QSI PhD Defense: Pradyoth Shandilya

TITLE:  Soliton Dynamics in Multi-Pumped Microresonators

ABSTRACT:  Optical frequency combs (OFCs) are indispensable tools in modern metrology, acting as co-herent bridges between high optical frequencies and lower microwave frequencies. This capability enables precise optical frequency measurements and underpins a range of applications, including high-resolution spectroscopy, low-noise microwave generation, and precision time-keeping. Early OFC implementations relied on bulky mode-locked lasers, which limited their use to laboratory environments due to their size and complexity. The drive for compact, power-efficient, and cost-effective solutions has brought microresonator-based OFCs to the forefront. These chip-scale devices generate dissipative Kerr solitons (DKSs) in dielectric ring resonators exhibiting anomalous group-velocity dispersion and third-order (Kerr) nonlinearity. The periodic extraction of the DKS results in an infinite train of identical pulses, producing a stable and broad frequency comb. For metrology applications, an OFC must have both of its key degrees of freedom, the repetition rate and the carrier-envelope-offset (CEO) frequency, precisely stabilized. The most widely used technique for detecting the CEO frequency is f -2f interferometry, which requires the OFC to span at least an octave. Thus, achieving octave-spanning, low-noise OFCs in microresonators remains a central research objective.

A promising recent development in this domain is the use of multi-pumped microres-
onators, where two or more pump lasers are used simultaneously. This approach has shown
great potential for generating octave-spanning combs and has revealed intriguing soliton dy-
namics. Our experimental collaborators observed the formation of multi-color solitons whose
corresponding OFCs consist of interleaved sub-combs, each sharing the same repetition rate.
Under certain conditions, the interleaving collapses into a single comb locked to the two pump
frequencies, a phenomenon termed Kerr-induced synchronization (KIS). While prior studies
modeled these behaviors using the multi-pumped Lugiato-Lefever equation (MLLE) and suc-
cessfully matched experimental results, the MLLE offered limited insight into the underlying
intracavity dynamics.

In this dissertation, we introduce a new theoretical framework consisting of a set of coupled
mode equations termed the three-wave equations, which accurately capture the formation and
behavior of multi-color solitons in microresonators. We demonstrate that these equations not
only reproduce the results of the MLLE but also support stationary solutions. This crucial fea-
ture allows us to perform a linear stability analysis of multi-color solitons, which was previously
infeasible using the MLLE. We then investigate soliton dynamics in the KIS regime. Using a
combination of linear stability analysis, Langevin equations, and Monte Carlo simulations, we
show that KIS significantly mitigates the impact of thermo-refractive noise (TRN), which is a
major source of noise in microresonator-based OFCs. We further extend our three-wave model to describe a novel class of solitons known as parametrically driven cavity solitons (PDCSs). Unlike traditional DKSs, which are primarily driven by a single pump laser, PDCSs emerge from the nonlinear parametric interactions between two pump lasers. The resulting frequency comb lies in the spectral region between the two pump frequencies. We demonstrate that the three-wave model accurately captures the formation and dynamics of these PDCSs. We also explore synchronization mechanisms for PDCSs using additional pump lasers, either directly or via nonlinear parametric interactions. We conduct a detailed analysis of the parameter space governing multi-color solitons, identifying regions of stability and instability. Finally, we study the soliton self-balancing effect that enhances high-frequency dispersive wave power when the DKS is synchronized with a reference laser at the low-frequency dispersive wave, enabling simplified f -2f self-referencing architectures. 

Together, the work presented here establishes a comprehensive theoretical framework for soliton dynamics in multi-pumped microresonators, with the ultimate goal of guiding the development of next-generation OFC systems.