High-Q double-disk microcavities for cavity optomechanics

We design a double-disk microcavity consisting of a pair of silica microdisks separated by a nanoscale gap region on a silicon chip for cavity optomechanics. We show that this type of photonic structure can provide a per-photon gradient force with a magnitude much larger than for scattering-force-based structures. Moreover, this device provides for nearly independent optimization of optical and mechanical properties. We present the processing details of fabricated devices. ©2009 Optical Society of America OCIS codes: (200.4880) Optomechanics; (140.3945) Microcavities. References and links 1. T. J. Kippenberg, and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-17172. 2. T. J. Kippenberg, and K. J. Vahala, “Cavity Optomechanics: Back-Action at the Mesoscale,” Science 321(5893), 1172–1176 (2008). 3. I. Favero, and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. 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Here we describe the design and fabrication of a double-disk microcavity for cavity optomechanics.The structure features a gradient-force-induced optomechanical coupling that enables improved optimization of coupling strength without adversely impacting other device properties.It also supports high optical quality factor whispering-gallery modes, provides for easy fabrication, and low thermo-optic effects.Beyond cavity optomechanics, this structure may also find applications in various fields such as cavity QED, biosensing, optomechanically tuned filters [24], and optical wavelength conversion [18].The double-disk microcavity is illustrated in Fig. 1, and consists of a pair of silica microdisks stacked on top of each other and separated by a nanoscale gap.Using silica as the disk material provides several benefits.First, the negligible optical loss in the silica material helps to support the extremely high optical quality factor of the microcavity, as has been shown in microdisks [25,26] and microtoroids [27].Second, its moderate refractive index provides sufficient mode confinement while also allowing the optical mode to spread out from each single disk, thereby enabling strong mode coupling even with a modest disk spacing.Third, silica has a high thermal resistance, significantly reducing the magnitude of possible thermaloptic and thermal-mechanical effects relative to the optomechanical effects [23,24].Finally, the amorphous nature of silica glass allows for flexible processing during device fabrication, which will be discussed in detail later.

Optical design and simulation
Well separated disks would feature whispering gallery modes on a spectral grid determined by the disk radius.In the coupled, double-disk geometry, two degenerate (or nearly degenerate) whispering gallery modes will couple evanescently, forming hybridized supermodes that are symmetric and anti-symmetric combinations of the original, uncoupled modes.The gradient force causes attraction of the disks when the symmetric mode is excited, and repulsion for the antisymmetric mode.As a result, these modes can also be called bonding and anti-bonding supermodes in analogy to a chemical bond.Mode profiles are shown in Fig. 2. The required level of degeneracy for the original, uncoupled modes is, in fact, easy to satisfy on account of the strong coupling of the modes.For example, given a 200 nm gap between two 400 nm thick silica microdisks a mode splitting of more than 24 THz occurs between the bonding and anti-bonding modes.This splitting is so large that even modes that are mismatched in frequency by several free-spectral-ranges will nonetheless experience strong coupling and setup the symmetric and anti-symmetric supermode states.This is particularly important as the actual double-disk structure (see Fig. 2(c), 2(d)) features disks that are distinctly different in diameter on account of side-wall etching that is angled.The dependence of bonding mode resonance on gap is plotted in Fig. 3(a  The optical gradient force between the two disks can be characterized through the cavity dispersion as F = -N£g OM , where N is the total photon number inside the cavity, £ is the reduced Plank's constant, and g OM = dω/dx is the optomechanical coupling coefficient characterizing the magnitude of the per-photon force.Figure 3(b) shows the optomechanical coupling coefficient versus gap in a double-disk structure with a diameter of 90 µm and a thickness of 400 nm for each disk.It is shown clearly that, with a disk spacing of 200 nm, the optomechanical coupling coefficient can be as large as 2π×27 GHz/nm.This value is about one order of magnitude higher than other cavities such as Fabry-Perot cavities and microtoroids, showing the extremely strong gradient force provided by the double-disk structure.More importantly, as the mode coupling is primarily determined by the lateral mode confinement, the per-photon force in the double disk is independent of cavity optical-pathlength (i.e., disk radius) [23,24].This is in strong contrast to other optomechanical cavities, in which the per-photon force scales inversely with the cavity size.For example, in Fabry-Perot cavities g OM scales inversely with cavity length (g OM = -ω/L), and in microtoroids it scales inversely with radius (g OM = -ω/R).Therefore, using double-disks it is possible to realize diverse disk geometries (large or small) while maintaining the same optomechanical coupling strength [24].For easy comparison to other structures, we introduce an effective length L eff defined by g OM = dω/dx = ω/L eff to characterize the gradient force in the double-disk structure [23].This effective length is given by L eff = ω/(dω/dx).The green curve in Fig. 3(a) shows the effective length as a function of gap for the bonding mode in a 90-µm-diameter microcavity with 400nm thickness silica disks.The effective length increases exponentially with the distance of the two disks.In principle, the minimum effective length can be as small as 4 µm: much smaller than in Fabry-Perot cavities or microtoroids.This value is achievable in practice since current fabrication technique allows the disk spacing to be as small as tens of nanometers.
Note that, in addition to the in-plane TE-like cavity modes presented in Fig. 2, the same device structure also supports orthogonal TM-like mode families.Figure 4 shows a typical mode profile of the TM-like bonding mode.Clearly, due to the distinctive boundary condition of the electromagnetic fields, the optical energy is more confined inside the gap region for the TM-like modes compared with the TE-like modes.This feature is similar to that in a slot waveguide [15].As a result, the TM-like cavity mode is more sensitive to variations in disk spacing, leading to a stronger optomechanical coupling [24].As shown clearly in Fig. 4, the optomechanical coupling coefficient in the TM-like mode is about 30-60% higher than that of the TE-like mode [24].Although various optomechanical photonic structures have been proposed and demonstrated to utilize the optical gradient force, in general, these structures exhibit either quite low optical quality factors or a small optomechanical coupling due to either their intrinsic geometric limitations or practical difficulties in device fabrication.As a result, these photonic structures generally has a dynamic backaction efficiency even lower than in conventional optomechanical cavities based on radiation pressure.In contrast, the whisperinggallery nature of the double-disk microcavity described here allows for extremely high quality optical modes circulating around the disk perimeter.In practice, the optical Q factor is primarily limited by the sidewall roughness.However, it can be significantly mitigated by applying a tilted angle to push the optical mode away from the disk perimeter region [26].FEM simulations show (Fig. 2) that the bonding mode profile remains nearly unchanged with the addition of this sidewall angle.However, the anti-bonding mode experiences significant mode hybridization with higher-order TM-like modes, leading to very low cavity Q factors.As a result, in practice, for devices with very small disk spacing ~100nm, the bonding mode is much easier to observe than the anti-bonding mode [23,24].The double-disk structure supports multiple mechanical normal motions.Some typical examples are shown in Fig. 5, obtained from mechanical FEM simulations.Figure 5(a) shows a lateral flapping mode in which the two disks move opposite to each other.Other modes are radial breathing modes with the two disks moving in parallel.It is clear that only the lateral flapping motion would be strongly actuated by the optical gradient force.In general, the frequency of the flapping mode is dominantly controlled by the length of undercut, while the frequencies of the radial breathing modes are primarily determined by the radius of the pedestal.Due to the whispering-gallery nature of the cavity, the optical mode is pushed to the disk edge and thus is relatively insensitive to the undercut length.This provides flexibility for nearly independent control of the mechanical and optical properties of the structure.By varying the undercut length, we are able to freely engineer the mechanical frequency of the (C) 2009 OSA 9 November 2009 / Vol.17, No. 23 / OPTICS EXPRESS 20916 flapping mode.Figure 6 shows the mechanical frequency as a function of undercut, showing clearly the free control of the mechanical frequency [23,24].The whispering-gallery nature of the structure pushes the cavity mode towards the disk edge, and thus maximizes the mechanical torque for the flapping mechanical motion.Moreover, as the gradient force is symmetric on the two disks, only the undercut regions are involved in the flapping motion.As a result, the flapping mode has a very small effective motional mass [23,24].For the example shown in Fig. 5(a), the effective mass is only 334 pg (see Ref [23].for details about the definition of effective mass), implying a significantly enhanced efficiency of the dynamic backaction.In addition to the undercut length, the effective motional mass also scales inversely with the disk diameter.As a result, by varying the disk diameter while maintaining the same undercut length, we can freely engineer the effective mass without affecting the mechanical frequency [23].Clearly, the double-disk geometry provides great freedom to independently engineer various aspects of the optomechanical properties of the device, enabling optimization of the structure for diverse applications [23,24].In practice, the mechanical quality is primarily determined by the squeeze-film damping from the surrounding gas and the clamping loss from the sandwiched silicon layer [23,24].The main fabrication process for the double disk structure is illustrated in Fig. 7. First, two layers of silica and the sandwiched amorphous silicon (α-Si) layer were deposited on a silicon wafer using plasma-enhanced chemical vapor deposition (PECVD).The wafer was then thermally annealed at 1050 °C for 6 hours under a nitrogen atmosphere in order to densify the PECVD films and improve their optical quality.The double-disk structures were then patterned using electron beam lithography and etched via an anisotropic inductively-coupled plasma reactive ion etch with a C4F8/SF6 gas chemistry.For the final step, the sandwiched αsi layer and the silicon pedestal were simultaneously undercut using a SF 6 chemical plasma release.Figure 8 shows a scanning electron microscope image of the fabricated double disk microcavity.[23,24,28,29].The cavity output is then measured by a fast detector.Figure 10 shows a typical linear transmission spectrum of a TE-polarized bonding mode in a 90-µmdiameter double-disk microcavity.The input optical power is maintained at a very low level (2.8 µW) to prevent any thermal nonlinearity.The measured free spectral range (FSR) is ~6 nm.A detailed scan (inset of Fig. 10(a)) of the bonding mode at a wavelength of 1512.80 nm indicates an intrinsic quality factor of about 1 million.The optical Q factor is primarily limited by the sidewall roughness, the structure uniformity, and the optical quality of the PECVD material.As discussed previously, the high mode hybridization prevents observation of the anti-bonding mode in this spectral region.

Conclusion
In conclusion, we have described and demonstrated a double-disk structure for cavity optomechanics.Both optical and mechanical analyses have been discussed.The mechanical frequency of the flapping mode can be tuned by controlling the undercut of the sandwiched α-Si layer without affecting the optical mode of the cavity.In addition, we have demonstrated the fabrication of a double-disk microcavity with a quality factor of about 1 million.Beyond cavity optomechanics, we believe that the double-disk structure can also find applications in various fields such as biosensing, tunable filtering [24], and optical wavelength conversion [18].

Fig. 2 .
Fig. 2. Mode profiles of the radial component of the electric field for the TE-like cavity mode in a double-disk cavity.(a) bonding and (b) antibonding mode in a cavity with a vertical sidewall.(c) bonding and (d) anti-bonding mode in a practical cavity with a angled sidewall.The mode hybridization is clearly visible for the anti-bonding mode.

Fig. 3 .
Fig. 3. (a) Resonance wavelength (blue) and effective length (green) as a function of disk spacing, for a TE-like bonding mode.(b) The corresponding optomechanical coupling coefficient.

Fig. 4 .
Fig. 4. (a) Mode profiles of the vertical component of the electric field for the TM-like cavity mode.(b) The optomechanical coupling coefficient gOM as a function of disk spacing for the TM-like mode.

Fig. 5 .
Fig. 5. FEM simulations of three typical mechanical modes in a 90-µm-diameter, double-disk cavity with 7 µm undercut, 400 nm thickness for each disk and 200 nm disk spacing.The color map shows the vertical displacement, exaggerated for clarity.

Fig. 6 .
Fig. 6.The mechanical frequency of the flapping mode as a function of undercut width.

Fig. 7 .
Fig. 7. Schematic description of the procedure for fabricating the double-disk microcavities.(a) Deposition of silica, α-silicon, and silica layers on top of a silicon wafer.(b) E-beam lithography to form the microdisk pattern on the mask.(c) RIE dry etching to produce double microdisks.(d) Plasma dry release to partially remove the silicon layers to form the silicon pedestal and partially undercut sandwiched α-silicon layer.

Fig. 9 .
Fig. 9. (a) Schematic of the experimental setup for optical and mechanical measurement.(b) Top-view optical image of the taper-disk coupling system.It is enclosed in a nitrogen environment at atmospheric pressure.VOA: variable optical attenuator.

Figure 9 (
Figure9(a) shows the experimental setup used to characterize the fabricated device.A continuous-wave tunable laser is launched into the cavity through a single-mode tapered fiber (Fig.9(b))[23,24,28,29].The cavity output is then measured by a fast detector.Figure10shows a typical linear transmission spectrum of a TE-polarized bonding mode in a 90-µmdiameter double-disk microcavity.The input optical power is maintained at a very low level (2.8 µW) to prevent any thermal nonlinearity.The measured free spectral range (FSR) is ~6 nm.A detailed scan (inset of Fig.10(a)) of the bonding mode at a wavelength of 1512.80 nm indicates an intrinsic quality factor of about 1 million.The optical Q factor is primarily limited by the sidewall roughness, the structure uniformity, and the optical quality of the

Fig. 10 .
Fig. 10.Linear scan of cavity transmission.The inset shows a detailed scan of the bonding mode at 1512.80 nm, with experimental data in blue and theoretical fit in red. ).