Octave-wide phase-matched four-wave mixing in dispersion-engineered crystalline microresonators

Abstract

In this Letter, we report phase-matched four-wave mixing separated by over one-octave in a dispersion engineered crystalline microresonator. Experimental and numerical results presented here confirm that primary sidebands were generated with a frequency shift up to 140 THz, and that secondary sidebands formed a localized comb structure, known as a clustered comb in the vicinity of the primary sidebands. A theoretical analysis of the phase-matching condition validated our experimental observations, and our results good agree well with numerical simulations. These results offer the potential to realize a frequency tunable comb cluster generator operating from 1 µm to mid-infrared wavelengths with a single and compact device.Phase-matched four-wave mixing (FWM) in a whispering gallery mode (WGM) microresonator driven by a continuous wave (CW) laser have been studied for decades [1]. In particular, a microresonator frequency comb (Kerr comb) realized via a cascade FWM process makes it possible to achieve broadband optical frequency comb sources characterized as having high repetition rates, compactness and low-energy consumption [2]. They provide fascinating applications including precise spectroscopy [3] and coherent data transmission [4]. A Kerr comb, and particularly a dissipative Kerr soliton (DKS), which is a stable low noise state, features a coherent broad comb spectrum with a smooth envelope [5]. However, spectral broadening over one octave remains a challenge mainly because of the limitation imposed by group velocity dispersion (GVD). Spectral broadening utilizing dispersion engineering has been achieved with Cherenkov radiation, which can be understood in terms of the coherent dispersive wave in the frequency domain emitted from a soliton propagating along a resonator [6]. A dispersive wave induces asymmetrical spectral profiles and occurs at the point where a simple phase-matching condition is satisfied, and it is determined by the signs and values of higher-order (i.e., third-, fourth-and fifthorder) dispersion parameters.Higher-order dispersion plays important roles not only as regards a Kerr soliton in an anomalous GVD regime, but also in a weak normal GVD regime. Since a normal dispersion usually does not allow modulation instability (MI) near the pump, phase-matched FWM may be considered to occur only in an anomalous dispersion resonator. However, higher-order dispersion, particularly even orders of dispersion, enables a resonant MI process, called clustered frequency combs, to occur far from the pump mode [7][8][9]. Clustered combs, characterized by FWM generation with parametric sidebands that have a * takasumi@elec.keio.ac.jp large-frequency shift, have been reported using an MgF 2 microresonator [7,9] and silica microtoroids [8]. The fact that clustered combs have the potential to utilize microcomb source emitting in the 1.0 to 3.5 µm wavelength region with just a near-infrared pump indicates interesting potential applications, for example laser processing and optical communication. In particular,...

Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics

“…This is in contrast to other wide-band nonlinear processes, e.g., nanophotonic SHG/THG, which have been extensively reported [12][13][14][15][16][17][18] . Recently, widely separated OPO has been achieved in whispering-gallery mode (WGM) platforms with larger footprints, including crystalline MgF 2 microcavities [19][20][21] and SiO 2 microtoroids 15 , but the threshold powers are relatively large and the spectra of the OPO output have been restricted to the infrared.…”

“…However, the above design principles do not guarantee that the targeted wide-band OPO process will occur. Critically, the targeted process also has to win over all other competing processes that are matched in phase and frequency, including OPO in the pump band 28,29 , clustered frequency combs in the signal and idler bands 15,20,30,31 , and other nonlinear processes (e.g., stimulated Raman scattering 19 and thirdharmonic generation 15 ). For example, recent work reporting telecom-to-visible spectral translation via stimulated dFWM did not exhibit widely-separated OPO, because without the seed telecom light, close-to-pump OPO processes dominate 28 .…”

Stretching the spectra of Kerr frequency combs with self-adaptive boundary silicon waveguides

“…14 and is thus used hereafter as the reference case. The primary comb lines 12,13,15 that are generated in the early stage of the comb generation process provide information that is useful for evaluating the bandwidth of parametric process; [24][25][26] it is also plotted for point 3 at the bottom of Fig. 1(d).…”

“…It is thus very interesting to reduce and engineer the dispersion coefficient D globally while keeping the other parameters fixed (γ, P in , etc.). [22][23][24][25][26] This matter is discussed in the next section of the article.…”

“…Consequently, addressing the problem of the spectral bandwidth of microcombs in silicon waveguides is an important point. Broadband phase-matching was shown based on the optimization of high order dispersion terms, e.g., by relying on fourth-order dispersive waveguides, [22][23][24][25][26] or by implementing slightly etched rib geometries. 6 Yet, the proposed solutions require complex fabrication processes, with deposition of different materials or a tight control of the rib and slab thicknesses, respectively.…”