We demonstrate and characterize a thermo-optomechanical oscillator based on a PMMA-coated silica microtoroid and employ it as a sensor. The observed thermo-optomechanical oscillation has a unique waveform that consists of fast and slow oscillation periods. A model based on thermal and optical dynamics of the cavity is used to describe the bi-frequency oscillation and experiments are conducted to validate the theoretical model in order to explore the origin of the two oscillatory phenomena. As opposed to previously shown hybrid toroidal microcavities, the excessive PMMA coating boosts the thermo-mechanical (expansion) effect that results in bi-frequency oscillation when coupled with the thermo-optical effect. The influences of the input power, quality factor, and wavelength detuning on oscillation frequencies are studied experimentally and verified theoretically. Finally the application of this oscillator as a sensor is explored by demonstrating the sensitivity of oscillation frequency to humidity changes.
© 2013 OSA
Low optical loss (high quality factor) and small mode volume make Whispering Gallery (WG) mode microresonators [1–3], such as microspheres and microtoroids, suitable for a variety of studies and applications such as microlasers , nonlinear optical phenomena , photonic biosensing  and cavity quantum electrodynamics (QED) . Specifically, the large circulating optical power inside these microresonators induces optical and thermal nonlinear effects at relatively low input powers [8,9]. In particular the interplay between circulating optical power, resonant wavelength through thermal effects can result in interesting dynamic behavior. Regenerative pulsation at low temperature (competition of Kerr effect and thermal expansion) , thermal and carrier induced optical nonlinearity with pulsed optical excitation , self-modulation of transmission in a silicon microdisk (free carriers and thermal nonlinearity) , thermo-mechanical oscillation in silicon nitride microdisks  oscillatory instability resulting from thermal nonlinearity  and dynamic thermal behavior  are examples of temperature induced phenomena observed in high-Q optical microresonators.
While most studies were focused on microcavities made of one structural material (silica, silicon nitride or silicon), recent developments in the hybrid silica/polymer microcavities have revealed a new class of thermal effects in these microcavities. For example it has been shown that a thin layer of polymer coating with negative thermo-optic coefficient can compensate the silica’s positive thermo-optic coefficient, resulting in an athermal silica microcavity . The large thermo-optical coefficient of polymer materials combined with high quality factor of silica microresonator can be used for sensitive temperature monitoring [15–17]. Recently periodic power variations of the transmission spectrum has been reported in a PDMS coated silica microtoroid . In this hybrid resonator the interplay between circulating power and the resonant wavelength through thermo-optical effect in silica and PDMS results in the oscillatory behavior of the transmitted optical power as the input wavelength is scanned through the resonant wavelength.
Using a similar approach with a different polymer (Poly-methylmethacrylate or PMMA) and coating technique, here we demonstrate a stable self-sustained thermo-optomechanical oscillator. In contrast to the previous report , in this device even at a fixed input wavelength, the optical output power is naturally modulated by a unique waveform that consists of fast and slow oscillation periods. Experimental characterization combined with theoretical analysis of the device has revealed the physical mechanisms responsible for specific waveform generated by this oscillator. Our study shows the slow oscillation is generated by the wavelength shift induced by thermo-mechanical deformation of the bimorph structure, while the fast oscillation is generated by the wavelength shift due to thermal dependence of optical refractive index (thermo-optic effect) in silica and PMMA. The latter phenomenon is similar to the one causing the power variation in Ref. 18 in the wavelength domain.
We study the influence of optical input power, quality factor, and wavelength detuning on oscillation frequencies both experimentally and theoretically. Next we demonstrate the application of this bi-frequency thermo-optomechanical oscillation in monitoring variations in relative humidity.
2. Observation and modeling of self-sustained thermo-optomechanical oscillation
The optical microresonator used in our experiment is a silica microtoroid cavity with a major diameter of D = 42µm, and minor diameter of d = 5.5µm. The silica microtoroid fabrication process is described in Ref. 19. A layer of PMMA (Microchem, PMMA950) is spin coated on chip that contained fifty silica microtoroids. The spin speed was 2000 rpm and after coating, the chip was baked at 90 °C for 10 minutes. Figure 1(a) shows the SEM picture of the bare and PMMA coated silica microtoroid. The estimated thickness (h) of the PMMA layer on the toroidal part is 200 nm (based on SEM imaging). Figure 1(b) shows the calculated cross-sectional optical power distribution for the fundamental WG mode in the hybrid microtoroid. About 4% of the optical power circulates in the PMMA layer. The original microtoroid had an intrinsic quality factor (Qint) of the 3.2 × 107. After PMMA coating, Qint dropped to 2.3 × 106 due to the absorption loss in PMMA. All the experiments in this paper are conducted on a single microtoroid. Note that we have tested several microtoroids with slightly different dimensions but we did not observe any difference in the overall behavior of the device.
A tunable near–IR laser (λ~1550 nm) with a linewidth of 300 kHz is used to study the hybrid microtoroid. The laser light is coupled into and out of the microcavity through a silica fiber-taper. The transmitted optical power is fed to a detector with a bandwidth of 120 MHz and the detected signal was monitored using an oscilloscope. When the laser wavelength was tuned close to the resonant wavelength of a high-Q WGM of the microcavity, self-sustained temporal oscillation of the transmitted optical power was observed as shown in Fig. 1(c). Two periodic variations can be identified in the resulting waveform: a slow oscillation (see the top panel) with a frequency of fL in the 10-300 Hz range and a fast oscillation fH in the 10-100 kHz range. The bottom panel shows the high-frequency oscillation with higher temporal resolution.
Note that in contrast to Ref. 18, where the periodic power variation was observed as the laser wavelength moved toward the resonant wavelength (with a speed of 40nm/s-120nm/s), here the laser wavelength is constant and is kept at a fixed detuning (Δλ = λr-hot-λlaser = 62 pm, where λr-hot is the resonant wavelength of the mode when cavity is in resonance with the laser or λr = λlaser). Since the resonant wavelength of the mode is thermally coupled to the circulating optical power inside the cavity choosing the resonant wavelength at largest circulating power (resulting in maximum local temperature) as a reference to simplify the measurements. While λr-hot can be larger or smaller than the cold-cavity resonant wavelength (λr), their variations are equal (i.e. Δλr = Δλr-hot). The resulting temporal oscillation of the optical output power is very stable and it can last as long as the Δλ remains within certain range (~5-100 pm for the device under test). Moreover in Ref. 18 only the toroidal section of a single silica microtoroid was coated using a fiber-taper (that carried a drop of PDMS) and a micro-positioner (to move the droplet on the microtoroid), while here the PMMA is spin coated using conventional spinner. The spin-coating technique is very simple and can be used to coat all the microresonators on a chip at the same time. However the extra PMMA that covers the silica disk and the silicon pillar has significant impact on the dynamic of the thermo-optomechanical oscillation as shown in this paper.
To understand the dynamics of thermo-optomechanical oscillator and the resulting waveform, we use a modified version of the formalism used in Ref. 18 to explain the periodic power variation during the laser scan for PDMS coated silica microtoroids. The resonant wavelength of the optical mode (λr) is controlled by the radius of the optical path and the effective optical refractive index of the WG mode:
For selective PDMS coated microtoroids (only the toroidal region) in Ref. 18, ΔReff was assumed to be zero. However in our device that is spin-coated with PMMA, finite element method (FEM) thermal modeling shows that absorption of the circulating optical power not only changes the local temperature but also deforms the structure and changes the effective radius (ΔReff) of the mode (Fig. 2(a) ).
Two effects contribute to ΔReff: expansion of the PMMA layer on the toroidal part that increases Reff, and bending of the bimorph (PMMA/silica) structure that decreases Reff. The bending is due to the large difference in thermal expansion coefficients of silica (αexp-1 = 0.55 × 10−6/K) and PMMA (αexp-2 = 2.02 × 10−4/K). Calculations show that for the hybrid microtoroid under test the resulting ΔReff is negative (dominated by the bending effect). The above-mentioned effects have different response times. The thermo-optic effect only depends on the local temperature change in the optical mode region resulting in a relatively fast response (τ1, μs range) while the bending of the bimorph structure (PMMA/silica) depends on the global temperature change and is relatively slow (τ2, ms range) [8, 20]. The schematic diagram in Fig. 2(b) shows the interplay between circulating optical power (Pcirc) and resonant wavelength (λres) through optical absorption and temperature change. Considering both the thermo-optic and thermo-mechanical effects, Eq. (1) can be written as follows:Equation (3) (m = 1: silica, and m = 2: PMMA) describes the heat dissipation from the mode volume; Eq. (4) (n = 3: silica, and n = 4: PMMA) denotes heat dissipation from the cavity structure. Here γth,m and γabs,m are the effective thermal relaxation and optical absorption rates in the optical mode volume; τr ( = 2πneffReff/c) is the cavity round trip time and Ec is the circulating optical field inside the cavity (|Ec(t)| = √Pc(t)/τr); γth,n and gcon,n are the effective thermal relaxation (due to the air and the substrate) and conduction (from the mode volume) rates for the entire structure. Here other high-order effects, such as Kerr nonlinearity, stress induced index variation, coupling between different modes are ignored. The dynamics of the optical field inside the cavity is governed by :Fig. 3 , the temporal oscillation of transmitted optical power predicted by Eqs. (2)-(6) is in good agreement with the experimental results. Specifically the slow and fast periodic variations can be identified in the resulting waveform similar to Fig. 1(c).
As shown in Ref. 18 the thermo-optic effect (dn/dT in PDMS and silica) alone can induce fast oscillatory behavior when the laser is scanned toward the resonant wavelength. Here the slow oscillation due to expansion effects is effectively a self-generated wavelength scanning mechanism that combined with the thermo-optic effect, results in the unique waveform shown in Fig. 3. To validate our physical assumptions and clarify the difference between these two response times (leading to the mixture of fast and slow oscillatory behaviors), two additional experiments are performed.
Figure 4(a) shows the measured resonant wavelength shift as the input power is increased very slowly to observe the impact of the thermo-mechanical effects. Since optical mode mainly resides in silica (that has a positive dneff/dT), in the absence of expansion effects (ΔReff = 0), the neff and therefore λr should increase as the power grows (similar to what is observed in a bare silica microtoroid). In contrary here the negative slope (dλr/dP < 0) indicates that |ΔReff/R| > Δneff/neff (see Eq. (1). Figure 4(b) shows the calculated change of the effective radius (for the device used in part a) plotted against input power.
As expected the value of (ΔReff/R)/P ( = −1.81 × 10−5 /mW) is very close to the value extracted from the experimental results of Fig. 4(a) (−2.09 × 10−5/mW, using Eq. (1), the fact that Δλr/λr = −1.75 × 10−5 and Δneff/neff = 3.4 × 10−6). To compare the effect of the fast thermo-optical and slow thermo-mechanical effects we have scanned the laser wavelength at different speeds near resonance. Figure 5(a) -5(c) show the transmitted optical power (black trace) and the laser wavelength (blue line) as a function of time. The laser wavelength is scanned from 1547.25 nm to 1547.45 nm and back to 1547.25 nm at various speeds (35, 3.5 and 0.35 nm/s).
At large scan speeds (Fig. 5(a)) the fast oscillations due to thermo-optic effect appear in the up-scan region (similar to what is observed in Ref. 18). Note that the red shift of the resonant wavelength (width of the black triangle on the left) shows that the positive thermo-optic effect (dn/dT > 0) is the dominant effect  (as opposed to Fig. 4(a) where the expansion was the dominant effect). When the scan speed is reduced (Fig. 5(b) and 5(c)), the slow expansion effects start playing a role in the thermo-optomechanical dynamic of the system. As a result the red shift is reduced in the up-scan region, while in the down-scan region the mixed oscillatory behavior appears. As shown in Fig. 5(d), when the laser wavelength is fixed (scan speed = 0 nm/s) the temporal behavior of the transmitted optical power resembles the behavior observed in the down-scan at very slow speed (Fig. 5(c)). In conclusion the competition between the inside bending effect and outside expanding effect results in a self-generated scanning thermo-mechanical mechanism that modulates the detuning, while the thermo-optic effect (competition between dn/dT in silica and PMMA) generates the fast oscillations as the detuning is scanned by the slow expansion effects.
3. Characterization of the thermo-optomechanical oscillator
In this section, we explore the influences of input power, loaded quality factor and wavelength detuning on the self-generated thermo-optomechanical oscillation.
3.1) Power dependence of oscillation frequencies
Figure 6(a) shows the fL and fH plotted against input optical power. Both frequencies decrease as we increase the power. The markers are the measured data and the solid lines are the simulation results (based on the frame work defined in 2). Figure 6(b) shows the temporal behavior of the transmitted optical power at different input powers. The time for the deformation to recover (go back to the initial shape/size) becomes longer as the input power increases. This is because more input power translates to a larger temperature increase in the mode volume and subsequently brings much more deformation to the microtoroid caused by thermal expansion.
3.2) Impact of quality factor on oscillation frequencies
Figure 7 shows the effect of total (loaded) quality factor (Qtot) on bi-frequency thermo-optical oscillation. Both frequencies decrease as we increase the power. Here the internal-Q (Qint) is constant and Qtot is varied by changing the coupling factor (coupling gap between fiber-taper and the microtoroid) or the external-Q (Qext). For all data points the microresonator is in the under-coupled regime (Qext > Qint). Qext quantifies the coupling strength and dictates how much power is coupled into the microcavity, so it affects the oscillation in the same manner as the input power. Figure 7(a) shows the fL and fH plotted against Qtot at a constant input optical power of 3.4 mW. Figure 7(b) shows the temporal behavior of the transmitted optical power for different values of Qtot. At large values of Qtot the high frequency oscillation disappears while the low frequency oscillation caused by thermal expansion always exists.
3.3) Impact of wavelength detuning on oscillation frequencies
Figure 8(a) shows fL and fH plotted against wavelength detuning (Δλ = λr-hot− λlaser) at constant input optical power and coupling strength. The markers are the measured data and solid lines are simulation results (based on the frame work defined in 2). Figure 8(b) shows the temporal behavior of the transmitted optical power at different wavelength detunings. The maximum observed value for fL in Fig. 8(a), can be explained by studying the temporal behavior in Fig. 8(b). As Δλ increases the time for the deformation to recover increases while duration of the high frequency oscillation in each period decreases. Therefore, fL reaches the maximum at a balance point during this process. The maximum wavelength detuning that maintains the oscillation is around 140 pm.
4. Application of thermo-optomechanical oscillator in sensing
The sensitivity of the thermo-optomechanical oscillation frequency to power, wavelength detuning and quality factor make this oscillator a potential candidate for a variety of sensing applications. Note that both quality factor and resonant wavelength (and therefore the wavelength detuning) are sensitive to the chemical composition of the surrounding medium [21–24]. The main advantage of this device and the corresponding method over the direct measurement of Q and wavelength shift used in previous resonant optical sensors, is the fact that quality factor and resonant wavelength variations are directly translated to frequency changes in electrical domain eliminating the need for a tunable laser for spectral monitoring. As a proof of concept we have used the thermo-optomechanical oscillator to monitor the humidity of the surrounding medium.
Figure 9 shows the experimental configuration used for humidity sensing. The PMMA-coated microtoroid and the fiber-taper are placed in a closed chamber (atmosphere pressure). A nitrogen bubbler is employed to carry water molecules into the chamber and gradually increase the relative humidity (RH) inside the chamber. A psychrometer (humidity sensor) is used to monitor the RH inside the chamber. Figure 10(a) shows the measured values of fL and fH in the detected waveform plotted against RH. Here laser wavelength, coupling strength (κ) and optical input power are constant. The combination of the parabolic behavior of fL - RH and the linear behavior of fH – RH, can serve as a powerful read-out mechanism for the gas sensing. Basically fH and fL individually can be used for measuring changes in RH while fH – fL crossing points provide references for measuring absolute RH values. Assuming a frequency resolution of 10 Hz the slope of fH – RH (612 Hz/RHU) corresponds to a minimum detectable RH change of about 0.016%. Beyond the resolution of frequency measurement, the sensitivity of the device is limited by the oscillation stability and phase noise. These parameters are dependent on the performance of laser and internal noise mechanisms (such as Brownian noise). So prediction of ultimate sensitivity of the device requires an in-depth study of contributing noise mechanisms that is beyond the scope of this paper.
As evident from the plot the behavior of fL and fH is similar to Fig. 8(a) suggesting that RH is mainly affecting Δλ. Basically as expected the adsorbed water vapor increases the effective refractive index of the mode resulting in the red shift of resonant wavelength (Δλ increases). However a comparison between the measured frequency changes and the expected changes from Fig. 8(a) reveals that quality factor change due to large optical absorption of water, also contributes in the observed frequency change. We have directly measured the cold-cavity resonant wavelength change (Δλr) as a function of relative humidity (Fig. 10(b)) and observed a slope of 11.16 pm/RHU (where RHU corresponds to a relative humidity unit of 1% or RH = 1%). For cold-cavity measurement the optical power is kept low enough to make the thermal effects negligible.
According to Fig. 8(a), ΔfH/Δλr-hot is ~38 Hz/pm (note that Δλr-hot = Δλr). So if ΔfH was only caused by wavelength shift then we should have observed a ΔfH of −424 Hz/RHU (~38 Hz/pm × 11.16 pm/RHU), while the fH-RH slope in Fig. 10(a) is –612 Hz/RHU. The difference (i.e. –188 Hz/RHU) is caused by the optical absorption due to adsorbed water molecules on the surface of the device. Basically the large absorption coefficient of water near 1550 nm (~1050 /m) degrades Qtot and therefore reduces fH (according to Fig. 8(a)).
In conclusion, we have demonstrated a thermo-optomechanical oscillator by spin coating PMMA on silica microtoroids. Using experimental results and theoretical modeling we have identified the mechanisms behind the unique waveform that consists of fast and slow oscillation periods. We have characterized this oscillator by exploring the effect of wavelength detuning, input power and quality factor on the fast and slow oscillation frequencies. Finally we have shown that by translating the quality factor and resonant wavelength variations to oscillation frequency change, the thermo-optomechanical oscillator can function as a sensor. The proof of concept experiment has shown that as a humidity sensor, the thermo-optical mechanical oscillator has a sensitivity of better than 0.016% (RH). By carefully selecting the wavelength, the same approach may be used to detect and quantify other molecules in gaseous form. Specifically when the laser wavelength is close to the unique absorption line of a molecule, optical quality factor and therefore the oscillation frequencies will strongly depend on the concentration of the corresponding molecule. Moreover since presence of nanoparticles on a high-Q optical microresonator can also degrade the quality factor of the optical mode , this device and the corresponding technique may have applications in nanoparticles detection.
Y. Deng thanks Mohammadhosein Ghasemi Baboly for help with FEM thermo-mechanical modeling. This work was in part supported by Air Force Office of Research (Grant#: FA9550-12-1-0049) and National Science Foundation (Grant#: 1055959).
References and links
1. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137(7–8), 393–397 (1989). [CrossRef]
2. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optical coupling to high-Q whispering-gallery-modes,” J. Opt. Soc. Am. B 16(1), 147 (1999). [CrossRef]
4. L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett. 83(5), 825–826 (2003). [CrossRef]
5. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004). [CrossRef] [PubMed]
7. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005). [CrossRef]
8. V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).
12. T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14(2), 817–831 (2006). [CrossRef] [PubMed]
13. C. Baker, S. Stapfner, D. Parrain, S. Ducci, G. Leo, E. M. Weig, and I. Favero, “Optical instability and self-pulsing in silicon nitride whispering gallery resonators,” Opt. Express 20(27), 29076–29089 (2012). [CrossRef] [PubMed]
14. L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93(20), 201102 (2008). [CrossRef]
15. C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett. 94(23), 231119 (2009). [CrossRef]
17. H.-S. Choi and A. M. Armani, “Thermal non-linear effects in hybrid optical microresonators,” Appl. Phys. Lett. 97(22), 223306 (2010). [CrossRef]
18. L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express 17(12), 9571–9581 (2009). [CrossRef] [PubMed]
21. N. A. Yebo, P. Lommens, Z. Hens, and R. Baets, “An integrated optic ethanol vapor sensor based on a silicon-on-insulator microring resonator coated with a porous ZnO film,” Opt. Express 18(11), 11859–11866 (2010). [CrossRef] [PubMed]
22. H. Wang, L. Yuan, C. W. Kim, Q. Han, T. Wei, X. Lan, and H. Xiao, “Optical microresonator based on hollow sphere with porous wall for chemical sensing,” Opt. Lett. 37(1), 94–96 (2012). [CrossRef] [PubMed]
23. H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004). [CrossRef]
24. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23(4), 247–249 (1998). [CrossRef] [PubMed]
25. J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010). [CrossRef]