Generation and stabilization of frequency combs in nonlinear microring resonators: Fundamentals and applications to astronomy

Optical frequency combs arise from the superposition of numerous continuous electromagnetic waves with equidistant frequency spacing (line spacing). In typical frequency comb sources, the phase relationship between the individual lines is fixed, so that in the time domain, a sequence of optical pulses with a well-defined temporal spacing (i.e., the repetition rate) emerges, determined by the line spacing. Beyond their central role in metrology and highprecision spectroscopy, frequency combs are currently becoming increasingly established in astronomy as calibration light sources for spectrographs. Conventional frequency combs generated by mode-locked lasers, however, usually have line spacings that are too small to be resolved by astronomical spectrographs. Microresonators offer an alternative: thanks to their compact dimensions in the micrometer to millimeter range, they can produce line spacings in the gigahertz or terahertz range when pumped by a laser. Silicon nitride (Si3N4)-based microresonators, integrated as ring-shaped waveguides in a silicon dioxide layer on optical chips, have been the focus of the research community for many years. Due to the high Kerr index of Si3N4 in combination with strong mode confinement, Si3N4 microring resonators are particularly well suited for frequency comb generation. This work investigates Si3N4 microring resonators as frequency comb sources in four topics: design and characterization of microring resonators, frequency comb generation in microring resonators, frequency stabilization of the comb, and development of analytical models with investigations related to the thermal behavior of microring resonators. Established methods were applied and combined for the first three topics: the geometrical design parameters were determined based on numerical calculations for 72 resonator variants, which were subsequently fabricated by a contract manufacturer as integrated elements on optical chips. A selection of these resonators was characterized via transmission measurements to validate simulations and determine parameters for modeling frequency comb generation. Practical generation was demonstrated on three resonators with free spectral ranges of 28.4 GHz and 172 GHz and compared with model calculations. To achieve stable soliton frequency combs, simulations considering thermal effects were conducted, from which the required pump-laser detuning rates of 0.013 to 0.069 GHz/µs were derived. To stabilize the comb line spacing, the use of modulated pump-laser light was investigated experimentally and in simulations. Simulations showed that the line spacing can be controlled within a range of 37.5 kHz. For the pump laser driving the microresonator, a frequency-offset locking scheme was implemented to stabilize its wavelength with respect to a reference laser. The reference laser operates at a wavelength of 1560 nm and was stabilized via frequency doubling relative to an atomic rubidium transition detected through saturated absorption spectroscopy. In the fourth topic three analytical models were developed and corresponding practical investigations were carried out: The first model allows calculation of the thermal conductivity of a microring resonator embedded in a three-layer structure of different materials. The second model serves to extract parameters from a pump-probe experiment describing the optical properties of the resonator under the influence of thermal and nonlinear effects. The third model describes the effect of mode interaction in an interferometrically coupled microring resonator as a function of the electrical power applied to a heater integrated into the optical chip.