# Spectral Broadening in a Continuously Pumped Singly Resonant Second-Harmonic Cavity
## 3 Experimental Results and Discussion
Hereafter, we focus our investigations on the maximum achievable wavelength broadening for high \(\Delta^{c}\) values, i.e., in the region where the pump laser is less blue detuned (Figure 4). We report spectral broadening for pump powers up to 6 W. For 0.3 W, 0.6 W,and 1 W, the acquired spectra correspond to \(\Delta^{c}\) values of 9, 15, and 30 MHz, respectively. For larger powers, we used a thermally induced self-locking of the optical cavity [40], and the \(\Delta^{c}\) values are, therefore, not measured exactly. Increasing the input power, the parametric sidebands arising far from the pump evolve into \"clustered\" optical frequency combs, and at the maximum power available, they extend over a wavelength range spanning up to 100 nm. Figure 4: Optical spectral power around the fundamental mode for 0.3 W, 0.6 W, 1 W, 4 W, 4.7 W, and 6 W of input power. Dashed lines show predicted sideband positions. Figure 3: Ikeda map simulation with \(P_{in}=2\) W and \(\delta_{1}=-0.0392\) showing comb generation similar to the pink panel in Figure 2. Panels show fundamental (**left**) and second harmonic spectra (**right**). The position of these sidebands can be estimated from the phase-matching condition \(\delta_{1}-(K_{1}^{\prime\prime}L/2)\Omega^{2}=m\pi\), where we neglect nonlinear phase shifts. We find that the sideband positions are approximately as follows:  
\[\Omega_{m}\approx\sqrt{\frac{2}{K_{1}^{\prime\prime}L}(\delta_{1}+m\pi)},\qquad m =0,1,2,\ldots \tag{4}\]  
with the pump detuning \(\delta_{1}\approx 0\) and where the order \(m=0\) corresponds to the ordinary MI. The predicted positions of the \(m=[1,2,3,4]\) sidebands are shown as dashed lines in Figure 4. The position of the first higher-order \(m=1\) sideband is approximately 6.7 THz, which is in good agreement with the measured frequency shift. Increasing the pump power leads to the generation of additional sidebands with even larger frequency shifts that approximately match with the higher-order positions of the model. This is a strong indication that the sidebands originate from boundary conditions induced MI. Sidebands with smaller frequency shifts are also observed at higher pump powers, but these intermediate sidebands are neither predicted by Equation (4) nor observed in the Ikeda map simulations. Furthermore, we observe that various nonlinear cascaded processes lead to wavelength emission that extends not just around the pump but also around 840 nm, a spectral range not previously observed. In Figure 5, we report spectral measurements in the maximum wavelength range of the optical spectrum analyzer, together with the radio-frequency (RF) spectrum of the pump frequency recorded at 6 W of input power. The RF spectrum reveals a frequency comb structure with an adjacent peak separation close to 501 MHz, corresponding to the FSR of the cavity. Additional processes can occur since the QPM grating phase-matches not only the primary SHG process, but also other combinations of waves. For example, using the Sellmeier equation for LiNbO3, we find the possibility of having additional sum-frequency generation and OPO processes [12]. In fact, the blue side of the SH supports nondegenerate OPO. Any wavelength \(\lambda_{3}<532\) nm will satisfy the energy conservation  
Figure 2:0 Measured wavelength emission in the maximum range of the optical spectrum analyzer with 6 W input power and in inset the radio frequency spectrum. and phase-matching condition \(k_{3}-k_{1}-k_{2}+k_{Q}=0\) (with \(k_{i}=2\pi/\lambda_{i}\), \(i=1,2,3\) and \(k_{Q}=2\pi/\Lambda\)), for some combination of frequencies. Additional three-wave mixing processes can moreover be phase-matched by multiple order wavevectors of the QPM grating. Unfortunately, the dynamics of these combs are outside the range of applicability of current models [13; 15; 41]. Their numerical simulation would require the use of a single envelope equation model or the development of a new multi-envelope Ikeda map model that is beyond the scope of the current investigation and will be the subject of upcoming works.