Supersymmetric transparent optical intersections

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.

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.

Linear response theory of open systems with exceptional points

Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M_s with M_s = 2, 3, …, M, depending on the choice of input and output channels.

The authors develop a closed-form expansion of the linear response associated with resonant non-Hermitian systems having exceptional points and demonstrate that the spectral response may involve different super Lorentzian lineshapes depending on the input/output channel configuration.

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.

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.

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.

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.

Metadisorder for designer light in random systems

Disorder plays a critical role in signal transport by controlling the correlation of a system, as demonstrated in various complex networks. In wave physics, disordered potentials suppress wave transport, because of their localized eigenstates, from the interference between multiple scattering paths. Although the variation of localization with tunable disorder has been intensively studied as a bridge between ordered and disordered media, the general trend of disorder-enhanced localization has remained unchanged, and the existence of complete delocalization in highly disordered potentials has not been explored. We propose the concept of "metadisorder": randomly coupled optical systems in which eigenstates can be engineered to achieve unusual localization. We demonstrate that one of the eigenstates in a randomly coupled system can always be arbitrarily molded, regardless of the degree of disorder, by adjusting the self-energy of each element. Ordered waves with the desired form are then achieved in randomly coupled systems, including plane waves and globally collective resonances. We also devise counterintuitive functionalities in disordered systems, such as "small-world-like" transport from non-Anderson-type localization, phase-conserving disorder, and phase-controlled beam steering.

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'.