IŶvestigatioŶ of Mode CoupliŶg iŶ Noƌŵal DispeƌsioŶ SiliĐoŶ Nitƌide MiĐƌoƌesoŶatoƌs foƌ Keƌƌ FƌeƋueŶĐy Coŵď GeŶeƌatioŶ YANG LIU 1 , YI XUAN 1,2 , XIAOXIAO XUE 1 , PEI -HSUN WANG 1 , STEVEN CHEN 1 , ANDREW J. METCALF 1 , J IAN WANG 1,2 , DANIEL E. LEAIRD 1 , MINGHAO QI 1,2 , AND ANDREW M. WEINER 1,2* 1 School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035 2 Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA *Corresponding author: amw@purdue.edu Kerr frequency combs generated from microresonators are the subject of intense study. Most research employs microresonators with anomalous dispersion, for which modulation instability is believed to play a key role in initiation of the comb. Comb generation in normal dispersion microresonators has also been reported but is less well understood. Here we report a detailed investigation of few-moded, normal dispersion silicon nitride microresonators, showing that mode coupling can strongly modify the local dispersion, even changing its sign. We demonstrate a link between mode coupling and initiation of comb generation by showing experimentally, for the first time to our knowledge, pinning of one of the initial comb sidebands near a mode crossing frequency. Associated with this route to comb formation, we observe direct generation of coherent, bandwidth-limited pulses at repetition rates down to 75 GHz, without the need to first pass through a chaotic state. Recently high quality factor (Q) microresonators have been intensively investigated for optical comb generation. Both whispering gallery mode resonators employing tapered fiber coupling and chip-scale microresonators employing monolithically fabricated coupling waveguides are popular. Tuning a continuous-wave (CW) laser into resonance leads to build-up of the intracavity power and enables additional cavity modes to oscillate through cascaded four-wave mixing (FWM) [1-15]. Modulational instability (MI) of the CW pump mode is commonly cited as an important mechanism for comb generation [16-18]. According both to experiment and to theoretical analysis, comb generation preferably occurs in resonators with anomalous dispersion. However, comb generation in resonators characterized with normal dispersion has also been observed experimentally [5, 8, 19-24]. Several models have been proposed to describe this phenomenon. Although MI gain is missing in fibers or waveguides with normal dispersion, when it comes to resonators, the detuning provides an extra degree of freedom which enables MI to take place in the normal dispersion regime, hence providing a route to comb generation [16, 18, 25]. However, this mechanism requires either a precise relationship between detuning and pump power, making it difficult to realize practically, or hard excitation, a nonadiabatic process under which pump photons must be initially present in the resonator [17]. Mode coupling has also been suggested as a mechanism enabling comb generation in resonators with normal dispersion [26]. When resonances corresponding to different families of transverse modes approach each other in frequency, they may interact due to imperfections in the resonator. The theory of mode coupling in resonators has been well-established [27], and frequency shifts and avoided crossings have been observed [28-33]. In the anomalous dispersion regime, mode coupling has been reported to affect the bandwidth scaling of frequency combs [34] and the process of soliton formation [35]. However, in these cases anomalous dispersion is still considered to be the determining factor for comb generation; mode coupling is considered to be detrimental, inhibiting the formation of solitons and limiting comb bandwidth. In the normal dispersion regime, measurements have been performed with CaF2 whispering gallery mode resonators [26]. The experiments demonstrate strong local frequency shifts that are attributed to mode interactions and show a correlation between the presence of such local frequency shifts and the ability to generate combs in these normal dispersion resonators. Significant changes in comb spectra have been observed when pumping different longitudinal modes spaced by only a few free spectral ranges (FSR), both in normal dispersion silicon nitride microring resonators [5] and in the whispering gallery mode resonators of [26]; in the latter case, such effects were specifically attributed to mode interactions. In the current report, we perform comb-assisted precision spectroscopy measurements [36] of few-moded silicon nitride microresonators in the normal dispersion regime over frequency ranges spanning dozens of FSRs. As a result we are able to