# Transformation of topological optical states via spiral modulation in fractional-diffraction systems

## TL;DR

This paper introduces a method to manipulate topological optical states in fractional systems using spiral modulation, enabling mode conversion and exploring nonlinear effects, with potential applications in optical topological control.

## Contribution

It presents a novel spiral modulation scheme for topological state manipulation in fractional optical systems, including analytical and simulation analyses of mode conversion mechanisms.

## Key findings

- Supports direct mode conversion with topological-charge difference Δm=1
- Requires intermediary mode for Δm=2 conversion with precise resonance tuning
- Nonlinear effects cause resonance-frequency shifts affecting conversion efficiency

## Abstract

We propose a scheme for manipulations of a variety of topological states in fractional optical systems through spiral modulation of the local refraction index. An analytical approximation, based on a truncated finite-mode system, and direct simulations reveal that the spiral modulation supports direct mutual conversion between eigenmodes with topological-charge difference \Delta m=1, driven by the resonant coupling between the modes and the underlying spiral modulation. The conversion between eigenmodes with \Delta m=2 requires involvement of an intermediary mode and precise tuning of the resonance condition. We further explore the conversion of degenerate modes under the action of azimuthal modulation. Modulated degenerate modes exhibit incomplete conversion, evolving into intermediate states with odd parity symmetry. Finally, we examine nonlinear effects on the spiral-modulation-induced mode conversion, identifying an essential nonlinearity-induced resonance-frequency shift that critically affects the conversion efficiency.