Abstract

Phase retrieval is the algorithmic process of recovering the phase of a signal from more accessible quantities, such as iterative transformations of its magnitude response. The phase often reveals far more about the underlying system than the magnitude alone, yet conventional retrieval methods rely on software approaches that use computationally expensive iterative algorithms or hardware solutions that are sensitive to manufacturing variations.  In this dissertation, we show that the phase can be retrieved via a Hilbert transform of the magnitude response, bypassing iteration entirely, provided that the underlying system structure satisfies the minimum-phase condition. We apply this to three classes of problems in integrated photonics: wavelength metrology, Fourier transform spectroscopy, and in situ calibration of unitary matrices. A central result is that when a photonic circuit is designed so that more optical power is routed through its shortest delay path than through any other path, the phase of its transfer function is uniquely determined by its magnitude, a condition known as minimum phase. This relationship, enforced by the Kramers-Kronig relations, eliminates the need for hardware phase-measurement techniques such as 90-degree hybrids, which are sensitive to manufacturing variations and consume significant chip area. We derive and experimentally validate the minimum-phase boundary condition for asymmetric Mach-Zehnder interferometers and demonstrate a sparse multi-$\Delta L$ wavemeter that achieves sub-picometer wavelength resolution in a single-stream circuit, without the signal-to-noise penalties of conventional narrowband filtering and dispersive-element architectures. Building on this, we show that the same minimum-phase framework enables complex-valued Fourier transform spectroscopy, recovering both the amplitude and phase of arbitrary optical spectra through interferogram alignment via complex multiplication, a lossless and interpolation-free alternative to the Mertz phase correction. We further apply delay engineering to the in situ calibration of unitary matrices in MZI mesh architectures, demonstrating single-shot extraction of all $2\times2$ matrix elements with $O(n)$ complexity and experimentally realizing Bar and Cross states with extinction ratios of 35~dB and 22~dB, respectively. Finally, we characterize the optical-electrical-optical (OEO) conversion circuit as a candidate nonlinear activation function for neuromorphic photonics. We perform large- and small-signal analyses of a micro-ring modulator driven by photogenerated current from a balanced photodetector pair, and introduce a total harmonic distortion minimization procedure to identify the optimal quiescent operating point across the full two-dimensional current bias-wavelength space. Small-signal electro-optic characterization shows poor RF performance, with RF degradation near \(\sim\) 50 MHz attributed to parasitic capacitance from an unconnected pad, which can be minimized by better pad design. These results establish the minimum-phase framework as a broadly applicable design paradigm for scalable, phase-aware photonic integrated systems.

Publication Date

7-12-2026

Document Type

Dissertation

Student Type

Graduate

Degree Name

Electrical and Computer Engineering (Ph.D)

College

Kate Gleason College of Engineering

Advisor

Stefan Preble

Advisor/Committee Member

Dorin Patru

Advisor/Committee Member

Cory Merkel

Comments

This dissertation has been embargoed. The full-text will be available on or around 7/12/2027.

Campus

RIT – Main Campus

Download

Share

COinS