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Updated: Aug 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Constant-Amplitude 2π Phase Modulation from Topological Pole-Zero Winding
1Florida International University, Florida International University, Department of Electrical and Computer Engineering, Miami, Florida 33174, USA and Knight Foundation School of Computing and Information Sciences, Miami, Florida 33174, USA.
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A resonant phase shifter should rotate a complex optical field without changing its magnitude, but loss and coupling usually make resonant phase tuning change the intensity as well. We introduce a pole-zero synthesis rule that produces a full 2π phase winding at a chosen scattering magnitude for a selected matrix element S_{ij}. The rule traces a closed iso-|S_{ij}| contour that encloses a scattering zero and excludes the relevant pole; Cauchy's argument principle fixes the phase winding, and the contour fixes the amplitude. For a single isolated resonance, this contour is an Apollonius circle, giving a closed-form design. We realize the rule either by finite-time complex-frequency waveform excitation of a static resonator or by adiabatic comodulation of detuning with damping or coupling at a real carrier. We also discuss the extra control-dimensionality needed for simultaneous multichannel operation.
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