Topological effects in 2D and 3D systems
Topology is a branch of mathematics focusing on how shapes can change without breaking or tearing. But with the discovery of the quantum Hall effect, scientists found that certain materials, called topological insulators, could also be described using a concept from topology. In these materials, a special property, known as a topological invariant, characterizes the existence of robust surface states that are immune to defects and disorder in the system.
Recently, these protected edge states were also found in photonics, where they promise robust light transfer, better data transmission, and improved optical devices. Moreover, photonic model systems can mimic the behavior of electrons in topological condensed matter. Probing into the fundamental properties of topological phases, we want to uncover insights into the collective behavior of electrons and the emergence of exotic quantum states.
Combining topology with 3D microprinting technology allows for the creation of quantum simulators, which are tiny devices that can be used for fundamental research. It also offers the unique opportunity to translate topological effects into practical applications due to the microscopic size and fast and easy fabrication of 3D microprinted systems.
Waveguide systems
Fig. 1: Fabrication of infiltrated waveguide arrays [1]. (a) The inverse of the waveguide array is 3D microprinted. After development, the sample contains empty channels arranged in a lattice structure: (b) Scanning electron micrograph from top (i) and side (ii) of typical structures. In a second step, the empty channels are infiltrated with a photoresist with a slightly higher refractive index (c). In the microscope image shown here, the unfilled channels appear dark, and the infiltrated channels appear light. (d) Typical measurement setup.
Model systems of photonic waveguide arrays are ideally suited for quantum simulation in two-dimensional systems, since the description of light propagation in such systems (the paraxial Helmholtz equation) is mathematically equivalent to that of electron motion in 2D materials (the Schrödinger equation). We developed a new platform for evanescently coupled waveguide arrays: The inverse of the desired waveguide array is 3D microprinted. The cavities are then infiltrated with another polymer with a slightly higher refractive index to create waveguides. This infiltration step allows great flexibility in the design of the waveguide arrays compared to existing systems. For example, the refractive index of the waveguides can be adjusted over a wide range and materials with Kerr nonlinearity can also be integrated into the waveguides. Another advantage is that the propagation axes of the waveguides can be shaped at will – for example, helically curved waveguides can be fabricated this way, and all waveguides in the lattice can be shaped individually.
Current projects
Fig. 2: Effects in waveguide lattices: a) Topological edge mode of light moving around/through a time-dependent defect. b) Donut-shaped waveguides transmitting orbital angular momentum. c) Selectively infiltrated waveguides [2] for researching spatially modulated nonlinearity.
Currently, we are exploring the effects of higher waveguide modes in such waveguide lattices. We want to determine how we can make use of higher modes and orbital angular momentum of light for switchable and more accurate quantum simulation.
We are also working on the integration of nonlinear materials in 3D photonic structures. High optical nonlinearities in photonic structures are important e.g. for optical neural networks, all-optical switching devices, and interesting new physics in metamaterials. Specific research questions include soliton-based topological states: Solion collisions in topological Thouless pumps and interaction-induced topological phase transitions in lattices with spatially modulated nonlinearity.
Photonic (quasi-)crystals
While (linear) 2D topological systems have already been studied in detail, relatively little is known about optical topological 3D systems. Until now, this was mainly due to limitations in the manufacturing possibilities. The technology of 3D microprinting opens up new opportunities for the investigation of complex structures in a topological context.
We also use dimensional extension in 1D photonic multilayer structures to make higher-dimensional topological physics accessible within a simple photonic platform. Such systems also offer the unique possibility to apply “unphysical” inhomogeneous magnetic fields or boundary conditions.
Photonic quantum computing
Together with the DFKI we are currently exploring how to alter quantum computing algorithms such that they can be usefully implemented in photonic computing chips.
Selected references
[1] J. Schulz, S. Vaidya, and C. Jörg, Topological photonics in 3D micro-printed systems. APL Photonics 6, 080901 (2021).
[2] Bachelor thesis Alaa Bayazeed, TU Kaiserslautern 2020.
[3] C. Jörg+, S. Vaidya+, J. Noh, A. Cerjan, S. Augustine, G. von Freymann, and M. C. Rechtsman, Observation of the Splitting of Charge-2 (Quadratic) Weyl Points in Near-Infrared Photonic Crystals. Laser & Photonics Reviews 16, 2100452 (2022).
[4] S. Vaidya+, C. Jörg+, K. Linn, M. Goh, M. C. Rechtsman, Reentrant delocalization transition in one-dimensional photonic quasicrystals. Phys. Rev. Research 5, 033170 (2023).