November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS
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Torsional optical spring effect in coupled nanobeam photonic crystal cavities Feng Tian,1 Guangya Zhou,1,* Fook Siong Chau,1 and Jie Deng2 1
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore 2 Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602, Singapore *Corresponding author: [email protected] Received June 2, 2014; revised October 3, 2014; accepted October 4, 2014; posted October 6, 2014 (Doc. ID 213327); published October 27, 2014 Compared to probe-tuned optomechanical cavity systems, coupled cavity systems have the merit of having much stronger optomechanical interactions. However, to date, the torsional optomechanical effects of coupled cavities have rarely been investigated. In this Letter, we report a torsional optical spring effect in coupled nanobeam photonic crystal cavities. One of the cavities is suspended by a multi-degree-of-freedom spring mechanism that supports torsional vibration modes. The cavities’ light field acts in reverse on the selected torsional mode, thus generating a torsional optical spring effect. The experimental results show that the third-order torsional mode of the spring mechanism is optically stiffened and a maximum frequency increase of 77.1 Hz is obtained. The device provides a novel configuration for the optomechanical design of a new degree of freedom (torsional motion) and the coupled cavities are favorable for strong optomechanical interactions in the torsional direction. © 2014 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (230.4685) Optical microelectromechanical devices. http://dx.doi.org/10.1364/OL.39.006289
Nanomechanical torsional resonators are increasingly important to a range of practical applications, including ultra-sensitive measurements. For example, a ferromagnetic–nonmagnetic hybrid nanotorsional resonator has been proposed to detect the electron spin flip [1]. More recently, a nanomechanical torsional resonator for frequency-shift-based infrared thermal sensing was investigated [2]. In the quantum field, the ultra-sensitive torsional resonator of a superconducting quantum interference device (SQUID) has such a strong back-action of measurement that the corresponding instability created self-sustained oscillations of the resonator [3]. Additionally, nanotorsional resonators have also been successfully applied in torque magnetometry and related fields of research [4,5]. The optical spring effect, a radiation-pressure-induced change in the stiffness of a “mirror spring,” is an important branch of optomechanics. The majority of the reported optical spring effects in nanophotonics are associated with translational motions [6–8]. Recently, torsional optomechanics have been reported [9] in which nanoscale torsional resonators are evanescently coupled to optical microdisk whispering gallery mode resonators. Another sophisticated torsional optomechanical device is the nanoseesaw system, which has one photonic crystal cavity (PCC) on each side [10]. However, optomechanical interactions between cavities and exotic probes [9] or bus waveguides [10] are weaker than those of coupled PCCs [11]. On the other hand, coupled PCCs are widely used in nanoscale optomechanics studies [6,8,12], but the torsional movement of one PCC relative to the coupled other and its related optomechanical interactions are still missing in the literature. In this Letter, we integrate double-coupled nanobeam PCCs suspended with a multi-degree-of-freedom (DOF) spring mechanism [12,13], and investigate the optical spring effects on a selected torsional mechanical mode. 0146-9592/14/216289-04$15.00/0
Figure 1(a) shows a schematic of torsional-motioninduced optomechanical interactions in the doublecoupled nanobeam PCCs, where torsion between the cavities causes a resonance shift of the optical mode. At the same time, the optical torque generated from the optical mode acts in reverse on the motion, thereby altering the cavities’ configuration. The vertical electrostatic force can drive an out-of-plane bend of the coupled cavities [14]. However, it is very difficult to experimentally realize a static torsion between the cavities, as that requires a pair of anti-symmetric vertical electrostatic forces on both sides of the cavity beam. This would be difficult to realize in a silicon-on-insulator (SOI) chip. Therefore, we instead studied the dynamic optomechanical properties of a selected torsional mode of the aforementioned multi-DOF spring mechanism. The fabricated coupled PCCs corresponding to the schematic in Fig. 1(a) are shown in Fig. 1(b). Figure 1(c) is the global SEM view of the whole device. For its schematic, we can refer to Fig. 1(a) in [15]. One of the coupled nanobeam PCCs, a1 , is fixed and connects with the input and output rib waveguides, while the other movable cavity, a2 , is attached to the mass m2 and driven by the multiDOF spring mechanism. Nanobeam PCCs are designed by the rules of high quality factor (Q factor) and high transmission [16]. The two nanobeam PCCs are identical; the beam width is 720 nm, the invariable lattice period is 300 nm for all holes, and the holes’ diameters are tapered from 200 nm in the center to 30 nm on both sides after 39 lattices. As shown in Fig. 1(c), the multi-DOF spring mechanism consists of three nanoelectromechanical system (NEMS) springs formed by folded beams, marked as k1 , k2 , and k3 . Parts of these three springs are magnified in Fig. 1(d). The beams of spring k1 have a length of 15 μm and a width of 375 nm, while springs k2 and k3 have identical beam dimensions of 15 μm in length and 220 nm in width. Using the finite element method (FEM), the spring constants of k1 , k2 , and k3 are found to be 1.996, 0.104, © 2014 Optical Society of America
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in Refs. [9] and [10], for example) are not only applicable but also have the advantages of simpler configuration and a smaller footprint over the spring mechanism reported here. A setup for testing the device is shown in the schematic in Fig. 2(a). The device is loaded into a vacuum chamber (10−7 bar), and a pair of fibers are used to couple light into and out of the device through grating couplers. Light from a tunable laser source (TLS, Ando AQ4321D) is amplified by an erbium-doped fiber amplifier (EDFA). Transverse electric (TE)-like modes in coupled nanobeam PCCs are excited by adjusting the fiber polarization controller, which is placed after the fiber polarizer. The light from the device is split into two routes, one of which is guided into an optical spectrum analyzer (OSA, Ando
Fig. 1. (a) Schematic of torsional optomechanical interactions in double-coupled nanobeam PCCs where the electric field profile of the fourth-order even optical resonance mode is overlapped. Cavity a1 is fixed, and cavity a2 rotates (red arrows) around the central axis of both cavities (red dotted line). (b) Scanning electron microscope (SEM) image of the fabricated coupled cavities corresponding to the schematic in (a). (c) SEM image of a whole device where a multi-degree-offreedom (DOF) spring mechanism supports torsional mechanical modes. The anchors of the mechanism are marked with red arrows. (d) and (e) Magnified SEM images of the three springs (d) and the comb drive (e).
and 0.207 N/m, respectively. To excite the mechanical resonance modes of the mechanism, a NEMS comb drive, as shown in Fig. 1(e), is integrated into the mass m1 . All structures have a uniform thickness of 260 nm. An SOI wafer with a device layer of 260 nm and BOX layer of 1 μm is used to fabricate the device. The first electron beam lithography (EBL) forms the patterns of the suspended cavities and NEMS structures. A process of inductively coupled plasma reactive ion etching (ICP– RIE) transfers the patterns onto the whole device layer. The second EBL writes the tapered rib waveguides and grating couplers, while the second ICP–RIE etches patterns into the device layer with a depth of 80 nm. Electrodes and isolation trenches for applying voltages to the NEMS comb drive are fabricated by the processes of photolithography, ICP–RIE, metal electron beam evaporation, and liftoff. Finally, the wafer is diced into 6 mm × 6 mm chips and the suspended cavities and NEMS structures are released from the buried oxide (BOX) layer by etching with hydrogen fluoride (HF) vapor. Compared with the torsional nanoseesaw system in [10], the spring mechanism in Fig. 1(c) looks complicated but is better able to cope with the surface tension that can cause the suspended PCCs to collapse onto the substrate during HF release. However, with the benefit of state-of-theart release processes, seesaw-like structures (the devices
Fig. 2. (a) Schematic of setup used to test the device. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; FP, fiber polarizer; FPC, fiber polarization controller; CUT, chip under test; OSA, optical spectrum analyzer; PD, photodetector; NA, network analyzer. (b) Measured mechanical mode spectrum of the spring mechanism. O1, the first-order out-of-plane mode; I1, the first-order in-plane mode; T1, the first-order torsional mode; T3, the third-order torsional mode. Insets: finite element method (FEM) simulated motions of O1, I1, and T1 modes. (c) FEM simulated motion of T3 mode. The motions of these four modes all are normalized to the maximum amplitude of the T3 mode.
November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS
AQ6317C). The other is launched into a high-speed photodetector (PD). A network analyzer (NA, Agilent 4395A) inputs an RF signal to the comb drive to excite resonances of the device and simultaneously acquire the cavities’ signal from the PD. To measure the mechanical mode spectrum of the presented spring mechanism, the TLS wavelength is detuned half an optical linewidth away from the fourth-order even cavities’ mode (TEe;4 ) [15]. The NA source provides an excitation of −30 dBm. The measured spectrum is plotted in Fig. 2(b). As shown, there are four detected mechanical modes below 800 kHz, which are at 328.6, 335.1, 397.8, and 750.1 kHz. Each mode is recognized by FEM simulations. The motions of the first three modes are plotted as insets in Fig. 2(b). The modes can be categorized into in-plane translational (I), out-of-plane translational (O), and torsional (T) modes, according to the directions of their motions. Clearly, the first three modes are the first-order out-of-plane translational (O1), the first-order in-plane translational (I1), and the first-order torsional (T1) modes, respectively. For the torsional modes of interest here, after T1 mode, there is T2 mode at around 700 kHz, but its motion is such that the spring k2 rotates by a large angle while springs k1 , k3 , and cavity a2 rotate very little, making it difficult to detect. T3 mode is observed at 750.1 kHz; its motion is plotted in Fig. 2(c). As opposed to T1 mode, in which springs k2 , k3 , and the cavity rotate in phase, T3 mode reverses the phase of spring k2 . However, the torsional amplitudes of the cavity in T1 and T3 modes are approximately equal. It has been found to be very hard to excite the torsional resonance
Fig. 3. (a) Measured transmission spectrum of the cavities’ fourth-order even (TEe;4 ) resonance mode, the black solid line is the Lorentz fit to the measured data (red dots). (b) Mechanical frequency and Q factor of the spring mechanism’s T3 mode probed by various detuned wavelengths across the peak in (a).
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mode for individual folded-beam-spring, but here, the excitations of the torsional modes benefit from the threespring configuration (k2 and k3 are more flexible than k1 ). The optical spectrum of the coupled nanobeam PCCs is recorded by OSA. A magnified peak of TEo;4 mode, shown in Fig. 3(a), is at 1594.37 nm and has Q factor of 6900. The measurement is conducted first at a low input power, which is estimated to be at 80 μW in the waveguide just before the cavities. The T3 mechanical mode is chosen to investigate the torsional optical spring effect. The mechanical frequency shift of T3 mode versus wavelength sweeping across the TEo;4 resonance while keeping the input laser power fixed is plotted in Fig. 3(b). There is an observable drop in frequency when the wavelength sweeps through the peak, which demonstrates a similar trend as the translational optical spring effects previously reported [6,8]. However, the frequency does
Fig. 4. (a) Measured nonlinear spectrum of TEe;4 mode at high input power. The solid blue line is the fit to the measured data (red dots). (b) Network analyzer recorded mechanical spectrum of T3 mode at different pump wavelengths. For display purposes, each curve is relatively shifted by 10 dB in the vertical axis. (c) Mechanical frequency and Q factor of the spring mechanism’s T3 mode versus pump wavelengths along the curve in (a).
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not shift more than 30 Hz, and the variations on both sides are not prominent, so the torsional optical spring effect is weaker than that in the translational one. Variations of the mechanical Q factor are also shown in Fig. 3(b), and have a minimum at around the peak wavelength. The input laser power is then increased to 370 μW in the waveguide, just before the cavities. As shown in Fig. 4(a), a nonlinear phenomenon appears. This is attributed to the optomechanical and thermo-optic effects [17]. The measured data in Fig. 4(a) are fitted by the optical bistable model of Eqs. 3 and 4 in [17]. Pumped at wavelengths of 1593.9, 1594.2, 1594.5, and 1594.8 nm, as shown in Fig. 4(b), the frequency of T3 mode is gradually changed and a maximum tuning of 77.1 Hz is obtained. The torsional optical spring effect pumped by wavelengths along the nonlinear curve in Fig. 4(a) can be seen in Fig. 4(c). As the wavelength and optical power inside the cavities increase, the mechanical frequency of the T3 mode increases, which means that the optical torque from the cavities’ TEo;4 mode stiffens the spring mechanism. Meanwhile, the T3’s Q factor decreases, which indicates an increased damping by the optical field in the torsional direction. As can be expected, if the wavelength is further increased, there will be a drop in the frequency curve of the T3 mode corresponding to the drop in Fig. 1(a). Here, however, after the drop in the optical spectrum, the light carrying the vibration signal is too weak to be detected. In the left region of the drop point, the wavelengths are blue-detuned [17], so they have the same stiffening effect on the T3 mode as the blue-detuned wavelengths at a weak input light in the left half of Fig. 3(b). In fact, at both weak and strong input light power, the basic theory of torsional optical spring effect is the same as those of translation [6,18]. In conclusion, we have experimentally investigated the dynamic interactions between a torsional mechanical mode and the light field in coupled nanobeam PCCs, and have demonstrated the torsional optical spring effect. The torsional mechanical mode is generated in a multiDOF spring mechanism and TEo;4 light mode applies a torque on the mechanism. At lower input light power, the torsional optical spring effect is weak but detectable, while at higher input light power, the torsional optical
spring effect is manifested as a stiffening and damping of the mechanical resonance. This work is supported by MOE Research grant R-265-000-416-112. Devices are fabricated in the SERC Nanofabrication and Characterization Facility (SNFC), Institute of Materials Research and Engineering, A*STAR, Singapore. References 1. G. Zolfagharkhani, A. Gaidarzhy, P. Degiovanni, S. Kettemann, P. Fulde, and P. Mohanty, Nat. Nanotechnol. 3, 720 (2008). 2. X. C. Zhang, E. B. Myers, J. E. Sader, and M. L. Roukes, Nano Lett. 13, 1528 (2013). 3. S. Etaki, F. Konschelle, Y. M. Blanter, H. Yamaguchi, and H. S. J. van der Zant, Nat. Commun. 4, 1803 (2013). 4. J. P. Davis, D. Vick, D. C. Fortin, J. A. J. Burgess, W. K. Hiebert, and M. R. Freeman, Appl. Phys. Lett. 96, 072513 (2010). 5. J. A. J. Burgess, A. E. Fraser, F. F. Sani, D. Vick, B. D. Hauer, J. P. Davis, and M. R. Freeman, Science 339, 1051 (2013). 6. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009). 7. D. V. Thourhout and J. Roels, Nat. Photonics 4, 211 (2010). 8. P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, Nat. Commun. 3, 846 (2012). 9. P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, Appl. Phys. Lett. 102, 053102 (2013). 10. H. Li and M. Li, in Conference on Lasers and Electro-Optics: 2014, OSA Technical Digest (Optical Society of America, 2014), paper FTH1K.5. 11. X. Chew, G. Zhou, H. Yu, F. S. Chau, J. Deng, Y. C. Loke, and X. Tang, Opt. Express 18, 22232 (2010). 12. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, X. Tang, and R. Akkipeddi, Opt. Express 21, 18398 (2013). 13. T. Tsuchiya, Y. Ura, K. Sugano, and O. Tabata, J. Microelectromech. Syst. 21, 523 (2012). 14. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, and R. Akkipeddi, Opt. Lett. 38, 2005 (2013). 15. F. Tian, G. Zhou, F. S. Chau, J. Deng, and R. Akkipeddi, Appl. Phys. Lett. 102, 081101 (2013). 16. Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010). 17. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, S. L. Teo, and R. Akkipeddi, Opt. Lett. 38, 3394 (2013). 18. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
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Torsional optical spring effect in coupled nanobeam photonic crystal cavities Feng Tian,1 Guangya Zhou,1,* Fook Siong Chau,1 and Jie Deng2 1
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore 2 Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602, Singapore *Corresponding author: [email protected] Received June 2, 2014; revised October 3, 2014; accepted October 4, 2014; posted October 6, 2014 (Doc. ID 213327); published October 27, 2014 Compared to probe-tuned optomechanical cavity systems, coupled cavity systems have the merit of having much stronger optomechanical interactions. However, to date, the torsional optomechanical effects of coupled cavities have rarely been investigated. In this Letter, we report a torsional optical spring effect in coupled nanobeam photonic crystal cavities. One of the cavities is suspended by a multi-degree-of-freedom spring mechanism that supports torsional vibration modes. The cavities’ light field acts in reverse on the selected torsional mode, thus generating a torsional optical spring effect. The experimental results show that the third-order torsional mode of the spring mechanism is optically stiffened and a maximum frequency increase of 77.1 Hz is obtained. The device provides a novel configuration for the optomechanical design of a new degree of freedom (torsional motion) and the coupled cavities are favorable for strong optomechanical interactions in the torsional direction. © 2014 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (230.4685) Optical microelectromechanical devices. http://dx.doi.org/10.1364/OL.39.006289
Nanomechanical torsional resonators are increasingly important to a range of practical applications, including ultra-sensitive measurements. For example, a ferromagnetic–nonmagnetic hybrid nanotorsional resonator has been proposed to detect the electron spin flip [1]. More recently, a nanomechanical torsional resonator for frequency-shift-based infrared thermal sensing was investigated [2]. In the quantum field, the ultra-sensitive torsional resonator of a superconducting quantum interference device (SQUID) has such a strong back-action of measurement that the corresponding instability created self-sustained oscillations of the resonator [3]. Additionally, nanotorsional resonators have also been successfully applied in torque magnetometry and related fields of research [4,5]. The optical spring effect, a radiation-pressure-induced change in the stiffness of a “mirror spring,” is an important branch of optomechanics. The majority of the reported optical spring effects in nanophotonics are associated with translational motions [6–8]. Recently, torsional optomechanics have been reported [9] in which nanoscale torsional resonators are evanescently coupled to optical microdisk whispering gallery mode resonators. Another sophisticated torsional optomechanical device is the nanoseesaw system, which has one photonic crystal cavity (PCC) on each side [10]. However, optomechanical interactions between cavities and exotic probes [9] or bus waveguides [10] are weaker than those of coupled PCCs [11]. On the other hand, coupled PCCs are widely used in nanoscale optomechanics studies [6,8,12], but the torsional movement of one PCC relative to the coupled other and its related optomechanical interactions are still missing in the literature. In this Letter, we integrate double-coupled nanobeam PCCs suspended with a multi-degree-of-freedom (DOF) spring mechanism [12,13], and investigate the optical spring effects on a selected torsional mechanical mode. 0146-9592/14/216289-04$15.00/0
Figure 1(a) shows a schematic of torsional-motioninduced optomechanical interactions in the doublecoupled nanobeam PCCs, where torsion between the cavities causes a resonance shift of the optical mode. At the same time, the optical torque generated from the optical mode acts in reverse on the motion, thereby altering the cavities’ configuration. The vertical electrostatic force can drive an out-of-plane bend of the coupled cavities [14]. However, it is very difficult to experimentally realize a static torsion between the cavities, as that requires a pair of anti-symmetric vertical electrostatic forces on both sides of the cavity beam. This would be difficult to realize in a silicon-on-insulator (SOI) chip. Therefore, we instead studied the dynamic optomechanical properties of a selected torsional mode of the aforementioned multi-DOF spring mechanism. The fabricated coupled PCCs corresponding to the schematic in Fig. 1(a) are shown in Fig. 1(b). Figure 1(c) is the global SEM view of the whole device. For its schematic, we can refer to Fig. 1(a) in [15]. One of the coupled nanobeam PCCs, a1 , is fixed and connects with the input and output rib waveguides, while the other movable cavity, a2 , is attached to the mass m2 and driven by the multiDOF spring mechanism. Nanobeam PCCs are designed by the rules of high quality factor (Q factor) and high transmission [16]. The two nanobeam PCCs are identical; the beam width is 720 nm, the invariable lattice period is 300 nm for all holes, and the holes’ diameters are tapered from 200 nm in the center to 30 nm on both sides after 39 lattices. As shown in Fig. 1(c), the multi-DOF spring mechanism consists of three nanoelectromechanical system (NEMS) springs formed by folded beams, marked as k1 , k2 , and k3 . Parts of these three springs are magnified in Fig. 1(d). The beams of spring k1 have a length of 15 μm and a width of 375 nm, while springs k2 and k3 have identical beam dimensions of 15 μm in length and 220 nm in width. Using the finite element method (FEM), the spring constants of k1 , k2 , and k3 are found to be 1.996, 0.104, © 2014 Optical Society of America
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in Refs. [9] and [10], for example) are not only applicable but also have the advantages of simpler configuration and a smaller footprint over the spring mechanism reported here. A setup for testing the device is shown in the schematic in Fig. 2(a). The device is loaded into a vacuum chamber (10−7 bar), and a pair of fibers are used to couple light into and out of the device through grating couplers. Light from a tunable laser source (TLS, Ando AQ4321D) is amplified by an erbium-doped fiber amplifier (EDFA). Transverse electric (TE)-like modes in coupled nanobeam PCCs are excited by adjusting the fiber polarization controller, which is placed after the fiber polarizer. The light from the device is split into two routes, one of which is guided into an optical spectrum analyzer (OSA, Ando
Fig. 1. (a) Schematic of torsional optomechanical interactions in double-coupled nanobeam PCCs where the electric field profile of the fourth-order even optical resonance mode is overlapped. Cavity a1 is fixed, and cavity a2 rotates (red arrows) around the central axis of both cavities (red dotted line). (b) Scanning electron microscope (SEM) image of the fabricated coupled cavities corresponding to the schematic in (a). (c) SEM image of a whole device where a multi-degree-offreedom (DOF) spring mechanism supports torsional mechanical modes. The anchors of the mechanism are marked with red arrows. (d) and (e) Magnified SEM images of the three springs (d) and the comb drive (e).
and 0.207 N/m, respectively. To excite the mechanical resonance modes of the mechanism, a NEMS comb drive, as shown in Fig. 1(e), is integrated into the mass m1 . All structures have a uniform thickness of 260 nm. An SOI wafer with a device layer of 260 nm and BOX layer of 1 μm is used to fabricate the device. The first electron beam lithography (EBL) forms the patterns of the suspended cavities and NEMS structures. A process of inductively coupled plasma reactive ion etching (ICP– RIE) transfers the patterns onto the whole device layer. The second EBL writes the tapered rib waveguides and grating couplers, while the second ICP–RIE etches patterns into the device layer with a depth of 80 nm. Electrodes and isolation trenches for applying voltages to the NEMS comb drive are fabricated by the processes of photolithography, ICP–RIE, metal electron beam evaporation, and liftoff. Finally, the wafer is diced into 6 mm × 6 mm chips and the suspended cavities and NEMS structures are released from the buried oxide (BOX) layer by etching with hydrogen fluoride (HF) vapor. Compared with the torsional nanoseesaw system in [10], the spring mechanism in Fig. 1(c) looks complicated but is better able to cope with the surface tension that can cause the suspended PCCs to collapse onto the substrate during HF release. However, with the benefit of state-of-theart release processes, seesaw-like structures (the devices
Fig. 2. (a) Schematic of setup used to test the device. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; FP, fiber polarizer; FPC, fiber polarization controller; CUT, chip under test; OSA, optical spectrum analyzer; PD, photodetector; NA, network analyzer. (b) Measured mechanical mode spectrum of the spring mechanism. O1, the first-order out-of-plane mode; I1, the first-order in-plane mode; T1, the first-order torsional mode; T3, the third-order torsional mode. Insets: finite element method (FEM) simulated motions of O1, I1, and T1 modes. (c) FEM simulated motion of T3 mode. The motions of these four modes all are normalized to the maximum amplitude of the T3 mode.
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AQ6317C). The other is launched into a high-speed photodetector (PD). A network analyzer (NA, Agilent 4395A) inputs an RF signal to the comb drive to excite resonances of the device and simultaneously acquire the cavities’ signal from the PD. To measure the mechanical mode spectrum of the presented spring mechanism, the TLS wavelength is detuned half an optical linewidth away from the fourth-order even cavities’ mode (TEe;4 ) [15]. The NA source provides an excitation of −30 dBm. The measured spectrum is plotted in Fig. 2(b). As shown, there are four detected mechanical modes below 800 kHz, which are at 328.6, 335.1, 397.8, and 750.1 kHz. Each mode is recognized by FEM simulations. The motions of the first three modes are plotted as insets in Fig. 2(b). The modes can be categorized into in-plane translational (I), out-of-plane translational (O), and torsional (T) modes, according to the directions of their motions. Clearly, the first three modes are the first-order out-of-plane translational (O1), the first-order in-plane translational (I1), and the first-order torsional (T1) modes, respectively. For the torsional modes of interest here, after T1 mode, there is T2 mode at around 700 kHz, but its motion is such that the spring k2 rotates by a large angle while springs k1 , k3 , and cavity a2 rotate very little, making it difficult to detect. T3 mode is observed at 750.1 kHz; its motion is plotted in Fig. 2(c). As opposed to T1 mode, in which springs k2 , k3 , and the cavity rotate in phase, T3 mode reverses the phase of spring k2 . However, the torsional amplitudes of the cavity in T1 and T3 modes are approximately equal. It has been found to be very hard to excite the torsional resonance
Fig. 3. (a) Measured transmission spectrum of the cavities’ fourth-order even (TEe;4 ) resonance mode, the black solid line is the Lorentz fit to the measured data (red dots). (b) Mechanical frequency and Q factor of the spring mechanism’s T3 mode probed by various detuned wavelengths across the peak in (a).
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mode for individual folded-beam-spring, but here, the excitations of the torsional modes benefit from the threespring configuration (k2 and k3 are more flexible than k1 ). The optical spectrum of the coupled nanobeam PCCs is recorded by OSA. A magnified peak of TEo;4 mode, shown in Fig. 3(a), is at 1594.37 nm and has Q factor of 6900. The measurement is conducted first at a low input power, which is estimated to be at 80 μW in the waveguide just before the cavities. The T3 mechanical mode is chosen to investigate the torsional optical spring effect. The mechanical frequency shift of T3 mode versus wavelength sweeping across the TEo;4 resonance while keeping the input laser power fixed is plotted in Fig. 3(b). There is an observable drop in frequency when the wavelength sweeps through the peak, which demonstrates a similar trend as the translational optical spring effects previously reported [6,8]. However, the frequency does
Fig. 4. (a) Measured nonlinear spectrum of TEe;4 mode at high input power. The solid blue line is the fit to the measured data (red dots). (b) Network analyzer recorded mechanical spectrum of T3 mode at different pump wavelengths. For display purposes, each curve is relatively shifted by 10 dB in the vertical axis. (c) Mechanical frequency and Q factor of the spring mechanism’s T3 mode versus pump wavelengths along the curve in (a).
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not shift more than 30 Hz, and the variations on both sides are not prominent, so the torsional optical spring effect is weaker than that in the translational one. Variations of the mechanical Q factor are also shown in Fig. 3(b), and have a minimum at around the peak wavelength. The input laser power is then increased to 370 μW in the waveguide, just before the cavities. As shown in Fig. 4(a), a nonlinear phenomenon appears. This is attributed to the optomechanical and thermo-optic effects [17]. The measured data in Fig. 4(a) are fitted by the optical bistable model of Eqs. 3 and 4 in [17]. Pumped at wavelengths of 1593.9, 1594.2, 1594.5, and 1594.8 nm, as shown in Fig. 4(b), the frequency of T3 mode is gradually changed and a maximum tuning of 77.1 Hz is obtained. The torsional optical spring effect pumped by wavelengths along the nonlinear curve in Fig. 4(a) can be seen in Fig. 4(c). As the wavelength and optical power inside the cavities increase, the mechanical frequency of the T3 mode increases, which means that the optical torque from the cavities’ TEo;4 mode stiffens the spring mechanism. Meanwhile, the T3’s Q factor decreases, which indicates an increased damping by the optical field in the torsional direction. As can be expected, if the wavelength is further increased, there will be a drop in the frequency curve of the T3 mode corresponding to the drop in Fig. 1(a). Here, however, after the drop in the optical spectrum, the light carrying the vibration signal is too weak to be detected. In the left region of the drop point, the wavelengths are blue-detuned [17], so they have the same stiffening effect on the T3 mode as the blue-detuned wavelengths at a weak input light in the left half of Fig. 3(b). In fact, at both weak and strong input light power, the basic theory of torsional optical spring effect is the same as those of translation [6,18]. In conclusion, we have experimentally investigated the dynamic interactions between a torsional mechanical mode and the light field in coupled nanobeam PCCs, and have demonstrated the torsional optical spring effect. The torsional mechanical mode is generated in a multiDOF spring mechanism and TEo;4 light mode applies a torque on the mechanism. At lower input light power, the torsional optical spring effect is weak but detectable, while at higher input light power, the torsional optical
spring effect is manifested as a stiffening and damping of the mechanical resonance. This work is supported by MOE Research grant R-265-000-416-112. Devices are fabricated in the SERC Nanofabrication and Characterization Facility (SNFC), Institute of Materials Research and Engineering, A*STAR, Singapore. References 1. G. Zolfagharkhani, A. Gaidarzhy, P. Degiovanni, S. Kettemann, P. Fulde, and P. Mohanty, Nat. Nanotechnol. 3, 720 (2008). 2. X. C. Zhang, E. B. Myers, J. E. Sader, and M. L. Roukes, Nano Lett. 13, 1528 (2013). 3. S. Etaki, F. Konschelle, Y. M. Blanter, H. Yamaguchi, and H. S. J. van der Zant, Nat. Commun. 4, 1803 (2013). 4. J. P. Davis, D. Vick, D. C. Fortin, J. A. J. Burgess, W. K. Hiebert, and M. R. Freeman, Appl. Phys. Lett. 96, 072513 (2010). 5. J. A. J. Burgess, A. E. Fraser, F. F. Sani, D. Vick, B. D. Hauer, J. P. Davis, and M. R. Freeman, Science 339, 1051 (2013). 6. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009). 7. D. V. Thourhout and J. Roels, Nat. Photonics 4, 211 (2010). 8. P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, Nat. Commun. 3, 846 (2012). 9. P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, Appl. Phys. Lett. 102, 053102 (2013). 10. H. Li and M. Li, in Conference on Lasers and Electro-Optics: 2014, OSA Technical Digest (Optical Society of America, 2014), paper FTH1K.5. 11. X. Chew, G. Zhou, H. Yu, F. S. Chau, J. Deng, Y. C. Loke, and X. Tang, Opt. Express 18, 22232 (2010). 12. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, X. Tang, and R. Akkipeddi, Opt. Express 21, 18398 (2013). 13. T. Tsuchiya, Y. Ura, K. Sugano, and O. Tabata, J. Microelectromech. Syst. 21, 523 (2012). 14. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, and R. Akkipeddi, Opt. Lett. 38, 2005 (2013). 15. F. Tian, G. Zhou, F. S. Chau, J. Deng, and R. Akkipeddi, Appl. Phys. Lett. 102, 081101 (2013). 16. Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010). 17. F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, S. L. Teo, and R. Akkipeddi, Opt. Lett. 38, 3394 (2013). 18. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).
