The three-wave equations that describe broadband microresonators with a nearly quartic dispersion are briefly derived. They are then applied to describe recent experimental results in which interleaved frequency combs are generated, from which a single broadband frequency comb can be generated under the right conditions [1,2].
1. G. Moille, et al., “Kerr-induced synchronization of a cavity soliton to an optical reference,” Nature 624, 267–274 (14 Dec. 2023) [doi: 10.1038/s41586-023-06730-0].
2. G. Moille, et al., “Ultra-broadband Kerr microcomb through soliton spectral translation,” Nat. Comm. 12, 7275 (2021) [doi: 10.1038/s4146-021-27469-0].
We present a terahertz-carrier frequency comb based on Kerr-Induced Synchronization (KIS) of an Optical Frequency Comb (OFC), wherein a commercially available C-band laser harnesses an OFC tooth and captures the repetition rate (frep) of the OFC. The linear relationship between the C-band laser modulation and the OFC frep modulation enables direct transfer of the C-band laser frequency to the OFC frep. In addition, the large KIS effect bandwidth facilitates frep tuning over a wide range of frequencies. This work addresses the THz gap by providing a direct path for millimeter wave generation, utilizing CMOS-compatible fabrication techniques and off-the-shelf components.
We show that in the Kerr-Induced Synchronization (KIS) regime, an external reference pump laser allows for the control of the opposite (in frequency) Dispersive Wave (DW) power and frequency, through self-balancing of the cavity soliton. We report an increase of more than 20~dB of the DW of an octave-spanning comb at 780 nm, with a reference pump in the telecom C-band, while tuning of the DW over three comb teeth. Our work paves the way for significant improvement of the carrier-envelope offset frequency detection of octave-spanning combs.
We demonstrate that a dissipative Kerr soliton comb tooth can be captured by another injected pump laser, resulting in Kerr induced synchronization. This regime is highly significant for metrology applications, where the soliton can passively lock onto a reference clock laser. The dynamics of the system also enable other forms of locking, where the comb tooth is captured at a fixed offset from the reference laser, entering the syntonization regime. Similar to breather entrainment, we establish that the syntonization frequency offset correlates with the soliton's repetition rate.
We present a study on the accuracy of three neural network architectures, namely fully-connected neural networks, recurrent neural networks, and attention-based neural networks, in predicting the coupling response of broadband microresonator frequency combs. These frequency combs are crucial for technologies like optical atomic clocks. Optimizing their spectral features, especially the dispersion in coupling to an access waveguide, can be computationally demanding due to the large number of parameters and wide spectral bandwidths involved. To address this challenge, we employ machine learning algorithms to estimate the coupling response at wavelengths not present in the input training data. Our findings demonstrate that when trained with data sets encompassing the upper and lower limits of each design feature, attention mechanisms achieve over 90% accuracy in predicting the coupling rate for spectral ranges six times wider than those used in training. This significantly reduces the computational burden for numerical optimization in ring resonator design, potentially leading to a six-fold reduction in compute time. Moreover, devices with strong correlations between design features and performance metrics may experience even greater acceleration.
We present the demonstration of elastic collisions between dissipative Kerr solitons at different repetition rates in an integrated microresonator. Their periodic collision results in a periodic inter-exchange of their repetition rate. We observe this phenomenon experimentally, and support it with numerical simulations, with each comb tooth is impacted by the periodic soliton collision, producing an interwoven frequency comb.
We present the creation of a two-dimensional frequency comb in a single integrated microring resonator through its dual pumping. We demonstrate experimentally and theoretically that dual-pumping allows for the creation of a multi-color soliton with a single group rotation velocity yet multiple phase rotation velocities, yielding multiple soliton eigenfrequencies (i.e. colors). We show that, thanks to the material's nonlinearity, its eigenfrequencies can cascade through four-wave mixing, creating a comb. Because this dimension is orthogonal to the azimuthal mode number dimension, the extracted frequency comb is ultimately a two-dimensional one.
Multi-mode optical microcavities have enabled the emergence of compact optical sources such as parametric oscillators and nonlinear combs for quantum information and metrology. Efficient nonlinear interactions take place, owing to a combination of large Q factor, small modal volume and large material index. The control of the frequency spacing of the resonances is also a critical aspect.
Here we demonstrate an effective harmonic potential for photons owning to the concept of bichromatic lattice in a photonic crystal structure. Wide gap semiconductor material, i.e. GaInP, is used here to prevent any detrimental non-linear absorption such as two photons.
The experimental evidence is given through the statistical analysis of the frequency spacing of high-Q resonances over 68 cavities.
For each structure, the complex reflection spectra is measured using Optical Coherent Tomography (OCT) with a resolution of 20 MHz.
The dispersion of the resonator is extracted through a polynomial fit. It appears to be small and more importantly crosses zero as the radius of the holes is changed.
Moreover, each of these resonators have many modes, typically four, with loaded Q factor in the 10^5 to 7x10^5 range and intrinsic Q factor well above one million.
Equi-spaced resonances in a very compact structure should lead to ultra-strong nonlinear interactions, particularly resonantly enhanced Four Wave Mixing and parametric oscillation.
We briefly review the technology of advanced nonlinear resonators for all-optical gating with a specific focus on the application of high-performance signal sampling and on the properties of III-V semiconductor photonic crystals
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