# Spectral Broadening in a Continuously Pumped Singly Resonant Second-Harmonic Cavity
## 1 Introduction  
The increasing demand of metrological and high-resolution spectroscopic measurements drives optical frequency combs (OFCs) synthesizers to be more and more performing in terms of pump power levels, wavelength ranges and chip-scale integration [1, 2]. In particular, OFCs act as a frequency ruler and allow to measure optical frequencies with radio frequency accuracy [3, 4]. A traditional way to generate OFCs is femtosecond mode-locked lasers, their development and applications having been awarded with the 2005 Nobel Prize in physics to [PERSON] and [PERSON] [5, 6]. Soon thereafter, in 2007, OFCs were demonstrated in microresonators pumped by a continuous-wave (cw) laser, exploiting the third-order nonlinear susceptibility \(\chi^{(3)}\), in so called Kerr combs [7, 8]. Recent theoretical studies and experimental investigations have demonstrated frequency comb generation also in quadratic nonlinear optical cavities, realizing quadratic frequency combs [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. These sources provide an interesting alternative to traditional comb generation techniques. They offer numerous advantages in terms of low pump power requirements, spectral versatility, and potential for miniaturization of the device [17, 18, 19, 20, 21, 22, 23]. Interestingly, they can generate simultaneous combs in different spectral ranges. However, so far, the observed local spectral broadening has been limited.  
A critical point is to extend the spectra of quadratic OFCs to meet the requirements of frequency metrology, molecular spectroscopy, and astronomical applications. Several methods have been developed to expand traditional OFCs to wider spectral regions via spectral broadening in optical fibers [24; 25], difference frequency generation schemes [26], and optical parametric oscillators (OPOs) [27; 28] and amplifiers [29]. Interestingly, spectral broadening was recently observed in a cw pumped OPO with an additional intracavity crystal, intentionally phase-mismatched for the second-harmonic process [30]. However, the possibility of direct broadband multifrequency emission in a second-order nonlinear cavity, shown here, provides important advantages in terms of device simplicity, size, and efficiency, which are worth exploring. Our system is furthermore attractive, in a long-term perspective, for the miniaturization of quadratic comb synthesizers through the chip-scale realization of photonic circuits [31].  
In this work, we present a novel mechanism of spectral broadening of quadratic frequency combs carried out directly in a continuous-wave pumped singly resonant second-harmonic cavity. Most significantly, we observe multifrequency parametric oscillations distant up to 50 nm from the pump wavelength, and a broad frequency emission intermediate between the pump and the second harmonic. The observed spectral dynamics of the quadratic OFC generation is explained by sideband generation through higher-order modulational instability (MI), induced by the cavity boundary conditions [32]. In the following, we report on the experimental observation of new unexplored regimes in a continuously pumped singly resonant second-harmonic cavity and discuss the results.