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][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Modulational instability (MI) of the CW pump mode is commonly cited as an important mechanism for comb generation [16][17][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][20][21][22][23][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][29][30][31][32][33]. In the anomalous dispersion regime, mode coupling has been reported to affect the bandwidth scaling of frequency combs [34] and the p...

Optical resonators with high quality factors (Qs) are promising for a variety of applications due to the enhanced nonlinearity and increased photonic density of states at resonances. In particular, frequency combs (FCs) can be generated through four-wave mixing in high-Q microresonators made from Kerr nonlinear materials such as silica, silicon nitride, magnesium fluoride, and calcium fluoride. These devices have potential for on-chip frequency metrology and high-resolution spectroscopy, high-bandwidth radiofrequency information processing, and high-data-rate telecommunications. Silicon nitride microresonators are attractive due to their compatibility with integrated circuit manufacturing; they can be cladded with silica for long-term stable yet tunable operation, and allow multiple resonators to be coupled together to achieve novel functionalities. Despite previous demonstrations of high-Q silicon nitride resonators, FC generation using silicon nitride microresonator chips still requires pump power significantly higher than those in whispering gallery mode resonators made from silica, magnesium, and calcium fluorides, which all have shown resonator Qs between 0.1 and 100 billion. Here, we report on a fabrication procedure that leads to the demonstration of "finger-shaped" Si 3 N 4 microresonators with intrinsic Qs up to 17 million at a free spectrum range (FSR) of 24.7 GHz that are suitable for telecommunication and microwave photonics applications. The frequency comb onset power can be as low as 2.36 mW and broad, single FSR combs can be generated at a low pump power of 24 mW, both within reach of on-chip semiconductor lasers. Our demonstration is an important step toward a fully integrated on-chip FC source. Kerr comb generation in microresonators starts when an external continuous-wave (CW) laser is tuned into a cavity resonance; this causes intracavity power to build, which enables additional cavity modes to oscillate through nonlinear wave mixing [10]. FC formation has now been demonstrated in a variety of Kerr nonlinear materials such as silica [9,14-18], silicon nitride (Si 3 N 4 ) [19-21], aluminum nitride [22], CaF 2 [23], and MgF 2 [24]. Recently, dissipative Kerr solitons have also been demonstrated in MgF 2 and Si 3 N 4 optical microresonators [25,26]. Out of these materials, stoichiometric Si 3 N 4 has distinctive 2334-2536/16/111171-10 Journal

The discovery and characterization of exoplanets around nearby stars is driven by profound scientific questions about the uniqueness of Earth and our Solar System, and the conditions under which life could exist elsewhere in our Galaxy. Doppler spectroscopy, or the radial velocity (RV) technique, has been used extensively to identify hundreds of exoplanets, but with notable challenges in detecting terrestrial mass planets orbiting within habitable zones. We describe infrared RV spectroscopy at the 10 m Hobby-Eberly telescope that leverages a 30 GHz electro-optic laser frequency comb with nanophotonic supercontinuum to calibrate the Habitable Zone Planet Finder spectrograph. Demonstrated instrument precision <10 cm/s and stellar RVs approaching 1 m/s open the path to discovery and confirmation of habitable zone planets around M-dwarfs, the most ubiquitous type of stars in our Galaxy. Fig.1. Instrumentation for precision infrared astronomical RV spectroscopy. (A) Starlight is collected by the Hobby-Eberly telescope and directed to an optical fiber. Lasers, electro-optics and nanophotonics are used to generate an optical frequency comb with teeth spaced by 30 GHz and stabilized to an atomic clock. Both the starlight and frequency comb light are coupled to the highly-stabilized Habitable Zone Planet Finder (HPF) spectrograph where minute wavelength changes in the stellar spectrum are tracked with the precise calibration grid provided by the laser frequency comb. (B) Components for frequency comb generation. (upper) A fiber-optic integrated electro-optic modulator and (lower) silicon nitride chip (5 mm × 3 mm) on which nanophotonic waveguides are patterned. Light is coupled into a waveguide from the left and supercontinuum is extracted from the right with a lensed fiber. (C) The HPF spectrograph, opened and showing the camera optics on the left, echelle grating on the right, and relay mirrors in front. The spectrograph footprint is approximately 1.5 m × 3 m. (D) The 10 m Hobby-Eberly telescope at the McDonald Observatory in southwest Texas.

We validate the discovery of a 2 Earth radii sub-Neptune-size planet around the nearby high proper motion M2.5-dwarf G 9-40 (EPIC 212048748), using high-precision near-infrared (NIR) radial velocity (RV) observations with the Habitable-zone Planet Finder (HPF), precision diffuser-assisted ground-based photometry with a custom narrow-band photometric filter, and adaptive optics imaging. At a distance of d = 27.9 pc, G 9-40b is the second closest transiting planet discovered by K2 to date. The planet's large transit depth (∼3500ppm), combined with the proximity and brightness of the host star at NIR wavelengths (J=10, K=9.2) makes G 9-40b one of the most favorable sub-Neptune-sized planet orbiting an M-dwarf for transmission spectroscopy with JWST, ARIEL, and the upcoming Extremely Large Telescopes. The star is relatively inactive with a rotation period of ∼29 days determined from the K2 photometry. To estimate spectroscopic stellar parameters, we describe our implementation of an empirical spectral matching algorithm using the high-resolution NIR HPF spectra. Using this algorithm, we obtain an effective temperature of T eff = 3404 ± 73K, and metallicity of [Fe/H] = −0.08 ± 0.13. Our RVs, when coupled with the orbital parameters derived from the transit photometry, exclude planet masses above 11.7M ⊕ with 99.7% confidence assuming a circular orbit. From its radius, we predict a mass of M = 5.0 +3.8 −1.9 M ⊕ and an RV semi-amplitude of K = 4.1 +3.1 −1.6 m s −1 , making its mass measurable with current RV facilities. We urge further RV follow-up observations to precisely measure its mass, to enable precise transmission spectroscopic measurements in the future.