A bulk acoustic mode single-crystal silicon microresonator with a high-quality factor

This paper details a bulk acoustic mode resonator fabricated in single-crystal silicon with a quality factor of 15 000 in air, and over a million below 10 mTorr at a resonant frequency of 2.18 MHz. The resonator is a square plate that is excited in the square-extensional mode and has been fabricated in a commercial foundry silicon-on-insulator (SOI) MEMS process through MEMSCAP. This paper also presents a simple method of extracting resonator parameters from raw measurements heavily buried in electrical feedthrough. Its accuracy has been demonstrated through a comparison between extracted motional resistance values measured at different voltage biases and those predicted from an analytical model. Finally, a method of substantially cancelling electrical feedthrough through system-level electronic implementation is also introduced. © 2008 IOP Publishing Ltd.

Binary excitation of a high-Q bulk acoustic microresonator by actuation polarity inversion

We present a technique for independently exciting two resonant modes of vibration in a single-crystal silicon bulk mode microresonator using the same electrode configuration through control of the polarity of the DC actuation voltage. Applications of this technique may include built-in temperature compensation by the simultaneous selective excitation of two closely spaced modes that may have different temperature coefficients of resonant frequency. The technique is simple and requires minimum circuit overhead for implementation. The technique is implemented on square plate resonators with quality factors as high as 3.06 × 106. Copyright © 2008 by ASME.

Absolute Absorption Cross-Section Measurement of a Submonolayer film on a silica microresonator

Conventional absorption spectroscopy is not nearly sensitive enough for quantitative overtone measurements on submonolayer coatings. While cavity-enhanced absorption detection methods using microresonators have the potential to provide quantitative absorption cross sections of even weakly absorbing submonolayer films, this potential has not yet been fully realized. To determine the absorption cross section of a submonolayer film of ethylene diamine (EDA) on a silica microsphere resonator, we use phase-shift cavity ringdown spectroscopy simultaneously on near-IR radiation that is Rayleigh backscattered from the microsphere and transmitted through the coupling fiber taper. We then independently determine both the coupling coefficient and the optical loss within the resonator. Together with a coincident measurement of the wavelength frequency shift, an absolute overtone absorption cross section of adsorbed EDA, at submonolayer coverage, was obtained and was compared to the bulk value. The smallest quantifiable absorption cross section is σmin 2.7 × 10−12 cm2. This absorption cross section is comparable to the extinction coefficients of, e.g., single gold nanoparticles or aerosol particles. We therefore propose that the present method is also a viable route to absolute extinction measurements of single particles.

Nanobump microresonator

We introduce a whispering gallery-mode (WGM) nanobump microresonator (NBMR) and develop its theory. This microresonator is formed by an asymmetric nanoscale-high deformation of the translationally symmetric optical fiber surface, which is employed in fabrication of surface nanoscale axial photonics (SNAP) structures. It is shown that an NBMR causes strong localization of WGMs near a closed ray (geodesic) at the fiber surface, provided that this ray is stable. Our theory explains and describes the experimentally observed localization of WGMs by NBMRs and is useful for the design and fabrication of SNAP devices.

5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million

This paper reports the design and electrical characterization of a micromechanical disk resonator fabricated in single crystal silicon using a foundry SOI micromachining process. The microresonator has been selectively excited in the radial extensional and the wine glass modes by reversing the polarity of the DC bias voltage applied on selected drive electrodes around the resonant structure. The quality factor of the resonator vibrating in the radial contour mode was 8000 at a resonant frequency of 6.34 MHz at pressure below 10 mTorr vacuum. The highest measured quality factor of the resonator in the wine glass resonant mode was 1.9 × 106 using a DC bias voltage of 20 V at about the same pressure in vacuum; the resonant frequency was 5.43 MHz and the lowest motional resistance measured was approximately 17 kΩ using a DC bias voltage of 60 V applied across 2.7 μm actuation gaps. This corresponds to a resonant frequency-quality factor (f-Q) product of 1.02 × 1013, among the highest reported for single crystal silicon microresonators, and on par with the best quartz crystal resonators. The quality factor for the wine glass mode in air was approximately 10,000. © 2009 Elsevier B.V. All rights reserved.

Low loss HF band SOI wine glass bulk mode capacitive square-plate resonator

This paper reports on the design and electrical characterization of a single crystal silicon micromechanical square-plate resonator. The microresonator has been excited in the anti-symmetrical wine glass mode at a resonant frequency of 5.166 MHz and exhibits an impressive quality factor (Q) of 3.7 × 106 at a pressure of 33 mtorr. The device has been fabricated in a commercial foundry process. An associated motional resistance of approximately 50 kΩ using a dc bias voltage of 60 V is measured for a transduction gap of 2 νm due to the ultra-high Q of the resonator. This result corresponds to a frequency-Q product of 1.9 × 1013, the highest reported for a fundamental mode single-crystal silicon resonator and on par with some of the best quartz crystal resonators. The results are indicative of the superior performance of silicon as a mechanical material, and show that the wine glass resonant mode is beneficial for achieving high quality factors allowed by the material limit. © 2009 IOP Publishing Ltd.

Square wine glass mode resonator with quality factor of 4 million

We report on the experimental characterization of a single crystal silicon square-plate microresonator. The resonator is excited in the square wine glass (SWG) mode at a mechanical resonance frequency of 2.065 MHz. The resonator displays quality factor of 9660 in air and an ultra-high quality factor of Q = 4.05 × 106 in 12 mtorr vacuum. The SWG mode may be described as a square plate that contracts along one axis in the fabrication plane, while simultaneously extending along an orthogonal axis in the same plane. The resonant structure is addressed in a 2-terminal configuration by utilizing equal and opposite drive polarities on surrounding capacitor electrodes, thereby decreasing the motional resistance of the resonator. The resonant micromechanical device has been fabricated in a commercial silicon-on-insulator process through the MEMSCAP foundry utilising a minimum electrostatic gap of 2 μm. © 2008 IEEE.

Characterizing a resonator bolometer array

High-background applications such as climate monitoring, biology and security applications demand a large dynamic range. Under such conditions ultra-high sensitivity is not required. The resonator bolometer is a novel detector which is well-suited for these conditions. This device takes advantage of the high-density frequency multiplexing capabilities of superconducting microresonators while allowing for the use of high-Tc superconductors in fabrication, which enables a modest (1-4 K) operating temperature and larger dynamic range than is possible with conventional microresonators. The moderate operating temperature and intrinsic multiplexability of this device reduce cost and allow for large pixel counts, making the resonator bolometer especially suitable for the aforementioned applications. A single pixel consists of a superconducting microresonator whose light-absorbing area is placed on a thermally isolated island. Here we present experimental results and theoretical calculations for a prototype resonator bolometer array. Intrinsic device noise and noise equivalent power (NEP) under both dark and illuminated conditions are presented. Under dark conditions the device sensitivity is limited by the thermal noise fluctuations from the bolometer legs. Under the experimental illuminated conditions the device was photon noise limited.

Nonlinear optics in planar silica-on-silicon disk resonators

Optical frequency combs (OFCs) provide direct phase-coherent link between optical and RF frequencies, and enable precision measurement of optical frequencies. In recent years, a new class of frequency combs (microcombs) have emerged based on parametric frequency conversions in dielectric microresonators. Micocombs have large line spacing from 10's to 100's GHz, allowing easy access to individual comb lines for arbitrary waveform synthesis. They also provide broadband parametric gain bandwidth, not limited by specific atomic or molecular transitions in conventional OFCs. The emerging applications of microcombs include low noise microwave generation, astronomical spectrograph calibration, direct comb spectroscopy, and high capacity telecommunications.

In this thesis, research is presented starting with the introduction of a new type of chemically etched, planar silica-on-silicon disk resonator. A record Q factor of 875 million is achieved for on-chip devices. A simple and accurate approach to characterize the FSR and dispersion of microcavities is demonstrated. Microresonator-based frequency combs (microcombs) are demonstrated with microwave repetition rate less than 80 GHz on a chip for the first time. Overall low threshold power (as low as 1 mW) of microcombs across a wide range of resonator FSRs from 2.6 to 220 GHz in surface-loss-limited disk resonators is demonstrated. The rich and complex dynamics of microcomb RF noise are studied. High-coherence, RF phase-locking of microcombs is demonstrated where injection locking of the subcomb offset frequencies are observed by pump-detuning-alignment. Moreover, temporal mode locking, featuring subpicosecond pulses from a parametric 22 GHz microcomb, is observed. We further demonstrated a shot-noise-limited white phase noise of microcomb for the first time. Finally, stabilization of the microcomb repetition rate is realized by phase lock loop control.

For another major nonlinear optical application of disk resonators, highly coherent, simulated Brillouin lasers (SBL) on silicon are also demonstrated, with record low Schawlow-Townes noise less than 0.1 Hz^2/Hz for any chip-based lasers and low technical noise comparable to commercial narrow-linewidth fiber lasers. The SBL devices are efficient, featuring more than 90% quantum efficiency and threshold as low as 60 microwatts. Moreover, novel properties of the SBL are studied, including cascaded operation, threshold tuning, and mode-pulling phenomena. Furthermore, high performance microwave generation using on-chip cascaded Brillouin oscillation is demonstrated. It is also robust enough to enable incorporation as the optical voltage-controlled-oscillator in the first demonstration of a photonic-based, microwave frequency synthesizer. Finally, applications of microresonators as frequency reference cavities and low-phase-noise optomechanical oscillators are presented.

Equilateral-Triangle and Square Resonator Semiconductor Microlasers

The characteristics of equilateral-triangle resonator (ETR) and square resonator microlasers are reported, which are potential light sources in the photonic integrations. Based on the numerical simulations, we find that high-efficiency directional emission can be achieved for the triangle and square microlasers by directly connecting an output waveguide to the resonators. The electrically injected InP/InGaAsP ETR and square resonator microlasers with a 2-mu m-wide output waveguide were fabricated by standard photolithography and inductively coupled plasma etching techniques. Room-temperature continuous-wave (CW) operations were achieved for the ETR microlasers with the side length from 10 to 30 mu m and the square resonator microlasers with the side length of 20 mu m. The output power versus CW injection current and the laser spectra are presented for an ETR microlaser up to 310 K and a square resonator microlaser to 305 K. The lasing spectra with mode wavelength intervals as that of whispering-gallery-type modes and Fabry-Perot modes are observed for two square lasers, which can lase at low temperature and room temperature, respectively.

Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator

The eigenmodes confined in the equilateral triangle resonator (ETR) are analyzed by deriving the eigenvalues and the mode field distributions and by the finite difference time domain (FDTD) technique. The analytical results show that the one-period-length for the mode light rays inside the ETR is the perimeter of the ETR, and the number of transverse modes is limited by the condition of total internal reflection. In addition, the sum of the longitudinal mode index and the transverse mode index should be an even number, which limits the number of confined modes again. Based on the FDTD technique and the Pade approximation, we calculate the mode resonant frequencies and the quality factors from the local maximum and the width of the spectral distribution of the intensity The numerical results of mode frequencies agree very well with the analytical results, and the quality factor of the fundamental mode is usually higher than that of the higher order transverse modes. The results show that the ETR is suitable to realize single-made operation as semiconductor microcavity lasers.

Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Pade approximation

The mode wavelength and quality factor (Q-factor) for resonant modes in optical equilateral triangle resonators (ETR's) are calculated by the finite-difference time-domain (FDTD) technique and the Pade approximation, For an ETR with the side length of 3 mu m and the refractive index of 3.2, we get the mode wavelength interval of about 70 nm and the Q-factor of the fundamental mode over 10(3), The results show that the ETR is suitable to realize single-mode operation, and that the radiation loss in the corner regions of ETR is rather low, In addition, the numerical results of the mode wavelength agree very well with our analytical formula.