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Abstract
Thermo-optic phase shifters (TOPSs) are commonly used in large-scale silicon photonic integrated optical phased arrays (OPAs). However, fast-response TOPSs consume relatively high power; the elevated temperature floor in the dense region of the TOPSs introduces thermal crosstalk between optical paths, which undermines the control accuracy. We propose a combined method that involves subarray design in the optical power distribution network and array control method to predict, optimize, and redistribute the phase shifts and mitigates thermal crosstalk. Thermal simulations and an array control method for generic OPA models are discussed. A silicon photonic chip prototype of a 4 × 4 OPA with three-level cascaded subarrays is fabricated to demonstrate the proposed method. The experimental and statistical results show that the method effectively reduces the average total power consumption by 31%, the maximum local temperature by 18.4%, and the thermal crosstalk within the OPA.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past decade, large-scale silicon photonic optical phased arrays with several thousands of emitter elements have been demonstrated [1–4] for applications in LiDAR [4,5], free space optical communication [5,6], and 3-D sensing [7]. This CMOS-compatible technology has the nature to be monolithically integrated with its electronic control circuits to realize small-size, low-cost, and energy-efficient but powerful devices [2,8]. Unlike mechanical rotational scanning systems, an OPA system operates entirely by electronic scanning, which is based on electrical manipulation of relative phases between emitters (a phase shift profile) to change the optical interference in the far-field. The electronic method enables rapid and precise beamsteering operations without the limitation of mechanical inertia and vibration. The steering speed is determined by the type of phase shifters, where Electro-Optic (EO) and Thermo-Optic (TO) phase shifters are typically used.
While EO phase shifters exhibit superior modulation speeds in the order of tens of GHz, their implementations come at the cost of higher optical loss, larger driving and bias voltages, and more chip area consumption [9–11]. Conversely, TOPSs, typically constructed as waveguides with metal or doped silicon heaters [12–17], offer a more compact alternative. The TOPSs require smaller driving voltages, exhibit lower optical loss, and use simpler fabrication processes. These characteristics make TOPSs highly desirable for cost-effective, large-scale OPAs. However, a large number of TOPSs operating in an OPA leads to an elevated temperature floor within the dense phase shifter region, resulting in thermal crosstalk and inaccurate phase controls.
Traditional approaches to resolve the high power consumption and thermal crosstalk issues are by re-engineering the TOPSs, such as introducing in-waveguide doped heater [12,18] to localize the heat within the target waveguide, multi-pass waveguide loops [13,16,19] to reuse the diffused heat and reduce the maximum tuning temperature, or adding air-trenches between the adjacent phase shifters [14,15,20] to isolate the heat diffusion. However, these modifications come with trade-offs. Re-engineering the TOPSs to improve the power efficiency usually further lowers the response speed, from tens of $\mu$s to more than a hundred of $\mu$s, or increases the overall footprint. Introducing in-waveguide dopings also increases the optical loss. The air trenches not only significantly increase the footprint but also reduce the response speed and require extra fabrication processes.
To overcome this fundamental challenge, we propose a combined approach that cooperates the photonic circuit design with the array control method. Firstly, we distribute phase shift control throughout the entire hierarchy of optical paths by adopting the cascaded subarray design in the optical power distribution network (OPDN) of the OPA. In this way, the common phase shifts of grouped emitters can be controlled by their subarray phase shifters. The generated heat will be distributed from the TOPS array to a larger region so that the maximum temperature is reduced. Secondly, we mathematically model and map the phase shift and mutual thermal crosstalk in matrix form, which represents the phase contribution of each phase shifter to all emitter phases. Finally, we globally optimize and redistribute the phase shift profile so that the thermal crosstalk effect and total power consumption can be minimized.
This paper is organized as follows. In Section 2, we describe the cascaded subarray design for OPA and introduce related new terms. Section 3 focuses on 2-D and 3-D finite-element thermal simulations of the TOPS performance and the thermal crosstalk modeling process. In Section 4, we introduce a mathematical model, phase coupling matrix, based on reference [21], and adopt this model to our cascaded subarray design. Thermal simulation results are extracted and mapped using this model. The 1-D and 2-D OPA performances with and without the cascaded subarray controls are predicted through two 16-element OPA examples. In Section 5, we show the experimental results of the prototype chip and compare the OPA performance with and without the subarray controls. In Section 6 and 7, we summarize the impact and benefits of our method.
2. Cascaded subarray design
Subarray techniques are frequently employed in RF phased arrays to reduce the number of active controls, devices, and signal processing [22] due to the high cost of RF components. For integrated OPAs, active controls and phase shifters can be produced at a much lower cost and smaller size, thanks to the CMOS-compatible silicon photonic process and the highly-temperature-dependent refractive index of silicon material. The easier access to more active controls and phase shifters enables more potential applications of subarray techniques on integrated OPAs.
In the past decade, a few research studies have been conducted on the subarray [2] and cascaded phase shifters [23–25] OPA design. These research studies focus on 1-D uniform linear OPAs, as shown in the upper part of Fig. 1(a), where the optical emitters are uniformly distributed in parallel so that the phase tunings follow a linear ramp relationship. The subarray techniques (or cascaded phase shifters in reference) are applied to reduce the number of control electronics and phase shifters as well as enable continuous steering by simply increasing the driving voltage to the serially connected phase shifters. To our best knowledge, there is no research study on applying subarray and cascaded phase shifters to 2-D OPA configurations. It is challenging because, in a 2-D OPA configuration, such as a rectangular grid OPA, as shown in the lower part of the Fig. 1(a), the relative phase shift profile in the emitter array now follows a 2-D plane relationship which has to map back into the linear phase shifter array. In addition, it is harder to align the initial phase of each emitter perfectly due to the non-equal waveguide path length routing and process non-uniformity. Equalized path length or active control compensation on each emitter is needed.
Fig. 1. (a) 1-D and 2-D OPA configurations and phase shift profiles at the emitter and phase shifter array. (b) Proposed cascaded subarray OPA design.
This work explores the cascaded subarray design in a 2-D rectangular OPA configuration. Figure 1(b) shows the proposed schematic. An input laser is coupled from a fiber into the OPA through an edge coupler, and evenly distributed through a 1:2:4:8:$\cdot \cdot \cdot$:N OPDN consisting of cascaded 1$\times$2 multi-mode interferometers (MMI). This schematic only shows up to 16 elements, but the design can be scaled up to $N=2^{S}$ elements, where $N$ is defined as the number of elements and $S$ as the number of MMI stages. After the OPDN, a linear array of TOPSs (TOPS array) controls individual phases of emitters. Because the size of OPDN is determined by the waveguide’s minimum bending radius and the number of elements, those stages before the last stage, Sub2, generally have large spacing between the waveguide branches. This space has not been utilized for another purpose except optical power splitting, hence, it can be potentially used for common phase tuning of the emitter groups, i.e., subarrays.
The subarrays are grouped into different stages in the OPDN’s branches, as shown in Fig. 1(b), named as Sub2 stage, Sub4 stage, Sub8 stage, and so on. The subscript indicates the number of emitters this subarray is controlling. Within the stage, the index of a particular subarray is also appended to the stage name, for example, Sub2-1. This cascaded subarray design distributes the phase shifts and spreads heat to a broader region and hence mitigates thermal crosstalk within the dense TOPS array region. Since phase shifts accumulate across a series of subarray TOPSs in the distribution tree, lower overall power consumption can be achieved in most cases. Meanwhile, the original footprint of the OPA design is maintained. In the following section, these ideas will be further analyzed and discussed.
3. Thermal crosstalk modeling
In this section, the TOPS performance, the thermal crosstalk of the TOPS array, and the TOPSs in the cascaded subarray are evaluated using 2-D and 3-D finite-element thermal simulations. The 2-D thermal simulation uses much less computational power and gives fast but good approximation of the TOPS array performance. The operations and thermal crosstalk of TOPSs in the cascaded subarray can only be simulated in 3-D.
3.1 2-D thermal simulation of a TOPS array
Figure 2(a-b) show the cross-section of a TOPS structure in the prototype chip and its 2-D thermal simulation heat distribution profile. The chip uses a standard silicon-on-insulator (SOI) multi-project wafer (MPW) foundry service from IMEC. The technology has a 220nm thick SOI layer and a 2$\mu$m buried oxide layer (BOX). A Tungsten heater, 600$\times$300nm (W$\times$H), is 1$\mathrm{\mu}$m above the 450$\times$220nm Si strip waveguide and 150$\mu$m in length. The TOPS array has a uniform spacing of 31$\mu$m to avoid excess thermal crosstalk. The temperature of the background, chip substrate, and air is set to 300K by default in the simulations.
Fig. 2. (a) 2-D TOPS cross-section profile. (b) 2-D thermal simulation heat distribution profile. (c) Phase shift induced in an adjacent 150-$\mathrm{\mu}$m waveguide near the heater over distance. (d) One case of TOPS array 2-D temperature profile in the SOI layer. TOPS indices are labeled in red. (e) The simulated phase shift efficiency. (f) The extracted phase shift efficiency from measurement. The OPA beam intensity and emitter phase shift (TOPS power) have a sine function relationship through optical interference. (g) Simulated and calculated phase shift map of the TOPS array.
The TOPS array operation can be well approximated by simulating the cross-section of a single TOPS in the 2-D thermal simulation and superposing its heat profile according to the array arrangement. This method, discussed in [26], assumes the superposition and linearity of the heat transport equations and ignores the vertical temperature variation across the 220nm thin layer. This approximation is effective because the TOPS and the array have simple geometry and are consistent over the length. To verify this assumption, one case of the TOPS array temperature profile with different TOPS input powers is simulated as shown in Fig. 2(d).
In Fig. 2(c), by sweeping the input power of the TOPS, the temperature variation maps of the SOI layer at different powers, $\Delta$T(x,y,P), can be obtained. The phase shift efficiency $P_\pi$ can be extracted by monitoring $\Delta$T in the waveguide region under the heater and calculating the phase shift:
Due to the nature of heat diffusion, the thermal crosstalk profile across the SOI layer can be modeled as a continuous two-term exponential decay curve over the distance from the source TOPS, $T_{XT}(x) = Ae^{Bx} + Ce^{Dx}$ (the vertical temperature variation is ignored), as shown in Fig. 2(c). The subscript $XT$ means thermal crosstalk. This fit model is valid for distances beyond the heater width. With this model, the thermal crosstalk from the source TOPS to other waveguides can be estimated over distance. (Unbalanced MZI test structure with TOPS aggressors at different distances could be used to further verify the thermal crosstalk, as discussed in [19,20]). Using the thermal crosstalk fit curve and the superposition method, arbitrary TOPS array operations can be quickly computed. The details of the computation will be discussed in Section 4.1. Figure 2(g) shows one case of simulated and calculated phase shift of TOPS array operation. The calculated results match the simulated results.
3.2 3-D thermal simulation of a cascaded subarray
To evaluate the cascaded subarrays’ thermal crosstalk within the OPDN, 3-D thermal simulations are necessary. Figure 3 shows the OPDN region of the prototype OPA and the simulated heat maps. The heaters are folded to reduce the area and localize the heat within the region without affecting the original MMIs’ arrangement. 3-D thermal simulations of different stages are performed separately to evaluate the phase shifter efficiency and thermal crosstalk within the OPDN. The large gold dash-line box indicates the simulation region. The 3-D simulations require much more computational resources. However, by fully utilizing the symmetry of the OPDN layout, much fewer cases are required. Simulated heat maps of subarray Sub2-3, Sub4-2, and Sub8-1 are overlaid on the design drawing, where the red circles indicate the regions of $\Delta$T about 1K and the green circles indicate the regions of $\Delta$T about 0.1K. From Fig. 3, there are enough clearances between the three stages, so the thermal crosstalk between them is negligible.
Fig. 3. Cascaded subarray design and thermal simulation illustration. The subarrays are labeled by their stage number and index. All TOPS simulations in the figure operate at 10mW.
Figure 4(a-b) further illustrate the phase shifts in the Sub2-3 TOPSs and the thermal crosstalk to its neighbors Sub2-4. The waveguide region data are extracted and segmented to calculate the segments’ temperature and accumulated phase shift along the waveguide due to the rise in temperature. From the simulation results, even for the nearest case of Sub2-3&4, the phase shift induced by the thermal crosstalk is lower than 0.1 degree at 10mW operation. This OPDN design can be further optimized by moving subarray TOPSs in Sub2 stages further away.
Fig. 4. (a) Sub2-3 waveguide heat map, $\Delta$T and cumulated phase shift along the waveguide. (b) Thermal crosstalk from Sub2-3 to its neighbor Sub2-4.
The thermal-crosstalk-induced phase shift and power imbalance of the MMI are not fully studied in this work, since the process involves more complicated thermal and EM simulations. However, [27,28] show that a 10K $\Delta$T creates less than 5% of the power imbalance between two ports and $P_{\pi }=60.4$mW for a traditional MMI structure. Therefore, the effects of thermal crosstalk in the MMIs are assumed to be negligible.
4. Phase coupling matrix method for subarray control
TOPSs in the TOPS array and cascaded subarray are simulated. The extracted results characterize the phase shift efficiency and thermal crosstalk. A comprehensive mathematical model is needed to merge the thermal simulation or experimental results into the OPA control signals to predict and compensate for the thermal crosstalk error presented in the TOPS array and cascaded subarray. To use the thermal simulation data, one should make sure that the OPA chip is operating under good heat dissipation conditions, so the chip temperature is well-controlled to match the simulation condition. For simplicity, an N-antenna OPA with a TOPS array without subarray configuration is considered first.
4.1 Phase coupling matrix
The phase status of the OPA emitters can be represented as a phase vector $\boldsymbol {\Phi } = [\Phi _1 \cdots \Phi _N]^{\mathrm {T}}$ which is also known as a steering vector, where $\Phi _i$ is the phase of the emitter. The phase tuning of the TOPS is represented as a phase shift vector $\Delta \boldsymbol {\Phi } = [\Delta \Phi _1 \cdots \Delta \Phi _N]^{\mathrm {T}}$. A phase coupling matrix [21] is introduced here to derive the phase tuning with thermal crosstalk effect:
To calculate $\mathbf {T}$, the phase shifter mutual distances $x_{i j}$ in the TOPS array are created as an $N{\times }N$ matrix and plugged into the thermal crosstalk model $T_{XT}(x)$ as discussed in Section 3.1. Notice that the diagonal terms $x_{i i}$ are zeros and should be replaced by the simulated center waveguide $\Delta$T as the self-induced temperature change. Then, using the phase shift equation, Eq. (1), mutual phase coupling $T_{i j}$ can be obtained. However, the present $\mathbf {T}$ only represents this specific simulation case, where the input phase shift vector is induced by the simulated TOPS power. Since the TOPS power and phase shift have a linear relationship. A normalization of $\mathbf {T}$ is required.
Using the array synthesis method [29], the OPA beamsteering control signals and beam patterns can be derived from array steering vectors $\boldsymbol {\Phi }$, element and array factors [30]. The steering vectors are calculated based on the OPA’s element positions and steering angles. Due to waveguide length differences and process variations, the OPA emitters’ initial phases also exhibit static phase errors $\boldsymbol {\Phi _0}$, where the non-static phase errors due to thermal crosstalk can be taken into account by the phase coupling matrix. To solve for the correct input phase shift vector $\Delta \boldsymbol {\Phi }$, the static phase errors should be removed first $\Delta \tilde {\boldsymbol {\Phi }} = \boldsymbol {\Phi } -\boldsymbol {\Phi _0}$; Then, the correct input phase shift vector is calculated as $\Delta \boldsymbol {\Phi }=\mathbf {T^{-1}}\Delta \tilde {\boldsymbol {\Phi }}$. With the TOPS efficiency $P_{\pi }$ and resistance, the electrical current and power through each TOPS can be calculated for the OPA control.
4.2 Phase coupling matrix for subarray control
To take into account the cascaded subarray, the subarray phase coupling matrix, $\mathbf {T_{Sub}}$, can be created in a similar manner as an $N{\times }M$ matrix, then horizontally concatenated to $\mathbf {T}$ as a $N{\times }(N+M)$ matrix, $\mathbf {T_{Combined}}$. $M$ is defined as the total number of subarray TOPSs, which is equal to $2^S-2$ but can be less for fewer stage operations. $S$ is defined as the number of MMI stages. Here, the maximum number of subarrays TOPSs is considered.
In Fig. 5, $\mathbf {T_{Sub}}$ consists of two parts, the self-phase-coupling and the mutual-phase-coupling due to thermal crosstalk. The column order of the subarray TOPSs can be defined arbitrarily but should be sorted thoughtfully for easier visual understanding. Here, the order goes from subarrays with fewer emitters to those with more emitters. The index $i$ of the coefficients indicates the emitter index. The index $j$, for example, Sub2-1, represents the source subarray of the coupling.
Although the generic forms of the $\mathbf {T_{Sub-Self}}$ and $\mathbf {T_{Sub-Mutual}}$ look complicated, after normalization, as shown in the lower part of the Fig. 5, the normalized $\mathbf {T_{Sub-Self}}$ simply indicates the mapping between the subarray control to the emitters, assuming the TOPSs all have the same tunning efficiency. Due to the fact that the thermal crosstalk level in the OPDN is low in this work, most of the mutual phase coupling coefficients in $\mathbf {T_{Sub-Mutual}}$ can be set to zero, except those adjacent neighbors. For a more compact design of the OPDN or high-heater-power operations, these coefficients could be significant and must be considered.
With this new $N{\times }(N+M)$ matrix, $\mathbf {T_{Combined}}$, obtained by horizontally concatenating $\mathbf {T}$ and $\mathbf {T_{Sub}}$, input phase shift vector $\Delta \boldsymbol {\Phi }$ can not be obtained simply by matrix inversion of $\mathbf {T_{Combined}}$ due to rank deficiency. A mathematical optimization technique, linear programming can be used to find the best possible solution by considering a linear objective function, bounds, and constraints. The optimizations are done through MATLAB linprog function [31]. The linear objective function is set to find the solution that minimizes the OPA total power consumption. The upper and lower bounds can be set to the hardware output range, such as the voltage or current range, the TOPS maximum operating temperature range, etc. The phase coupling matrix $\mathbf {T_{Combined}}$, and emitter phase vector $\boldsymbol {\Phi }$ further provide linear equality constraints to the problem. For not strict constraints, the linear programming solver usually finds a solution for input phase shift vector $\Delta \boldsymbol {\Phi }$ within a few iterations.
4.3 Theoretical cascaded subarray performance
The performances of 1-D linear and 2-D rectangular OPAs with cascaded subarray are evaluated with different stage configurations in this section. The stage configuration is defined as the stage(s) of the subarray in operation. For example, Sub8 means only the subarray Sub8-1 and Sub8-2 are in operation; Sub2,4,8 means all the subarray stages are in operation. The stage configurations provide a flexible way for the circuit implementation when the number of controls is limited. The cascaded subarray design and performance are the same as the one from the thermal simulations. Assuming the static phase errors $\boldsymbol {\Phi _0}$ of the OPA are zeros in the calculation. The key indicators of the performance are the OPA total power consumptions of beamsteerings and the maximum temperature changes within waveguides. By comparing these values with and without the subarray controls, power consumption reduction and maximum temperature change reduction can be derived. The reduction is defined as the percentage change from the original value without the subarray configuration. These two indicators reflect how well the subarray design and proposed control method reduce the OPA power consumption and temperature.
4.3.1 1-D linear OPA
Consider a 1-D linear OPA with 16 emitters spacing at a 1.55 $\mu$m pitch size. The azimuth steering is by phase tuning of TOPSs and the elevation steering is by wavelength tuning of the input laser. 240-point azimuth ($\pm$12$^{\circ }$) steering vectors with 0.1-degree step size are calculated to evaluate the steering performance with and without the cascaded subarray. Statistical results are summarized in Fig. 6(a-b). From the results, the cascaded subarray with Sub2,4,8 configuration reduces the average total power consumption by 39.98% and the maximum temperature change in the waveguide by 20.89%. Even for the Sub8 configuration with two TOPSs, a 12.95% reduction in power consumption and 9.63% in maximum temperature change can be achieved. Notice that the solver occasionally can not find the solutions. This situation happens more for the subarray stage configurations with fewer TOPSs. For Sub2,4,8, Sub2,4, and Sub2 configurations, 98.75% of solutions out of 240 cases can be found. Sub4 and Sub4,8 configurations both give 97% of the solutions. Whereas Sub8 configuration gives 88% of solutions. For those cases without solutions, their results are not included in the statistics.
Fig. 6. (a) 1-D OPA subarray configurations and power consumption reduction box plot. (b) Max. temperature change reduction box plot. (Note: The blue vertical line inside of each box is the sample median, whereas the red vertical line is the mean. The left and right edges of each box are the lower and upper quartiles. The box range is defined by the interquartile range (IQR). The outliers are values that are more than 1.5$\times$IQR away from the edges of the box.)
For the input phase shift vectors without solutions, the main reasons are due to either a very small slope of phase difference or multiple near zero phase shifts (very large slope of phase difference after unwrapping the phase). In other words, those phase shifts contain little common phase shift between emitters, so the solver cannot find a proper combination of the subarray controls. Fortunately, those cases usually have lower power consumption and maximum waveguide temperature change than most of the general cases.
4.3.2 2-D rectangular OPA
The 2-D rectangular OPA performance is calculated using the prototype design. Both azimuth steering and elevation steering are controlled through phase tuning of TOPSs. 3835-point azimuth and elevation steering vectors with 0.25-degree step size are computed and evaluated. The results are summarized in Fig. 7(a-b). Similar to the 1-D OPA, the Sub2,4,8 configuration reduces the power consumption by 35.55% and maximum waveguide temperature change by 25.2%. For Sub2,4,8, Sub2,4 and Sub2 configurations, 99.69%, 98.62%, and 98.51% of solutions out of 3835 cases can be found, respectively. Sub4 and Sub4,8 configurations give 97.34% and 97.37% of the solutions, whereas Sub8 configuration gives 90.51% of solutions. To conclude this section, the phase coupling matrix method for subarray control is an effective method to take thermal crosstalk into account, as well as to optimize and reduce power consumption and OPA maximum temperature. The matrix nature of the method enables fast computations during the OPA beamsteering operations.
Fig. 7. (a) 2-D OPA subarray configurations and power consumption reduction box plot. (b) Max. temperature change reduction box plot.
5. Experimental results
5.1 Prototype chip
In order to demonstrate the concept of the cascaded subarray OPA, a 2-D 16-emitter OPA (4x4 rectangular array) prototype chip was fabricated. The OPA layout is shown in Fig. 8(a). Sub2,4,8 configuration cascaded subarray is implemented in the OPDN. There are 30 TOPSs in this OPA design. As shown in Fig. 8(b), the emitter size is 3.7$\mu m \times 2.5 \mu m$ with a row pitch of 10$\mu m$ and column pitch of 3.5$\mu m$ in the emitter array. The emitter array aperture size is 33.7$\mu m \times 13 \mu m$. The OPA operates at 1550nm wavelength and its cross-section profile has been discussed in Section 3.
Fig. 8. (a) Micrograph of the prototype OPA chip. (b) OPA aperture region. (c) OPA experimental test setup.
5.2 Experimental test setup
The OPA experimental test setup, as shown in Fig. 8(c), consists of an OPA driver package, control and power supply electronics, and an NIR microscopic imaging system for OPA beam pattern capture. The prototype OPA chip is mounted on a copper chip mount atop a thermoelectric cooler (TEC) and is wirebonded to its driver circuit PCB inside the package. A thermistor is attached to the copper chip mount near the chip to monitor the temperature. A PID temperature controller maintains the chip temperature at around 20$^{\circ }$C. The driver circuit consists of two parts, voltage generation using DACs, and current sensing using an ADC. Each TOPS is controlled by a DAC channel. The control voltage errors are then corrected by the current sensing feedback. The current sensing is done by cooperating low resistance sense resistors, fix-gain sense amplifiers, multiplexers (MUXs), and an ADC. The current and power consumption of each TOPS can be monitored by measuring the voltage across the sense resistor and calculating through pre-measured calibration data. The whole system operates at 3.3V and 5V supply voltages.
5.3 Calibration process and beamsteering results
A calibration is required to compensate for the static phase error $\boldsymbol {\Phi _0}$ before the beamsteerings. Because the OPA beamsteering is confined by the element pattern envelope which is determined by the grating emitter characteristics, a maximum intensity exists at a certain emission direction. The grating emitter emits at around 7$^{\circ }$ in our design. Here, we perform iterative coarse and fine-phase tuning scans of each individual OPA emitter phase and use the NIR microscopic imaging system to capture far-field beam intensity patterns. By maximizing the beam intensity at the azimuth $\phi$=0$^{\circ }$ and elevation $\phi$=7$^{\circ }$ (a hill-climbing optimization process), the static phase error can be extracted based on the known direction and hence, known steering vector. The images of before and after calibration are shown in Fig. 9(a). The measured $\boldsymbol {\Phi _0}$ are then used for all the input phase shift vector $\Delta \boldsymbol {\Phi }$ calculations. Notice that $\Delta \boldsymbol {\Phi }$ is still a 16-element vector where the subarray is not controlled. The OPA beamsteering capability is further verified by performing a fast scanning of a "U" and an "R" pattern (451 points in total). Each point is exposed for around 350$\mu$s. By synchronizing the pattern scan time and the camera exposure time (around 95$ms$), the patterns are as shown in Fig. 9(b).
5.4 Cascaded subarray performance
Once $\boldsymbol {\Phi _0}$ and $\Delta \boldsymbol {\Phi }$ are known, 30-element $\Delta \boldsymbol {\Phi }$ with the subarray control can be computed using the phase coupling matrix method and the linear programming solver discussed in Section 4.2. Different combinations of stage operations are performed and evaluated through the 241-point cases of azimuth steering ($\pm$12$^{\circ }$) with 0.1$^{\circ }$ step size. Finally, 1421-point cases of azimuth ($\pm$12$^{\circ }$) and elevation ($\pm$7.5$^{\circ }$) steerings with 0.5$^{\circ }$ step size in Sub2,4,8 configuration are performed to further verify the statistics. The OPA total power consumptions are measured using the current sensing of the driver circuit. The maximum waveguide temperature changes are derived from the phase shift & temperature model.
Figure 10 shows the image captures of azimuth and elevation beamsteering with and without the subarray controls using an IR camera. The steering angles are relative to the calibration point. The subarray controls reproduce the same steering behaviors. No significant deviation and intensity change is observed. Figure 11 compares the different performances of the subarray configurations from case to case and from a statistical perspective. The statistics of different stage configurations are summarized in Fig. 11(b). The experiment results show the same trend as the theoretical prediction. The reason for the results not being as good as the calculated ones is most likely due to the additional static phase error $\boldsymbol {\Phi _0}$ from the unequal waveguide length and fabrication imperfection. So the common phase shifts between emitters are reduced.
Fig. 10. (a-b) Azimuth beamsteerings ($\theta$=7$^{\circ }$), (c-d) and Elevation beamsteerings ($\phi$=0$^{\circ }$) with (Sub2,4,8 configuration) and without subarray controls. (To fit multiple beamsteering images in a row$/$column, images’ aspect ratios are changed, so they are visually different from Fig. 9(a)).
Fig. 11. (a) Experimental data of different subarray configurations from case to case. (b) Box plots of different subarray configurations. (AzEl) indicates the 1421-point beamsterring cases.
6. Discussion
The proposed method increases the degree of freedom of the OPA controls and enables redistribution of the phase tunings from TOPS array to subarray TOPSs. The effect is beneficial in various aspects. From a thermal aspect, the heat spreads to a much larger region for dissipation which leads to lower hot spot temperature and chip temperature. The thermal crosstalk will decrease accordingly. Lower chip temperature also means less pressure on the cooling system. From a layout aspect, this generic method is scalable for larger OPA designs since the OPDN also scales with increasing number of emitters. Lower thermal crosstalk enables a more compact OPA footprint so that more emitters and TOPSs can fit in a given area. In the case of large-scale 2-D OPA, sparse array technique [32] is a potential option to overcome the 2-D routing challenge. The proposed method is applicable to the sparse array design since the common phases exist between emitters. For the power efficiency and control aspect, the method can be further combined with more power-efficient TOPS to achieve even lower power consumption and drive voltage. The OPDN has large unused space for the large-size power-efficient TOPSs. In this way, the OPA can use TOPS array to achieve fast scanning and searching while running in low-power mode using the subarray operation for long-duration communication.
7. Conclusion
In this work, the subarray design and its control method for optical phase array are investigated in detail to resolve the thermal crosstalk and relatively high power consumption when thermo-optic phase shifters are used. Theoretical calculations and experimental results show that the proposed method significantly reduces the average total power consumption and maximum chip temperature by 31% and 18.4%, respectively. In theory, higher average reductions above 35% and 20% are possible when all waveguide lengths are equalized. This work provides a new direction and guideline to design and optimize integrated OPAs for lower power consumption and optimized thermal crosstalk.
Funding
L3Harris Technologies; National Science Foundation; Center for Emerging and Innovative Sciences (530863).
Acknowledgments
This research is partially supported by NSF grants ECCS-1842691 and IIS-1722847. We also acknowledge funding support by L3Harris Space and Airborne Systems and CEIS. The authors would like to thank J. Daniel Newman, Andrew Sacco, and Daniel Sundberg for providing resources and support to our works; Dr. Wenhui Hou, Dr. Tara Peña, and Professor Stephen Wu for PIC wirebondings; Dr. Jingwei Ling and Professor Qiang Lin for equipment; Yujia Yan and Ge Zhu for enlightening discussions; IMEC for PIC fabrication.
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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