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Microresonator-based Kerr frequency comb (microcomb) generation can potentially revolutionize a variety of applications ranging from telecommunications to optical frequency synthesis. However, phase-locked microcombs have generally had low conversion efficiency limited to a few percent. Here we report experimental results that achieve ~30% conversion efficiency (~200 mW on-chip comb power excluding the pump) in the fiber telecommunication band with broadband mode-locked dark-pulse combs. We present a general analysis on the efficiency which is applicable to any phase-locked microcomb state. The effective coupling condition for the pump as well as the duty cycle of localized time-domain structures play a key role in determining the conversion efficiency. Our observation of high efficiency comb states is relevant for applications such as optical communications which require high power per comb line.
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The model, that is usually called Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs - first observed in 2007, i.e. 20 years after the original formulation of the LLE. - and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton induced broadening phenomena. Combined with the ability to miniaturize and integrate on chip, microresonator based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.
Taking advantage of an extended Lugiato--Lefever equation with third-order dispersion, we numerically show that dark cavity solitons formed in normal dispersion of microresonators are capable of emitting dispersive waves in both normal and anomalous dispersion regions, resembling the behavior of the commonly encountered bright cavity solitons. The generated dispersive waves can be accurately predicted by the dissipative radiation theory. In addition, we demonstrate the stability enhancement of Kerr frequency combs in normal dispersion regime in case the dispersive wave is emitted by dark solitons in presence of third-order dispersion.
Kerr optical frequency combs with multi-gigahertz spacing have previously been demonstrated in chip-scale microresonators, with potential applications in coherent communication, spectroscopy, arbitrary waveform generation, and radio frequency photonic oscillators. In general, the harmonics of a frequency comb are identically polarized in a single microresonator. In this work, we report that one comb in one polarization is generated by an orthogonally polarized soliton comb and two low-noise, orthogonally polarized combs interact with each other and exist simultaneously in a single microresonator. The second comb generation is attributed to the strong cross-phase modulation with the orthogonally polarized soliton comb and the high peak power of the intracavity soliton pulse. Experimental results show that a second frequency comb is excited even when a continuous wave light as a seed-with power as low as 0.1 mW-is input, while its own power level is below the threshold of comb generation. Moreover, the second comb has a concave envelope, which is different from the sech2 envelope of the soliton comb. This is due to the frequency mismatch between the harmonics and the resonant frequency. We also find that the repetition rates of these two combs coincide, although two orthogonal resonant modes are characterized by different free spectral ranges.
We numerically investigate the influence of high-order dispersion on both temporal and spectral characterizations of microresonator-based optical frequency combs. The moment method is utilized to study the temporal dynamics of intracavity solitons. The theoretical and numerical results indicate the temporal shifts are induced by high-odd-order dispersion rather than high-even-order dispersion. The role of high-order dispersion on the frequency comb envelopes is carefully elucidated through analyzing the intracavity Cherenkov radiations. We further demonstrate that the spectra envelope of an ultrabroadband optical frequency comb can be engineered by using dispersion profiles with multiple zero dispersion wavelengths.
We study optical parametric oscillations in Kerr-nonlinear microresonators, revealing an intricate solution space -- parameterized by the pump-to-signal conversion efficiency -- that arises from an interplay of nonlinear processes. Using a three-mode approximation, we derive an efficiency-maximizing relation between pump power and frequency mismatch. To move beyond a three-mode approximation, a necessity for geometries such as integrated microring resonators, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We observe and characterize two nonlinear phenomena linked to parametric oscillations in multi-mode resonators: Mode competition and cross phase modulation-induced modulation instability. Both processes may impact conversion efficiency. Finally, we show how to increase the conversion efficiency by tuning the microresonator loss rates. Our analysis will guide microresonator designs that aim for high conversion efficiency and output power.
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