Observation of supersymmetric scattering in photonic lattices

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.

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.

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.

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.

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.

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.

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.

Reflectionless and invisible potentials in photonic lattices

An arbitrarily shaped optical potential on a discrete photonic lattice, which transversely drifts at a speed greater than the maximum speed allowed by the light cone of the lattice band, becomes reflectionless. Such an intriguing result, which arises from the discrete translational symmetry of the lattice, is peculiar to discretized light and does not have any counterpart for light scattering in continuous optical media. A drifting non-Hermitian optical potential of the Kramers-Kronig type also is an invisible potential, i.e., a discrete optical beam crosses the drifting potential without being distorted, delayed, nor advanced.

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.

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'.

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.