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A wide-range split-ladder photonic crystal cavity which is tuned by changing its intrinsic gap width is designed and experimentally verified. Different from the coupled cavities that feature resonance splitting into symmetric and anti-symmetric modes, the single split-ladder cavity has only the symmetric modes of fundamental resonance and second-order resonance in its band gap. Finite-difference time-domain simulations demonstrate that bipolar resonance tuning (red shift and blue shift respectively) can be achieved by shrinking and expanding the cavity’s gap, and that there is a linear relationship between the resonance shifts and changes in gap width. Simulations also show that the split-ladder cavity can possess a high Q-factor when the total number of air holes in the cavity is increased. Experimentally, comb drive actuator is used to control the extent of the cavity’s gap and the variation of its displacements with applied voltage is calibrated with a scanning electron microscope. The measured wavelength of the second-order resonance shifts linearly towards blue with increase in gap width. The maximum blue shift is 17 nm, corresponding to a cavity gap increase of 26 nm with no obvious degradation of Q-factor.
©2012 Optical Society of America
1. Introduction
Photonic crystal cavities have the capability to achieve light resonance with high quality (Q) factors and confine light to a very small region, which can be used making them very useful in a wide range of applications including optical switches [1–3], filters [4–6], modulators [7, 8], ultra-small lasers [9, 10], quantum electrodynamics [11, 12], nonlinear optics [13, 14], and biological and chemical sensors [15, 16]. Tuning of photonic crystal cavities is an attractive topic of research, because it can actively and dynamically control the cavities’ resonances. Up to now, various tuning approaches employing microfluidics [17], liquid-crystal [18], magneto-optic [19], thermo-optic [20], and electro-optic [21, 22] effects have been reported. In addition, mechanical approaches to tune the resonance have also been proposed. Initially, nanoprobes, such as atomic force microscope (AFM) [23, 24] and scanning near-field optical microscope (SNOM) [25], have been utilized as tuning tools by perturbing the evanescent field of the cavity. Subsequently, on-chip-integrated micro/nano-electromechanical systems (MEMS/NEMS) driven nanoprobes were successfully introduced [26–29], with in-plane nanoprobe tuning [30] demonstrating generally better integration than their out-of-plane tuning counterparts. Although various probe shapes have been explored for expanding the tuning range, the widest tuning range reported for this scheme is still very limited (about several nanometers) coupled with significant degrading of the cavity’s Q due to scattering of light and leakage through the probe [30, 31]. Another integrated MEMS tuning scheme involved double-coupled cavities, which could achieve a tuning range up to 18 nm [30, 32]. Further enhancements such as utilizing triple-coupled cavities can improve the tuning range to 24 nm [33]. Generally, resonance tuning through cavity coupling leads to less degradation of Q-factor because light inside the cavities involved in tuning is well confined. However, the resonance shift through coupled cavities is accompanied by a resonance split, which can be explained by the Coupled-Mode Theory (CMT). For many applications, such as filters and lasers, this split resonance is undesirable. Recently, a tunable slotted slab photonic crystal cavity has been reported to alleviate the problem of resonance split and at the same time maintain wide-range tuning and high-Q properties [34, 35].
The quasi-1D photonic crystal cavity has attracted much attention lately because of its merits, such as small dimension, easy fabrication and better integration with optical waveguides [36]. Recently, more advanced quasi-1D photonic crystal cavities with ultrahigh-Q have been reported [37–39]. One of them, the “zipper” cavity (double-clamped ladder structures), can simultaneously localize mechanical and optical energy at the nanoscale [40]. In addition, a deterministic design method for cavities with ultrahigh Q and ultrahigh transmission has been proposed and experimentally demonstrated [41, 42]. This design method is ideally suited for coupling to the feeding waveguide due to its ultrahigh transmission. Moreover, the cavity parameters can be determined directly, hence avoiding trial-based parameter-search simulation. Besides, there are theoretical analyses and simulations available for a slotted quasi-1D photonic crystal cavity, which can be tuned by a nano-electromechanical system (NEMS) based actuator [43]. In this paper, we describe the design of a novel tunable quasi-1D photonic crystal cavity, which we call a split-ladder cavity. Its optical resonance can be tuned over a large range by changing its intrinsic gap width. We first describe the design and simulation of the proposed split-ladder cavity, followed by its fabrication and characterization. Finally, we experimentally demonstrate that the resonance of such cavity can be tuned over a large spectral range by means of an on-chip integrated NEMS actuator.
2. Design methods
The design of the split-ladder cavity is based on Silicon-on-Insulator (SOI) wafers, which has a device layer of 260 nm and buried oxide of 1 µm. This SOI-based design is desirable for future large scale integration of photonic and electronic devices. As shown in Fig. 1(a) , the split-ladder cavity is formed in the silicon device layer as a ladder-like structure with an air-slot in the middle splitting the structure into two symmetrical parts. The oxide layer under the split-ladder is removed at the end of the fabrication process, thereby creating a released air-suspended cavity. The resonance of the split-ladder cavity can be tuned through a NEMS actuator that changes its intrinsic gap g. The geometry of the holes in the dielectric, shown in Fig. 1(a), is favorable for transverse-electric-like (TE-like) band gaps, and hence in this paper, we study a TE-like field and represent it with the electric field component in the x-direction (Ex). All the dimensions except the device thickness (t) of the proposed split-ladder cavity are annotated in Fig. 1(a). Figure 1(b) shows the axial TE-like band structure of the quasi-1D split-ladder lattice, calculated by 3D RSoft BandSOLVE. All the lattice dimensions used for band calculations are normalized by the lattice constant as follows: a/a = 610/610, w/a = 730/610, t/a = 260/610, g/a = 120/610, hz/a = 280/610, and hx/a = 520/610; the unit of these values is nanometer. Thirty-two axial calculation steps are made for one lattice period, which is sufficiently fine to obtain convergent band structures. The refractive index of silicon is set at 3.46. The Ex profile of the first TE-like band (lowest-order band) is shown in the inset in Fig. 1(b). For traditional quasi-1D photonic crystals having holes in dielectric, the first band should concentrate the Ex field in the dielectric region, but for the split-ladder cavity, there is an air-slot along its z-axis. As can be seen here, the Ex field is mostly concentrated in the air-slot of the dielectric region.
Fig. 1 (a) Local scanning electron microscope (SEM) image of split-ladder cavity, where a is the photonic crystal lattice constant; w is the cavity width; g is the slot width; hz is the axial hole lengths; hx is the transversal hole widths. (b) Axial TE-like band structure of split-ladder lattice. Inset: normalized electric field component in x direction of first (lowest-order) band edge. (c) Normalized lattice periods of half cavity (from center to one side). (d) Normalized wavelengths corresponding to first band edges of lattices in (c). (e) Fundamental and (f) second-order resonance mode of split-ladder cavity with 35 holes. The contour plot of the cavity’s refractive index is shown by dark outline.
The resonance of photonic crystal cavity is formed by introducing a “defect” into the photonic lattice. There are many design methods for various ultrahigh Q quasi-1D photonic crystal cavities, including the lattice-constant-modulated [40], the hole-size-modulated [41] and the beam-width-modulated [42]. Here, we adopt the lattice-constant-modulated method as demonstrated by Chan et al [40]. We set the central 15 holes out of the total number of 35 in the split-ladder cavity as the “defect” region. The lattice period of the cavity’s Bragg mirror region is denoted by am and that of the “defect” region by an, (n has values from 0 to 7, corresponding to number of holes from the center to either sides in the “defect” region). The lattice periods in the “defect” region is modulated according to the equation:
The normalized lattice periods of the half cavity are plotted in Fig. 1(c). As shown, the lattice an in the cavity’s center is 90% that of am. Reducing the lattice period can shift the first band up into the band gap of the mirror region, and a resonance can thus be formed by this localized first band mode. The normalized wavelengths corresponding to first band edges of half cavity’s lattices are plotted in Fig. 1(d). The 3D FDTD simulations for this split-ladder structure are carried out using RSoft FullWAVE, and its fundamental and second-order resonance modes are shown in Figs. 1(e) and 1(f) respectively.The dependence of Q-factor on the total number of holes in the proposed split-ladder cavity structure is investigated by keeping the design of the defect region unchanged and gradually increasing the number of air-holes in the mirror region from 3 to 15 on each side. The results are shown in Fig. 2(a) . It can be seen that the Q-factor increases as the total number of holes increases, until it finally saturates at around 105 for air-hole numbers greater than 39. Here, the cavity’s Q-factor consists of axial and transverse Q-factors. The axial Q-factor characterizes the radiation loss through the two ends of cavity while the transverse Q-factor corresponds to the radiation loss transverse to the length of the cavity. Their relationship can be represented by
where Qaxial represents axial Q-factor, Qtransverse represents transverse Q-factor, and Qtotal represents total Q-factor. Increasing the number of air-holes enhances the mirror strength along the cavity. When the air-hole number is large enough, the axial Q-factor will be much higher than the transverse Q-factor and the total Q-factor will be eventually limited by the transverse Q-factor.Fig. 2 (a) Simulated Q-factor of fundamental resonance versus total number of cavity holes. Cavity gap is fixed in 120 nm. (b) Simulated resonant wavelength (fundamental and second-order) λ versus cavity gap change Δg. The number of cavity holes is 25. The cavity dimensions are consistent with those in the previous discussion.
We also investigated the tuning of the cavity resonance by varying cavity gap. For easy device fabrication and characterization, a split-ladder cavity with a total number of 25 air-holes is selected for proof-of-concept demonstration. Figure 2(b) shows the simulated resonant wavelength of the cavity as a function of the cavity gap change. The blue and red data denote respectively the fundamental and second-order resonances. The symbols in the Fig. 2(b) are simulated data obtained by 3D FDTD, whereas the solid lines are linear fitting results. It can be seen that narrowing and widening of the cavity’s gap g produce the red and blue shift of resonance wavelength, respectively. The slope of the fundamental resonance fit line is −0.8088, while that of the second-order resonance fit line is −0.7862, indicating that their movement keeps paces with each other.
3. Fabrication and characterization
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. ZEP 520A is coated on the SOI wafer, forming a 350 nm-thick layer that acts as E-beam resist. The patterns of the split-ladder cavities and NEMS comb drive actuators are produced by electron beam lithography (EBL). The writing current is 200 pA and the exposure dose is 320 μC/cm2. The device pattern is transferred to the wafer’s device layer by an inductively coupled plasma reactive ion etching (ICP-RIE) system, which uses plasma of C4F8/SF6 chemistry. The etch depth is 260 nm, ie until the dioxide layer is exposed. The residual E-beam photoresist is removed by Microposit 1165 remover. A second EBL and ICP-RIE etch are used to fabricate rib waveguides and grating couplers. The etching depth in this step is controlled to be at 80 nm. Next, the residual E-beam photoresist is removed, also by 1165. The peripheral structures for charactering the device, including the isolation trench, electrodes, etc, are fabricated through a series of lithography, RIE etching, metal E-beam evaporating and lift-off processes. Finally, the wafer is diced into 6 × 6 mm chips, and put into hydrofluoric (HF) acid vapor to etch the silicon dioxide below the cavities and actuators.
Figure 3 shows a schematic of the setup for characterizing the tunable split-ladder cavity. Light from a tunable laser source (ANDO AQ4321D) is launched into a single-mode fiber. A fiber polarization controller is utilized to adjust the polarization to selectively excite the TE-like modes of the split-ladder cavity. A pair of XYZ-stages holds the coupling fibers, each tilted 10 degrees from the normal to the device surface as shown in the Fig. 3. The fibers are aligned manually under a microscope with the grating couplers on the chip. Light coupled into the waveguide through the input grating coupler is directed to the cavity, and the cavity’s output is collected by another waveguide and launched into a multi-mode fiber through the output grating coupler. It is finally recorded by an optical spectrum analyzer (ANDO AQ6317C). The TLS and the OSA can synchronously sweep through wavelengths from 1520 nm to 1620 nm, with the smallest sweep interval at 1 pm. Although a photodetector combined with a TLS can also be utilized to characterize the spectrum [44], in the current setup, the spectrum can be immediately displayed on the OSA screen after the sweep, thus making it speedy and convenient.
Fig. 3 Schematic of setup used to characterize the tunable split-ladder cavity. TLS, tunable laser source; FPC, fiber polarization controller; CUT, chip under test; OSA, optical spectrum analyzer.
4. Experimental results and discussion
Figure 4(a) shows a global SEM image of the fabricated device. The NEMS comb drive actuator is located at the right side of a 25-hole split-ladder cavity. The electrostatic pulling force is generated by the potential difference between the two sets of comb drive fingers. Normally the movable part of the comb drive is connected with the ground to avoid bending it towards the grounded substrate, while a positive voltage is applied to the fixed part of the comb drive. The right half of the cavity is connected with the movable part of the comb drive, and left half of the cavity is fixed. Thus, the gap of the cavity can be widened when a voltage is applied to actuate the comb drive. In actual fact, the current design allows unidirectional movement. If the two sets of fingers are re-positioned to the opposite side of the fixed slab of the comb drive, the two halves of the cavity can be pushed closer, so bipolar tuning is feasible experimentally. The key dimensions of the NEMS comb drive are provided in Fig. 4(b).
Fig. 4 (a) Global SEM image of electrically tunable split-ladder cavity with NEMS comb drive actuators. The white outline shows the released region. (b) The magnified SEM image for actuator’s critical dimensions. The thickness, width and length of the folded beams are 260 nm, 463 nm and 10.2 µm respectively; the thickness and width of comb drive fingers are 260 nm and 182 nm respectively; initial finger overlap is 197 nm; the air gap between two adjacent fingers is 211 nm; the finger number is 25. (c) Supporting region of split-ladder cavity. The cavity is supported by NEMS actuator and disconnect with coupling waveguide. (d) Grating coupler designed for coupling light between chip under test and fibers. (e) Joint of rib waveguide and air-suspended waveguide. A misalignment can be seen clearly.
The relationship between displacement and applied voltage can be approximately calculated by [45]:
where Fe is the electrostatic force produced by the comb drive actuator, k is the spring constant of the folded beams, n is the number of comb drive fingers, ε is the permittivity in air, t is the device thickness, Va is the applied voltage, s is the air gap between two adjacent fingers, E is the Young’s modulus, w is the width of the folded beams, and L is the length of the folded beams. The magnified coupling region between cavity and waveguide is shown in Fig. 4(c). The waveguide is fixed while the cavity is movable, so they must be disconnected. The gap between them, shown in Fig. 4(c), is 65 nm. Obviously, there will be losses caused by the gap and the supports in this coupling region. As shown by FDTD calculations, the loss caused by the gap and the supports is 3 dB. Figure 4(d) is the SEM image of the grating coupler, whose area, period, filling factor (groove fraction of grating period) and groove depth are 12 µm × 12 µm, 600 nm, 50% and 80 nm respectively. This grating coupler has an experimentally-measured maximum of 30% coupling efficiency at a wavelength of ~1570 nm and a 3 dB-bandwidth of 105 nm. The light launched from the grating coupler is guided by a rib waveguide, which has the same etched depth (80 nm) as the grating coupler. The width of the rib waveguide then gradually tapers down to 700 nm, where it is connected to the air-suspended silicon waveguide. The joint between rib waveguide and air-suspended waveguide is shown in Fig. 4(e). The loss arising from this joint, calculated by FDTD, is 0.6 dB.The transmission spectrum of the device is experimentally characterized and the results obtained are given in Fig. 5 . The resonances at 1523.4 nm (fundamental) and 1592.2 nm (second-order) are shown in Figs. 5(a) and 5(b) respectively. As can be seen, the transmission of the fundamental resonance is much lower than that of second-order resonance, so it has a worse visibility. However, we can ascertain that the peak shown in Fig. 5(a) is indeed the fundamental resonance. First, it coincides with the simulated value obtained for the wavelength of the fundamental resonance. Second, when we apply voltage to the actuator, there is a stable movement of the position of the peak. The spectral interval between the fundamental and second-order resonances is 68.8 nm, which is a relatively large free spectral range and is advantageous for applications such as filters. The Q-factor of the fundamental resonance is about 1500, which is lower than the simulated value of 8600. And the Q-factor of the second-order resonance also has a lower value of 930, compared with the simulated Q-factor of 1900. As shown in Fig. 1(e), most of the resonance mode is concentrated in a very narrow gap, and this narrow mode volume can enhance the interaction between the light and the dielectric [44]. However, the sidewalls of the gap formed by etching with ICP-RIE, resulting in them being rougher than the polished top surface. The strong interactions between the resonance mode and the rough sidewalls severely increase the cavity’s inner loss, leading to very low values of experimental Q-factors. It is observed that the peak is very close to 1520 nm, which is the lower bound of the TLS’s measurement range. So although the blue shift of the fundamental resonance can be observed, it will fall outside the measurement range when a slightly larger voltage is applied. Therefore, we chose the second-order mode to carry out the measurement. Figure 5(c) shows the second-order resonance shifts under various applied voltages. It can be seen that applied voltages of 9.7 V, 19 V and 24.2 V induce resonance wavelength shifts of 4.3 nm, 10.9 nm and 16.9 nm respectively. As shown in the graph, the shifted resonances have lower transmissions, but there is no obvious degradation of Q-factor. The loss mechanisms of the slotted photonic crystal waveguides are useful to explain these situations of the transmissions and the Q-factors [46].
Fig. 5 Experimentally-measured transmission spectrum of a 25-hole split-ladder cavity. (a) Fundamental resonance peak and (b) second-order resonance peak with zero applied voltage. Both of them are normalized by the second-order resonance peak. (c) Normalized second-order resonance peaks with various applied voltages. Both of them are normalized by the second-order resonance peak with zero applied voltage.
In Fig. 6(a) , the change in the cavity’s gap, measured under SEM, is plotted against under applied voltage and data fitted with the equation Δg = 0.0449Va2. We then experimentally investigated the wavelength shift of the second-order resonance (Δλ = λshift-λinitial, λshift is the resonance wavelength with non-zero applied voltage, λinitial is the initial resonance wavelength without applied voltage), and Q-factor as a function of cavity gap change (Δg). The gap Δg is derived from the above calibrated data with a given applied voltage Va. In Fig. 6(b), the blue diamonds are the measured data of Δλ versus Δg, and we linearly fit them with the equation Δλ = −0.649Δg (blue solid line).
Fig. 6 (a) Cavity gap change Δg versus applied voltage Va, which is calibrated by SEM. The green triangles are the measured data; the solid curve is a parabola fit, Δg = 0.0449Va2. (b) Second-order resonance wavelength shift Δλ versus cavity gap change Δg. The blue diamonds are the measured data; the solid line is a linear fit, Δg = −0.649Δλ. (c) The Q-factor versus cavity gap change Δg.
The slope of the line for the measured data is −0.649, while the slope of the simulated data in Fig. 2(a) is −0.786. This discrepancy is possibly caused by the calibration errors of Δg versus Va and imperfect fabrication. The optomechanical coupling coefficient (gOM), defined as dωc/dx (differential frequency shift of the cavity resonance with mechanical displacement of the beams), is a figure of merit for optomechanical systems with optical force. In Fig. 6(b) the gOM/2π = 256 GHz/nm, which is twice the value demonstrated by the “zipper” cavity described in ref [47]. Thus, the split-ladder cavity may also have the potential to be utilized to study optical forces in the future. The maximum blue shift in this experiment is 17 nm, which corresponds to a cavity gap increase of 26 nm. Note that this value is not the limit of the proposed resonance tuning approach; it is, rather, limited by the stroke of our current NEMS actuator design. Had the actuator been optimized for stiffness and stroke, it would have been possible to achieve larger resonance shifts with relatively small applied voltages. As shown in Fig. 6(c), even when the cavity’s gap is changed, the Q-factors are consistently around 1000 and no obvious degradation is observed. This is because, in contrast with tip tuning approaches [30–33], this scheme is based on a single cavity’s tiny deformation, so no extra loss mechanism is introduced in the cavity. Compared with coupled-cavity approaches, this proposed scheme has the advantage of not producing resonance splitting, hence resulting in shifting of a single resonance over a wide range.
5. Conclusion
In this paper, we present a wide-range-tunable split-ladder cavity that can be tuned by changing its intrinsic gap width. It can be tuned over a range that is much larger than those using the tip-tuning approach, and unlike the coupled-cavity approach, there is no resonance splitting. These properties are advantageous to filter applications. The FDTD simulations show that when the cavity gap is narrowed or widened, the resonance will be red shifted or blue shifted respectively, which gives applications more flexibility. A Q-factor of more than 105 is demonstrated when the total number of holes in the cavity is enhanced. Using a NEMS comb drive actuator to control the gap distance of the split-ladder cavity, an experimentally measured wavelength shift of the second-order resonance of 17 nm, corresponding to a cavity gap increase of 26 nm, is obtained with no obvious degeneration of the Q-factor.
Acknowledgments
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. Sincere thanks to Dr. Rongguo Xie for calibrating the nano-scale displacement of the NEMS actuator.
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