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Nanoscale all-optical circuits driven by optical forces have broad applications in future communication, computation, and sensing systems. Because human society faces huge challenges of energy saving and emission reduction, it is very important to develop energy-efficient nano-optomechanical devices. Due to their high quality (Q) factors, resonance modes of cavities are capable of generating much larger forces than waveguide modes. Here we experimentally demonstrate the use of resonance modes of double-coupled one-dimensional photonic crystal cavities to generate bipolar optical forces. Attractive and repulsive forces of −6.2 nN and 1.9 nN were obtained with respective launching powers of 0.81 mW and 0.87 mW in the waveguide just before cavities. Supported by flexible nanosprings (spring constant 0.166 N/m), one cavity is pulled to (pushed away from) the other cavity by 37.1 nm (11.4 nm). The shifts of the selected resonance modes of the device are mechanically and thermally calibrated with an integrated nanoelectromechanical system actuator and a temperature-controlled testing platform respectively. Based on these experimentally-obtained relations, probe mode shifts due to the optomechanical effect are decoupled from those due to the thermo-optic effect. Actuated by the third-order even pump mode, the optomechanical shift of the second-order even probe mode is found to be about 2.5 times its thermal shift, indicating a highly efficient conversion of light energy to mechanical energy.
©2013 Optical Society of America
1. Introduction
Based on the state-of-the-art nanofabrication platform, nano-optomechanical devices combining nanophotonics and nanomechanics have been advanced rapidly [1–16]. Optical gradient forces produced in these nano-optomechanical devices can mechanically reconfigure nanophotonic circuits, which unfolds new dimensions for innovations in future photonic communication and signal processing [17–19]. Recently, the optical gradient force has been experimentally demonstrated in various photonic devices, such as waveguides [1, 2], photonic crystal cavities [3], ring resonators and disk resonators [4–6]. The optical force can be switched between attraction and repulsion by adjusting the optical mode, which is favorable to the versatile control of photonic structures. Bipolar tunings of coupled waveguides [1, 2] and coupled ring resonators [4] have been experimentally demonstrated, in which anti-symmetric and symmetric optical modes produce repulsive and attractive forces respectively. However, to the best of our knowledge, bipolar optical forces based on coupled one-dimensional photonic crystal cavities (1D PCCs) has not been reported. In fact, 1D PCCs are well suited for the construction of optomechanical devices due to their small footprint, high Q-factor, small mass, and design flexibility. Additionally, in double-coupled 1D PCCs, there are intrinsic odd (anti-symmetric) and even (symmetric) superposition modes corresponding to the repulsive and attractive forces respectively [20–22], whereas in coupled waveguides, bipolar optical forces must resort to an additional Mach-Zehnder interferometer to form anti-symmetric and symmetric propagating modes. Filters of double-coupled 1D PCCs actuated by optical forces of propagating waveguide modes have been successfully demonstrated [17]. However, theoretical analysis shows that cavity resonance modes can generate extremely larger optical forces due to their high Q-factors [16, 17]. Here, we first realize the bipolar optical forces in double-coupled 1D PCCs utilizing their resonance modes with high energy efficiency.
Optomechanical devices exploiting ultrahigh frequency operation of mechanical modes of nanoscale structures is attractive for high-speed sensors with ultimate sensitivity [23, 24]. Besides this, another important aspect of optomechanical devices is tuning magnitude, which is catered for applications such as optical filters and routers [7, 16]. In the work reported here, we recorded, as far as we know, the largest bipolar displacements driven by much lower optical pump power. This due to not only the high optical forces generated as a result of using the resonance modes, but also the design of suspended beams of low rigidity to support one of the coupled 1D PCCs. Additionally, in previously reported work, there was no direct measurement of the displacement, so the measured optical signal is combined with numerical simulation to determine the optical-force-induced displacement [4, 17]. In our design, a nanoelectromechanical system (NEMS) actuator is integrated with the cavity suspension structures, which enables us to precisely and straightforwardly calibrate the relation between the shift of probe resonance and the cavities’ gap by means of a scanning electron microscope (SEM).
2. Design, fabrication and characterization
A schematic of the experimental setup for characterizing the developed device is shown in Fig. 1(a). Light from a tunable laser source TLS-1 (Santec TLS-510) amplified by an erbium-doped fiber amplifier is used as pump light, while another tunable laser source TLS-2 (ANDO AQ4321D) operating at a much lower power is used as probe light. To excite transverse electric (TE) mode in the device, both arms of pump and probe light are adjusted by polarization controllers before they are combined into an input fiber to the chip through a 2 × 1 fiber coupler. Input and output fibers which are separately secured on two XYZ-stages are coupled with the device through their respective grating couplers. Light collected by the output fiber is divided into two halves by a 1 × 2 fiber splitter, one of which is acquired by an optical spectrum analyzer OSA (ANDO AQ6317C) and the other is detected by a power meter used to monitor the pump power. The TLS and OSA can synchronously sweep through wavelengths from 1520 nm to 1620 nm with the smallest sweep interval at 1 pm. A DC power supply connected with the device is used to apply DC voltage to the NEMS actuator. The microscope image on the lower right side of Fig. 1(a) shows an overview of the device under test, in which the two grating couplers, tapered rib waveguides, and central suspended structures are displayed. The patterns surrounding the device are parts of isolation trenches and electrode pads which are used to electrically characterize the device.
Fig. 1 (a) Schematic of setup used to characterize 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. Inset: microscope image of the CUT. (b) Scanning electron microscope (SEM) image of the suspended structures in the central region of the device, where springs, rigid masses, and comb drives are annotated. (c) Magnified SEM image showing the double-coupled cavities with a central gap width of 144.2 nm.
An SEM image of the suspended structures of the device is shown in Fig. 1(b). One of the double-coupled 1D PCCs is integrated with the suspended rectangular waveguides which is further connected with the rib waveguides, while the other 1D PCC is movable since it is supported by the folded free-standing beams that act as NEMS springs. There are three springs with spring constants of k1, k2 and k3 respectively, forming a displacement shrinkage mechanism with nanometer resolution [25, 26]. The force of the NEMS comb drive (F) is applied to the mass m1 and the displacement ratio of m2 and m1 is k2: k2 + k3. The cavities’ gap change (Δg) can be represented as . The beams of spring k1 has a length of 15 µm and width of 374 nm while springs k2 and k3 have identical beam dimensions of 15 µm length and 165 nm width, thereby making k1: k2: k3 ≈47: 1: 2 from theoretical calculation. The value of is calculated as 7.7 N/m by means of a finite-element method (FEM) simulation. In the comb drive region, there are 84 movable fingers with an initial finger overlap of 480 nm, finger width of 180 nm and finger gap spacing of 230 nm.
The design of the 1D PCC complies with the principles of high Q and high transmission cavities which require considerable mirror strength and strong coupling between the cavity and feeding waveguide [27]. However, there is a contradiction in that having a wider beam for the cavity is favorable for high transmission, but a narrow beam is preferred to ensure a high optomechanical coupling coefficient (gOM) which is proportional to optical force. As a compromise, cavity beams of 670 nm width are fabricated. A close-up SEM image showing the central region of double-coupled 1D PCCs is given in Fig. 1(c), where a gap of 144.2 nm between the two cavities is marked. All the periods of the photonic crystal lattices are the same (300 nm). The diameter of the hole in the center of cavity is 190 nm and on either side, their diameters are gradually tapered to 40 nm after 39 lattices.
The device is fabricated on a silicon-on-insulator (SOI) wafer, which consists of a device layer of thickness 260 nm and a 1 µm-thick silicon dioxide layer. The patterns of the suspended structures are written by electron beam lithography (EBL), after which they are etched by C4F8/SF6 plasma until the silicon dioxide layer is exposed. The second EBL forms the patterns of rib waveguides and grating couplers which are subsequently etched into the device layer at a depth of 80 nm. Afterwards, isolation trenches and electrode pads are fabricated by a series of lithography, RIE etching, metal E-beam evaporating and lift-off processes. After that, the wafer is diced into small chips and the suspension structures shown in Fig. 1(b) are released by hydrofluoric (HF) acid vapor. Finally, the chip is fixed onto a dual in-line package and the device electrodes are connected to package pins by wire bonding.
Figure 2(a) shows a measured transmission spectrum of the device shown in Fig. 1, where the resonance peaks of the second-order even (TEe,2), the third-order odd (TEo,3), the third-order even (TEe,3), the fourth-order odd (TEo,4), the fourth-order even (TEe,4), the fifth-order odd (TEo,5) and the fifth-order even (TEe,5) TE modes are marked. All these resonance modes are identified by finite-difference time-domain (FDTD) simulations. When wavelength is above the band edge (around 1602 nm), the propagating modes will exist. Here, we choose the first four resonances to carry out the experiments. TEe,2 and TEo,3 are used as probe signals, while TEe,3 and TEo,4 are used as pumps. Based on SEM-measured cavity geometries, the FDTD-simulated electric field profiles of these four resonance modes, shown in Fig. 2(b), have corresponding wavelengths at 1558.8 nm, 1571.9 nm, 1574.8 nm and 1585.5 nm respectively. As shown, even modes have more electric field energy concentrated in the slot gap than those of odd modes, while the electric field of odd modes have zero values along the slot’s central axis since the odd modes are anti-symmetric about the axis. Figures 2(c)-2(f) are the magnified resonance peaks of TEe,2, TEo,3, TEe,3 and TEo,4 marked in Fig. 2(a). The measured data are fitted by Lorentz curves and the apexes of these curves are determined to be 1554.052 nm, 1563.003 nm, 1567.936 nm and 1574.423 nm respectively. The slight discrepancies between the measured results and the simulated results are attributed to measurement inaccuracies of the cavities’ holes. The Q-factors of these measured resonance peaks are 61500, 61900, 16300 and 14800 respectively. Obviously, the Q-factor of TEe,2 are close to that of TEo,3 and higher than those of TEe,3 and TEo,4. The narrower peaks of TEe,2 and TEo,3 make them more suitable as probe signals for precise measurement of resonance shift. Lower-order resonances cannot be experimentally detected in this device as they were submerged by system noise. This is due to the fact that the lower-order resonances locate in the relatively low efficiency region of the grating coupler spectrum in our design and they inherently have lower transmission comparing to the other modes.
Fig. 2 (a) Experimentally-measured transmission spectrum of the fabricated double-coupled cavities shown in Fig. 1(c), where various resonance modes and propagating modes are marked. TEe,2, second-order even mode; TEo,3, third-order odd mode; TEe,3, third-order even mode; TEo,4, fourth-order odd mode; TEe,4, fourth-order even mode; TEo,5, fifth-order odd mode; TEe,5, fifth-order even mode. The spectrum is normalized to the highest transmission of TEe,4. (b) Calculated electric field profiles for TEe,2, TEo,3, TEe,3 and TEo,4. (c,d,e,f) detailed resonance peaks of TEe,2 (c), TEo,3 (d), TEe,3 (e) and TEo,4 (f) and their respective Lorentz fits. (g) Wavelength shifts of the TEe,2, TEo,3, TEe,3, and TEo,4 modes versus cavities’ gap width. Experimental results are plotted with discrete symbols and the solid lines are their respective fitted curves. (h) The optomechanical coupling coefficient gOM/2π versus cavities’ gap width.
The data points shown in Fig. 2(g) are the measured wavelength shifts (Δλ) of the selected modes at different gap widths (g). Gap widths versus voltages applied to NEMS actuator are first calibrated under a SEM and then wavelength shifts with corresponding voltages are measured, so relations between shifts and gap widths can be derived [26]. It is observed that even modes (TEe,2 and TEe,3) varies significantly as a function of the gap, while the odd modes (TEo,3 and TEo,4) are tuned slightly although the cavities’ gap decreases more than 40 nm. The measured data are fitted to quartic curves in Fig. 2(g) which are subsequently utilized in the calculations of gOM [26]. The curves of gOM/2π versus the gap width are plotted in Fig. 2(h). Compared with the gOM of odd modes, not only is the gOM of even modes much higher, but it also can be dramatically increased by narrowing the cavities’ gap.
4. Results and discussion
Resonance modes result in much larger optical forces than propagating modes due to their high Q-factor, but a wavelength-tracking mechanism is needed to keep the pump laser in tune with the resonance modes [17]. It is not cumbersome to adjust wavelength when varying the pump power, but the optimal wavelength for each pump power should be calibrated in advance. Figure 3(a) shows the spectra of TEe,3 under various incident light powers which are estimated in the waveguide just before the 1D PCCs. When the incident power is more than 0.46 mW, optical bistability can be clearly observed. Both thermo-optic and optomechanical effects contribute to the bistability [28, 29]. There would be a hysteresis loop by sweeping the wavelength forward and reversely, but just the forward swept curve can be experimentally acquired [Fig. 3(a)] since TLS cannot sweep wavelength reversely. As our experimental observations, in the curve of Fig. 3(a), the pump wavelength with higher transmission generates the bigger optical force. However, when pump wavelength is selected inside the hysteresis loop, the cavities’ system will be unstable and may suddenly jump from the high transmission state to the low transmission state. Thus, wavelength just below the hysteresis loop, which is approximately obtained by manually adjusting the TLS wavelength and observing the cavities’ transmission, is chosen as the optimal pump wavelength. For example, 1569.33 nm is determined to be the optimal wavelength for the TEe,3 mode with power of 0.81 mW. Pumped by this mode and power, the probe mode of TEe,2 redshifts 1.448 nm [Fig. 3(b)], while the other probe mode of TEo,3 redshifts 0.504 nm [Fig. 3(c)]. Compared to their original spectra, the Q-factors of TEe,2 and TEo,3 remain unchanged. Figure 3(d) shows the spectra of TEo,4 excited with various powers. Figures 3(e) and 3(f) show the redshifts of probe TEe,2 and TEo,3 pumped by TEo,4 at a wavelength of 1574.59 nm with an incident power of 0.87 mW, the magnitudes of which are 0.078 nm and 0.203 nm respectively. Shift of TEe,2 pumped by TEe,3 is more than that of TEo,3, whereas probes pumped by TEo,4 exhibit opposite behaviour. TEe,3 applies an attractive force to the two cavities and the gap between them is diminished, therefore the optomechanical and thermo-optic effects combine to produce constructive redshift. On the contrary, TEo,4 applies a repulsive force and the wavelength shifts due to optomechanical effect is opposite to those due to thermo-optic effect, so destructive redshifts occur. TEe,2 has a more significant optomechanical effect than TEo,3, so its redshift is more when the shift components due to respective effects are constructed and less when components are destructed.
Fig. 3 (a) Transmission spectrum of the TEe,3 pump mode under different incident light powers (just before the cavities). Ordinate represents the power detected by OSA. (b,c) Tuned probe TEe,2 (b) and TEo,3 (c) by the TEe,3 pump mode at wavelength of 1569.33 nm with power of 0.81 mW. Magnitude of each peak is normalized by maximum of itself. (d) Transmission spectrum of the TEo,4 pump mode under different incident light powers (just before the cavities). Ordinate represents the power detected by OSA. (e,f) Tuned probe TEe,2 (e) and TEo,3 (f) by the TEo,4 pump mode at wavelength of 1574.59 nm with power of 0.87 mW. Magnitude of each peak is normalized by maximum of itself.
Next, the device is tested under the influence of the selected pump modes of TEe,3 (for attractive force) and TEo,4 (for repulsive force) with various pump powers and corresponding tracked wavelengths. To better match the bipolar displacements that are a result of the optical forces with the SEM-calibrated displacement range shown in Fig. 2(g), a bias voltage of 3 V is applied to the NEMS actuator and the initial gap width between the cavities is set at 139.4 nm. The shift of the probe resonance that is directly measured comprises both thermal shift and optomechanical shift. To decouple the optomechanical shift from thermal shift, we use the following [26]:
where ΔλoT and ΔλeT are respectively the total shifts of odd and even modes; ΔλoTh and ΔλeTh are the components of thermal shifts; ΔλoOM and ΔλeOM are the components of optomechanical shifts; α is the ratio of the temperature shift of the even and odd modes, which has been measured to be 0.96 by heating the device; and β(ΔλoOM), a function of ΔλoOM, represents the ratio of the optomechanical shift of the even and odd modes, which is known from the data shown in Fig. 2(g). Therefore, based on all the experimentally measured parameters, the problem of determining how much is optomechanical shift alone can be solved from the Eqs. (1) and (2). Figures 4(a) and 4(b) show the measured total shifts, the solved optomechanical shifts, and the solved thermal shifts of TEe,2 and TEo,3 pumped by TEe,3, while Figs. 4(c) and 4(d) show those of TEe,2 and TEo,3 pumped by TEo,4. When pumped by TEe,3, thermal shift and optomechanical shift have the same signs, whereas when pumped by TEo,4, they have opposite signs, the reason being that TEe,3 and TEo,4 apply attractive and repulsive forces respectively. In Fig. 4(a), the ratio of optomechanical shift to thermal shift is around 2.5; in Fig. 4(b), the ratio is around 0.15; in Fig. 4(c), the ratio is around −0.55 and in Fig. 4(d), the ratio is around −0.07. TEe,3 has a higher gOM than that of TEo,4, so it generates a stronger force than TEo,4 with the same input power and has a higher conversion efficiency of light energy to mechanical energy.Fig. 4 (a,b) Total shift, decoupled thermal shift, and optomechanical shift of the probe TEe,2 (a) and TEo,3 (b) pumped by the TEe,3 with various powers and tracked wavelengths. (c) Diminishing of gap width pumped by TEe,3 with various powers and tracked wavelengths. Attractive force generated by TEe,3 are calculated by Fopt = kopt × Δg, in which Fopt is optical force, kopt = 0.166 N/m is optical force related spring constant calculated by finite-element method (FEM) and Δg is change of gap width. (d,e) Total shift, decoupled thermal shift, and optomechanical shift of the probe TEe,2 (d) and TEo,3 (e) pumped by the TEo,4 with various powers and tracked wavelengths. (f) Enlarging of gap width pumped by TEo,4 with various powers and tracked wavelengths. Repulsive force generated by TEo,4 are calculated by Fopt = kopt × Δg.
By combining the decoupled optomechanical wavelength shift with the known relation between the wavelength shift and the cavities’ gap [Fig. 2(g)], the variation of the gap width by the attractive optical force generated from TEe,3 mode is derived and plotted in Fig. 4(e). Similarly, the gap change by the repulsive force generated from TEo,4 mode is determined and plotted in Fig. 4(f). It is observed that the gap is shrunk by a maximum of 37.1 nm (for pump mode of TEe,3) and expanded by a maximum of 11.4 nm (for pump mode of TEo,4). In Fig. 4(f), the gap expansion is slightly out of the SEM-calibrated range, and the data above the dashed line is determined based on extension of the curves in Fig. 2(g). A spring constant, kopt = 0.166 N/m, simulated by FEM, is used to calculate the optical force Fopt by Fopt = kopt × Δg, where kopt is the mechanical spring constant of the suspended structures supporting the movable cavity. From Figs. 4(e) and 4(f), the maximum optical forces generated by the selected resonant modes are found to be around −6.2 nN (attractive) and 1.9 nN (repulsive), respectively.
Compared with the ring resonators (attractive force of 7.5 nN and repulsive force of 600 pN at input power of ~3 mW) [4], the coupled 1D PCCs demonstrated here, which generate attractive force of 6.2 nN at input power of 0.81 mW and repulsive force of 1.9 nW at input power of 0.87 mW, have higher efficiency of transferring light power to optical forces. The recently demonstrated metal-dielectric hybrid plasmonic waveguides extremely enhance the optical force between them (100 pN/µm/mW) [30]. However, considering the cavity length (24 µm), the optical forces of our device, 320 pN/µm/mW for attractive force and 90 pN/µm/mW for repulsive force, are the same order of magnitude as the hybrid plasmonic waveguides.
4. Conclusion
In summary, we have experimentally demonstrated the energy-efficient utilization of bipolar optical forces that exist in resonance modes of double-coupled 1D PCCs. TEe,2 and TEo,3 are taken to be the probe modes while TEe,3 and TEo,4 act as pump modes. A wavelength-tracking mechanism is adopted to further enhance the force, and unstable pump caused by bistability is avoided. The maximum shift of TEe,2 pumped by TEe,3 is 1.448 nm (57 times the TEe,2 resonance linewidth), which is attributed to both the large force generated by resonance with high Q-factor and having NEMS springs with less rigidity (spring constant is 0.166 N/m). By using a NEMS actuator, the relation between shift of the probe resonance and the gap width is directly calibrated by means of the SEM. Based on the relation, optomechanical shift is decoupled from thermal shift. Results show a highly efficient conversion of light energy to mechanical energy, in which optomechanical shift of TEe,2 pumped by TEe,3 is 2.5 times its thermal shift. The maximum attractive and repulsive forces produced by TEe,3 at 0.81 mW and TEo,4 at 0.87 mW (power values in the waveguide just before the cavities) are −6.2 nN and 1.9 nN respectively with corresponding gap changes of −37.1 nm and 11.4 nm. It is feasible to further enhance the optical force and improve the energy efficiency by increasing cavities’ gOM, and the technique demonstrated here is hopefully utilized in large scale reconfigurations of all optical circuits.
Acknowledgments
The authors acknowledge financial support by Singapore 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. Fabrication support by Ms. Siew Lang Teo and Mr. Yi Fan Chen is gratefully acknowledged. SEM characterization support by Dr. Dan Liu is gratefully acknowledged.
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