2D b roadband b eamsteering with l arge-s cale MEMS o ptical p hased a rray: supplementary material

.


Section I. Comparison of OPAs in Literature and in This Work
Table S1 compares the performance of the OPA reported here with other works reported in the literature.
Liquid crystal (LC) OPAs have been developed more than two decades ago [1].LC OPAs offer 2-D beamforming, large apertures and broad transmittance spectrum [2], [3].However, the response time of LC OPAs is limited to milliseconds, too slow for many applications.Fast beamsteering with ferroelectric-liquid-crystal has been reported [4], but the response time is still on the order of hundreds of microseconds.Most of the reported silicon photonic OPAs are 1-D arrays.Scanning in the orthogonal axis relies on wavelength scanning [5], [6].Some 2-D OPAs were reported, but they are limited to small arrays [7].Waveguide-based OPAs also suffer from high optical coupling losses.
MEMS-actuated piston mirror arrays have been reported for both 1-D and 2-D OPAs [8]- [12].Phase shift is achieved by vertical displacement of the individual mirrors.However, large displacement for long wavelength application is challenging for small MEMS mirrors due to pull-in effect, and the vertical displacement is large compared to the mirror size.the z-axis.Let us consider a collimated light wave illuminating the grating, as shown above, with an angle of incidence θi, the complex wavefield can be written as (dropping the time-dependent harmonic term e -i ω t ), ( ) ( ) ( )

Section II. Grating Phase Shifter Characteristics
Where r is the position vector r = (x,y,z), A is the wave amplitude, and k is the wave vector with amplitude equal to k = 2π/λ.At the grating plane y = 0, the incident wavefield is, The grating then adds its spatial modulation g(x) to the incident wave.The function g(x) is periodic with a period Λ, which can be expanded in to a Fourier series as follows, ( ) where the coefficients ηn is determined by, ( ) The outgoing light wave field at the grating plane then can be expressed as, ( ) ( ) From the angular spectrum of the wavefield point of view, the above equation represents a set of out-going plane waves from the grating, i.e. the diffracted beams.Taking the n th order diffracted beam from the grating shown in the figure as an example, the out-going wavefield can be written as, ( ) where θd is the diffraction angle, which can be shown from the above equation to fulfil the condition that, sin sin / ( ) Clearly, the diffraction efficiency of this order is related to |ηn| 2 .Then if the grating is shifted along the x-axis with a displacement of d as shown in the figure, the grating modulation function then becomes g(x+d) instead.Since this shift does not change the periodicity, the Fourier expansion Eq. ( 3) remains the same.However, the coefficient in each order now changes to ηn', where Liquid Crystal [1]  1-D 20 × 20 10° 78% 10.6 µm 0.1° <5 V 1 s Liquid crystal dynamics LC Liquid Crystal [2]  2-D 20 × 15 1.1° × 1.1° 87% 632.5 nm, and 1550 nm 1.32× diffraction limit 0.02 s for Visible, 0.2 s for IR Liquid crystal dynamics LC Liquid Crystal [3]   Cascaded 1-D 40 × 40 2.5° 100% @ 0deg 1550 nm 0.010° 32 V 2 ms Electronic controller LC Liquid Crystal [4]  1-D 9.9 × 9.9 0.12° 91% 658 nm 0.004° ±45 V <200 us Liquid crystal dynamics LC Silicon Photonics [5]  1-D +tuning 0.194 × 0.197

Polysilicon
Changing variable is used in the last step of the above equation.Since, g(x) is periodic, it is obvious that, ( Because g is period, i.e. g(t+Λ) = g(t), and replacing t back to x, we can obtain, Hence, a phase shift of Δφ = 2πnd/Λ will be imposed on the n th order diffracted beam.The n th order out-going diffracted wavefield can then be written as, ( ) Fig. S2 shows the calculated and measured diffraction efficiency of the grating versus (a) the operating wavelength and (b) etching depth of the grating.Compared with silicon grating, Au and Al gratings exhibit larger difference between their simulation and experimental values.This is attributed to the poor step coverage of the metal coating as the Au and Al gratings are made by evaporating gold and aluminum on top of silicon grating structure.Next the MEMS layers were deposited and pattered on top of the interconnect and via layers.First, a 500 nm thick polysilicon layer were deposited and patterned as ground shield between the interconnects and the combdrive actuators to suppress the electrical crosstalk.Then a sacrificial oxide was deposited and planarized with CMP for a thickness of 500 nm.Polysilicon plugs are formed by a damascene process to anchor the MEMS structures on top as well as to provide electrical contacts for the actuators.The MEMS structures comprising 2-µm-thick doped polysilicon were formed by DUV lithography and deep reactive ion etching (DRIE).The resolution of our DUV stepper (ASML 5500/300) is 250 nm.This enabled us to pattern 300nm wide comb fingers with 300nm spacing.

Section III. Device Fabrication
To add gratings on top of the MEMS actuators, a 2-µm-thick high-temperature oxide (HTO) sacrificial layer was first deposited and then planarized by CMP.Next, polysilicon plugs (posts) were formed by the same damascene process as the anchors.Gratings were patterned on a 1-µm-thick polysilicon deposited on top of the posts.Finally, the MEMS structures were released in liquid HF followed by critical point drying (CPD).

Section IV. Electrical Characteristics
160 × 160 OPA consists of 25,600 unit cells.The schematic of the unit cell is depicted in Fig. 2 of the main text.The grating is attached to the movable comb which is suspended by a folded spring.The combdrive actuators are designed for analog operation, exploiting its large displacement without pull-in.The schematic of the actuator without bias and under maximum bias voltage for π phase shift are shown in Fig. S4a and Fig. S4b, respectively.Fig. S4c shows the measured displacement-vs-voltage curves of 12 OPA elements.The average voltage to achieve ±0.5μm displacement for ±π phase shift is 10.5 V, with a standard deviation of 0.64 V.The voltage variations are mainly due to fabrication nonuniformity.The spring constant of the folded-beam flexure design is calculated by: Fill the via trenches with doped polysilicon, followed by CMP.Then deposit another 500nm of doped polysilicon, followed by deep-UV (DUV) patterning and silicon etch to create grounded shield layer to block electrical interferences between interconnect wires and combdrive actuators on top.6. LPCVD of sacrificial silicon dioxide layer (500 nm SiO2) followed by CMP planarization, and then DUV patterning and etching to create anchor holes for MEMS combdrives.7. LPCVD of 2 µm thick doped polysilicon, followed by CMP planarization.8. Silicon deep reactive ion etching (DIRE) to define the combdrive and spring beam structures, the critical dimension (CD) is 300nm.9. LPCVD of 2 µm thick high temperature oxide (HTO) to encapsulate the MEMS combdrive structures, followed by CMP planarization.Then the top sacrificial oxide layer was patterned with DUV lithography and etched to create top grating layer anchor mold (500nm deep).10.Formation of the top grating structure with a thickness of 500 nm, a grating depth of 380 nm.The red layer is 50nm thick gold coating.11.HF release.where E is the Young's modulus of polysilicon (169 GPa), b is the width (300 nm), h is the thickness of the spring layer (2 μm), and L is the length of one spring segment (17 μm).The resonance frequency of the OPA element is 1 2 where k and m are the spring constant and mass of the movable portion of the OPA element, respectively.With a spring constant k = 1.86 N/m and a mass of 4.52 ng, the calculated resonance frequency is 102.1 kHz.This agrees well with value obtained from the finite-elementmethod (FEM) simulation using ANSYS ® software, 98.8 kHz, as shown in Fig. S5a.The frequency response is measured with a Lyncée Tec ® digital holographic microscope (DHM).The resonance frequency is measured to be 55.0 kHz, as shown in Fig. S5b.This measured resonance value is 40% lower than the theoretical calculation and the numerical FEM simulated value.
The difference is due to the sidewall thinning of the folded beam springs during DRIE, resulting in a lower spring constant.The measured phase difference between high-and low-frequency regions is close to 180°, as shown in the frequency response of Fig. S5b.This phase difference fits well with the theoretical phase response of a typical 2 nd order harmonic oscillator.The high resonance frequency enables a fast response time.Fig. S6 shows the measured temporal response of a MEMS OPA element for a step-function input voltage with an amplitude of Vpp = 12 V.A steady-state displacement of 0.5μm is reached at 12 V.This displacement agrees well with the static transfer curve in Fig.  S4c.The actuator is under-damped and significant ringing is observed in Fig. S6a.To suppress the ringing, we used a three-step voltage waveform as shown in Fig. S6b.A smooth step response is obtained with a rise time of 5.7 μs for π phase shift, the maximum amount needed for our bi-directional actuator.The combdrive actuator has a capacitive load.During steady state, it does not consume any power, just like complementary metal-oxidesemiconductor (CMOS) circuits.If we operate the OPA at f = 20 kHz, the dynamic power consumption is 7 nW for each phase shifter, where C is the total capacitance of the combdrive actuator (1.89 fF) and Vmax is the voltage required for π phase shift (12 V).The power consumption of the entire OPA with 25,600 phase shifters is 69 μW.For the entire system including drive circuits, the capacitance of the interconnect wires also needs to be considered.Even including this capacitance, the device level power consumption is still orders of magnitude lower than typical silicon photonics OPA described in [6] in Table S1.

Section V. Optical Performance Characterization
With a uniform, overfilled incident light, the diffractive aperture can be modeled as a rectangular shape aperture.With 45° diffraction angle, the effective aperture of the MEMS OPA is 2.2 × 3.2 mm 2 .The theoretical divergence angle of the diffracted beam is thus 0.040°×0.027°.The experimental optical divergence angle of the OPA is characterized by two methods, both agree well with the theoretical value.
The first method images the output beam on an IR camera with a lens.When a monochromatic plane wave passes through a thin lens, the field at the focal plane of the lens can be modeled as the Fourier transform of the input wavefront.Fig. S7 shows the measured beam profile with 0.042°×0.031°divergence angle using a thin lens (Thorlabs AC254-150-C).The second method is to measure the beam spot size at a distance of 5m in free space propagation.The measured beam spot size is then compared with that is theoretically calculated using Fresnel simulation.Fig. S8 demonstrates the experimentally characterized beam spot profile compared with the theoretical beam profile modeled by Fresnel propagation.The broadening of the beam width is attributed to the non-uniformity of the displacements, which can be compensated by calibrating the translation of the OPA pixels.

Section VI. Electronic Control and Optimization of the OPA's Control Voltage Array
Due to fabrication imperfections, the displacements of different   OPA pixels have a distribution under the same voltage bias, as illustrated in Fig. S4c.To compensate this non-uniformity, an optimization program was developed to fine tune the voltage applied on each specific OPA pixel.The merit function of this optimization program is to maximize the main-to-sidelobe suppression ratio (MSSR) of the diffracted beam in the desired steered direction.
In practice, the optimization program enhances the intensity of the beam in the desired direction, while suppressing the intensity level of the undesired sidelobes and background noise floor through tuning of the voltage map for the OPA.The detailed optimization flow is illustrated in Fig. S9a.First, a complete list of digital-to-analog converter (DAC) code for all starting positions derived from theoretical calculation was generated.After applying the DAC codes to the drive board and waiting for the device to stabilize, which typically takes ~100 ms, the program takes an image of the captured diffracted patterns for all possible angles on the IR camera.Then, the optimization program uses the SimpleBlobDetector® feature in OpenCV to identify nonoverlapping spots in the image, and then bin the detected spots into a 2-D matrix representing all possible unique spot locations.Afterwards, the program identifies the pattern files to generate the brightest point for each spot, and uses the pattern files as the start location of each particle in the particle swarm optimization (PSO) instead of random start positions.To acquire the PSO fitness value for each optimization step, the program calculates the MSSR by summing the pixel intensity values inside and outside of the region of interest (ROI) around the spot.Fig. S9b and c illustrate the improvement of MSSR for the steered beam locating at the angle of (-1.65°, 0.42°), after the PSO treatment, the MSSR was improved from 0.54 dB to 9.66 dB.

Section VII. Hologram Generation Details
In principle, any arbitrary holographic patterns can be generated in the far field by tailoring the phase shift of all OPA elements.size change due to the wavelength dependence of FOV (shown in Fig. S11 d-e).In contrast, if the phase shifts were wavelength dependent, there would be significant side-lobe spots observable in the far-field pattern.

Fig
Fig.S1shows the schematics of the grating phase shifter.The phase shift of the diffracted beam is dependent on the pitch and displacement of the grating element:

Fig
Fig.S3shows the fabrication process flow.The starting n-type single crystalline silicon wafers were pre-cleaned in piranha solution to remove any organic contaminants.Then the wafer was coated with low stress nitride (LSN) by low-pressure chemical vapor deposition (LPCVD) for electrical insulation.Trenches were patterned on LSN by deep-UV (DUV) photolithography and dry etching for interconnect wires.Those trenches were filled with doped polysilicon by LPCVD, followed by chemical mechanical polishing (CMP) to expose the un-etched LSN.Likewise, a second LSN layer was coated to cover the polysilicon interconnect wires, then patterned with via structure, etched, refilled with polysilicon, and chemical-mechanically polished to create via contact between interconnect wires and the MEMS actuators.

Fig. S2 .
Fig. S2.Simulated and experimentally measured optical efficiencies of the grating versus a. wavelengths and b. grating etched depth.All data are measured with TM-polarized incident light.The colors of the curves and symbols represent data from gold (red), aluminum (blue), Si (black), respectively.
Fig. S3.Schematic diagram showing details of the fabrication process.1. Starting n-type Si wafer.2. DUV photolithography and trench etch to create interconnect lines with linewidth of 2 µm (turquoise: low-pressure chemical vapor deposition (LPCVD) low-stress nitride (LSN) layer of 1 µm thickness and 0.5 µm etching depth).3.LPCVD of doped polysilicon filling the etched LSN trenches, followed by chemical mechanical polishing (CMP).4. Deposition of the 2nd LSN, followed by via trench patterning and etching. 5. Fill the via trenches with doped polysilicon, followed by CMP.Then deposit another 500nm of doped polysilicon, followed by deep-UV (DUV) patterning and silicon etch to create grounded shield layer to block electrical interferences between interconnect wires and combdrive actuators on top.6. LPCVD of sacrificial silicon dioxide layer (500 nm SiO2) followed by CMP planarization, and then DUV patterning and etching to create anchor holes for MEMS combdrives.7. LPCVD of 2 µm thick doped polysilicon, followed by CMP planarization.8. Silicon deep reactive ion etching (DIRE) to define the combdrive and spring beam structures, the critical dimension (CD) is 300nm.9. LPCVD of 2 µm thick high temperature oxide (HTO) to encapsulate the MEMS combdrive structures, followed by CMP planarization.Then the top sacrificial oxide layer was patterned with DUV lithography and etched to create top grating layer anchor mold (500nm deep).10.Formation of the top grating structure with a thickness of 500 nm, a grating depth of 380 nm.The red layer is 50nm thick gold coating.11.HF release.

Fig. S5 .
Fig. S5.MEMS OPA Resonance Frequency.Electrostatic MEMS actuator design.a. Lateral displacement mode resonance frequency simulated using ANSYS.b.Measured frequency response of gain and phase.

Fig. S4 .
Fig. S4.Electrostatic MEMS combdrive actuator design.a. Schematic of the actuator without bias.b.Schematic of the actuator under max bias for π phase shift.c.Measured transfer curves of 12 OPA elements.

Fig. S6 .
Fig. S6.Transient response of an OPA cell.a. OPA temporal response in lateral displacement with reference to a 12 V voltage step.b.Oscillations were eliminated with a shaped signal, rise time of the OPA from zero bias to π phase shift is 5.7 μs.

Fig. S8 .
Fig. S8.Long distance beam profile measurement.a.The beam profile measured at 5m distance.b.Theoretical beam spot profile calculated using Fresnel simulation.c. and d. simulated (dotted curve) and measured (solid curve) beam profiles along x-and y-direction, respectively.

Fig. S7 .
Fig. S7.Beam divergence measurement.The diffracted beam is collected by a thin lens with a focal length of 300mm, as shown in a.The diffracted beam is focused onto an IR camera at the focal plane as shown in d.By measuring the diffracted beam spot size in both x-and y-direction as shown in the bold dots in b and c, the divergence angle is calculated to be 0.042°×0.031°,and compared to the unbold theoretical divergence curve (dotted Sinc function) from a rectangular aperture.

Fig. S9 .
Fig. S9.Electronic control optimization of the OPA.a. Optimization flow chart.b.Steered beam profile in the far-field FOV before optimization.The main lobe is located at (-1.65°, 0.42°), within the white box enclosed.c.Steered beam profile in the far-field FOV after optimization.The main-to-sidelobe suppression ratio (MSSR) is enhanced.
Fig. S10.SEMs of part of the 3 × 3 mm OPA system fabricated on a Silicon wafer.Different element pitches of a. 3 μm b. 5 μm c. 10 μm, and d. 20 μm are fabricated and characterized.

Fig. S11 .
Fig. S11.Experimental holographic patterns from MEMS OPA.a. Far-field diffractive patterns from checkboard phase profiles with different FOVs captured with 1260 nm wavelength, corresponding to different OPA pitch designs, b. and d.The far-field diffractive pattern of the "Cal" logo and Golden Gate Bridge using 320 × 320 OPAs with 10 μm element pitch captured with 1260 nm wavelength.c. and e.The far-field diffractive patterns generated by the same samples with 1550 nm wavelength.

Video 1 :Video 2 :Video 4 :
Dynamic movement of the MEMS grating OPA under low frequency actuation.Video captured in the experiment showing top view of a laterally moving MEMS OPA element.The time scale is 0-9 seconds.The actuation voltage is a 6Hz sinusoidal signal with Vpp = 10V.Sweeping of the OPA diffracted beam spot in diagonal direction.Video captured in the experiment showing the far-field of the OPA with the output beam sweeping from the upper left to the bottom right of the FOV.Video 3: Raster scan of OPA.The video shows raster scan of the OPA diffracted beams through 17 x 9 addressable angles.Residue spots at angles other than the steering angle are due to the mismatch of the grating and the pixel pitches.They can be eliminated by making the pixel pitch an integral multiple of the grating pitch, which we have confirmed in a separate short-loop experiment.Steering of the OPA diffracted beam for various wavelengths.Video captured in experiment showing the far-field spots of the OPA for various optical wavelengths.

Table S1 .
Comparison of the MEMS grating OPA reported here with other OPAs in the literature.