Optical phased arrays (OPAs) based on silicon photonics have promoted the development of integrated solid-state light detection and ranging (LiDAR). Silicon-photonics technology has the advantages of high integration density and compatibility with the CMOS process, which enables a broad prospect for the large-scale, low-cost production of LiDAR chips [1-4]. As an important part of an integrated OPA, the emitter is used to emit the phase-modulated light into free space. There are two types of emitters: The end-fire (EF) structure that radiates the light from the facets of a waveguide, and the waveguide grating antenna (WGA) that radiates nearly vertically [5]. An OPA with EF structures can only achieve one-dimensional (1D) beam forming and steering through phase modulation [6-10]. Using the WGA as emitters instead, a 1D OPA can achieve 2D beam forming and steering by using both phase modulation and wavelength tuning [11, 12].

High diffraction efficiency, high bandwidth, long radiation length, and robustness to fabrication errors are important parameters for a WGA [13, 14]. About half of the light is radiated to the substrate, without breaking the symmetry in the vertical direction in the WGA [15]. Any downward radiation will result in a reduction of the efficiency. Recently a scheme for replacing conventional distributed Bragg reflectors [16] or metal layers [17] with high-contrast gratings [18] as bottom reflectors has been reported, which achieves 87.6% directionality. A dual-layer millimeter-scale Si₃N₄ WGA with 93% upward radiation directionality at 1.55 µm was proposed [19], in which the perturbation strength was apodized so that the radiation length is on the order of millimeters, achieving a uniform and efficient emission for the first time [19]. But the dual-layer WGA has the problem of incompatibility with other traditional integrated photonic devices [20]. By offsetting the grating structure on the upper and lower surfaces of the silicon nitride waveguide along the waveguide direction, the designed chain and fishbone structure can achieve 95% directionality, and apodized gratings achieve a radiation length of 3 mm [21]. By placing the subwavelength segment in the evanescent field of a conventional strip waveguide, the WGA can achieve a radiation length at the millimeter level or even the centimeter level, but the directionality of such schemes reported at present is not ideal [22-24]. A three-layer silicon nitride structure of a recently reported grating-waveguide-grating achieves about 92% of the upward directionality at the wavelength of 1,540 nm, and has a flat near field [25]. A dual-layer structure with the waveguide separated from the grating is simpler, achieving more than 89% directionality and a millimeter-scale radiation length [13], while there is still the room for performance improvement.

In this paper, we propose a multilayered WGA based on interleaved etching. Compared to a traditional silicon WGA, the silicon nitride grating is less sensitive to variations in the fabrication process [26], so we use silicon nitride to fabricate the grating. In the silicon nitride layer, deep etched trenches and shallow etched trenches are interleaved, and therefore constructive interference in the upward direction is achieved by optimizing the design of the deep and shallow trenches. The multilayered structure breaks the symmetry in the vertical direction, and utilizes the reflection of multiple boundaries to minimize the leakage of light to the substrate direction, so that no additional bottom reflectors are needed. The WGA exhibits excellent performance: The directionality can reach more than 97%, while the 1-dB bandwidth of the WGA reaches 305 nm. The radiation length reaches 1.65 cm, based on the near-field emission profile fitted by the finite-difference time-domain (FDTD) simulation results with a simulation length of 1,000 µm, which can ensure a small divergence angle. The proposed structure is promising for improving the performance of an OPA system.

The side and 3D views of the WGA structure are shown in Figs. 1(a) and 1(b) respectively. The silicon nitride layer and the silicon waveguide layer are separated by a silicon dioxide layer. Both the buried and top oxide layers are made of silicon dioxide, and the thickness h_box of the buried oxide layer h_box is 2 μm. Since the waveguide width limits the minimum waveguide spacing in the OPA for a large field of view, the waveguide cannot be arbitrarily wide [27], yet if the waveguide is too narrow the diffraction efficiency will be reduced [20], so the waveguide width is fixed to 1.5 μm. The refractive indices of silicon, silicon nitride, and silicon dioxide at 1,550 nm are 3.48, 1.99, and 1.44 respectively, and the thicknesses of the corresponding layers are h_wg, h_Si3N4 and h_SiO2. On the silicon nitride layer, deep etched trenches and shallow etched trenches are interleaved, the etch depths being represented by the parameters h_DE and h_SE, and the etch widths represented by the parameters W_DE and W_SE. The distance between shallow and deep etched trenches in each period Λ is called Space.

Figure 1. The proposed waveguide grating antenna (WGA) structure. (a) Side viewand (b) 3D view.

The Fundamental transverse electric (TE) mode is injected into the silicon waveguide, as shown in Fig. 2. The light propagates along the x axis in the silicon waveguide and is coupled into the silicon nitride grating and coupled out through the silicon nitride grating.

Figure 2. The modal field of the input light.

The radiation field of the interleaved etched grating is a linear superposition of the radiation fields of two rectangular gratings with different etching depths and mutually offset in the propagation direction of the waveguide mode [28]. The principle of using interleaved etching to improve directionality of the grating is to utilize deep and shallow trenches to control the interference conditions. Specifically, by utilizing different etching depths and the offset of deep and shallow trenches in the propagation direction of the waveguide, the spatial and temporal phase delays are introduced, thus achieving constructive and destructive interference in the upward and downward directions respectively [1-30].

The separation of the grating structure from the waveguide reduces the strength of the mode perturbation, compared to direct perturbation of the waveguide, which is beneficial for increasing the radiation length of the WGA and provides an additional degree of freedom for optimizing the optical path length [20]. The downward radiation is reflected multiple times by the multilayered structure, which minimizes the leakage to the substrate. Except for layers whose parameters are limited by the standard silicon-on-insulator (SOI) wafers, the reflectivity can be maximized by optimizing the thicknesses of the other layers, thereby improving the directionality of the WGA.

The 3D FDTD is used to simulate the WGA. It is difficult to simulate a centimeter-scale WGA due to limitations in computing resources. Therefore, we optimize a WGA with a length of 50 μm to estimate the performance of the whole WGA [13, 20].

3.1. Optimization

We place six monitors in the six directions ±x, ±y, ±z of the WGA to obtain the transmission power in each direction. The residual power in the waveguide after being radiated by the WGA is collected by the +x-direction monitor. We define the +z direction as the top, the −z direction as the bottom, the ±y directions corresponding to the two sides, and the −x direction as the reflection. The sum of the optical power collected by the monitors in the five directions −x, ±y, ±z is the total outward radiated power. The directionality Γ of the WGA is thus defined as the ratio of the light power collected by the monitor in the +z direction to the total power radiated from the WGA [25],

The geometrical parameters of the WGA are optimized to find the maximum upward directionality for the fundamental TE mode at a wavelength of 1,550 nm. We utilize a particle-swarm optimization (PSO) algorithm for optimization. Commonly used thicknesses of the silicon waveguide layer on the SOI platform include 90 nm, 150 nm, and 220 nm, determined by the typical different silicon etch thicknesses. Therefore, we optimize other structural parameters under these thicknesses of the silicon waveguide layer, and the optimization design space is defined as X = [Λ, Space, W_SE, W_DE, h_Si3N4, h_SiO2, h_SE, h_DE]. To ensure that the evaluated devices are physically meaningful while considering fabrication capability, we restrict the search range for each parameter as shown in Table 1.

Table 1 . The search ranges of structural parameters.

Parameter	Λ	Space	WSE	WDE
Search Range (nm)	[600, 900]	[180, 420]	[54, 294]	[54, 294]
Parameter	hSi3N4	hSiO2	hSE	hDE
Search Space (nm)	[300, 600]	[50, 500]	[30, 200]	[200, 300]

In the PSO we take the upward directionality as the fitness function, the population size is chosen as 10 individuals, and the number of generations is chosen as 25. Figure 3 shows the directionality optimization process curves at different waveguide thicknesses.

Figure 3. Directionality variation with the number of generations.

As shown in Fig. 3, the directionality of the grating rapidly improves over the generations, with the optimization relying on the search ability of the PSO, and converging within 25 generations. The directionality of the optimized WGA is 97.8%, 91.4%, and 81.5% when the thickness of the silicon waveguide is 90 nm, 150 nm, and 220 nm respectively. It can be seen that the directionality of the WGA is highest when h_wg is 90 nmafter optimization, so we fix h_wg to 90 nm, and the optimized structural parameters are as follows X = [600 nm, 420 nm, 210 nm, 90 nm, 600 nm, 50 nm, 178 nm, 300 nm].

We evaluate the directionality as a function of the waveguide width for the optimized design, as shown in Fig. 4. The directionality of WGA reaches its highest when the waveguide width is 1.5 μm. The directionality of the WGA is above 91% for waveguide widths from 1 μm to 1.5 μm. The upward directionality of the optimized WGA exceeds 97%.

Figure 4. Directionality as a function of waveguide width.

We then perform wavelength scans of the optimized structure. Figure 5 shows the directionality for a wavelength range from 1,300 nm to 1,800 nm; The grating directionality peak reaches nearly 98% near 1,550 nm. The directionality is above 94% over a 100-nm band from 1,500 nm to 1,600 nm, and the 1-dB bandwidth reaches 305 nm. The steering of the emission angle depends on the wavelength sweeping; Larger bandwidth means that the light power diffracted from the WGA during the wavelength sweep has less fluctuation, and the WGA does not need to be redesigned when it is applied to other specific wavelengths within the bandwidth range.

Figure 5. Directionality as a function of wavelength.

A one-dimensional OPA assisted by the WGA can be a feasible solution to realize 2D beam steering, by controlling both the phase difference and the wavelength of the input light. The large bandwidth of the WGA is beneficial for increasing the steering range in the wavelength-controlled dimension.

3.2. Near-field Analysis

Another key parameter of a WGA is the radiation length of the grating. The detection resolution of LiDAR is related to the divergence angle of the beam emitted into space. It is necessary to reduce the divergence angle of the emitted beam as much as possible. The divergence angle of the far-field beam of the WGA can be calculated using the following equation:

where L is the radiation length of the WGA. The divergence angle of the beam can be reduced by increasing the radiation length of the WGA. It is difficult to simulate a WGA with a length of centimeters, due to the limitations of computing resources in 3D FDTD analysis. At the wavelength of 1,550 nm, we estimate the performance of the entire WGA by simulating results for a WGA with a length of 1000 μm, which is shown in Fig. 6(a).

Figure 6. Near field. (a) Simulated near-field electric field of the top emission. (b) Simulated (red) and fitted (blue) near-field profile. (c) Fitting curve for the profile of the near field.

The near-field electric field distribution above the WGA follows an exponential decay of e^−βx, where β is the perturbation strength of the grating and x is the propagation distance of the light along the waveguide propagation direction [19, 20]. A perturbation strength of 1.215 × 10⁻⁴/μm can be obtained from exponential fitting of the near-field electric field of the WGA, and then it can be calculated that the radiation length of the designed WGA reaches 1.65 cm when the near-field electric field decays to e⁻² [20], as shown in Figs. 6(b) and 6(c). The divergence angle of the estimated radiation length of 1.65 cm is 0.0054°, which is slightly larger than in the case of the uniform radiation (0.0048°).

To check the perturbation strength’s dependence on wavelength, we analyze the perturbation strength over a wavelength range of 100 nm near 1,550 nm with the same method, as shown in Fig. 7. In the wavelength range of 1,500 nm to 1,600 nm the perturbation strength fluctuates slightly, between 1.169 ×10⁻⁴/μm and 1.505 ×10⁻⁴/μm, indicating that the wavelength has little influence on the perturbation strength of the WGA. The radiation length of the silicon WGA with a 70-nm shallow etch in a SOI platform with 220-nm-thick top silicon is usually only tens of micrometers, and ultra-shallow etching methods with an etching depth of only a few nanometers must be used to achieve a radiation length of millimeters [4]. In contrast, the etching depths of the interleaved etched gratings we propose are 178 nm and 300 nm respectively, which are easier to fabricate.

Figure 7. Perturbation strength as a function of wavelength.

3.3. Far-field Analysis

According to the grating-emission equation of Eq. (3), the beam-emission angle of the WGA can be controlled by changing the wavelength of the light source:

where n_eff is the effective refractive index of the fundamental mode of the waveguide, n_c is the refractive index of the cladding, and λ is the wavelength of the injected light from free space. The far-field projections at wavelengths of 1,500 nm and 1,600 nm are shown in Fig. 8.

Figure 8. Far-field projections at different wavelengths: (a) 1,500 nm, and (b) 1,600 nm.

The beam-steering range in the silica cladding is 9.1° when the wavelength is scanned from 1,500 nm to 1,600 nm, as shown in Fig. 9. When light is injected into the air from the silicon dioxide, it can be calculated according to Snell’s law that the beam-steering range in air is 13.2°.

Figure 9. Far field at different wavelengths: (a) 1,500 nm, and (b) 1,600 nm.

3.4. Fabrication-tolerance Analysis

An important aspect of WGA design is the evaluation of tolerance to fabrication variations. The offset of the deep and shallow etched trenches in the interleaved etching structure in the propagation direction adds a temporal phase delay, and the difference between the two etching depths adds a spatial phase delay. The high directionality of the WGA is achieved by adjusting the structural parameters of the deep and shallow trenches to achieve constructive interference. Therefore the effect of process variations in the interleaved etched structure, in the propagation direction as well as the vertical substrate direction, are mainly considered, as shown in Fig. 10.

Figure 10. Different types of fabrication errors: (a) Etching depths, (b) critical dimensions, (c) overlay, and (d) thickness of the silicon dioxide layer.

The first important process variation is that of the etching depth. Figure 11(a) shows the effect of the etching-depth error δ₁. The fluctuation of the directionality does not exceed 2.5% and 10% when the etching depth is within the variation range of ±25 nm and ±50 nm respectively. Another source of uncertainty is the critical dimensions (CDs) of the shallow (W_SE) or deep (W_DE) etched trenches W_DE, as shown in Fig. 11(b).The directionality is over 95% and 90% when the variation δ₂ is within the range of ±25 nm, and over 90% and 80% when δ₂ is within the range of ±50 nm, for W_SE and W_DE respectively. We also consider the impact of the overlay variation δ₃ between the two etched patterns, and the variation δ₄ of the silicon dioxide layer’s thickness h_SiO2 between the silicon waveguide layer and silicon nitride layer as well, as shown in Figs. 11(c) and 11(d) respectively. The directionality is over 90% and 67% when δ₃ is within the range of ±40 nm and ±80 nm respectively. The fluctuation in directionality does not exceed 2% when δ₄ is within the variation range of ±50 nm. The fabrication-tolerance analysis supports that this WGA structure has large tolerance to variations in etching depths, h_SiO2, and W_SE. It is sensitive to changes in W_DE and overlay: The variation needs to be controlled within −50~+25 nm and ±40 nm respectively to ensure more than 89% directionality. If 193-nm deep ultraviolet (DUV) lithography is used, it can not only meet the CD requirement of 90 nm, but also control smaller fabrication errors, so this highly directional WGA design can be implemented.

Figure 11. Directionality for different types of fabrication errors: (a) Etching depths, (b) critical dimensions, (c) overlay, and (d) thickness of the silicon dioxide layer.

The proposed WGA is compared to simulation results for several WGAs that have been reported in recent years, as shown in Table 2. It can be seen that the WGA we propose in this paper has better performance in directionality, 1-dB bandwidth, and the estimated radiation length. The directionality of the grating is effectively improved by utilizing the interleaved etching structure and reflection at multiple interfaces. The grating structure is separated from the waveguide and the gap between the two layers is increased to reduce the perturbation strength of the grating, and thereby increase the radiation length of the WGA.

Table 2 . Comparison of the performance of WGAs.

Grating Antenna Structure	Directionality (%)	1-dB Bandwidth (nm)	Radiation Length	Far-field Deflection Angle (1,500 nm–1,600 nm) (°)
Separation Structure [20]	Over 70	-	1 mm	15
Dual-layer Structure [13]	Over 89	-	4 mm	12.5
Offset Structure [21]	95	-	3 mm	-
This Work	Over 97	305	1.65 cm	13.2

In conclusion, we propose a highly directional multilayered WGA based on interleaved etching. The grating structure is formed by interleaved etching of the silicon nitride on the upper layer of the waveguide. The interleaved-etching method is utilized to generate constructive interference in the upward direction, and the multilayered structure can reflect the light leaked toward the substrate, thereby effectively realizing high directionality of the WGA. The directionality of the proposed WGA is more than 97%, and the WGA exhibits large tolerance to fabrication variations. The 1-dB bandwidth of the WGA near the center wavelength of 1,550 nm is 305 nm, which is beneficial for increasing the beam-steering range by expanding the scanning-wavelength range. The perturbation strength can be controlled by changing the distance between the grating and the waveguide, and thus the radiation length reaches 1.65 cm, ensuring a small divergence angle. The far-field deflection angle is 13.2° when tuning the wavelength from 1,500 nm to 1,600 nm.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

Key Project of National Natural Science Foundation of China (61935003); the Strategic Pioneer Research Projects of Defense Science and Technology (XDB43020500); and the Shanghai Sailing Program (20YF1456900).