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Abstract
A waveguide-based multi-beam steering device is proposed for light detection and ranging (LIDAR). The device integrates binary gratings with an optical phased array (OPA), thus enabling a single-chip LIDAR system. The device can provide an N×M beam array that covers a wide angular range while phase shifters help realize steering over a narrow angle range between the beams. The antenna structure for 1D beam splitting is realized by combining the design of a grating coupler and a beam splitter grating, and a uniform beam splitting is achieved along the other dimension using non-uniformly distributed antennas. To illustrate the design, an OPA with an 11×11 beam array is designed at a wavelength of 905 nm. The OPA achieves a wide total field of view (FOV) of 68.8° × 77° with a narrow beam-array-steering angle of 6.5°, enabling a wide-FOV 3D sensing with a high frame rate.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Beam steering plays an important role in light detection and ranging (LIDAR) systems. Mechanical beam steering devices [1] are no longer suitable to meet the increasing requirement of a more compact LIDAR system with low cost and high resolution, because of moving parts and complicated calibration. Although steering mechanisms with digital mirror devices (DMDs) [2,3] are suitable for single-chip LIDAR, the mechanical loss may limit their service life. On the other hand, optical phased arrays (OPAs) [4–7], which can be integrated with lasers and other optical components on a single chip, can overcome the shortcomings of conventional mechanical steering devices. Two-dimensional (2D) beam steering in OPA can be implemented either by phase modulators or by wavelength tuning [8,9]. However, because of the irreducible gap between two adjacent radiating antenna gratings, an OPA typically has a narrow scanning angular range and lacks a wide field of view (FOV) [6].
Scanning multiple beams can help reduce the scanning angle, ensure a wide FOV, and improve the frame rate. This can be realized by adopting an OPA with large element spacing and utilizing higher-order grating lobes [8]. However, simply reducing the element spacing will cause power decline in high-order lobes. Multi-beam steering can also be achieved using a multiple-wavelength laser source [9], though this method requires a wide wavelength range, which is typically infeasible for on-chip lasers. A metasurface [10] may be a candidate for multi-beam formation; however, the manufacturing accuracy should be high. Vertical cavity surface emitting laser (VCSEL) arrays with diffractive optical elements (DOEs) [11] can also provide multi-beam output; however, the spacing between the beams cannot be swept. Therefore, it is important to develop an on-chip multi-beam steering system with a wide FOV and one that is high yield compatible with conventional manufacturing technologies.
In this work, a multi-beam-emitting OPA comprising non-uniformly distributed antennas with specially designed gratings is proposed to solve the aforementioned problems. With a single-mode laser input, a 2D beam array can be emitted vertically from the chip. The specially designed gratings, which are optimized using the finite-difference time-domain (FDTD) method [12] with the simulated annealing (SA) algorithm, enable 1D beam splitting. The antenna gratings are non-uniformly placed to ensure a flat-top envelope during steering. To illustrate this idea, an OPA operated at a wavelength of 905 nm with an 11×11 beam array is designed and simulated. The beam array, which covers a static FOV of 68.8° × 68.8° and a total scanning FOV of 68.8° × 77°, can be steered over a 6.5° angular range perpendicular to the antenna gratings. This FOV is much wider than those of currently used OPAs, and a narrow scanning angle can be easily achieved. The multi-beam steering device enables a single-chip solid-state LIDAR with a wide FOV, and the frame rate of the system can be improved owing to the increased number of output beams.
2. Operating mechanism and design rules
Figure 1(a) shows a schematic layout of the proposed multi-beam steering OPA, comprising four repeating units along the y direction, each containing five non-uniformly distributed 32-µm-long antenna gratings. The device is based on SiNx waveguides with SiO2 cladding. The power from a 905 nm laser is equally split into four repeating waveguide-based units. Each unit is equipped with a phase shifter followed by power dividers with a special splitting ratio, and a fixed set of waveguide modes is injected into the antenna gratings, as shown in Fig. 1(b). The specially designed antenna gratings are identical and can generate a 1D (11×1) beam array along the x direction. The five non-uniformly distributed antenna gratings in one unit ensure a flat-top envelope, which provides a 1D (1×11) beam array when the units are repeated along the y direction. Thus, the entire structure can transform an in-plane single-mode laser input into a far-field 11×11 spot pattern, which can be continuously steered along the y direction by adjusting the phase shifters. For design feasibility, beam splitting along the x and y directions of the 2D beam array is separately designed as follows.
Fig. 1. Scheme design of a 2D multi-beam steering OPA. (a) Schematic layout of the designed OPA. (b) Architecture of one unit of the OPA. The units are repeated along the y direction. The waveguide modes propagate along the x direction, and the beam array is emitted along the z direction.
2.1 Beam splitting along the x direction
The structure of a conventional grating coupler is composed of finite teeth with either regular or irregular periods, depths, and duty cycles, through which only a single beam can be emitted into free space [13,14]. Figure 2 depicts a segment of a grating coupler with a period of ${T_x}$, with each period comprising L ridges. The permittivity distribution $\varepsilon (x )$ in one period can be expressed as a function of the transition points $({{a_l},{b_l}} )$:
Based on the phase matching condition expressed by the Bragg law [15,16], the angle of the output beam ${\theta _m}$ is given by
where ${n_{eff}}$ is the effective index of the waveguide in the grating area, m is the diffraction order, and ${\lambda _0}$ is the wavelength in air. The characteristics of Bragg gratings have been analyzed using the coupled-wave theory [16]. The coupling efficiency of the m-th order diffraction can be expressed as where ${k_0}$ is the wave vector in air, $\Gamma $ is the power confinement factor in the grating regionSince multiple beams are emitted in our case, the optimization objective is to obtain a uniform efficiency distribution among the desired diffraction orders. The antenna grating can be optimized directly by calculating the efficiency of the diffraction orders through Eq. (3). To simplify the calculation, this problem can be separated into two parts: the design of a one-beam vertically emitting grating coupler and the introduction of a beam splitter grating into the grating coupler.
Fig. 2. Segment of a grating coupler. The period is ${T_x}$, with each period comprising L ridges. $({{a_l},{b_l}} )$ pairs represent the transition points in one period.
The concept of Dammann grating [17–20] is introduced here to create a multi-beam-emitting antenna grating. The Dammann grating is a beam splitter grating containing special distribution of ridges in one period, providing uniform multiple diffraction beams from the normally incident plane wave. Typically, both Dammann gratings and grating couplers change the propagation status of light by manipulating its phase and amplitude, with the only difference being the direction of the incident light. Therefore, we propose the design of a multi-beam-emitting antenna grating by combining the grating coupler with the beam splitter grating. Thus, it is easier to determine the transition-point pairs $({{a_l},{b_l}} )$ in the grating structure.
First, a nearly vertical emitting grating coupler and a beam splitter grating with a wide angular coverage are designed and optimized. Since the conventional scalar diffraction method cannot provide precise results for large incidence or departure angles, the FDTD method with the SA algorithm is applied to deal with this issue. The final grating structure can be obtained by carrying out an XOR operation between the two structures. Further adjustment is required since the effective index varies with the grating structure, which affects the efficiency distribution and emergence angles of different diffraction orders.
2.2 Beam splitting along the y direction
Beam splitting along the y direction is implemented via an OPA with non-uniformly and sparsely placed waveguide antennas. The far-field pattern of an OPA is defined by both the array pattern and the element pattern [21]. The two patterns are associated with two main problems in OPAs: the existence of side lobes and the power decline of the main lobe during scanning.
The emergence angle of the n-th side lobe ${\theta _n}$ depends on the period of the array ${T_y}$, which can also be given by the Bragg law:
where ${\theta _0}$ is the emergence angle of the main lobe.In a conventional OPA emitting only one beam, the period ${T_y}$ should be less than ${\lambda / {({1 + \sin {\theta_0}} )}}$ to avoid side lobes and ensure a full scan in a given angular range of $2{\theta _\textrm{0}}$ [5,6]. Fortunately, this is no longer required in a multi-beam-emitting device because the side lobes are exactly the additionally utilized beams. Meanwhile, the power variation problem during scanning becomes even more important, because the power should be uniformly maintained over all the lobes.
Therefore, the arrangement of the waveguide antennas in one repeating unit is prioritized. The gap between adjacent waveguide antennas should be larger than half the wavelength; otherwise, the high crosstalk between the two adjacent waveguides will lead to an undesirable far-field pattern. The waveguides should be sufficiently wide for good optical confinement, and the waveguides employed in our design have the same width, thus providing a constant effective index for a desirable interference. A regular arrangement of waveguide antennas can be utilized to form a flat-top element pattern, as demonstrated in our previous work [22]. However, more waveguides are required for such a wide angular coverage and splitting ratio along the y direction, in which case the crosstalk between the waveguides cannot be ignored. An irregular sparse distribution of the waveguide antennas [23] can help overcome the above problems. Meanwhile, the amplitude and phase of the light in each waveguide are adjusted to ensure a flat-top far-field power distribution in the given angular range.
3. Results and discussion
3.1 Structure of antenna grating
To determine the initial value of the grating period for optimization, the average effective index ${n_{eff}}$ is estimated by calculating the effective index of a SiNx waveguide with a height varying between 0 nm and 500 nm, since the entire thickness of the waveguide layer is set to 500 nm. A fundamental TE mode was selected in this simulation so that this OPA can be integrated with on-chip lasers, which are typically TE polarized. With the estimated ${n_{eff}}\textrm{ = 1}\textrm{.72}$, the initial grating period can be derived using Eq. (2); the value is found to be 0.52 µm for $m = 1$ and ${\theta _m} = 0^\circ $. Subsequently, the grating period and etch depth were optimized for better efficiency. Figure 3(a) shows the optimized result. A single beam at θ = −4.7° with an emission efficiency of 50.9% can be realized for a 32-µm-long grating coupler with a 0.53 µm grating period, 400 nm etch depth, and 29% duty cycle. The beam divergence is 1.38°, which can be further reduced by increasing the grating length. Here, a grating length of 32 µm is chosen to keep the calculation burden acceptable.
Fig. 3. Calculated far-field pattern of two grating structures. (a) A grating coupler with 0.53 µm period, 400 nm etch depth, and 29% duty cycle; (b) A beam splitter grating with 8 µm period, 457 nm etch depth, and five ridges in one period.
A beam splitter grating for normal incidence with a splitting ratio $SR = 11$ and a period of 8 µm is optimized, corresponding to a full angular range of 68.8° using Eq. (6). Here, an evaluation factor ${E^\textrm{2}}$ is employed to monitor the performance of the beam splitter grating, which can be written as:
After the XOR operation between the two grating structures, the resultant antenna grating has an undesirable ${E^\textrm{2}}$ value. Figure 4(a) shows the far-field patterns for the antenna grating with etch depths varying from 100 to 450 nm. The grating structure with an etch depth of 200 nm has a relatively good performance and, as shown in Fig. 4(b), the corresponding ${E^\textrm{2}}$ is 0.21. This multi-beam antenna grating generates a set of uniformly distributed light beams corresponding to the different diffraction orders, as shown in Fig. 4(c). The angular range of the beam array is 68.8°, which is the same as that of the beam splitter grating.
Fig. 4. Calculation results of the 1D multi-beam-emitting antenna grating. (a) Far-field pattern and (b) evaluation factor ${E^2}$ of the antenna grating with etch depths varying from 100 nm to 450 nm. (c) Far-field efficiency distribution of the antenna grating with an etch depth of 200 nm, which is a relatively good result.
As shown in Fig. 3(b) and Fig. 4(c), the non-uniformity increases after transplanting a beam splitter grating for normal incidence to the waveguide-based grating coupler. Although a preliminary optimization is carried out, the results are far from ideal. We suppose the main reason is that the electrical component normal to the waveguide plane ${E_z}$ is not zero in the antenna region, which is not considered in the design of the beam splitter grating. The electrical components of the incident light are ${E_x}$ and ${E_y}$ in the beam splitter grating designed above. Moreover, the effective index varies considerably through the simple XOR operation between the two structures, which may cause an undesirable efficiency distribution, as shown in Fig. 4(c).
Iterative algorithms, such as the Weighted Gerchberg–Saxton (GSW) algorithm [24], can help improve the performance of the antenna grating. The SA algorithm used above is a random optimization algorithm, which can theoretically find a global optimized solution but through a lot of calculation attempts. Because of the huge amount of calculation, only limited means are available to optimize the 1D multi-beam-emitting antenna grating. The GSW algorithm has advantages of fewer computations and fast convergence but is sensitive to the initial value. Setting the XOR result as the initial value can help overcome the sensitivity, and this algorithm can be made more useful in future work.
3.2 Non-uniform arrangement of waveguide antennas
The width of the waveguide antennas is set to 600 nm, while the minimum spacing is set to 500 nm, which is slightly wider than half the wavelength in free space, to reduce the crosstalk. The FDTD method with the SA algorithm is used to optimize the arrangement. Table 1 lists the parameters of the optimal arrangement and structure.
Table 1. Parameters of optimal structure
Figure 5(a) shows the 1D calculation results. With four units repeated along the y direction, a 1×11 beam array (black line) can be emitted that can scan along the envelope (red dashed line) formed by one unit, i.e., the element pattern, with an angular range of 68.8°. Figure 5(b) shows the 2D radiation pattern of the 1D multi-beam-emitting OPA. The emitting angle is near 0°, which is slightly different from that of the grating coupler shown in Fig. 3(a), because of the change in the effective index from the 2D calculation to the 3D one. As shown in Fig. 5(c), the evaluation factor ${E^\textrm{2}}$ and total efficiency remain at approximately 0.1 and 40%, respectively, as the phase shift between adjacent units varies, indicating that the OPA exhibits good performance during steering.
Fig. 5. Calculation results of the 1D multi-beam-emitting OPA. (a) Far-field pattern (black line) and element pattern (red dashed line) of the OPA. (b) 2D radiation pattern of the OPA. (c) Calculated evaluation factor ${E^2}$, total efficiency, and non-uniformity of the diffraction orders with phase shift varying from $- \pi $ to $\pi $. The inset shows the sparsely placed waveguide antennas.
3.3 Two-dimensional multi-beam steering OPA
By combining the structures described in Sections 3.1 and 3.2, the antenna structure of the 2D multi-beam-emitting OPA is formed. Figure 6(a) shows the 2D radiation pattern of the multi-beam-emitting OPA, exhibiting a fairly clear 11×11 spot pattern. The angular separation between the zeroth- and first-order beams in the y direction is 6.5°, as obtained using Eq. (6). By setting the phase difference between adjacent units to ${\pm} \pi $, the zeroth order can be steered to ±3.25°, as given by
In other words, the entire pattern can cover the gaps between the dots in the y direction with phase control. Figure 6(b) shows the 2D radiation pattern of the OPA with a phase difference of $\pi $, and the entire beam array is shifted by approximately 3.25° along the y direction. Figure 6(c) shows the far-field pattern of a single unit in the OPA. The total FOV, indicated by the white dashed box, is 68.8° × 77°, consistent with our design. The ${E^\textrm{2}}$ value of the multi-beam-emitting OPA is approximately 0.46, which is much higher than that of the 1D multi-beam-emitting antenna grating shown in Fig. 4(c), but largely the same as that of the 1D splitting array shown in Fig. 5(b). This is attributed to the relatively high ${E_z}$ component, which is inevitable in practice. The average divergence angle along both the directions is approximately 1.5°, which is largely the same as that in the case of the single-beam-emitting grating coupler described in Section 3.1. Similarly, the beam divergence can be further reduced by increasing the grating length and the number of repeating units along the y direction.
Fig. 6. Calculated results of the 2D multi-beam steering OPA. (a) 2D radiation pattern of the OPA with a phase difference of 0. (b) 2D radiation pattern of the OPA with a phase difference of $\pi $. (c) Far-field pattern of a single unit of the OPA, and the white dashed box indicates the total FOV. (d) Calculated evaluation factor ${E^2}$, total efficiency, and non-uniformity of the diffraction orders while the 2D beam array steers. The inset indicates the waveguide antennas in one unit of the OPA.
Figure 6(d) shows the evaluation factor ${E^\textrm{2}}$, total efficiency, and non-uniformity of the diffraction orders during steering. The total efficiency remains approximately 18%, which is much lower than the estimated efficiency of 40% described in Section 3.2. This is because some beams are outside the target angular range of the OPA, as shown in Figs. 6(a) and 6(b). This is also because of the high ${E_z}$ component in the imperfect 1D multi-beam-emitting antenna grating.
Notably, compared with a typical OPA with the same angular range and beam divergence, the proposed multi-beam steering OPA contains fewer phase shifters, and the gaps between adjacent antenna gratings are larger; thus, the fabrication difficulty and cost can be substantially reduced. This advantage is also strengthened by the minimum feature size of 91 nm of the antenna gratings. A smaller feature size may help improve the efficiency and uniformity of the beam array, as the design freedom is increased. However, for a design to exhibit acceptable device performance using conventional manufacturing technologies, we set an adequate feature size in this work.
Concerning the future applications of this design in LIDAR systems, there are several points that need to be further discussed. First, a relatively large waveguide height of 500 nm is adopted in this work; hence, there is sufficient margin for the phase difference to ensure a feasible multi-beam output design. This waveguide structure supports multiple modes at 905 nm; however, the total power of the excited high-order modes is fairly low when the laser source is TE polarized, and these modes have an insignificant effect on the multi-beam output. Overall, a single-mode waveguide is preferred in the design, and a Si waveguide with a higher refractive index can be adopted in future work to ensure both a single mode and a sufficient phase difference.
The steering along the second dimension is important for a fully functional LIDAR system and is typically achieved by wavelength tuning [9]. However, in this multi-beam steering device, different wavelengths also indicate different output angles and angular spacings along the y direction, which may cause a disordered beam-array-steering along with phase modulation. In addition, a wide wavelength-tuning range is required for steering over the entire angular spacing, which will be challenging for on-chip laser sources. Further work is required on methods that can realize steering along the second dimension.
In the design of the multi-beam LIDAR presented in this work, the multiple pulsed laser beams are transmitted simultaneously. To differentiate the scattered return from different angles, a detector array can be used. For example, an 11×11 detector array can be applied corresponding to the 11×11 beam array in this work, and each detector can be mapped with the space angle range illuminated by each beam through a specially designed lens, e.g., a freeform optical lens. The light received by each detector would represent the signal from a specific direction; thus, the 3D information of the target can be generated through subsequent data processing. Considering the losses due to waveguide coupling and propagation, power divider, and grating diffraction, the detection range of this OPA is estimated to be approximately 10 m, which is competitive compared with those of existing VCSEL arrays.
The performance of the multi-beam array can be further improved through several approaches. In the design of a nearly vertical-emitting grating coupler, as described in Section 3.1, an irregular etch depth can be utilized to ensure a uniform emission from the decay field. Since the light lost to the substrate severely affects the grating efficiency, the efficiency can be further enhanced by breaking the up–down symmetry [5,13,14]. Other algorithms can be used to optimize the arrangement of the waveguide antennas in the OPA, such as the alternating projection algorithm (APA) [23].
4. Conclusion
In this work we presented a detailed design process of a multi-beam steering OPA with a splitting ratio of 11×11, a static FOV of 68.8° × 68.8°, and a narrow scan range of 6.5°, covering a total scanning FOV of 68.8° × 77°. The 2D splitting problem was divided into two parts. For beam splitting along the x direction, the concept of Dammann grating was introduced into the waveguide grating. For the splitting along the y direction, a non-uniform sparse placement of the waveguide antennas was adopted to form a flat-top element pattern across the entire angular range. Compared with the flash LIDAR [25], which provides flood illumination over the entire FOV, both the detection range and viewing field of the proposed beam steering scheme could be improved, owing to the concentrated energy of the illumination spots brought about by the beam array. Since the OPA is a waveguide-based structure, it can be easily integrated with edge-emitting lasers and on-chip modulators. The design rules can be adapted to different wavelengths, and the angular range as well as the splitting ratio can be further improved. We believe that our multi-beam steering OPA design provides a constructive approach to realize single-chip LIDAR systems.
Funding
National Natural Science Foundation of China (61991443, 61822404, 61875104, 61904093, 61927811, 61975093, 61974080); Tsinghua University Initiative Scientific Research Program (20193080036); Beijing National Research Center For Information Science And Technology (BNR2019ZS01005).
Acknowledgment
This work was supported by the Collaborative Innovation Centre of Solid-State Lighting and Energy-Saving Electronics.
Disclosures
The authors declare no conflicts of interest.
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