Piezo-optomechanical cantilever modulators for VLSI visible photonics

There is currently an increasing demand for very large-scale integration (VLSI) photonic circuits^1,2 that provide precise, rapid, and low-power control of visible optical fields. Quantum information applications from quantum computing and networks to sensing^3–5 increasingly rely on atom^6–8 and atom-like^9–11 systems, which make use of optical transitions in the visible wavelength regime. In chemical sensing and imaging, visible light is required to interact with particular molecular species¹² and to achieve higher resolution than possible with longer wavelengths. A leading approach for large-scale optical control is programmable Mach–Zehnder meshes (MZMs),¹ built from cascaded Mach–Zehnder interferometers (MZIs) [Fig. 1(a)]. Each MZI performs the unitary operation U(2) as the fundamental building block for different types of meshes,^13–16 such as multi-port interferometers [Fig. 1(b)] and binary trees [Fig. 1(c)]. The complexity of scaling these circuits requires high-quality individual MZIs and has led to the development of many modulation schemes. In the near-infrared (NIR), phase modulation in MZIs has been demonstrated at large-scale with thermo-optic phase shifters^17–21 and in individual devices using free-carriers,²² χ⁽²⁾ nonlinearities,^23–25 and MEMS.²⁶ In the visible regime, previous reports on thermo-optic^27–29 and thin-film lithium niobate³⁰ MZIs show promise for VLSI photonics, but there remains an open challenge to build reliable MZMs that satisfy application requirements of high switching bandwidths (>10 MHz), high contrasts (>40 dB), and low losses (<1 dB) per modulator.

To address this need, we previously introduced a programmable MZM platform³¹ based on visible-spectrum silicon nitride (SiN_x) waveguides with high-speed (>100 MHz) aluminum nitride (AlN) piezo-modulation.³² However, the modulators in this mesh have a high voltage-loss product (175 V dB), defined as VLP = V_π × α_m, where V_π is the voltage required for a π-phase shift and α_m is the modulator insertion loss. The VLP metric governs the limit on possible mesh circuit depths, given the maximum voltage (e.g., set by CMOS driver circuitry) and optical loss requirements. Conversely, for a set mesh size, cascading high-VLP modulators to reduce V_π or improve unitary fidelity³³ may not be possible due to increasing photon losses. As the number of optical components in a mesh generally increases quadratically with the number of input/output fields,¹⁵ modulators with low VLPs are highly desirable.

In this work, we demonstrate a visible-spectrum phase and amplitude modulator using piezo-actuated mechanical cantilevers. An improved undercut process in the fabrication enables reliable, singly clamped cantilevers with large released regions (>500 µm) and lower VLPs in the 20–30 V dB range, an order of magnitude improvement over our previous work.^31,34 The optically broadband modulator has a 6 V_π cm, up to >40 dB extinction, low hold-power consumption (<30 nW), −1.5 to −2 dB insertion loss, and minimal modulation losses. Moreover, the modulator exhibits a nearly flat frequency response from DC to a peak mechanical eigenmode (up to tens of MHz) for nanosecond switching or resonantly enhanced actuation to further reduce operating voltage (down to 0.15 V_π cm or 0.8 V dB). We arrange the phase modulators for differential operation¹³ in an MZI configuration [microscope image shown in Fig. 1(d)] with the four possible phase shifts labeled. The device consists of 400 nm wide × 300 nm thick SiN_x waveguides coupled to an AlN piezo-stack [Fig. 1(e)]. The modulator operates by applying a voltage V_s across the piezo-layer, which mechanically deforms the cantilever and induces a path length change ΔL and phase shift θ in the waveguides. We characterize the device across the 700–780 nm wavelength range and explore different cantilever designs to target various operating regimes.

We illustrate the cantilever design in Fig. 2. A scanning electron microscope (SEM) image is shown in Fig. 2(a) of the fully fabricated and released cantilever with false-colored SiN_x waveguides, which are looped several times across the surface of the cantilever to increase the phase shifter response. Figure 2(b) maps out a cross section of our entire layer stack.

The fabrication is based on a 200 mm-wafer optical lithography process at Sandia National Labs, which we briefly summarize. First, a bottom aluminum metal layer (M1) is patterned and etched for routing electrical signals and grounds. We then deposit and pattern a sacrificial amorphous-Si (a-Si) layer for defining the cantilevers. Next, a stack of aluminum, aluminum nitride, aluminum (Al/AlN/Al) forms the electrodes and piezo-layers for optomechanical actuation. After some buffer oxide, we deposit and etch the SiN_x waveguides to form the optical waveguides. We next etch a set of small release holes through the entire stack [Fig. 2(b)], exposing additional a-Si to facilitate device release. Finally, post wafer dicing, a xenon difluoride (XeF₂) process removes the a-Si, undercutting all cantilever devices on a single die.

The physical mechanisms that contribute to the optical phase shift is primarily due to waveguide path length deformations induced by applying voltages across the piezo-layer, in addition to stress-optic effects.³⁵ Using finite-element models (COMSOL Multiphysics^®) of our cantilever geometry, we calculate the displacement tensor ∇u, defined as the gradient of the mechanical displacement vector field u, for a given applied voltage V_s. Integrating the displacement tensor along the meandering waveguide path [Fig. 2(a)], which we define as a curve C, we find the path length change ΔL to be

where $ŝ$ is the unit vector parallel to the path C. This length deformation then induces a phase shift

where n_eff = 1.68 is the effective modal index of our waveguide. Based on our simulations, for an h = 30 µm overhang cantilever at V_s = 10 V, we estimate a total ΔL = 0.89 nm for a single waveguide loop, corresponding to θ ∼ 0.004π radians at 737 nm wavelength. We note that at lower wavelengths, the phase-shifter becomes more effective, ultimately limited by the transparency window of our SiN_x. We also find in the linear elastic regime (applicable for the small strain values present in our system) that ΔL scales approximately linearly with cantilever overhang h and the number of waveguide loops N_L.

The induced phase shift’s dependence on the cantilever and waveguide geometric parameters h and N_L allows for a trade-off between device size, operating voltage, optical losses, and mechanical resonance frequency. Accordingly, we design two different cantilever geometries: design 1 is a high-displacement cantilever, optimized for DC, low voltage operation with a lower peak mechanical frequency, while design 2 is a low-displacement cantilever, optimized for AC, fast switching with a higher peak mechanical frequency. Table I summarizes the geometries and measured characteristics of the two devices based on experiments described in Sec. III.

We characterize our cantilever modulator’s performance by measuring MZIs with both design 1 and design 2 parameters by actuating the two internal phase shifters per MZI, each contributing a phase of θ_1,2 [Fig. 1(c)], while the additional phase shifts ϕ_1,2 are unused. We use a 250-µm pitch fiber array to couple a broadly tunable continuous-wave (CW) Ti:sapphire laser into our SiN_x waveguides through on-chip gratings designed for the 700–780 nm range. DC and AC electrical signals are delivered with a ground-signal-ground (GSG) RF probe touching down onto electrical pads connected to the phase shifters for active modulation. Insertion losses measured at 737 nm wavelength typically range from −1.5 to −2 dB per modulator after subtracting the grating coupler efficiencies.

We first characterize a design 1 MZI by applying a single voltage signal V_s connected in opposite polarities to the two phase shifters such that nominally θ₁ = −θ₂. Figure 3 shows the normalized optical transmission from the MZI’s cross-port as the voltage V_s is swept from 0 to 30 V at a 0.25 V step size. We plot modulation performances across 705, 737, and 780 nm wavelengths [Fig. 3(a)] and find the V_π values via a sinusoidal fit of the data to be 14.0, 15.2, and 16.3 V, respectively, increasing with wavelength. The total SiN_x waveguide length for design 1 is 3.9 mm (accounting for all loops), and thus, we calculate V_πL ranging from 5.5 to 6.3 V cm. The passive directional couplers in our modulator are optimized (50:50 splitting) around 737 nm, and thus, the depth of modulation decreases as the wavelength moves farther away from this wavelength.³³ The splitting ratios, seen more clearly in log scale [Fig. 3(b)], vary by wavelength and dip below 40 dB for 780 nm, while 737 and 705 nm show 28–30 dB, respectively. We attribute the variation to differences in polarization and frequency stability of the laser at different wavelength set points.

We next investigate a design 2 MZI to determine the temporal response and mechanical resonances present in the cantilever. For the experiments in this section, we apply an AC signal to modulate phase shifter θ₁ only, while the other phase shifter θ₂ is set to a specific DC bias point depending on the measurement.

The switching behavior of our modulator is characterized by applying various switch signals. Here, the phase θ₂ is biased such that the modulator turns “on” and “off” as θ₁ is modulated. When a simple square wave is applied [Fig. 4(a)], we observe many excited mechanical resonances, including a long-lived oscillation at ∼23 MHz. The high frequency components in the sharp square edge can be suppressed by tailoring a smoothed (hyperbolic tangent) switch signal, resulting in a clean transition with a 250 ns rise time [Fig. 4(b)] more suitable for applications requiring faster time scales.

We next measure the modulator’s frequency transfer function using small-signal (0.5 V pk–pk) sinusoids on θ₁ while setting θ₂ to the maximum slope of the MZI’s amplitude response for enhanced contrast. Figure 5(a) plots the device’s modulation amplitude as the small-signal sine is swept in frequency, normalized to the DC response. Several piezo-mechanical resonances³⁶ are clearly seen at 1.8, 4.4, 8.3, 14.1 MHz, and the long-lived 23.3 MHz resonance responsible for the oscillations observed in Fig. 4(a). Finite-element modeling of the cantilever confirms eigenmodes close to the measured frequencies, showing the resonances belong to the same family of modes. We show two lower order resonances at 1.8 and 4.4 MHz [Fig. 5(b)], simulated on a cantilever subsection, to illustrate the mechanical deformations. The number of ripples along the free-hanging portion of the cantilever increases for the higher frequency eigenmodes. We note that the measured resonance peaks are similar to those observed in other piezo-electronic systems.^37,38

The presence of cantilever mechanical eigenmodes particular to each phase shifter allows for the resonances to greatly enhance the phase shift per voltage response. We focus on the peak mode at 23.3 MHz, for which the mechanical ripples and the waveguide loops are spatially aligned approximately in a 1:1 ratio. We record a time-resolved trace of the cross port output while applying sine waves at 20 MHz (off-resonance) and 23 MHz (on-resonance) to θ₁ [Fig. 5(c)]. A large enhancement (∼15 dB) of the modulator response is seen due to the mechanical resonance effects. By adjusting the amplitude of the applied sine wave until the modulator output saturates, we measure the single cantilever V_π to be 0.8 V. The total SiN_x waveguide length for design 2 is 3.62 mm, corresponding to a V_πL of 0.3 V cm (or 0.15 V cm for two cantilevers in differential operation). Comparing the resonant V_π to the static V_π of a single cantilever (36 V) for design 2 (see supplementary material), the mechanical Q is estimated to be ∼40. The interaction between the optics and the mechanical resonance further contributes to the path displacement effect as well as strain-optic effects—we are currently investigating the detailed theory of the resonant piezo-optoelectronic physics.

We presented two specific designs for our piezo-optomechanical modulator, highlighting its versatility and overall suitability for large programmable photonic mesh circuits in the visible regime. The robustness of our fabrication process enables reliable cantilever performance and engineering of several important device parameters, including peak resonance frequency and V_π. We characterize additional cantilevers with varying overhang lengths from three different batches of wafers. Figures 6(a) and 6(b) show the measured single-loop V_π values at DC and peak cantilever resonance, respectively. Each data point is the average of three to five different cantilever modulators, with ±1 standard deviation error bars shown. Based on a least-squares fit, both the DC V_π and peak mechanical resonance f_R have a predictable inverse relationship with cantilever overhang, given by

where h is the cantilever overhang, N_L is the number of waveguide loops, and a_V and a_R are the slope coefficients of the V_π and peak resonance equations, respectively. We calculate a_V and a_R to be 42.7 V mm-loops and 1.81 MHz mm, respectively. From Eqs. (3) and (4), the critical parameters of V_π and f_R are quickly estimated by simply dividing a by the cantilever overhang and in the case of V_π, further divided by the number of waveguide loops. Unlike V_π, the peak mechanical resonance of the cantilever does not strongly depend on the number of waveguide loops. This behavior is explained by the resonance mode deformations [Fig. 5(b)], which is affected predominantly by the density of loops (nominally constant across all measured devices) over the cantilever area.

Despite the overall predictability of device performance, we see that the error bars in Fig. 6 increase as the cantilever overhang lengths get smaller. We attribute this effect to the smaller devices’ increased sensitivity to fabrication variations. This uncertainty applies strongly to the V_π measurements and, to a lesser degree, the resonance frequency measurements. However, these MHz-range mechanical resonance frequencies maintain an uncertainty of less than one linewidth from the measured devices, making them more robust to fabrication variations compared to typical optical resonance structures.³⁹ 

The broad ranges in operating voltage and bandwidth available to our cantilever modulator by simply adjusting parameters h and N_L allow for the engineering of larger photonic meshes to application-specific needs. Ultra-low-V_π MZMs are promising candidates for monolithically integrated photonics and CMOS electronic drivers⁴⁰—a single-chip solution that allows for a small number of electronic inputs to control a large number of complex circuits. Optogenetics⁴¹ and display technologies⁴² would not require >1 MHz responses and would be well served by a larger cantilever with lower actuation voltage and power consumption. Other applications, such as optical switches and optical neural networks,⁴³ would benefit from shorter cantilevers with >10 MHz resonance frequencies for high-speed reconfiguration. Moreover, quantum network switches likely prefer modulators with shorter waveguides and low optical loss at the expense of higher drive voltages. Finally, driving multiple engineered cantilevers on-resonance would be beneficial for phased arrays and light ranging applications,^44,45 which require fast and cyclical control of many output beams.

See the supplementary material for additional device performance data.

Major funding for this work was provided by MITRE for the Quantum Moonshot Program. D.E. acknowledges partial support from the DARPA ONISQ program, Brookhaven National Laboratory, supported by U.S. Department of Energy, Office of Basic Energy Sciences (Contract No. DE-SC0012704), and the NSF RAISE TAQS program. M.E. acknowledges partial support from the Center for Integrated Nanotechnologies, an Office of Science User Facility operated by the U.S. Department of Energy Office of Science. M.D. thanks Adrian Menssen, Ian Christen, and Artur Hermans for helpful technical discussions. M.D. also thanks Julia M. Boyle for characterizing the electrical impedances.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding authors upon reasonable request. The data are not publicly available.