Crystalline Resonators Research Articles

Elastic moduli from crystalline micro-mechanical oscillators carved by focused ion beam.

The elastic moduli provide unique insights into the thermodynamics of quantum materials, particularly into the symmetries broken at their phase transition. Here, we present a workflow to carve crystalline resonators via focused ion beam milling from small and oddly shaped crystals unsuitable for traditional measurements of elasticity. The accuracy of this technique is first established in silicon. Next, we showcase the capacity to probe changes in the electronic state with a resolution on the measured resonance frequency as small as 0.01% on YNiO3, a rare-earth perovskite nickelate, in which bulk single crystals have typical length scales of ≈40μm. Here, we observe a sharp 0.2% discontinuity in Young's modulus of an YNiO3 cantilever at a magnetic phase transition. Finally, an additional potential of using free-standing cantilevers as a tool for examining the time-dependence of chemical changes is illustrated by laser-heating YNiO3.

Frequency comb generation via synchronous pumped χ(3) resonator on thin-film lithium niobate

Resonator-based optical frequency comb generation is an enabling technology for a myriad of applications ranging from communications to precision spectroscopy. These frequency combs can be generated in nonlinear resonators driven using either continuous-wave (CW) light, which requires alignment of the pump frequency with the cavity resonance, or pulsed light, which also mandates that the pulse repetition rate and cavity free spectral range (FSR) are carefully matched. Advancements in nanophotonics have ignited interest in chip-scale optical frequency combs. However, realizing pulse-driven on-chip Kerr combs remains challenging, as microresonator cavities have limited tuning range in their FSR and resonance frequency. Here, we take steps to overcome this limitation and demonstrate broadband frequency comb generation using a χ(3) resonator synchronously pumped by a tunable femtosecond pulse generator with on-chip amplitude and phase modulators. Notably, employing pulsed pumping overcomes limitations in Kerr comb generation typically seen in crystalline resonators from stimulated Raman scattering.

High-power Raman lasing and efficient anti-Stokes generation in mm-sized crystalline disk resonators.

We have previously experimentally observed high-power Stokes and second-order Stokes output from a mm-sized CaF2 disk using stimulated Raman scattering. A pump laser at a wavelength of 1.06 µm was coupled via a tapered fiber to the whispering gallery modes (WGM) of the disk. In this Letter, we extend this work and demonstrate the production of the first anti-Stokes sideband at power levels as high as 60 µW in near continuous-wave (CW) operation. The result is a four-component Raman comb at the output, with a wavelength range covering from 1.023 to 1.14 µm. We discuss the threshold dependence of the observed Raman lines on the crystal orientation and provide experimental validation. These advances enable the use of such mm-sized resonators as compact, efficient sources for terahertz-level frequency modulation.

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution.

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

Controlling the propagation asymmetry of hyperbolic shear polaritons in beta-gallium oxide

Structural anisotropy in crystals is crucial for controlling light propagation, particularly in the infrared spectral regime where optical frequencies overlap with crystalline lattice resonances, enabling light-matter coupled quasiparticles called phonon polaritons (PhPs). Exploring PhPs in anisotropic materials like hBN and MoO3 has led to advancements in light confinement and manipulation. In a recent study, PhPs in the monoclinic crystal β-Ga2O3 (bGO) were shown to exhibit strongly asymmetric propagation with a frequency dispersive optical axis. Here, using scanning near-field optical microscopy (s-SNOM), we directly image the symmetry-broken propagation of hyperbolic shear polaritons in bGO. Further, we demonstrate the control and enhancement of shear-induced propagation asymmetry by varying the incident laser orientation and polariton momentum using different sizes of nano-antennas. Finally, we observe significant rotation of the hyperbola axis by changing the frequency of incident light. Our findings lay the groundwork for the widespread utilization and implementation of polaritons in low-symmetry crystals.

Pressure-based fast tuning of high-Q crystalline whispering gallery mode resonator

The whispering gallery mode resonator based on a fluoride crystalline material offers the advantage of an ultrahigh quality factor, however, its fast tuning remains a challenge. We propose a tuning method for a CaF2 crystalline resonator using external pressure loading. Through our theoretical calculations and simulations, we discovered that the frequency shift induced by deformation during the pressure tuning of the crystalline resonator is greater than that induced by changes in refractive index. Both shifts were of the same order of magnitude, indicating that both factors must be considered. The experimental results show tuning rates of 1114.6 and 888.2 MHz/MPa in the transverse electric and transverse magnetic modes, respectively. The tuning system can respond to a signal frequency of up to 1.2 MHz.

Compact on-chip crystalline resonator integration with etching of tapered fiber waveguide.

Whispering-gallery-mode crystalline resonators currently maintain the best quality factor (Q) record; however, compact on-chip packaging is still a challenge, although various coupling architectures have been developed. Here, a chemical etching method is proposed to fabricate a miniaturized tapered fiber waveguide on silicon substrate. The Marangoni effect is implemented to reduce the surface roughness of the cone region. The optical loss of 0.1dB/mm is obtained, and the Q of the on-chip crystalline resonator exceeds 108. Additionally, thermoelectric cooler (TEC) is implanted in the package to actively customize the temperature, and the temperature response of 18pm/°C is consistent with the theoretical calculation.

Evolution of the Cellulose Microfibril through Gamma-Valerolactone-Assisted Co-Solvent and Enzymatic Hydrolysis

Biomass recalcitrance during deconstruction remains a key bottleneck to affordable biomass processing technologies. A clear connection between the cell wall structure and biomass deconstruction is necessary to understand how lignocellulosic material is broken down to valuable monomeric components. Here, we monitor changes in the cellulose microfibril domains of poplar, sorghum, and switchgrass throughout gamma-valerolactone (GVL)–water co-solvent pretreatment and enzymatic hydrolysis using solid-state 13C cross-polarization magic angle spinning nuclear magnetic resonance spectroscopy (CP/MAS 13C-NMR) and wide-angle X-ray scattering (WAXS). Spectral fitting of NMR peaks corresponding to different cellulose microenvironments at the C4 carbon center suggests that a mildly acidic GVL–water co-solvent pretreatment of poplar leads to nearly full removal of xylan–cellulose linkages, which primes the cellulose for enzymatic attack. The spectral fitting also suggests that the pretreatment causes significant depletion of the inaccessible fibril surface domains with an increase in more thermally stable crystalline resonances (Iβ). WAXS confirmed a decrease in the lattice spacing between (200) crystalline planes with increasing co-solvent pretreatment severity. These results are interpreted as an opening of bound microfibril surfaces previously inaccessible to the co-solvent system, which leaves behind a more thermally stable, crystalline domain that is potentially prone to relaxation and recrystallization. Full conversion of residual GVL-pretreated biomass was achieved after the GVL co-solvent pretreatment at 140 °C using a commercial enzyme cocktail, CTec2, which contains different cellulases and other enzymes. Spectral fitting of enzymatically hydrolyzed samples by a single engineered cellulase, CelR, suggests that the residual cellulose recalcitrance is mainly due to the inability of CelR to digest the Iβ crystalline domain present in pretreated samples. This work helps to provide new information regarding the structure of the cell wall and recalcitrance throughout GVL–water mild acidolysis and CelR enzymatic biomass deconstruction by tracking the evolution of structural domains within the cellulose microfibril. This work further directs recommendations for improving the conversion and sugar yields in future studies. Our findings inform inquiry into larger questions of cellulose recalcitrance through GVL pretreatment and CelR enzymatic hydrolysis and give insight into subsequent required steps for full cellulose conversion with attention to the most recalcitrant cellulose structures.

Subharmonic instabilities in Kerr microcombs.

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns. We perform a theoretical analysis based on eigenvalue decomposition that evidences the mechanism leading to the excitation of these combs.

Optical microcombs in whispering gallery mode crystalline resonators with dispersive intermode interactions

Soliton microcombs have shown great potential in a variety of applications ranging from chip-scale frequency metrology to optical communications and photonic data center, in which light couplings among cavity transverse modes, termed as intermode interactions, are long-existing and usually give rise to localized impacts on the soliton state. Of particular interest are whispering gallery mode-based crystalline resonators, which with dense mode families, potentially feature interactions of all kinds. While effects of narrowband interactions such as spectral power spikes have been well recognized in crystalline resonators, those of broadband interactions remain unexplored. Here, we demonstrate microcombs with broadband and dispersive intermode interactions, in home-developed magnesium fluoride microresonators with an intrinsic Q -factor approaching 10 billion. In addition to conventional soliton comb generation in the single-mode pumping scheme, comb states with broadband spectral tailoring effect have been observed, via an intermode pumping scheme. Remarkably, footprints of both constructive and destructive interference on the comb spectrum have been observed, which as confirmed by simulations, are connected to the dispersive effects of the coupled mode family. Our results would not only contribute to the understanding of dissipative soliton dynamics in multi-mode or coupled resonator systems, but also extend the access to stable soliton combs in crystalline microresonators where mode control and dispersion engineering are usually challenging.

Miniaturizing Ultrastable Electromagnetic Oscillators: Sub- 10−14 Frequency Instability from a Centimeter-Scale Fabry-Perot Cavity

The best performance from compact, portable, and repeatably manufactured electromagnetic (EM) oscillators has for decades been built upon crystalline quartz resonators operating at radio frequencies. Such a source of frequency-stable EM waves has enabled a wide range of applications of significant technical and societal benefit, such as navigation and communication systems, distributed sensing, geodesy, and fundamental physics. However, meeting demands for increased measurement sensitivity requires pushing beyond a fractional frequency stability of ${10}^{\ensuremath{-}13}$, typical of the best ovenized quartz. To date, such performance has been available in the microwave domain only with the use of complex cryogenic systems, or in the optical domain at the expense of larger volume and weight. In either case, the size, weight, and power of state-of-the-art EM oscillators has relegated their use to laboratory experiments. Here we demonstrate the validity of a manufacturable, compact Fabry-Perot reference that improves upon all other centimeter-scale oscillators by more than a factor of 10, including those based on solid-state optical resonators as well as quartz. In a specific implementation, we show an 8 ml bonded assembly containing three vacuum-gap Fabry-Perot optical cavities with mirrors lithographically fabricated on a single substrate, each with quality factor exceeding 10 billion. A laser stabilized to one of the cavities exhibits thermal-noise-limited phase noise for offset frequencies ranging from 1 Hz to nearly 1 kHz, and fractional frequency stability of $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ at 1 s. Our advance with lithographically defined and microfabricated mirrors is validated by rigorous models, which highlight a path to oscillators with size comparable to ovenized quartz, but with significantly improved performance. For example, we predict sub-${10}^{\ensuremath{-}14}$ performance is readily attainable with a Fabry-Perot cavity volume less than 2 ml.

Raman lasing and other nonlinear effects based on ultrahigh-QCaF2 optical resonator

The calcium fluoride (CaF2) whispering gallery mode crystalline resonator is an excellent platform for nonlinear optical applications because of the decreasing in threshold caused by ultrahigh quality (Q) factor. In this paper, we achieved the observation of Raman lasing, first-order Raman comb, and second-order Raman lasing in a CaF2 disk resonator with a diameter of 4.96 mm and an ultrahigh-Q of 8.43×108 at 1550-nm wavelength. We also observed thermal effects in CaF2 disk resonator, and the threshold of thermo-optical oscillation is approximately coincident with Raman lasing, since the intracavity power increases rapidly when the power reaches the threshold, and higher input pump power results in longer thermal drift and higher Raman emission power. With a further increase in pump power, the optical frequency combs range is from 1520 nm to 1650 nm, with a wavelength interval of 4×FSR. It is a promising candidate for optical communication, biological environment monitoring, spectral analysis, and microwave signal sources.

Narrow linewidth self-injection locked fiber laser based on a crystalline resonator in add-drop configuration.

Strong and narrow spectral feedback plays a key role in self-injection locking (SIL) single-frequency lasers, especially in the stabilization of single longitudinal mode (SLM) operation of a multi-mode laser. Here, we report on a narrow linewidth SIL fiber laser that adopts a fiber add-drop configuration composing of two tapered fibers and a high-Q MgF2 crystalline whispering-gallery-mode resonator. The feedback from the drop port could be controlled and optimized for stable SLM lasing of multi-mode fiber lasers. A stable single-frequency fiber laser with white frequency noise as low as ∼0.4 Hz2/Hz, corresponding to an instantaneous linewidth of ∼1.26 Hz, is demonstrated. Compact, controllable, and all-fiber configuration in this work to achieve an ultra-narrow linewidth laser will attract interest in many applications.

Strained crystalline nanomechanical resonators with quality factors above 10 billion

In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, called dissipation dilution, is employed in mirror suspensions of gravitational-wave interferometers and at the nanoscale, where soft clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far been applied only to amorphous materials, specifically Si3N4. Crystalline materials exhibit substantially lower intrinsic damping at cryogenic temperatures. Applying dissipation dilution engineering to strained crystalline materials could, therefore, enable extremely low loss nanomechanical resonators, as they combine low internal friction, high intrinsic strain and high yield strength. This potential has not yet been fully exploited. Here we demonstrate that single-crystal strained silicon—a material developed for high-mobility transistors—can be used to realize mechanical resonators with ultralow dissipation. We fabricate strained silicon nanostrings with high aspect ratios supporting megahertz mechanical modes with quality factors exceeding 1010 at 7 K, a tenfold improvement over values reported in Si3N4. We estimate a thermal-noise-limited force sensitivity of (5 ± 2) × 10–20 N Hz–1/2 at 7 K—approaching that of carbon nanotubes—and a heating rate of only 60 quanta per second. The low mass and high quality factors of our nanomechanical resonators make them particularly promising for quantum sensing and transduction. Soft clamping reduces the dissipation of nanomechanical resonators, but this method has been limited to amorphous materials. When applied in crystalline silicon, it enables resonators with quality factors beyond ten billion.

Pockels soliton microcomb

Kerr soliton microcombs have recently emerged as a prominent topic in integrated photonics and have enabled new horizons for optical frequency metrology. Kerr soliton microcombs, as the name suggests, are based on high-order cubic optical nonlinearity. It is desirable to exploit quadratic photonic materials, namely Pockels materials, for soliton generation and on-chip implementation of 1f–2f comb self-referencing. Such quadratically driven solitons have been proposed theoretically, but have not yet been observed in a nanophotonic platform, despite recent progress in quadratic comb generation in free-space and crystalline resonators. Here, we report photonic-chip-based Pockels microcomb solitons driven by three-wave mixing in an aluminium nitride microring resonator. In contrast to typical Kerr solitons, the Pockels soliton features unity soliton generation fidelity, two-by-two evolution of multi-soliton states, favourable tuning dynamics and high pump-to-soliton conversion efficiency. Photonic-chip-based microcomb solitons driven by Pockels nonlinearity—the quadratic χ(2) effect—instead of the Kerr soliton are demonstrated in an aluminium nitride microring resonator with a conversion efficiency of 17%.

Effect of structure evolution of starch in rice on the textural formation of cooked rice

The content and composition of rice kernels are closely related to the textural properties of cooked rice. In this study, the mechanistic explanations of textural changes were linked to proton mobility, leaching behavior, and the molecular features of rice components during cooking. The decreasing trend of hardness and the formation of stickiness was mainly determined by the molecular mobility of components. The molecular weight (Mw) of starch and protein in leached solids increased with the leaching at 70–100 °C. The Mw of rice kernels at different cooking temperatures and times was similar, but the molecular size and volume varied at different stages of cooking. The dismission of the crystalline structure, C1 resonance, and lamellar structures after cooking at 100 °C for 10 min indicated that the structural evolution of starch in rice kernels was time- and temperature-dependent. These results provide a promising foundation for developing strategies to control rice cooking.

Epitaxial Aluminum Scandium Nitride Super High Frequency Acoustic Resonators

This paper demonstrates super high frequency (SHF) Lamb and surface acoustic wave resonators based on single-crystal orientation Aluminum Scandium Nitride (AlScN) thin films grown on silicon substrates by molecular beam epitaxy (MBE). We report on the experimental frequency response and electromechanical properties of 400 nm-thick crystalline AlScN acoustic resonators with up to 12% Sc/(Sc+Al) ratio. The film thickness is optimized for operation at the SHF range, targeting emerging wireless communication standards, such as 4G LTE/5G. We report on high-performance acoustic devices that take advantage of the crystallinity, and high piezoelectric properties of 400 nm-thick epitaxial AlScN films. Our work presents enhanced effective electromechanical coupling coefficients (k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) up to 5.3% and unloaded quality factors (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ) of ~192 at 3-10 GHz. However, fabrication challenges due to the high-stress levels of sub-micron AlScN epi-layers grown on Si substrates remain challenging and will be discussed in this paper. [2019-0231].

The coolest of vibrations

Optomechanics Shifts in the resonance frequency of micrometer-sized mechanical resonators provide a platform for high-resolution sensing and detection applications. To exploit optomechanical resonators for quantum technologies, the temperature of the system needs to be very low, ideally well below an occupancy of just one phonon, so that the system is in its ground state. From there, selection and control of the transitions between quantized energy levels provide for quantum-enhanced precision measurement. Qiu et al. demonstrate laser cooling of a crystalline silicon optomechanical resonator to its zero-point energy. With a mean thermal phonon occupancy of just ∼0.09 quantum, corresponding to ∼92% ground state probability and −7.4 decibels of the zero-point energy, the stage is now set for exquisite quantum-sensing applications as well as fundamental tests of quantum mechanics. Phys. Rev. Lett. 124 , 173601 (2020).

Observation of low-temperature magnetomechanic effects in crystalline resonant phonon cavities

We observe magnetic effects in ultra-high quality factor crystalline quartz Bulk Acoustic Wave resonators at milli-Kelvin temperature. The study reveals existence of hysteresis loops, jumps and memory effects of acoustical resonance frequencies. These loops arise as a response to the external magnetic field and span over few Hertz range for modes with linewidths of about $25$mHz, which constitute a frequency shift of order 60 linewidths. The effects are broadband but get stronger towards higher frequencies where both nonlinear effects and losses are limited by two level systems. This suggests that the observed effects are due to ferromagnet-like phase of a spin ensemble coupled to mechanical modes. The observed coupling between mechanical and spin degrees of freedom in the ultra low loss regime brings new possibilities for the emerging class of quantum hybrid systems.

Hybrid silicon on silicon carbide integrated photonics platform

We demonstrate a hybrid on-chip photonics platform based on crystalline silicon resonators and waveguides patterned on top of silicon carbide. The devices were fabricated with membrane transfer followed by standard electron beam patterning procedures. The platform allows the integration of high quality silicon photonics with color centers in silicon carbide operating in the near infrared for spin-photon interfaces used in quantum information processing applications. We measure waveguide-coupled ring resonators with loaded quality factors up to 23 000 at cryogenic temperatures.