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Abstract
Optical phased array (OPA) based on silicon photonics is considered as a promising candidate for realizing solid-state beam steering. However, the high refractive index contrast of the silicon waveguides leads to conventional silicon based OPA suffering from large random phase errors, which require complex post-processing such as time-consuming phase calibration. We propose and demonstrate a calibration-free silicon OPA with optimized optical waveguides width as well as the compact 90° waveguide bends beyond the single mode regime. By using grouped cascaded phase shifters, it is able to reduce the number of control electrodes from N to log2(N). A 16-channel OPA has been demonstrated with continuous beam steering over the field of view controlled by only four control voltages without any calibration.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Beam steering is a key technology for many applications such as light detection and ranging (LiDAR) [1,2], free-space optical communication [3], image projection [4], etc. Optical phased array (OPA) enables fast and stable beam control with compact size, low cost, and low power consumption [5]. Among various material platforms, OPA based on silicon photonics is considered as one of the most competitive solutions to realize all-solid-state beam steering systems due to its high integration density and superior CMOS compatibility. Recently, many high-performance silicon OPAs have been demonstrated, showing great advances in array element scale [6–9], antenna aperture size [10–12], scanning speed [8,13,14], and scanning range [15–20].
The high refractive index contrast of the silicon-on-insulator (SOI) platform is usually considered to be an advantage, which makes the waveguides have strong optical field confinement, allowing for high density integration. However, the enhancement of the optical field confinement also makes the silicon photonic devices sensitive to the geometry size variation [21,22]. OPAs achieve beam steering by controlling the relative phase difference between the adjacent array element, while the accumulated phase error will seriously affect the beam quality in the far field. Most of the current silicon based OPAs require complex and time-consuming feedback control to calibrate the phase error, which limits the large-scale deployment of OPA [23–25].
In order to achieve arbitrary angle within the field of view (FOV), a typical N-channel OPA requires N independent voltage control units. As the number of array channel increases, the electronic arrangement and packaging of the OPA chip becomes complex and difficult. Therefore, reducing the control complexity is of great importance to realize large scale OPAs. A triangular heater with only one control electrode is proposed to generate a linearly varying temperature field, achieving continuous scanning of the OPA far-field beam [26,27]. But such a method greatly increases the power consumption and is not scalable. Poulton et al. have reported a bus waveguide based beam splitting structure, in which the phase shifter is located between two adjacent directional couplers to control the relative phase difference between adjacent channels [1]. It also requires only one control signal to achieve arbitrary direction beam scanning. This structure has good scalability, but it is quite challenging to precisely control the specific power splitting ratio of the utilized directional couplers. It should also be noted that the above-mentioned cascaded structures require additional independently controlled voltages and optimization algorithms to suppress the effect of phase errors on the far-field. Therefore, reducing the random phase error in OPA is significantly important for the realization of control architectures with low-complexity. OPA based on dispersive array waveguide gratings has also been proposed to achieve two-dimensional beam steering with wavelength scanning, which has the advantage of simple structure and low power consumption [28,29]. However, it is difficult to scaling-up and the footprint is relatively large.
In this paper, we propose a silicon based OPA with calibration-free phase shifters. By widening the optical waveguides beyond the single mode regime, the influence of structure variations on the phase errors can be significantly reduced. To realize a compact device size and suppress the excitation of the higher order modes in the multimode waveguide, the taper waveguide bend and multimode waveguide bend based on the third-order Bezier contour trajectory are optimized by using particle swarm optimization (PSO) algorithm. Due to the negligible phase error, a cascaded phase-shifter structure can be used to reduce the number of control electrodes from N to log2(N). Here, we demonstrate a 16-channel OPA with optical waveguides width of 2 µm and antenna array pitch of 2.5 µm. By using only four control electrodes, a steering range of 36.2° has been achieved without any phase calibration.
2. Design and optimization
The whole design is based on a 220 nm SOI platform with a buried-oxide layer thickness of 2 µm. Figure 1 shows the schematic of the proposed OPA, which consists of cascaded multimode interference (MMI) splitter tree, grouped cascaded phase shifters, a 2.5 µm pitch end-fire waveguide array, the taper waveguide bends (TWB), and the multimode waveguide bends (MWB).
Fig. 1. Schematic diagrams of the proposed OPA: (a) the overall view, (b) taper waveguide bend (TWB), (c) multimode waveguide bend (MWB), and (d) third-order Bezier curves.
To reduce the phase error, all straight optical waveguides in the device are widened to 2 µm and connected by MWB. The input signal light at 1550 nm wavelength is launched into the OPA through a grating coupler. The cascaded MMI splitter tree then divides the optical power equally into N channels, where the output of the MMI are connected to the straight multimode waveguides via TWB. One phase shifter is utilized for every two adjacent waveguides at each splitter stage. All the phase shifters of ith stage are connected together in parallel to the same electrodes. Optical delay lines are utilized to connect the MMI tree and the end-fire antenna array to ensure that all channels have the same optical path.
In an optical phased array, the accumulated phase error along the optical waveguides is mainly caused by the random variations of the waveguide dimensions. When the waveguide width variations is taken as the main consideration, the phase error can be expressed as [30]:
The waveguide structures are optimized to reduce the sensitivity of the waveguide propagation constant to the waveguide width variations and the random phase errors. Figure 2(a) shows the effective refractive index (Neff) of the TE fundamental mode as a function of the waveguide width calculated by the finite difference eigenmode (FDE) method. As the width of the waveguide increases, the derivation of Neff over the waveguide width is monotonically decreased. Thus, a widened waveguide can significantly reduce the sensitivity of the Neff to the waveguide width variations and the accumulated random phase error. Figure 2(b) shows the phase error in OPA with different waveguide widths and the sidelobe suppression ratio (SLSR). According to previous results, the sidewall roughness of silicon waveguides is generally around 1-10 nm and the correlation length is around 50 nm [31]. Here we assume that the standard deviation of the waveguide width is 10 nm, the correlation length Lc is 50 nm, and the waveguide length L is 4 mm for the 16-channel OPA. From Fig. 2(b), it can be found that the phase deviation decreases exponentially when the waveguide width increases. For example, when the waveguide width is chosen as 0.4 µm, the accumulated phase error for the 4 mm-long waveguide can be as high as 85° and the corresponding SLSR is about 0, which means that the main lobe is drowned in noise. In contrast, when the waveguide is wider than 1 µm, the SLSR is no longer affected by the phase noise and reaches a theoretical limit of about -13 dB. Here we choose the waveguide Wm to be 2 µm.
Fig. 2. (a) Calculated effective refractive index and the derivation of dNeff /dw with different waveguide width w. (b) Calculated phase deviation and sidelobe suppression ratio as the waveguide width varies.
Since the wider waveguides support not only the fundamental mode but also high-order modes, the intermodal crosstalk can also lead to degradation of OPA far-field beam quality. Conventionally, a large bend radius is usually required to suppress the excitation of higher-order modes, but phase errors will accumulate along the waveguide length and the layout footprint will also be large. The realization of low-crosstalk, low-loss and compact bends for wider waveguides is also important.
The Bezier profile trajectory-based approach is widely utilized for bending waveguide optimization [32,33]. There are two bend structures need to be optimized: TWB and MWB. The input of the TWB is a single-mode waveguide (Ws) and the output is a wider multimode waveguide (Wm), which is used to connect the output port of the MMI to the 2 µm wide straight waveguide. The MWB is multimode waveguides (Wm) at input and output, which is used for 90° bend. The third-order Bezier curves is used to optimize the inner and outer contours of the bend waveguide independently. The third-order Bezier curve is defined by four discrete points (from A to D) whose positions are represented by the Cartesian coordinate system (xi, yi), as shown in Fig. 1(d). It should be noted that two 90° bent Bezier curves define the two boundaries of the TWB. Two 45° bent Bezier curves are used to represent the boundaries of the MWB in order to increase the degree of freedom of optimization, and then the complete MWB is obtained by symmetry of the angle bisector. The locations of the terminal points and control points are optimized by PSO algorithm. In order to obtain low loss and low intermodal crosstalk, the figure of merit (FOM) function is defined as:
The variation of curvature radius R and waveguide width w with waveguide length L for the optimized TWB and MWB are shown in Fig. 3(a) and 3(b). The waveguide width of the TWB can rapidly widen from 0.45 µm to 1 µm with the length of 1.4 µm. The width of the MWB is greater than 1 µm throughout the waveguide length. Compared to conventional single-mode waveguide bends, such bends have less sensitivity to variations of the waveguide width. The footprints of TWB and MWB are as compact as ∼3.69 × 11.62 µm2 and ∼8.31 × 8.31 µm2. The field propagation in the TWB and MWB is shown in Fig. 3(c) and 3(d). The calculated performance of the optimized TWB and MWB with three-dimensional finite-different time-domain (3D FDTD) is shown in Fig. 3(e) and 3(f). The insertion loss for both TWB and MWB are less than 0.01 dB, while the intermodal crosstalk is less than -27 dB at the central wavelength of 1550 nm and less than -21 dB within the 100 nm wavelength band.
Fig. 3. The curvature radius R and the core width w of the (a) TWB and (b) MWB as functions of the curve length L. Calculated light propagations of the TE0 mode in the (c) TWB and (d) MWB. The excess loss and intermodal crosstalk of the (e) TWB and (f) MWB calculated by 3D FDTD.
We calculate the far-field distribution of OPA with different array numbers (N = 16, 64 and 256) in the condition of 50° phase deviation. As shown in Fig. 4(a), when the array number increases, the SLSR is more robust to the random phase error. We also compare the effect of waveguide width on SLSR for different array numbers. From the Fig. 4(b), we can find that even for large scale OPAs (with N = 256), the SLSR is still < -12 dB with the wide waveguide. Thus, the calibration-free design of the multimode waveguide is promising for scaling to large-scale OPA with high resolution.
Fig. 4. (a) The far-field distribution of OPA with the phase deviation of 50°. (b) Sidelobe suppression ratio as the waveguide width varies.
Based on the low phase error waveguide structures, a 16-channel end-fire OPA with periodic array element is designed as an example. The pitch for the antenna is chosen to be 2.5 µm considering a reasonable crosstalk between the waveguides. As shown in Fig. 5, the far-field distribution is calculated for different phase gradients (Δφ). Since the array element spacing is larger than half of the operating wavelength, grating lobes exist at ±38.3° for 0° phase gradient. The FOV is 36° and the full width at half-maximum (FWHM) of the main lobe is 1.97° at 0°.
3. Fabrication and characterization
The designed silicon OPA was then fabricated on a 220 nm SOI platform. The patterns are defined with the electron beam lithography (EBL), followed by the inductively-coupled-plasma reactive ion etching (ICP-RIE) process. Then, a 1.2-µm thick silica thin film was deposited as the upper cladding. The 200-nm thick titanium-tungsten (TiW) alloy was then deposited on the top as the thermal heaters. It should be noted that the thickness of the cladding should ensure that the metal of heaters and electrodes do not affect the optical modes in the waveguide, and the length of the wiring should be as short as possible to reduce the voltage division to the heater. Figure 6(a) shows the microscope image of the fabricated calibration-free silicon-photonic OPA. The detailed views of the MMI region, grouped phase shifters, and antenna region are shown in Fig. 6(b)-(d), respectively.
Fig. 6. (a) Optical microscope image of the fabricated calibration-free silicon OPA. Detailed view of (b) the MMI region, (c) grouped phase shifters, and (d) antenna.
Figure 7(a) is the schematic diagram of measurement setup. Figure 7(b) shows the Fourier imaging system utilized to characterize the far-field image of the OPA. As shown in Fig. 7(c), a fiber array was packaged on the input grating coupler and the chip was wire-bonded to a print circuit board (PCB) connected to the multi-channel voltage source. The far-field distribution is imaged by the microscope objective (MO), two lenses (Lens1, Lens2) with a focal length of 20 cm, and the infrared CCD (Hamamatsu, C10633-23). The imaging system has a large field of view of 100° and a relatively small resolution of 0.36°. It should be noted that our measurement system does not include any phase calibration component.
Fig. 7. (a) Schematic diagram of the measurement setup for far-field measurement, (b) the measurement system, (c) optical microscope image of the packaged OPA.
There are two OPAs fabricated on the same chip side-by-side with the same settings except that one optical waveguide width is 2 µm and the other is 500 nm. To demonstrate the optimization of phase error suppression, we first compared the initial far-field distribution of the single-mode waveguide and the widen waveguide OPA, as shown in Fig. 8. From the far-field image shown in the Fig. 8 (a) and 8(b), it can be found that the single mode waveguide based OPA has many side lobes in the far-field due to severely random phase errors and there is no obvious main lobe. In contrast, the widen waveguide based OPA has obvious main lobe and grating lobes at the expected position, as shown in Fig. 8(c) and 8(d). The SLSR is 6.68 dB at 0° and the FWHM is 2.21°, which is close to the calculated value 1.97°. Such SLSR corresponding to a phase deviation of 45° is worse than the simulation results. The relatively phase error may be induced from the fabrication error of the EBL process and the nonuniform light intensity of the different channels.
Fig. 8. Measured far-field distribution of the OPA with optical waveguide width of (a)-(b) 500 nm and (c)-(d) 2µm.
The fabricated 16-channel silicon OPA has fifteen grouped cascaded phase shifters, and only four independently controlled voltages are required to achieve continuously varying phase gradient. To avoid thermal crosstalk of phase array, the minimum spacing between adjacent array elements is chosen to be 30 µm . The measured modulation efficiency of the phase modulator is 20.3 mW/π. Based on the linear relationship between phase shift and electrical power, the voltage applied in the ith stage is:
Fig. 9. (a) The image of far-field distribution and (b) the measured optical power distribution versus angle at different phase gradient Δφ.
4. Conclusion
In conclusion, we have proposed and demonstrated a calibration-free silicon optical phased array. The optical waveguide is widened from single mode to multimode, which reduces the sensitivity of the effective refractive index to the variations of waveguide width and effectively suppresses the random phase error of the optical field in the array elements. The contour trajectory and PSO optimization based taper waveguide bend and multimode waveguide bend are utilized to ensure a compact device size. Due to the low phase error, cascaded and grouped phase shifters have been utilized to significantly reduce the number of control voltages from N to log2(N), which greatly simplify the control complexity and can be extended to two-dimensional beam steering. A 16-channel OPA with only 4 control voltages has been fabricated and characterized. A continuous high-quality beam steering in a 36.2° FOV without any calibration has been demonstrated. In particular, the proposed concept is also suitable for standard multi-project wafer (MPW), making it possible to realize large scale integrated LiDAR system.
Funding
National Natural Science Foundation of China (61922070, 62105286).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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