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Abstract
We present an on-chip optoectromechanical phase shifter with low insertion loss and low half-wave voltage using a silicon nitride platform. The device is based on a slot waveguide in which the electrostatic displacement of mechanical structures results in a change of the effective refractive index. We achieve insertion loss below 0.5 dB at a wavelength of 1550 nm in a Mach-Zehnder Interferometer with an extinction ratio of 31 dB. With a phase tuning length of 210 µm, we demonstrate a half-wave voltage of Vπ = 2.0 V and a 2π phase shift at V2π = 2.7 V. We measure phase shifts up to 13.3 π at 17 V. Our devices can be operated in the MHz range and allow for the generation of sub-µs pulses.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic integrated circuits (PICs) have received considerable attention over the past decades for the realization of chip-based classical and quantum optical architectures. Modulation of the optical phase is one key functionality of PICs and is used for important applications such as tunable filters [1–3], switches [4,5], power modulators [6–8], stabilization schemes [9] and beam steering [10]. Although a phase difference can be controlled mechanically by tuning the physical distance between two optical elements [11], integrated optical devices generally rely on tuning the effective refractive index. Over the past years, different mechanisms and techniques have been explored: Electro optic modulators (EOMs) based on the Pockels effect [7,12–14] can be operated in the GHz regime while having low power dissipation and are orders of magnitude faster than other physical mechanisms. In addition, low-loss phase shifters have been realized [7]. However, because of relatively weak electro-optical coefficients, large phase-tuning lengths of several mm or even cm are typically required in order to induce a moderate phase shift, resulting in limited scalability in photonic circuits. Alternatively, injecting carriers is a modulation method often used in silicon photonic devices and, similar to the Pockels effect, allows for obtaining fast modulation speeds [6,15,16]. However, due to the free carriers, additional loss and thus amplitude modulation is induced. In addition, carrier injection lacks compatibility with important insulating materials used for low-loss photonic circuits, such as for example silicon nitride. Phase shifters based on the thermo-optic effect (TOPs) [17–19] allow for more compact designs but are limited in operation speed and suffer from large power dissipation and thermal crosstalk. Moreover, they lack cryogenic compatibility, which is essential for low-temperature operation, required for example for photonic circuits employing superconducting nanowire single-photon detectors (SNSPDs) [20]. A more power effective solution are microelectromechanical systems (MEMS) [4,11,21–27]. These systems provide compact footprint, high power efficiency, cryogenic compatibility, and modulation speed in the MHz range. Typically, a microstructure is placed in the vicinity of a waveguide, perturbing the evanescent field of the propagating mode. By tuning the distance between the waveguide and the microstructure, the effective refractive index and thus the accumulated optical phase can be controlled. Different approaches have been explored thus far: On the silicon nitride platform, an H-resonator was placed next to a waveguide, which can be actuated electrostatically in-plane [22]. On the same platform, better performance in terms of reconfigurability was achieved by placing a microbridge above the waveguide [25]. However, this comes at the cost of extra absorption loss induced by the metal cover of the bridge. Alternatively, MEMS phase shifters on silicon-on-insulator (SOI) have been proposed theoretically [23] and been realized experimentally [11,21,24,26]. These implementations, however, either suffer from high insertion loss or require high voltage for achieving π phase shift. Another design based on a microstructure placed above a waveguide was shown to generate a decent phase shift for an indium phosphide on silicon platform, but also with relatively high insertion loss [4]. Here, we demonstrate a low-loss MEMS phase shifter, which is based on a mechanically movable slot waveguide. We show that we can achieve a phase shift of π at a half-wave voltage of only 2 V with an insertion loss of 0.5 dB at a wavelength of 1550 nm. By optimizing the phase shifter’s parameters, our structures can generate a phase shift of more than 13π with a phase tuning length of 250 µm. In the first part of this paper, we discuss the working principle, design, and fabrication process of our device. In the following sections, we describe the optimization of the core components of our phase shifter with respect to the loss, first based on simulations and second based on experiments. We analyze our phase shifter in static and dynamic mode and compare our device to other phase shifters with focus on MEMS, but also to EOMs and TOPs.
2. Approach
In the design of our phase shifter, we exploit the strong dependence of the effective refractive index neff on the gap width of a slot waveguide wslot. We simulate this dependence using the two-dimensional finite-element method (FEM) in COMSOL Multiphysics [see Fig. 1(a)]. A phase shift is generated by tuning the effective refractive index, which is achieved by actively manipulating the gap width of the slot waveguide via electrostatic actuation. A sketch of our structure is depicted in Fig. 1(b). The design comprises two gold electrodes, one fixed and one movable, which are separated by a distance of del. By applying a voltage to the electrodes, an electric field is generated, and the free-standing electrode is displaced with respect to the fixed electrode. A bridge connects the free-standing electrode to the upper rail of the slot waveguide [see Fig. 2(a)], which follows the displacement, and the slot width is increased, resulting in a decrease of the effective refractive index. The free-standing electrode, the bridge and the upper rail form an H-shaped mechanical structure that can be brought into oscillation, similar to Ref. [22]. Contrary to MEMS devices as those in Ref. [25], the electrodes are placed at a distance of a few micrometers to prevent optical absorption of the propagating mode in the gold. Since in general, strip waveguides show lower propagation loss compared to slot waveguides [28–31], most of the components that are used for integrated photonics are based on strip waveguides. Because a slot waveguide is the key component of our structure, efficient mode conversion between slot and strip modes is essential. Therefore, our design comprises one strip-to-slot mode converter and one slot-to-strip mode converter [32,33] to match the mode of a strip waveguide to a slot waveguide and vice versa over a taper length Lmc. The converters are located directly prior to and after the phase tuning section [see Fig. 2(b)]. While the slot waveguide is completely suspended, both mode converters are only partially suspended to stabilize the free-standing mechanical structure. Before the first and behind the second mode converter, the etch window, in which the structures are suspended, is tapered over a length of Ltt to reduce loss induced by off-plane scattering at the oxide/air transition.
Fig. 1. (a) The effective refractive index of the fundamental TE mode in dependence of the slot width simulated with COMSOL Multiphysics at a wavelength of 1550 nm. A typical mode profile is shown in the inset (rail width = 425 nm, slot width = 150 nm). (b) 2D sketch of our phase shifter structure. The light blue area denotes regions in which the structures are suspended. By applying a voltage V between the electrodes, an electric field is generated, and the movable (bottom) electrode is displaced in-plane towards the fixed (top) electrode. One rail of the slot waveguide is connected by a bridge with the movable electrode and is thus displaced as well. The increase of the slot width results in a decrease of the effective index and thus a phase shift is induced. Two mode converters are used for strip-to-slot mode conversion and vice versa. In addition, we use a taper to reduce loss due to off-plane scattering at the oxide/air transition.
Fig. 2. False color SEM image, taken under an angle of 45°, of (a) the suspended slot waveguide, bridge and electrodes and (b) the partially free-standing slot-to-strip mode converter. (c) Optical micrograph of a photonic circuit with an MZI and a phase shifter (Lpt = 250 µm). Three grating couplers are used for coupling TE polarized light into the structure, for reference measurements and to couple light out of the MZI. We use three contact pads with a ground (G) signal (S) ground (G) configuration to contact the electrodes. The inset shows a 2D sketch of the cross section of the phase shifter.
3. Device design
An optical microscope image of a fabricated device is depicted in Fig. 2(c). We use grating couplers optimized for a wavelength of 1550 nm for coupling transverse-electric (TE) polarized light into and out of the photonic structures. Split by a 50/50 multimode interference coupler (MMI), one part of the in-coupled light (In) is coupled out of the chip into an optical fiber for reference measurements (Ref). The second part is guided to a Mach-Zehnder Interferometer (MZI) with a built-in path length imbalance of 170 µm on the upper arm, where two MMIs split and combine light into and from the two MZI channels. The phase shifter is placed in the upper arm. A 2D sketch of the phase shifter’s cross section is depicted in the inset of Fig. 2(c). Light combined at the second MMI is guided to a third grating coupler (MZI out), where the spectrum of the MZI and thus the phase shift can be analyzed. Based on 3D FEM simulations, we estimate the insertion loss of our MMIs to be around 0.18 dB at a wavelength of 1550 nm. Three large contact pads with a ground (G) signal (S) ground (G) configuration are placed above the phase shifter for contacting the electrodes. The footprint of our device is 360×15 µm2 without and 360×240 µm2 with contact pads for a phase tuning length of 250 µm.
4. Sample fabrication
We create the design layout for our samples with the python based package GDShelpers [34] and fabricate the devices at the Münster Nanofabrication Facility (MNF). We start with silicon nitride-on-insulator templates (high stress LPCVD Si3N4) with a layer thickness of 330 nm on 3.3 µm buried silicon dioxide on a 525 µm silicon handle wafer. Three steps of exposure are carried out using electron beam lithography (Raith EBPG5150). First, the contact pads, electrodes and markers are patterned using the positive resist PMMA (Allresist). Cr, Au and Cr thin films (7nm, 80nm, 7nm) are deposited via electron beam physical vapor deposition, followed by a lift-off process. We use negative AR-N 7520.12 resist (Allresist) and reactive ion etching (Oxford 80) in CHF3 chemistry to fabricate the photonic structures. The SiN layer is partially etched down to a remaining layer thickness of 50 nm, which acts as a hard mask during a subsequent wet etching step. Afterwards, the resist is not removed but remains on the photonic structures. Using PMMA, the windows for the wet etching step are defined and the remaining SiN in these windows is removed in a second RIE process. The residual resist is removed via oxygen plasma cleaning. The final step is the release of the suspended structures, which is done via wet etching (BOE 1:7) followed by critical point drying (Leica EM CPD 300) to prevent stiction.
5. Numerical optimization of the phase shifters
Prior to fabrication, we optimize the transmission of our phase shifter by tuning the parameters of the individual elements by means of numerical simulations. Three components contribute predominantly to the insertion loss: First, off-plane scattering at the oxide/air transition, second, loss at the mode converter and, third, scattering at the bridge (see Fig. 3). Note that due to symmetry, an oxide/air transition leads to similar transmission as an air/oxide transition. For this reason, we do not consider the latter transition separately but refer to it as oxide/air transition. In this section, we focus on the 3D FEM simulations, which we carry out in COMSOL Multiphysics using the electromagnetic waves, frequency domain module. All simulations are based on the power in the waveguide. An experimental characterization will be given in the next section. Since the oxide/air transition, the mode converter and the bridge can be optimized independently, we only simulate the transmission of one of the three sections instead of the whole phase shifter. In the following, the given transmission refers only to the transmission of the section under test and not the whole phase shifter. All simulations are carried out at a wavelength of 1550 nm.
Fig. 3. Simulated transmission of different sections of the phase shifter. If not stated otherwise, we use wslot = 150 nm, wr1 = wr2 = 425 nm, and wbridge = 250 nm. (a) Transmission of the oxide/air transition section as function of the taper length Ltt. (b) Transmission of the mode converter as function of the mode converter taper length Lmc. From Lmc = 5 µm on, loss is close to 0.05 dB. Transmission of the bridge section as function of (c) the bridge width wbridge and (d) of the rail widths wr1/2. (c) While for a small bridge width of wbridge = 200 nm loss of only 0.1 dB is simulated, it increases with increasing wbridge. (d) When wr1 and wbridge are kept constant and wr2 is varied, no significant variation in the transmission can be observed. On the other hand, loss decreases down below 0.1 dB when wr1 is increased.
To reduce loss at the oxide/air transition, we introduce a taper with length Ltt [see Fig. 1(b)] and simulate the transmission for varying Ltt [see Fig. 3(a)]. The width and height of our waveguide are kept constant at 1.3 µm and 330 nm, respectively, which is the cross section of our fabricated strip waveguide. For the simulation, we use a circular shaped SiO2 profile, similar to the profile shown in the inset of Fig. 2(c). Our simulation predicts loss of 0.43 dB at the transition without taper, while adding a taper of 36 µm reduces loss down to 0.16 dB. At this length, loss is close to constant and no significant transmission improvement can be observed at longer taper lengths.
The second component we characterize is the mode converter. We simulate the transmission for taper lengths ranging from Lmc = 2 µm to Lmc = 14 µm and wr1 = wr2 = 0.425 µm and wslot = 0.150 µm [Fig. 3(b)]. According to the results, from Lmc = 5 µm on, the transmission is close to constant and a taper length of Lmc = 10 µm yields loss of only 0.04 dB, which is close to what is achieved on SOI with a similar design [32]. For shorter taper lengths, loss increases up to 0.13 dB at Lmc = 2 µm.
Also, scattering at the bridges induces loss. We study two ways to reduce loss at this component: First, one can decrease the width of the bridge and second, one can increase the width of the rails. We simulate loss at the bridge using wr1 = wr2 = 0.425 µm and wslot = 150 nm, so that the slot waveguides supports the fundamental TE mode, and varying wbridge from 100 nm to 1 µm [see Fig. 3(c)]. Clearly, a narrow bridge is crucial for achieving high transmission. While a small bridge with a width of 200 nm yields loss of 0.10 dB, loss increases strongly with increasing width by approximately 0.12 dB per 100 nm of additional width. For a width of 1 µm, the loss due to scattering reaches 1 dB. Furthermore, we vary the width of one rail and keep the width of the other rail constant [wbridge = 250 nm, wslot = 150 nm, see Fig. 3(d)]. First, we set wr1 to 0.425 µm and sweep wr2 from 200 nm to 650 nm. From the results, we conclude that this has almost no influence on the loss at the bridge, which is close to 0.3 dB for all wr2. However, when keeping wr2 constant at 0.425 µm and sweeping wr1, loss is reduced from 0.66 dB (wr1 = 200 nm) to 0.04 dB (wr1 = 650 nm).
Based on these simulation results, we estimate that a phase shifter with Ltt = 36 µm, Lmc = 10, wslot = 150 nm, wbridge = 250 nm, wr1 = 525 nm and wr2 = 425 nm will have insertion loss of around 0.5 dB at 1550 nm.
6. Experimental characterization of the transmission
Following the simulation presented in the previous section, we characterize the losses of each component of our phase shifter (oxide/air transition, mode converter, bridge) experimentally with respect to their design parameters by cascading these structures, similar to the cutback method [35]. In analogy to the simulation, we cascade and characterize each structure of interest individually.
We fabricate several devices with a varying number of test structures and systematically varied design parameters. To study the impact of the transition taper length Ltt on the loss at the oxide/air transition, we sweep Ltt from 0 µm to 39 µm in 13 steps of 3 µm. For each taper length Ltt, we cascade up to 9 etch windows [N = 18 oxide/air transitions, see Fig. 4(a)], resulting in 14×10 = 140 devices. We keep the length of the waveguide constant to prevent additional loss due to waveguide sidewall roughness. For each taper length, we measure the transmission as a function of number of transitions n. This is shown exemplarily in Fig. 4(b) for a taper length Ltt = 0 µm. By employing a linear fit function, we obtain the loss per oxide/air transition, which is given by the slope of the fit a. This procedure is repeated for all taper lengths Ltt. The offset b takes into account losses due to grating couplers, waveguide roughness and the setup. The transmission of the oxide/air transition section as function of the taper length Ltt is shown in Fig. 4(c). We find that a longer taper length results in a higher transmission. While no taper would result in around (0.53 ± 0.02) dB loss, a taper length of 36 µm decreases loss down to (0.24 ± 0.02) dB per transition, which agrees well with our simulations. This loss is slightly higher compared to the results of our simulation, which might be explained by fabrication imperfections.
Fig. 4. Experimental results of the characterization of the phase shifter’s components. If not stated otherwise, we use wslot = 150 nm, wr1 = wr2 = 425 nm, and wbridge = 250 nm. (a) Schematic of the chip layout for the cut-back method. The number of oxide/air transitions n and the length of the transition taper are varied from 0 to N = 18 and 0 µm to 38 µm, respectively. Note that in this figure only the variation of the number of transitions n is depicted. (b) Transmission as function of number of oxide/air transitions for a taper length of Ltt = 0 µm. The loss per oxide/air transition is given by the slope of a linear fit function. (b) Transmission of one oxide/air transition as function of the taper length Ltt. We measure loss of 0.24 dB in the best case (Ltt = 36 µm). (c) Transmission of a strip-to-slot mode converter as function of the converter length Lmc. From Lmc = 6 µm, we measure loss smaller than 0.1 dB. (d) Transmission of a slot waveguide at the bridge as function of the bridge width wbridge. (c) Transmission of a slot waveguide at the bridge as function of the width of the rails. Only a small transmission improvement can be observed when wr1 is increased. An increase of wr2 has a much higher impact on the transmission.
The mode converter is a key element of our phase shifter. Repeating the procedure described above by cascading up to 14 mode converters, we sweep the taper length Lmc from 2 µm to 12 µm. The rail and slot width are kept constant at wr1 = wr2 = 0.425 µm and wslot = 0.150 µm, respectively. From Fig. 4(d) we conclude that a taper length of 10 µm is sufficient for low loss of (0.06 ± 0.01) dB, which is close to the simulated 0.04 dB. Even for a reduced taper length of Lmc = 6 µm we achieve loss close to 0.1 dB. However, for shorter lengths, loss drastically increases up to (0.64 ± 0.02) dB at Lmc = 2 µm. Our results are close to the reports on SOI [32], where a different approach has shown similar loss [36] but with a larger footprint. By optimizing the taper of our design, our mode converter achieves lower loss compared to other converter designs [33,37–41].
Apart from the window transition and the mode converter, the bridge is the third component with major contribution to loss due to scattering. By varying the width wbridge, while keeping the rail widths constant and vice versa, we study two ways to improve the loss at the bridge, as was done in the simulation section. We sweep wbridge from 100 nm to 1.1 µm, while keeping the rail and slot width constant at wr1 = wr2 = 0.425 µm and wslot = 0.150 µm, respectively. Up to 12 bridges are cascaded for each wbridge. The transmission of this section as function of wbridge is shown in Fig. 4(e). For the given parameters we find a strong influence of the bridge on the overall transmission, where a bridge width of 100 nm yields around (0.13 ± 0.01) dB scattering loss, while a bridge width of 1 µm already results in (3.62 ± 0.26) dB loss. This makes it clear that a narrow bridge is essential for a high transmission. In addition, we keep the width of the bridge and the first rail constant (wbridge = 250 nm and wr1 = 425 nm) and vary wr2 from 325 nm to 600 nm [see Fig. 4(f)]. As in the case of the simulation, this only has a relatively small impact on the scattering loss. While wr2 = 325 nm yields loss of (0.49 ± 0.02) dB, increasing the width wr2 to 600 nm reduces loss down to (0.37 ± 0.03) dB. On the contrary, when wr2 is constant at 425 nm and wr1 is increased from 325 nm to 600 nm, loss at the bridge decreases from (0.63 ± 0.02) dB to (0.13 ± 0.01) dB.
Finally, we determine the transmission spectrum of a full phase shifter (Ltt = 35 µm, Lmc = 10, wslot = 150 nm, wr1 = 550 and wr2 = 450 nm) by cascading up to 10 phase shifters. According to our previous results, higher wr1 should result in slightly lower losses. However, we noticed that in these cases (wr1 > 550 nm), the rails tend to stick together. So far, the reason is unknown and further investigations remain to be done. For each device, we measure the transmission in the wavelength range from 1500 nm to 1580 nm at 1 mW laser power and for each wavelength we plot the transmission as function of number of phase shifters n. For a wavelength of 1550 nm this is shown exemplarily in Fig. 5(a). The transmission of one phase shifter at a specific wavelength is given by the slope of the linear fit function. As before, the setup, grating couplers and propagation loss result in an offset, in this case (23.74 ± 0.09) dB. The final transmission spectrum of our phase shifter (without MZI) is shown in Fig. 5(b). We conclude that over the whole wavelength range we achieve a transmission better than (−0.68 ± 0.06) dB, which we measure at 1580 nm. For smaller wavelengths, we achieve slightly better values of (−0.47 ± 0.01) dB at 1550 nm and (−0.37 ± 0.05) dB at 1500 nm, which agrees well with our expectation from our previous simulation and measurements. We note that in the measurements we are limited in wavelength by the transmission spectrum of the grating couplers, as their transmission decreases drastically beyond the given limits of 1500 nm and 1580 nm.
Fig. 5. (a) Transmission as function of number of cascaded phase shifters for a target wavelength of 1550 nm. The slope of the linear fit function denotes the loss per phase shifter at 1550 nm. (b) Spectrum of a phase shifter (without MZI). Over the whole wavelength range, we achieve loss below 0.7 dB. The grey area denotes the standard deviation.
7. Characterization of the static phase shift
To study the performance of our phase shifter devices, we embed a device within a Mach-Zehnder interferometer. We analyze the spectrum of the MZI by tuning the wavelength of the laser from 1535 nm to 1575 nm and measuring the transmission at the third grating coupler [Fig. 2(c) MZI out] with a photo detector. The MZI spectrum of one device (Lpt = 250 µm, del = 0.45 µm) as function of the applied voltage is depicted in Fig. 6(a). Fringes, which result from interference at the second MZI beam splitter, with a free spectral range of 9.8 nm and an extinction ratio of 26 dB at 1550 nm are visible. When a voltage is applied to the electrodes, the gap width between the rails of the slot waveguide is increased and the effective refractive index decreases. The spectrum is shifted to smaller wavelengths, due to the decreased optical path length in the upper, longer arm of the MZI. Because the extinction ratio remains constant over this shift [see Fig. 6(a)], we conclude that the applied voltage and thus the slot gap width have only little influence on the loss of our device. The phase shift is calculated from the position of the fringes and is shown as function of the voltage in Fig. 6(b). For the device under test, we measure a half-wave voltage of Vπ = 4.5 V, equivalent to a half-wave-voltage-length product VπLpt of 0.113 Vcm. Furthermore, we obtain a phase shift of 2π at V2π = 6.4 V and a maximum phase shift of 13.3π at 17 V. We estimate the pull-in voltage to be 18.4 V, meaning that the device is already operated close to the maximum. As in the case of other MEMS phase shifter [22], our device features a phase shift that is proportional to V2.
Fig. 6. (a) Normalized MZI spectrum as function of the applied voltage. Due to interference, fringes with a free spectral range of 9.8 nm and an extinction ratio of 26 dB are visible. (b) Phase shift as function of the applied voltage along with a quadratic fit function. A half-wave voltage of Vπ = 4.5 V is achieved. (c) Phase shift as function of the applied voltage for devices with different phase tuning lengths and electrode gap widths.
In addition, we compare two phase shifters with different phase tuning lengths Lpt of 150 µm and 210 µm and electrode gaps del of 280 nm and 150 nm, respectively. Smaller electrode gaps allow for a smaller half-wave voltage. On the other hand, shorter phase tuning lengths result in compacter and faster devices while having an increased half-wave voltage. The phase shift as function of the voltage for all three devices is shown in Fig. 6(c). In the case of the first device (Lpt = 150 µm, del = 280 nm), we measure a half-wave voltage of Vπ = 5.6 V, equivalent to a half-wave-voltage-length product of VπLpt = 0.084 Vcm. For the second device (Lpt = 210 µm, del = 150 nm), we obtain Vπ = 2.0 V and VπLpt = 0.042 Vcm. In both cases a 2π phase shift is achievable (V2π = 8.0 V for Lpt = 150 and V2π = 2.7 V for Lpt = 210 µm). Both devices provide an extinction ratio of 31 dB at 1550 nm, which is 5 dB larger compared to what we obtain with our longest device (Lpt = 250 µm). This device is on another sample, on which we notice a slightly higher waveguide side wall roughness, which the extinction ratio difference may be attributed to.
8. Dynamic response of the phase shifter
To further study the dynamic behavior of our devices, we place the sample in a vacuum chamber (pressure approx. 2.0×10−5 mbar) and drive our phase shifter with a network analyzer. The measured response of the device under test (Lpt = 150 µm, del = 280 nm) is depicted in Fig. 7(a). We use a laser power of 10 mW and set the wavelength to the slope of one of the MZI transmission fringes. Several resonances can be seen in the response at the eigenfrequencies of our system. . The first mode, at which the entire H-resonator is moving, is found at 1.177 MHz, whichis close to the eigenfrequency of 1.325 MHz, which we simulate in COMSOL Multiphyiscs using FEM. The 3 dB point occurs at around 2.85 MHz. We determine the Q factor to be 1132 ± 5 in vacuum, which at this condition is mostly limited by clamping loss. At atmospheric pressure, the Q factor is 15 ± 1 at an eigenfrequency of 1.175 MHz. For our longer structures (210 µm and 250 µm) we measure lower eigenfrequencies of 0.885 MHz and 0.779 MHz, respectively. To demonstrate the generation of pulses at atmospheric pressure, we place the wavelength of our laser to the minimum of an MZI fringe and apply a pulsed signal of 3 V with a frequency of 100 kHz, a pulse width of 850 ns and rising and falling slopes of 10 ns [see Fig. 7(b)] top, resulting in the output signal shown in the bottom panel of Fig. 7(b). A pulse full width at half maximum (FWHM) of 380 ns and a height of 60% of the full MZI transmission range is achieved. By increasing the length of the driving pulses, longer optical pulses can be generated. In combination with a driving voltage of 5.6 V, the entire transmission range of the MZI can easily be covered [see Fig. 7(c)]. With rising and falling slopes of 10 ns, the transmission signal shows high amplitude ringing with a period of 880 ns, which corresponds well to the first in-plane mode 1.175 MHz. To suppress this ringing, we use a sinus-shaped pulse edge with a width of 1.5 µs, which eliminates overshooting.
Fig. 7. (a) Driven response of a phase shifter with a phase tuning length of Lpt = 150 µm measured in vacuum (approx. 2.0×10−5 mbar).. The first fundamental in-plane mode is found at 1.177 MHz with a Q factor of 1132 ± 5. The 3 dB point occurs at 2.85 MHz. (b) Generation of optical pulses with a frequency of 100 kHz and a FWHM of 380 ns at atmospheric pressure. The bottom panel is normalized by the peak transmission of the MZI. (c) Generation of optical pulses with varying pulse length normalized by the peak transmission of the MZI. A sinus-shaped pulse flank is used to reduce overshooting.
9. Discussion
Finally, we want to compare our phase shifters to other reported MEMS phase shifters (see Table 1) [4,11,21,22,24–26]. With the optimized design, we achieve a half-wave voltage of only 2 V, which is smaller by a factor of almost two or more compared to other MEMS phase shifting devices. In addition, with a phase tuning length of 210 µm, we demonstrate a half-wave voltage length product of 0.042 Vcm, which is very competitive within MEMS phase shifters. Other devices with insertion loss comparable to the 0.47 dB at 1550 nm in our case require a much higher half-wave voltage Vπ. Only for the second device reported in [25], much lower insertion loss of 0.07 dB at a π phase shift is found. However, in this case a half-wave voltage of 33 V is needed, which is significantly higher compared to our devices. Differing from other reports, we do not observe a significant change in the insertion loss, when the applied voltage and hence the phase shift are increased. By tuning the parameters of our devices, we can demonstrate a phase shift of up to 13.3π at 17 V, which exceeds other reported maximum phase shifts by a factor of more than two and is, to best of our knowledge, the highest reported so far. To achieve this large phase shift, this device features a long phase tuning length along with a small slot width. Compared to our other two devices, we use a large gap between the electrodes, which allows for a higher displacement and phase shift. In addition, a large gap results in a higher pull-in voltage. We note that our phase tuning lengths, which range from 150 µm to 250 µm, are relatively long compared to other reported MEMS devices. However, we want to emphasize that this is a design choice, since shorter devices show in general a smaller phase shift and higher half-wave voltage. On the other hand, this could be compensated by using a smaller gap between the electrodes. For a more detailed comparison between different MEMS devices we refer to Errando-Herranz et al. [42].
Table 1. Comparison of different MEMS phase shifters reported in the literature. Since not all reports include a measurement of the insertion loss IL and this is a key figure, we estimate this value or adapt it from Errando-Herranz et al. [42]. Since a π phase shift is not demonstrated or the half-wave voltage is not given in all reports, these values along with VπLpt are omitted in some cases.
A half-wave voltage of 2 V and a half-wave-voltage length product VπLpt of 0.042 Vcm compares favorably with other phase shifter approaches. With electro-optic modulators on lithium niobate losses of less than 0.5 dB and Vπ = 1.4 V have been achieved [7] and recently a half-wave voltage of only 0.875 V with on-chip loss of 5.4 dB on a silicon nitride lithium niobate hybrid platform was presented [13]. However, due to the long phase tuning length of usually several mm, the half-wave-voltage-length product of EOMs is typically still over 1 Vcm [7,8,13]. For this reason, when a compact structure is needed, our design is much more favorable while having low loss and a low half-wave voltage. Despite that, using silicon-organic hybrid devices, VπLpt below 0.1 Vcm were reported [12,43].
We estimate the energy Es required for one switching process by using Es=ɛ0AVs2/(del-ds), where ɛ0 is the vacuum permittivity, A is the area of the capacitor and Vs and ds are the voltage and the displacement required for switching. For our device with Lpt = 150 µm and a switching voltage of Vs = 5.6 V, we obtain Es = 22 fJ, which results in a power of 22 nW, assuming a driving frequency of 1 MHz. This is significantly smaller compared to thermo-optic phase shifters, which typically require a power in the mW range for both during switching and at steady state [17,18]. For our devices, we estimate the static dissipated power to be in the nW range, since no current apart from a small leakage current is flowing. The comparably high power consumption of thermo-optic phase shifters makes our MEMS device much more attractive when a larger number of phase shifters is required. In addition, thermo-optic phase shifters are not suitable for cryogenic applications, which is essential for SNSPDs. On the contrary, operating MEMS structures at these temperatures is comparably simple [44].
Finally, by using a longer phase tuning length, a smaller electrode gap width or a decreased slot gap width, the half-wave voltage might be decreased even further. However, smaller slot gaps present fabrication challenges because the gaps tend to be not fully etched even after a relatively long dry etching time and the rails may stick together. In addition, higher eigen frequencies and thus higher driving frequencies and shorter pulses can easily be achieved by decreasing the length of our suspended structure, while the hence reduced phase shift can be compensated for by cascading several devices.
10. Conclusion
We have experimentally demonstrated a silicon nitride MEMS phase shifter based on a slot waveguide. We have shown that these structures feature high transmission, while generating a high phase shift at low driving voltages. Our phase shifters have low insertion loss of (0.47 ± 0.01) dB at 1550 nm. A maximum phase shift of 13.3π at 17 V and a half-wave voltage of only 2 V are reported. Using our devices, we have demonstrated the generation of pulses with a FWHM of 380 ns. Longer pulses can be generated, while ringing is suppressed by using an improved drive signal. Reducing the phase tuning length, even shorter pulses are possible. Due to the small half-wave voltage, the full transmission range of 31 dB of the MZI can be covered easily for fast amplitude modulation. We envision several of our phase shifters being operated along with single photon sources and SNSPDs on one single chip. Being compact, having a small half-wave voltage and having low loss makes our design an excellent candidate for different applications such as on-chip routing, multiplexing and quantum simulation.
Funding
Volkswagen Foundation (A123235, A126874); European Research Council (724707); Deutsche Forschungsgemeinschaft (PE 1832/5-1, PE 1832/6-1); Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen (421-8.03.03.02 - 130428).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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