Baets, Roel

Van Laer, Raphaël

Van Thourhout, Dries

English

Ghent University Academic Bibliography

An ultra-high frequency optomechanical oscillatorR. Van Laer, D. Van Thourhout and R. BaetsGhent University-IMEC, Photonics Research Group, 9000 Gent, BelgiumThe coupling of optical and mechanical degrees of freedom has applications rangingfrom mass spectroscopy and force detection to even tests of quantum mechanics. Rapidadvances in the past years have shown conclusively that the strong field gradient nearwaveguides can be exploited for actuating optomechanical devices. Most devices studiedso far oscillate at megahertz-frequencies. We aim to increase the speed of these vibrationsby several orders of magnitude. To this end, we consider very stiff devices. In orderto compensate for their smaller deflections, we enhance the optical gradient force byconfining the light into a nanogap.IntroductionOptomechanics has attracted a great deal of interest in recent years. Research has tar-geted both practical applications, such as mass spectroscopy and signal processing, andfundamental research, such as mesoscale quantum mechanics. [1] The main idea is to uselight to make on-chip nanostructures move. The force light exerts on a body comes in twovarieties. First, the scattering force is simply the result of momentum transfer betweena photon and the body on which it impinges. This is the force that makes a comet’s tailpoint away from the sun, as noted by Kepler in the 16th century.On the other hand, the gradient force is related to variations in the electromagnetic fieldintensity. To get a feeling for this force, one can think of a polarizable particle entering aregion with strong field gradients. The field induces a dipole in the particle. Subsequentlythe particle will be accelerated towards the region with the strongest field. This is the prin-ciple underpinning optical tweezers, which trap microparticles like living cells, DNA andbacteria in the waist of a powerful laser beam. Since macroscopic structures such as in-tegrated photonic wires are a collection of dipolar subunits, they are also affected by avarying optical field intensity. We put this effect to work in the ultra-high mechanical fre-quency range. Such fast oscillations are necessary to realize high-speed sensing devicesand to further progress towards the quantum regime of mechanical oscillators. [2]Partially underetched slot waveguideThe nanostructure we treat here is a silicon-on-insulator slot waveguide, see figure 1. Thecross-section of such a waveguide is typically a square of side 220 nm. The waveguidesare separated by a gap of size g ≈ 100 nm. This device is interesting for optomechanicsfor two reasons:• The small gap allows for strong confinement of the optical mode, which enhancesthe optical gradient force.• The waveguides are extremely stiff, which results in vibration frequenties exceed-ing 1 GHz. However, their displacement is also smaller. This is a fundamentaltrade-off: frequencies and mechanical displacements are inversely related.Figure 1: Top view (left) and cross-section of a slot waveguide (right).To increase the mechanical movement, we consider a scenario in which the waveguidesare partially underetched with hydrofluoric acid (HF). Such structures have been studiedbefore [2], but only in the case they were completely underetched. The novelty of ourapproach lies in the partial underetch.Mechanical eigenmodesWe calculate the mechanical eigenmodes of these waveguides with the commercial finite-element package COMSOL. The first three eigenmodes are shown in figure 2. We areparticularly interested in the left flexural mode. This mode couples best to the opticalmode and is predicted to have the largest mechanical quality factor, see further on. Figure3 depicts the dependency of the eigenfrequencies of these modes on the undercut. Theyall vibrate faster than 1 GHz for undercuts below 45%.Figure 2: First three mechanical eigenmodes of a partially underetched waveguide. Thecolors indicate the size and the arrows the direction of the displacement.Mechanical quality factorThe mechanical Q-factor determines the amplitude of the vibration under resonant ex-citation. It is critical to engineer this factor properly. Unfortunately, predicting this pa-rameter is notoriously hard. Many mechanisms are at play. Among the most importantare air damping, thermoelastic damping and clamping loss. However, nanofluidic theorypredicts reduced air damping in the microwave regime. [3] Furthermore, a simple modelfor thermoelastic damping [4] suggests a minimal Q-factor of 104 associated with thisloss mechanism. Therefore we expect clamping loss to be dominant.In a COMSOL eigenfrequency study, it is possible to introduce a matching layer with animaginary Young’s modulus and density. This layer absorbs the incoming elastic waves,ideally without reflections. Using such a layer, we calculate the clamping loss limitedQ-factor of the fundamental mode, see figure 4. The other modes have a significantlylower Q, as expected given the larger pillar displacement. Our intuition is confirmedFigure 3: Underetch dependency of the mechanical eigenfrequencies. Note that the sec-ond and third mode switch color near an undercut of 85%.in this case: larger undercuts result in smaller support loss. Other studies have shownexcellent agreement of such simulations with experiment. [5] Simulations based on aphenomenological parameter related to acoustics [6] can also be reproduced this way.Another trade-off is encountered here. At low undercuts we get large frequencies, butlow Q-factors. The choice of undercut depends on the application.Figure 4: Clamping loss limited Q-factor of the fundamental mode.Optical gradient forceA seminal paper in 2005 [7] showed how the optical gradient force can be calculatedas F = 1cdndg , with n the effective index. The derivative ought to be calculated at fixedfrequency. Thus we calculate the gradient force for the TE-mode of this slot waveguide.At low gaps there is also a TM-mode, but its optical force is much smaller. Indeed, the TE-mode is strongly confined in the gap due to the discontinuity of the Ex-component at thetransition silicon-air. The results are shown in figure 5. The graph clearly demonstratesthe need to explore structures with smaller gaps.Figure 5: Dependency of the optical gradient force on the gap size.ConclusionWe have studied the optical and mechanical properties of a novel high-frequency me-chanical oscillator. Simulations of the optical gradient force show the need to pursuesmaller slot-gaps. Mechanically we encounter a trade-off between frequency, stiffnessand Q-factor. The experimental verification of these predictions is in the pipeline.References[1] Dries Van Thourhout and Joris Roels. Optomechanical device actuation through the optical gradientforce. Nature Photonics, 4(4):211–217, April 2010.[2] Mo Li, W. H. P. Pernice, and H. X. Tang. Ultrahigh-frequency nano-optomechanical resonators in slotwaveguide ring cavities. Applied Physics Letters, 97(18):183110, 2010.[3] K L Ekinci, V Yakhot, S Rajauria, C Colosqui, and D M Karabacak. High-frequency nanofluidics: auniversal formulation of the fluid dynamics of MEMS and NEMS. Lab on a chip, 10(22):3013–25,November 2010.[4] Ron Lifshitz and ML Roukes. Thermoelastic damping in micro-and nanomechanical systems. PhysicalReview B, 61(8):5600–5609, 2000.[5] Xiankai Sun, Xufeng Zhang, and Hong X. Tang. High-Q silicon optomechanical microdisk resonatorsat gigahertz frequencies. Applied Physics Letters, 100(17):173116, 2012.[6] G. Anetsberger, R. Rivie`re, a. Schliesser, O. Arcizet, and T. J. Kippenberg. Ultralow-dissipationoptomechanical resonators on a chip. Nature Photonics, 2(10):627–633, September 2008.[7] Michelle L Povinelli, Marko Loncar, Mihai Ibanescu, Elizabeth J Smythe, Steven G Johnson, FedericoCapasso, and John D Joannopoulos. Evanescent-wave bonding between optical waveguides. OpticsLetters, 30(22):3042–4, November 2005.

An ultra-high frequency optomechanical oscillator

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An ultra-high frequency optomechanical oscillator

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