Winding coupling phase for pseudo-spin-derived topological photonics

Topological phases derived from spin or pseudo-spin typically leverage specific effects like spin-orbit interaction or antiferromagnetism. Here, we propose a flexible theoretical framework capable of designing pseudo-spin-derived topological phases. We reveal that the evanescent coupling between nearby resonators exhibits a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>π</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msup> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> topology characterized by a quantized coupling winding number. By tailoring the coupling winding number in photonic crystals, we propose silicon-on-insulator designs for the spin-valley Hall phase (SVHP), its anomalous variant, the anomalous Hall phase, and anti-helical edge states. Notably, the SVHP is obtained in a non-antiferromagnetic system without the need of time-reversal symmetry breaking, and the anti-helical edge states are designed independently of next-nearest coupling tuning. The results are compatible with conventional fabrication processes, demonstrating the simplicity and versatility of this framework and its potential for applications in spin-valley protected light transport and slow light guiding.