Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators

TL;DR

The paper addresses extending photonic quantum simulators beyond single-mode sites by exploiting higher-order spatial modes and orbital degrees of freedom to realize synthetic gauge fields. It surveys photonic waveguide arrays and exciton-polariton lattices, detailing inter-orbital coupling, phase engineering, and synthetic flux arising from $s$/$p$/$d$ and OAM modes. Key demonstrations include $\pi$ flux and Aharonov–Bohm caging with OAM modes, and the emergence of Möbius topological insulators and other higher-order topologies via inter-orbital hopping, with dynamic control enabled by structured pumping and nonlinearities. The perspective argues that multimode photonic platforms enable orbitronics and robust photonic devices, providing a versatile platform for orbital-based quantum simulations, non-Hermitian and Floquet engineering, and soliton–Wannier connections for future studies.

Abstract

Photonic platforms have emerged as versatile and powerful classical simulators of quantum dynamics, providing clean, controllable optical analogs of extended structured (i.e., crystalline) electronic systems. While most realizations to date have used only the fundamental mode in each site, recent advances in structured light - particularly the use of higher-order spatial modes, including those with orbital angular momentum - are enabling richer dynamics and new functionalities. These additional degrees of freedom facilitate the emulation of phenomena ranging from topological band structures and synthetic gauge fields to orbitronics. In this perspective, we discuss how exploiting the internal structure of higher-order modes is reshaping the scope and capabilities of photonic platforms for simulating quantum phenomena.

Figures (4)

• Figure 1: Orbital degrees of freedom in waveguide lattices. a) In a quantum mechanical potential well, modes are classified according to their symmetry. The same can be done in step-index waveguides, where the effective refractive index plays the role of negative energy (i.e., the well is flipped). Due to this analogy, we can label different Hermite-Gauss (HG) modes according to the notation used for atomic orbitals (b). Blue and red color stand for phases with a difference of $\pi$. c) Modes carrying a winding phase front, so-called OAM-modes, are composed of superpositions of HG modes with complex coefficients. d) Coupling between different orbitals can be achieved when their propagation constants $\beta$ match. The propagation constants can be tuned via the refractive index difference $\Delta n$ between two waveguides, or the shape of the waveguides. d) Adapted with permission from Guzman-Silva. Copyrighted by the American Physical Society.
• Figure 2: Phases in the coupling amplitude appear depending on the orientation of the orbitals in the transverse plane. a) The coupling amplitude $J$ of an $s$- to a $p_y$- and back to an $s$-mode gains a $\pi$-phase flip, i.e. a negative sign (top). The coupling of $s$- and OAM-modes depends on the angle between waveguides and the OAM quantum number (bottom). b) The phase in the coupling between two $p_y$-modes depends on the angle between them. It can range from positive coupling, when two $p_y$-modes are aligned along the x-axis (coupling $J_\pi$), to a negative one for alignment along the y-axis (coupling $J_\sigma$). At a certain "magic" angle $\theta_m$, the coupling vanishes completely. c) Coupling between a detuned and lossy $s$-mode waveguide and an elliptical $p$-mode waveguide has been predicted to lead to non-Hermitian states wang_non-hermitian_2023. b) Adapted with permission from invisibility. Copyright 2025 American Chemical Society. c) Adapted with permission from wang_non-hermitian_2023 © Optica Publishing Group.
• Figure 3: Gauge fields induced via higher orbitals or OAM in photonic waveguide lattices. a) In a diamond chain, light with OAM of $|l|=1$ creates a $\pi$-flux, leading to Aharonov-Bohm caging (a return of the intensity to the excited waveguide after a certain propagation distance period), while light with vanishing OAM disperses Joerg_LightSciAppl_2020. b) Similarly, $p_y$-modes in a diamond chain create a flux of $\pi$PhysRevLett.128.256602. c) Elliptical waveguides in a 2D SSH lattice create fluxes that lead to the formation of corner states in higher-order topological insulators Schulz_NatCommun_2022. d) $d$-modes in a 2D lattice give rise to a topological Möbius insulator Jiang_OpticsLetters_23 b) Adapted with permission from PhysRevLett.128.256602. Copyright 2022 by the American Physical Society. d) Adapted with permission from Jiang_OpticsLetters_23. © Optica Publishing Group.
• Figure 4: Higher modes in polariton lattices. a) A zig-zag array of coupled polariton cavities with $p$-modes acts as a Su-Schrieffer-Heeger system. The sketch on the side shows the different layers of an exciton-polariton cavity, a quantum well (QW) in an optical cavity consisting of two dielectric Bragg gratings (DBR). The picture on the bottom shows the light emission of the spectrally isolated and localized topological edge mode St-Jean_NatPhoton_2017. b) Dispersion relation: The dispersion relation of a photon in the cavity is parabolic, while that of an exciton is, in comparison, flat. Due to the coupling between the two particles, the polariton dispersion relation splits into an upper and a lower polariton branch (UPD and LPB, respectively). c) Sketch of how a structured pump beam acts as a repulsive potential for polaritons. Lattices can be constructed such that polaritons populate vortex modes on each lattice site. Alyatkin_SienceAdvances_2024. d) Measured emission (intensity right and phase left) of a polariton vortex lattice. The OAM of the vortex modes arrange themselves in the same way as spins would do in an Ising lattice. Alyatkin_SienceAdvances_2024. a) Reprinted with permission from St-Jean_NatPhoton_2017, Copyright © 2017 Springer Nature. c), d) Copyright © 2024, The American Association for the Advancement of Science.