Systematic dispersion engineering of crystalline microresonators for broadband and coherent frequency comb generation

TL;DR

The paper tackles the challenge of achieving coherent broadband microcombs in crystalline resonators by addressing fabrication-induced dispersion variability and mode interactions. It introduces computer-controlled ultraprecision machining to sculpt MgF2 resonators with diverse cross-sections, enabling tailored dispersion profiles and suppression of avoided mode crossings. The authors demonstrate mode-interaction-free dissipative Kerr soliton generation across multiple FSRs, along with dispersion engineering that extends microcomb operation from near-IR into the mid-IR and enables widely tunable optical parametric oscillation pumped at 1 μm. This work provides a general, reproducible design toolkit for crystalline microresonator-based coherent broadband microcombs with broad application potential in spectroscopy, metrology, and quantum photonics.

Abstract

Ultraprecision machining offers a powerful route to dispersion control in crystalline microresonators, allowing the design of waveguide geometries for tailoring the spectrum of microresonator frequency combs. By precisely designing the geometry, both group-velocity and higher-order dispersions can be engineered across a broad wavelength range. However, despite their promising features, such advantages have remained largely unexplored due to fabrication challenges. Here, we demonstrate that resonators shaped by ultrapecision machining exhibit high precision and strongly suppressed spatial mode interactions, facilitating the generation of smooth dissipative Kerr soliton combs and broadband frequency combs beyond the telecommunication C-band. These results underscore the effectiveness of precision geometry control for realizing coherent and broadband microcombs on crystalline photonic platforms.

Figures (7)

• Figure 1: (a) Schematic illustration of a soliton microcomb in a crystalline WGM microresonator. (b) Group velocity dispersion $\beta_2$ and $D_2/2\pi$ values of $\mathrm{MgF_2}$ resonators for different FSRs. All simulations were performed for a fundamental mode. (c-e) Experimentally observed single soliton spectra with FSRs of 7.48 GHz, 13.89 GHz, and 61.08 GHz, respectively. (f) Mode field distributions with FSRs of 100 GHz (top) and 10 GHz (bottom) under a fixed curvature radius of 25 µ m. (g) Effective mode area as a function of the resonator diameter for TE and TM modes with a curvature radius of 25 µ m. (h) Mode field distributions with curvature radii of 25 µ m (top) and 100 µ m (bottom) under a fixed FSR of 25 GHz. (i) Effective mode area as a function of the curvature radius for TE and TM modes with an FSR of 20 GHz.
• Figure 2: (a,b) Mode structures of 25 GHz-FSR $\mathrm{MgF_2}$ microresonators fabricated by machining and hand-shaping. A significant reduction in the number of mode families is confirmed for a machine-shaped resonator. (c,d) Magnified plots (blue) and fitting curves (red) for the machine-shaped (c) and the hand-shaped (d) resonators. A large deviation from a parabolic curve due to mode coupling is observed only in a hand-shaped resonator. (e) The Q-factors gradually improved with additional polishing. (f) 3D profile of the machine-shaped microresonator. (g) Measured surface roughness (top) and the cross-sectional shape (bottom) of the resonator. (h) A single soliton spectrum with a smooth $\mathrm{sech^2}$ envelope generated in a machine-shaped resonator. The fitting result yields a 3-dB bandwidth of 2.61 THz, corresponding to a pulsewidth of 121 fs. The insets show the magnified optical spectrum and the beat-note spectrum, yielding a repetition rate of 25.88 GHz. (i) Phase noise comparison with other free-running DKS-based photonic microwaves scaled to 25.9 GHz. Performances of a 19.6 GHz DKS in $\mathrm{Si_3N_4}$Liu2020NP, a 15.2 GHz DKS in $\mathrm{SiO_2}$Yang2021, a 14.1 GHz DKS in $\mathrm{MgF_2}$PhysRevLett.122.013902, an 11.4 GHz DKS in $\mathrm{SiO_2}$Yao2022, a 9.9 GHz DKS in $\mathrm{MgF_2}$Liang2015, and a 25.9 GHz DKS in $\mathrm{MgF_2}$ (this work).
• Figure 3: (a) Mode field distributions for different WG structures of interest. The scale bar represents 5 µ m. (b,c) Simulated group velocity dispersion $\beta_2$ and corresponding integrated dispersion $D_\mathrm{int}/2\pi$ for 100 GHz FSR resonators. The dashed black line is the material dispersion of an $\mathrm{MgF_2}$ crystal for reference. (d,e) Contour maps for GVDs showing the dependence on the apex angle $\theta$ for triangular shapes and the height $h$ for rectangular shapes. (f) Contour map for GVDs as a function of the angle $\varphi$ and the height $h$ of trapezoidal shapes. The 100 GHz FSR is assumed for (d-f).
• Figure 4: (a) Ultraprecision lathe for microresonator fabrication. (b-d) SEM images for $\mathrm{MgF_2}$ resonators fabricated by fully computer-controlled machining. (e-g) Measured and simulated dispersion $D_\mathrm{int}/2\pi$. A triangular shape with an apex angle of 120$^\circ$ for (b,e). A spheroid shape with a curvature radius of 36 µ m for (c,f). A trapezoidal shape with $h=$8 µ m and $\varphi=45^\circ$ for (d,g).
• Figure 5: (a-c) Colormaps of GVDs with respect to rectangular height $h$ for 50, 100, and 300 GHz-FSRs at $\sim$1300 nm. The dashed black lines represent zero dispersion boundaries. (d,e) Simulated GVD $\beta_2$ and corresponding integrated dispersion $D_\mathrm{int}/2\pi$ for 50 GHz FSR resonators. The black line indicates the GVD of the spheroid shape with a curvature $r$=25 µ m for comparison. (f) Simulated comb spectra for $h=4$ µ m and $h=8$ µ m. The LLE is numerically solved to produce optical spectra including higher-order dispersions.