Shows Valley Photonic Crystals Co-Optimise Band Gap and Chern Number Using PSO

Researchers are tackling the challenge of creating robust on-chip optical circuits that function reliably despite manufacturing flaws and complex designs. Devansh Satra from IIT Bombay, alongside Abhishek Kumar from the Jawaharlal Nehru Centre for Advanced Scientific Research, and Anshuman Kumar from IIT Bombay, present a new design framework for valley photonic crystals (VPCs) that simultaneously optimises both bandwidth and topological protection. Their work, detailed in a recent paper, introduces a modified particle-swarm optimisation technique to engineer VPCs with a substantial band gap and a high valley Chern number, paving the way for more stable and efficient light-based integrated circuits. This innovative approach consolidates topology-aware geometry optimisation, promising a significant advance in robust on-chip optical guiding.

Researchers addressed the critical need for stable wave propagation in integrated photonic circuits, particularly in the presence of fabrication imperfections, tight bends, and dense routing.

The team achieved this by leveraging VPCs, which engineer guided modes confined to domain walls, reducing backreflection at corners. This breakthrough reveals a modified particle-swarm optimization (PSO) algorithm used to navigate a complex design space while evaluating the photonic band structure via plane-wave expansion and topological characteristics using a gauge-invariant lattice discretization to compute the Berry curvature.
The optimization process focuses on simultaneously maximizing bandwidth and valley-protected transport, crucial for efficient device operation. Experiments show the optimized structures exhibit a clean valley-Hall gap with edge bands traversing the gap, demonstrating high interface transmission in full-wave simulations.

The study establishes that topology-aware geometry optimization can significantly enhance the performance of on-chip photonic devices. Specifically, the research consolidates a method for creating robust waveguides, splitters, and multiplexers compatible with standard dielectric slab processes. These results open possibilities for footprint reduction in photonic systems without sacrificing link margin, offering a pathway to denser and more reliable integrated circuits.

The work demonstrates wide-bandgap waveguides with single-mode, low bend loss, and confined transport validated through FDTD simulations using Tidy3D. Researchers introduced a topological figure of merit that jointly optimizes the bulk bandgap with valley topological characteristics, exploring a broader design space than previously investigated.

The PSO algorithm effectively identifies optimal configurations within a six-dimensional parameter space defined by the geometry of inversion-broken unit cells. This approach addresses the challenge of balancing usable bandgap and valley-protected transport, crucial for practical applications and enabling a new generation of compact, high-performance photonic interconnects.

Optimisation of valley crystal topology using particle-swarm optimisation and plane-wave expansion reveals novel band structures

Scientists developed a novel design framework to co-optimise the bulk band gap and valley Chern number in valley crystals (VPCs), enabling robust on-chip light guiding. The research team employed a modified particle-swarm optimisation (PSO) technique, a gradient-free method, to navigate complex, multi-dimensional design spaces and identify optimal VPC configurations.

This approach overcomes limitations in existing methods that struggle with broad parameter exploration. To characterise the VPCs, the study utilised plane-wave expansion (PWE) to compute the bulk band structure of the inversion-broken unit cell, focusing on TE-like modes within a 2D photonic crystal description.

Researchers extracted features relevant to the K and K’ points of the hexagonal Brillouin zone, ensuring consistency throughout the manuscript, with detailed derivations and convergence tests available in supplementary information. The team then quantified valley topology by computing Berry curvature on a discrete k-mesh using a gauge-invariant lattice formulation, avoiding ambiguities and ensuring numerical stability during large-scale parameter sweeps.

The optimisation process involved searching a six-parameter unit-cell design, defined by variables including normalised feature sizes, in-plane rotations, and polygon side counts. Continuous variables were bounded relative to the lattice constant, while angles were folded to maintain fundamental symmetry, and discrete values were selected from a fixed set of regular polygons.

Each particle evaluation consisted of unit-cell construction, PWE band calculations, gauge-invariant Berry curvature and valley Chern number determination, and objective scoring, utilising a topological figure of merit, T(x) = ∆f/f0² |Cv|, where ∆f represents the minimum bulk direct gap, f0 is the mid-gap frequency, and Cv is the valley Chern number. Finally, the optimised structures underwent validation using full-wave simulations with Tidy3D, specifically examining defect-type domain-wall interfaces for fabrication simplicity and consistently high transmission, demonstrating wide-bandgap waveguides with single-mode, low bend loss, and confined transport. This methodology consolidates topology-aware geometry optimisation, paving the way for practical applications of VPCs in future on-chip technologies and revealing the importance of employing such figures of merit for photonic structure optimisation.

Co-optimisation of photonic band gaps and valley Chern numbers in valley photonic crystals enables robust valley-selective unidirectional propagation

Scientists have developed a design framework to co-optimise the photonic bulk band gap and valley Chern number in valley photonic crystals (VPCs) using a modified particle-swarm optimization (PSO) technique. The research focuses on engineering guided modes confined to domain walls, reducing backreflection around corners in on-chip integrated circuits.

Experiments revealed that optimized structures exhibit a clean valley-Hall gap with edge bands traversing it, demonstrating high interface transmission in full-wave simulations. The team measured the quantum geometric tensor (QGT) to analyse Bloch modes, calculating Berry curvature and the quantum metric to understand the geometric properties of the VPCs.

Results demonstrate that inversion-symmetry breaking generates sharply peaked Berry curvature at the K and K’ valleys, reshaping the metric and influencing device robustness. Specifically, the study quantified the valley Chern number, finding it is not strictly quantized to ±1/2 in practical dielectric slabs due to delocalization of berry curvature.

Tests prove that even with non-quantized valley Chern numbers, strong protection against bend-induced backscattering and lithographic disorders is achievable in a regime termed “weak topology”. Measurements confirm that reciprocal valley-Hall interface modes can exhibit backscattering when disorder induces intervalley coupling, highlighting the importance of careful design.

The breakthrough delivers a topological figure of merit that simultaneously maximizes usable bandgap and valley-protected transport, exploring a six-dimensional unit-cell parameterization with both continuous and discrete variables. The optimized structures were validated through full-wave simulations, benchmarking domain-wall waveguides across straight and sharp-bend routes.

This work consolidates topology-aware geometry optimization for robust on-chip guiding, promising footprint reduction without sacrificing link margin and retaining compatibility with standard dielectric slab processes. The research provides a systematic approach to enhancing the topological performance of VPCs by exploring a broader design space than previously investigated.

Balancing Bandgap and Valley Topology for Robust Photonic Waveguiding offers new possibilities

Scientists have developed a design framework for valley photonic crystals that addresses the challenge of robust on-chip light guiding, even with fabrication imperfections and complex routing. This research introduces a multiobjective inverse-design methodology, explicitly navigating the trade-off between bandwidth and valley topology.

By jointly evaluating the bandgap and a valley topology indicator, the team generated a Pareto frontier that visualises optimisable design parameters within specific geometric constraints. The optimised structures demonstrate a clean valley-Hall gap with edge bands and high interface transmission in simulations, exceeding the performance of several comparable topological photonic-crystal waveguides detailed in existing literature.

The findings suggest that increasing the bandgap can delocalise Berry curvature, potentially degrading valley-Chern numbers, and highlight the importance of balanced designs retaining strong valley character. The authors acknowledge limitations related to disorder robustness, slab radiation loss, and manufacturability, suggesting these could be incorporated into future work. Further research could extend this approach to optimise performance objectives, topological descriptors, and practical limitations simultaneously, moving valley topological photonics towards a more established engineering discipline.