimode optomechanical system. Mechanically mediated optical mode conversion in a silica microtoroid provides a synthetic gauge bias for light, enabling four-port circulation that exploits tailored interference between appropriate light paths. We identify two sideband conditions under which ideal circulation is approached. This allows to experimentally demonstrate ~10 dB isolation and <3 dB insertion loss in all relevant channels. We show the possibility of actively controlling the circulator properties, enabling ideal opportunities for reconfigurable integrated nanophotonic circuits.

Nonreciprocity and magnetic-free isolation based on optomechanical interactions.

Nonreciprocal components, such as isolators and circulators, provide highly desirable functionalities for optical circuitry. This motivates the active investigation of mechanisms that break reciprocity, and pose alternatives to magneto-optic effects in on-chip systems. In this work, we use optomechanical interactions to strongly break reciprocity in a compact system. We derive minimal requirements to create nonreciprocity in a wide class of systems that couple two optical modes to a mechanical mode, highlighting the importance of optically biasing the modes at a controlled phase difference. We realize these principles in a silica microtoroid optomechanical resonator and use quantitative heterodyne spectroscopy to demonstrate up to 10 dB optical isolation at telecom wavelengths. We show that nonreciprocal transmission is preserved for nondegenerate modes, and demonstrate nonreciprocal parametric amplification. These results open a route to exploiting various nonreciprocal effects in optomechanical systems in different electromagnetic and mechanical frequency regimes, including optomechanical metamaterials with topologically non-trivial properties.

Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices.

We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.

Integrable nonlinear parity-time-symmetric optical oscillator.

The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.

Systematic approach for designing zero-DGD coupled multi-core optical fibers.

An analytical method is presented for designing N-coupled multi-core fibers with zero differential group delay. This approach effectively reduces the problem to a system of N-1 algebraic equations involving the associated coupling coefficients and propagation constants, as obtained from coupled mode theory. Once the parameters of one of the cores are specified, the roots of the resulting N-1 equations can be used to determine the characteristics of the remaining waveguide elements. Using this technique, a number of pertinent geometrical configurations are investigated to minimize intermodal dispersion.

Observation of discrete diffraction patterns in an optically induced lattice.

We have experimentally observed the discrete diffraction of light in a coherently prepared multi-level atomic medium. This is achieved by launching a probe beam into an optical lattice induced from the interference of two coupling beams. The diffraction pattern can be controlled through the atomic parameters such as two-photon detuning and temperature, as well as orientations of the coupling and probe beams. Clear diffraction patterns occur only near the two-photon resonance.

Observation of optical solitons in PT-symmetric lattices.

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.