Constant-Amplitude $2\pi$ Phase Modulation from Topological Pole--Zero Winding

TL;DR

This paper introduces a topological method to achieve a full 2π phase shift with constant amplitude in resonant devices by winding a scattering zero in the complex-frequency plane, avoiding amplitude variation.

Contribution

A novel topological synthesis technique that guarantees constant amplitude and full phase swing by zero winding, applicable to integrated photonic and quantum devices.

Findings

Achieves full 2π phase shift at constant scattering magnitude.

Suppresses amplitude modulation to prevent AM--PM conversion.

Applicable to integrated resonant modulators and quantum interferometers.

Abstract

Resonant phase shifters inevitably mix phase and amplitude. We present a topological synthesis that guarantees a full $2\pi$ phase swing at a prescribed constant scattering magnitude $|S_{ij}|=C$ by winding a scattering zero around the operating point in the complex-frequency plane while avoiding pole windings. We realize this either by complex-frequency waveform excitation on an iso-$|S_{ij}|$ (Apollonius) loop or by adiabatic co-modulation of detuning and decay at fixed carrier, suppressing AM--PM conversion and quantizing $\Delta\phi$ by the Argument Principle. The approach targets integrated resonant modulators, programmable photonic circuits, and quantum/beam-steering interferometers that require amplitude-flat phase shifts.