Supersymmetric mode converters

Loss-tailoring single-mode high-power supersymmetric lasers

Diode lasers with high beam quality and high power have many promising applications. However, high beam quality is always in conflict with high power. In this Letter, we theoretically and experimentally confirm the mode instability property of supersymmetric structures at higher operating currents. Meanwhile, we propose a loss-tailoring diode laser based on a supersymmetric structure, which enables the higher-order lateral modes to obtain higher losses, raises the excitation threshold of the higher-order lateral modes, and achieves a stable fundamental-lateral-mode output at higher current operation. The device obtained a quasi-single-lobe lateral far-field distribution with the full width at half maximum (FWHM) of 7.58° at 350 mA under room temperature, which is a 65% reduction compared to the traditional Fabry-Perot (FP) diode lasers. Moreover, the M2 of 2.181@350 mA has an improvement of about 37% over traditional FP and supersymmetric structure lasers.

Perfect Excitation of Topological States by Supersymmetric Waveguides

Topological photonic states provide intriguing strategies for robust light manipulations, however, it remains challenging to perfectly excite these topological eigenstates due to their complicated mode profiles. In this work, we propose to realize the exact eigenmode of the topological edge states by supersymmetric (SUSY) structures. By adiabatically transforming the SUSY partner to its main topological structure, the edge modes can be perfectly excited with simple single-site input. We experimentally verify our strategy in integrated silicon waveguides in telecommunication wavelength, showing a broad working bandwidth. Moreover, a shortcut-to-adiabaticity strategy is further applied to speed up the adiabatic pump process by inverse-design approaches, thus enabling fast mode evolutions and leading to reduced device size. Our method is universal and beneficial to the topology-based or complex eigenmodes systems, ranging from photonics and microwaves to cold atoms and acoustics.

Electrically driven supersymmetric semiconductor laser arrays with single-lobe far-field patterns

Semiconductor laser arrays based on the third-order supersymmetric (SUSY) transformation are proposed to increase the mode discrimination between fundamental supermode and high-order supermodes. The distance between the edge waveguide of the main array and that of the superpartners is optimized. Then, the electric field distributions of different modes are also calculated, which show that, except for the fundamental supermode, the high-order supermodes penetrate deeper into the superpartner arrays, which accounts for the increased loss of high-order supermodes. The fabricated third-order SUSY laser array can emit light with a single-lobe far-field pattern under an injection current of 70 mA, which is a promising candidate for optical couplings between lasers and optical elements.

Guiding flow of light with supersymmetry

The continuous supersymmetry transformation is applied to the silicon waveguides, and the guidance and conversion of any mode in a wide spectral range are successfully realized in experiments. This proves its great potential in optical spatial mode modulation and space division multiplexing in optical communication.

On-chip beam rotators, adiabatic mode converters, and waveplates through low-loss waveguides with variable cross-sections

Photonics integrated circuitry would benefit considerably from the ability to arbitrarily control waveguide cross-sections with high precision and low loss, in order to provide more degrees of freedom in manipulating propagating light. Here, we report a new method for femtosecond laser writing of optical-fiber-compatible glass waveguides, namely spherical phase-induced multicore waveguide (SPIM-WG), which addresses this challenging task with three-dimensional on-chip light control. Fabricating in the heating regime with high scanning speed, precise deformation of cross-sections is still achievable along the waveguide, with shapes and sizes finely controllable of high resolution in both horizontal and vertical transversal directions. We observed that these waveguides have high refractive index contrast of 0.017, low propagation loss of 0.14 dB/cm, and very low coupling loss of 0.19 dB coupled from a single-mode fiber. SPIM-WG devices were easily fabricated that were able to perform on-chip beam rotation through varying angles, or manipulate the polarization state of propagating light for target wavelengths. We also demonstrated SPIM-WG mode converters that provide arbitrary adiabatic mode conversion with high efficiency between symmetric and asymmetric nonuniform modes; examples include circular, elliptical modes, and asymmetric modes from ppKTP (periodically poled potassium titanyl phosphate) waveguides which are generally applied in frequency conversion and quantum light sources. Created inside optical glass, these waveguides and devices have the capability to operate across ultra-broad bands from visible to infrared wavelengths. The compatibility with optical fiber also paves the way toward packaged photonic integrated circuitry, which usually needs input and output fiber connections.

High-efficiency topological pumping with discrete supersymmetry transformations

Making use of the isospectrality of Supersymmetry transformations, we propose a general and high-fidelity method to prepare gapped topological modes in discrete systems from a single-site excitation. The method consists of adiabatically connecting two superpartner structures, deforming the input state into the desired mode. We demonstrate the method by pumping topological states of the Su-Schrieffer-Heeger model in an optical waveguide array, where the adiabatic deformation is performed along the propagation direction. We obtain fidelities above F = 0.99 for a wide range of coupling strengths when pumping edge and interface states.

Electrically injected supersymmetric semiconductor lasers with narrow vertical divergence angle

Electrically injected supersymmetric (SUSY) semiconductor lasers are proposed and fabricated. Two successive SUSY transformations are applied to the main array arranged along the direction of epitaxial growth, which can remove the propagation constants of the fundamental mode and the leaky mode of the main array from the superpartner while keeping those of other high-order modes. The SUSY laser possesses an excellent mode discrimination and favors the lasing of the fundamental mode. The fabricated SUSY laser can emit light with a single-lobe vertical far-field pattern with the full width at half maximum of 16.87° under an injection current of 1.4 A.

Quantum-inspired multicore optical fiber

We introduce a new, to the best of our knowledge, type of multicore optical fiber having a quantum-inspired network topology and unique spectral features. Particularly, the connectivity between the cores is generated by unfolding a circular array of coupled quantum oscillators in Fock space. We show that in such a fiber geometry, the eigenvalues of the optical supermodes exhibit partial degeneracy and form a ladder. In turn, this leads to revival dynamics, allowing for a periodic re-imaging of the input intensity. As an example, we present a realistic design with six cores in silica glass platforms.

Supersymmetry-enhanced stark-chirped rapid-adiabatic-passage in multimode optical waveguides

We propose a method to efficiently pump an excited mode of a multimode optical waveguide starting from a fundamental-mode input by combining Stark-Chirped Rapid Adiabatic Passage (SCRAP) and Supersymmetry (SUSY) transformations. In a two-waveguide set, we implement SCRAP by modulating the core refractive index of one waveguide, which is evanescently coupled to its SUSY partner. SCRAP provides an efficient transfer of light intensity between the modes of different waveguides, while SUSY allows to control which modes are supported. Using both techniques allows to achieve fidelities above 99% for the pumping of the excited mode of a two-mode waveguide. Additionally, we show that SCRAP can be exploited to spatially separate superpositions of fundamental and excited modes, and how SUSY can also improve the results for this application.

PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case.

Waveguide-lattice-based architecture for multichannel optical transformations

We consider waveguide lattices as the architecture to implement a wide range of multiport transformations. In this architecture, a particular transfer matrix is obtained by setting step-wise profiles of propagation constants experienced by a field evolving in a lattice. To investigate the capabilities of this architecture, we numerically study the implementation of random transfer matrices as well as several notable cases, such as the discrete Fourier transform, the Hadamard, and permutation matrices. We show that waveguide lattice schemes are more compact than their traditional lumped-parameter counterparts, thus the proposed architecture may be beneficial for photonic information processing systems of the future.

Higher-dimensional supersymmetric microlaser arrays

The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers-collectively oscillating in the fundamental transverse supermode-which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes.

Landau-Zener Transition in the Dynamic Transfer of Acoustic Topological States

Topological notions in physics often emerge from adiabatic evolution of states. It not only leads to fundamental insight of topological protection but also provides an important approach for the study of higher-dimensional topological phases. In this work, we first demonstrate the transfer of topological boundary states (TBSs) across the bulk to the opposite boundary in an acoustic waveguide system. By exploring the finite-size induced minigap between two TBS bands, we unveil the quantitative condition for the breakdown of adiabaticity in the system by demonstrating the Landau-Zener transition with both theory and experiments. Our results not only serve as a foundation of future studies of dynamic state transfer but also inspire applications leveraging nonadiabatic transitions as a new degree of freedom.

Fermionic time-reversal symmetry in a photonic topological insulator

Much of the recent attention directed towards topological insulators is motivated by their hallmark feature of protected chiral edge states. In electronic (or fermionic) topological insulators, these states originate from time-reversal symmetry and allow carriers with opposite spin-polarization to propagate in opposite directions at the edge of an insulating bulk. By contrast, photonic (or bosonic) systems are generally assumed to be precluded from supporting edge states that are intrinsically protected by time-reversal symmetry. Here, we experimentally demonstrate counter-propagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is the design of a Floquet driving protocol that incorporates effective fermionic time-reversal symmetry, enabling the realization of the photonic version of an electronic topological insulator. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby offering alternative opportunities for photonics as well as acoustics, mechanical waves and cold atoms.

Stepped laser-ablation fabrication of concave micromirrors in rectangular optical waveguides for low loss vertical coupling

In this report, we present a stepped laser-ablation method for the fabrication of concave micromirrors in rectangular optical waveguides. The numerically simulated vertical coupling loss of the reflection of the concave micromirror can be reduced to 1.53 dB. The processing parameters of the utilized excimer laser, such as the step number, width, and depth, were optimized to fabricate the concave micromirrors. After the thermal reflow process, the measured curve of the circular concave micromirrors obtained using a 3D optical profiler agreed well with a standard circle with a surface roughness of 39.56 nm. Furthermore, vertical coupling for 62.5 µm MMF revealed that the loss of the circular concave micromirror coated with a 50 nm thick Au film is as low as 1.83 dB, corresponding to a high coupling efficiency of 65.61%. This new, convenient, and efficient fabrication technology for the fabrication of concave micromirrors can be applied to vertical coupling for optical printed circuit board (OPCB) interconnection technology.

Parity-Time Symmetry in Non-Hermitian Complex Optical Media

The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.

Supersymmetry in the time domain and its applications in optics

Supersymmetry is a conjectured symmetry between bosons and fermions aiming at solving fundamental questions in string and quantum field theory. Its subsequent application to quantum mechanics led to a ground-breaking analysis and design machinery, later fruitfully extrapolated to photonics. In all cases, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we demonstrate that Maxwell's equations, as well as the acoustic and elastic wave equations, also possess an underlying supersymmetry in the time domain. We explore the consequences of this property in the field of optics, obtaining a simple analytic relation between the scattering coefficients of numerous time-varying systems, and uncovering a wide class of reflectionless, three dimensional, all-dielectric, isotropic, omnidirectional, polarisation-independent, non-complex media. Temporal supersymmetry is also shown to arise in dispersive media supporting temporal bound states, which allows engineering their momentum spectra and dispersive properties. These unprecedented features may enable the creation of novel reconfigurable devices, including invisible materials, frequency shifters, isolators, and pulse-shape transformers.

Mode-sorter design using continuous supersymmetric transformation

We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation constants while being spatially separated. This global matching of the propagation constants, in conjunction with the adiabatic modification of the refractive index landscape along the propagation direction, results in the negligible modal cross-talk and low scattering losses in the sorter. We show that a properly optimized SUSY mode sorter outperforms a standard asymmetric Y-splitter by reducing the cross-talk by at least two orders of magnitude. Moreover, the SUSY sorter is capable of sorting either transverse-electric or transverse-magnetic polarized modes and operates in a broad range of wavelengths. At the telecommunication wavelength, the 300-μm-long SUSY sorter provides the cross-talk of -35 dB and a broad operation bandwidth. The design proposed here paves the way toward efficient signal manipulation in integrated photonic devices.

Single-mode lasing by selective mode pairing

High-order laser modes are suppressed by pairing them with lossy “superpartners”

Supersymmetric laser arrays

Scaling up the radiance of coupled laser arrays has been a long-standing challenge in photonics. In this study, we demonstrate that notions from supersymmetry—a theoretical framework developed in high-energy physics—can be strategically used in optics to address this problem. In this regard, a supersymmetric laser array is realized that is capable of emitting exclusively in its fundamental transverse mode in a stable manner. Our results not only pave the way toward devising new schemes for scaling up radiance in integrated lasers, but also, on a more fundamental level, could shed light on the intriguing synergy between non-Hermiticity and supersymmetry.

Supersymmetric Polarization Anomaly in Photonic Discrete-Time Quantum Walks

Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a system. These anomalies are at the heart of topological effects in electronic, photonic, and atomic systems, where they result in a unique response to external fields but generally escape a more direct observation. Here, we implement an optical-network realization of a discrete-time quantum walk, where such an anomaly can be observed directly in the unique circular polarization of a topological midgap state. We base the system on a single-step protocol overcoming the experimental infeasibility of earlier multistep protocols. The evolution combines a chiral symmetry with a previously unexplored unitary version of supersymmetry. Having experimental access to the position and the coin state of the walker, we perform a full polarization tomography and provide evidence for the predicted anomaly of the midgap states. This approach opens the prospect to dynamically distill topological states for quantum information applications.

Integrated photonic devices based on adiabatic transitions between supersymmetric structures

We introduce adiabatic transitions connecting two supersymmetric partner profiles by smoothly modifying the transverse refractive index profile along the propagation direction. With this transformation, one of the transverse electric modes evolves adapting its shape and propagation constant without being coupled to other guided or radiated modes while the rest of the modes are radiated. This technique offers a systematic way to manipulate the modal content in systems of optical waveguides and engineer efficient and robust photonic devices such as tapered waveguides, single-waveguide mode filters, beam splitters and interferometers. Numerical simulations show that very high fidelities and transmitted powers are obtained for a broad range of devices lengths and light's wavelengths.

Supercharge optical arrays

We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state below the ground state of the super-partner array. This zero mode, which is pinned deep in the mid-gap of the corresponding supercharge array owing to the square-root spectral relationship between a supercharge and a super-Hamiltonian array, is shown to be protected because of the chiral symmetry inherent to a supercharge array. A supercharge array can be used in practical applications to design a discrete optical system of waveguides or coupled resonators where the mid-gap zero mode facilitates robust light dynamics in either spatial or time domain.

Supersymmetry-guided method for mode selection and optimization in coupled systems

Single-mode operation of coupled optical systems, such as optical-fiber bundles, lattices of photonic waveguides, or laser arrays, requires an efficient method to suppress unwanted super-modes. Here, we propose a systematic supersymmetry-based approach to selectively eliminate modes of such systems by decreasing their lifetime relative to the lifetime of the mode of interest. The proposed method allows to explore the opto-geometric parameters of the coupled system and to maximize the relative lifetime of a selected mode. We report a 10-fold increase in the relative lifetime of the fundamental modes of large one-dimensional coupled arrays in comparison to simple "head-to-tail" coupling geometries. The ability to select multiple supported modes in one- and two-dimensional arrays is also demonstrated.

Symmetry in optics and photonics: a group theory approach

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.

Parity–time symmetric photonics

The establishment of non-Hermitian quantum mechanics (such as parity–time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to complex quantum potentials, photonics provides an ideal platform for the visualization of many conceptually striking predictions from non-Hermitian quantum theory. A rapidly developing field has emerged, namely, PT-symmetric photonics, demonstrating intriguing optical phenomena including eigenstate coalescence and spontaneous PT-symmetry breaking. The advance of quantum physics, as the feedback, provides photonics with brand-new paradigms to explore the entire complex permittivity plane for novel optical functionalities. Here, we review recent exciting breakthroughs in PT-symmetric photonics while systematically presenting their underlying principles guided by non-Hermitian symmetries. The potential device applications for optical communication and computing, biochemical sensing and healthcare are also discussed.

Unscrambling light-automatically undoing strong mixing between modes

Propagation of light beams through scattering or multimode systems may lead to the randomization of the spatial coherence of the light. Although information is not lost, its recovery requires a coherent interferometric reconstruction of the original signals, which have been scrambled into the modes of the scattering system. Here we show that we can automatically unscramble optical beams that have been arbitrarily mixed in a multimode waveguide, undoing the scattering and mixing between the spatial modes through a mesh of silicon photonics tuneable beam splitters. Transparent light detectors integrated in a photonic chip are used to directly monitor the evolution of each mode along the mesh, allowing sequential tuning and adaptive individual feedback control of each beam splitter. The entire mesh self-configures automatically through a progressive tuning algorithm and resets itself after significantly perturbing the mixing, without turning off the beams. We demonstrate information recovery by the simultaneous unscrambling, sorting and tracking of four mixed modes, with residual cross-talk of -20 dB between the beams. Circuit partitioning assisted by transparent detectors enables scalability to meshes with a higher port count and to a higher number of modes without a proportionate increase in the control complexity. The principle of self-configuring and self-resetting in optical systems should be applicable in a wide range of optical applications.

Mode-division (de)multiplexing using adiabatic passage and supersymmetric waveguides

The development of mode-division multiplexing techniques is an important step to increase the information processing capacity. In this context, we design an efficient and robust mode-division (de)multiplexing integrated device based on the combination of spatial adiabatic passage and supersymmetric techniques. It consists of two identical step-index external waveguides coupled to a supersymmetric central one with a specific modal content that prevents the transfer of the fundamental transverse electric spatial mode. The separation between waveguides is engineered along the propagation direction to optimize spatial adiabatic passage for the first excited transverse electric spatial mode of the step-index waveguides. Thus, by injecting a superposition of the two lowest spatial modes into the step-index left waveguide, the fundamental mode remains in the left waveguide while the first excited mode is fully transmitted to the right waveguide. Output fidelities ℱ > 0.90 are obtained for a broad range of geometrical parameter values and light's wavelengths, reaching ℱ = 0.99 for optimized values.

Kerr self-cleaning of pulsed beam in an ytterbium doped multimode fiber

We experimentally demonstrate that Kerr spatial self-cleaning of a pulsed beam can be obtained in an amplifying multimode optical fiber. An input peak power of 500 W only was sufficient to produce a quasi-single-mode emission from the double-clad ytterbium doped multimode fiber (YMMF) with non-parabolic refractive index profile. We compare the self-cleaning behavior observed in the same fiber with loss and with gain. Laser gain introduces new opportunities to achieve spatial self-cleaning of light in multimode fibers at a relatively low power threshold.

Low-dimensional gap plasmons for enhanced light-graphene interactions

Graphene plasmonics has become a highlighted research area due to the outstanding properties of deep-subwavelength plasmon excitation, long relaxation time, and electro-optical tunability. Although the giant conductivity of a graphene layer enables the low-dimensional confinement of light, the atomic scale of the layer thickness is severely mismatched with optical mode sizes, which impedes the efficient tuning of graphene plasmon modes from the degraded light-graphene overlap. Inspired by gap plasmon modes in noble metals, here we propose low-dimensional hybrid graphene gap plasmon waves for large light-graphene overlap factor. We show that gap plasmon waves exhibit improved in-plane and out-of-plane field concentrations on graphene compared to those of edge or wire-like graphene plasmons. By adjusting the chemical property of the graphene layer, efficient and linear modulation of hybrid graphene gap plasmon modes is also achieved. Our results provide potential opportunities to low-dimensional graphene plasmonic devices with strong tunability.

Non-Hermitian engineering of single mode two dimensional laser arrays

A new scheme for building two dimensional laser arrays that operate in the single supermode regime is proposed. This is done by introducing an optical coupling between the laser array and lossy pseudo-isospectral chains of photonic resonators. The spectrum of this discrete reservoir is tailored to suppress all the supermodes of the main array except the fundamental one. This spectral engineering is facilitated by employing the Householder transformation in conjunction with discrete supersymmetry. The proposed scheme is general and can in principle be used in different platforms such as VCSEL arrays and photonic crystal laser arrays.

Optical revivals in nonuniform supersymmetric photonic arrays

We investigate the problem of wavepacket revivals in coupled nonuniform linear optical structures. Starting from the photonic Bloch lattices and J(x) arrays, whose propagators are fully periodic, we use cascaded discrete supersymmetric transformations to generate a family of nonuniform isospectral lattices. These new structures exhibit perfect imaging for any initial condition despite the apparent lack of order in their physical parameters. We note, however. that the SUSY-induced disordered coefficients are not random but, rather, inherit some of the features associated with the original array.

On-chip data exchange for mode division multiplexed signals

Data exchange is an important function for flexible optical network, and it has been extensively investigated for the time and wavelength domains. The mode division multiplexing (MDM) has been proposed to further increase the transmission capacity by carrying information on different modes with only single wavelength carrier. We propose and experimentally demonstrate a novel on-chip data exchange circuit for the MDM signals by utilizing two micro-ring resonator (MRR) based mode converters. For demonstration, single and four wavelengths non-return-to-zero on-off-keying (NRZ-OOK) signals at 10 Gb/s carried on different modes are successfully processed, with open and clear eye diagrams. Measured bit error ratio (BER) results show reasonable power penalties. The proposed circuit can be potentially used in advanced and flexible MDM optical networks.

Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example

In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solution of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. We believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.

Bloch-like waves in random-walk potentials based on supersymmetry

Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this restriction was disproven by the discoveries of amorphous media and quasicrystals. While network and liquid models have been suggested for the interpretation of Bloch-like waves in disordered media, these approaches based on searching for random networks with bandgaps have failed in the deterministic creation of bandgaps. Here we reveal a deterministic pathway to bandgaps in random-walk potentials by applying the notion of supersymmetry to the wave equation. Inspired by isospectrality, we follow a methodology in contrast to previous methods: we transform order into disorder while preserving bandgaps. Our approach enables the formation of bandgaps in extremely disordered potentials analogous to Brownian motion, and also allows the tuning of correlations while maintaining identical bandgaps, thereby creating a family of potentials with 'Bloch-like eigenstates'.

Supersymmetry-inspired non-Hermitian optical couplers

Supersymmetry has been shown to provide a systematic and effective framework for generating classes of isospectral optical structures featuring perfectly-phase-matched modes, with the exception of one (fundamental) mode which can be removed. More recently, this approach has been extended to non-Hermitian scenarios characterized by spatially-modulated distributions of optical loss and gain, in order to allow the removal of higher-order modes as well. In this paper, we apply this approach to the design of non-Hermitian optical couplers with higher-order mode-selection functionalities, with potential applications to mode-division multiplexing in optical links. In particular, we highlight the critical role of the coupling between non-Hermitian optical waveguides, which generally induces a phase transition to a complex eigenspectrum, thereby hindering the targeted mode-selection functionality. With the specific example of an optical coupler that selects the second-order mode of a given waveguide, we illustrate the aforementioned limitations and propose possible strategies to overcome them, bearing in mind the practical feasibility of the gain levels required.

Supersymmetric transparent optical intersections

Supersymmetric (SUSY) optical structures provide a versatile platform to manipulate the scattering and localization properties of light, with potential applications to mode conversion, spatial multiplexing, and invisible devices. Here we show that SUSY can be exploited to realize broadband transparent intersections between guiding structures in optical networks for both continuous and discretized light. These include transparent crossing of high-contrast-index waveguides and directional couplers, as well as crossing of guiding channels in coupled resonator lattices.

Observation of supersymmetric scattering in photonic lattices

Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing schemes. Here, we experimentally investigate the scattering characteristics of SUSY photonic lattices. We directly observe the light dynamics in such systems and compare the reflection/transmission properties of SUSY partner structures. In doing so, we demonstrate that discrete settings constitute a promising testbed for studying the different facets of optical supersymmetry.

Absorption-assisted mode transformation in butterfly compound eyes

The ommatidium of the butterfly's afocal apposition eye exhibits angular performance that can only be achieved by transforming the diffraction pattern of its corneal lens into the fundamental mode of its rhabdom waveguide. A graded index model of the ommatidium has been proposed and verified but the efforts to extract the transformation's underlying physics from it have been hindered by its extreme complexity. Here we numerically investigate the ommatidium model and reveal that the current model, involving only the graded index distribution, is insufficient for the transformation. We further find that adding spatially varying absorption to the existing model dramatically improves its transformation performance, producing near-perfect mode matching with overlap integral exceeding 0.96. Such a combined action of spatially varying index and absorption for microscale mode transformation is new to researchers in optics and biology and will benefit both disciplines.

Bent waveguides for matter-waves: supersymmetric potentials and reflectionless geometries

Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found whose geometry-induced potentials share the same scattering properties. As a result, reflectionless waveguides, dual to the straight waveguide, are identified. Strictly isospectral waveguides are also found by modulating the depth of the trapping potential. Numerical simulations are used to demonstrate the efficiency of these approaches in tailoring and controlling curvature-induced quantum-mechanical effects.