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 $2\pi$ 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.

Close

PrevNext

View figure in article

• Coherent control
• Photonics
• Topological effects in photonic systems
• Real & complex analysis