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Abstract
To build advanced all solid-state LiDAR, optical phased arrays (OPAs) with a large field of view are highly desirable. As a critical building block, a wide-angle waveguide grating antenna is proposed here. Instead of aiming at the elimination of downward radiation of waveguide grating antennas (WGAs) to improve efficiencies, we in turn utilize the downward radiation and double the range of beam steering. In addition to widened field of views, the steered beams in two directions come from a common set of power splitters, phase shifters and antennas, which greatly reduces chip complexity and power consumption, especially for large-scale OPAs. Beam interference and power fluctuation in the far field due to downward emission can be decreased by specially designed SiO2/Si3N4 antireflection coating. The WGA exhibits balanced emissions in both the upward and downward directions, in which the field of view in each direction is more than 90°. The normalized intensity remains almost the same with a small variation of 10% from -39° to 39° for the upward emission and from -42° to 42° for the downward emission. This WGA is featured by a flat-top radiation pattern in far field, high emission efficiency and good tolerance to device fabrication errors. It holds good potential to achieve wide-angle optical phased arrays.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Phased array antennas at radio frequencies have been widely developed for many years before being transferred to the optical domain. Based on the same principle but in a drastically different frequency range, optical phased arrays (OPAs) have attracted a great deal of attention, stimulated by great advances in agile and precise free-space beam steering, which is free of any moving parts [1–13]. Many pioneering demonstrations of chip-scale OPAs have been reported for a wide range of applications, from Light detection and ranging (LiDAR) [8,14], free-space optical communication [8,15], imaging [16–18], to biology sensing [19,20], which have been categorized and analyzed in details in a recent review paper [21].
One of the building blocks of on-chip OPAs is an antenna, which is typically based on grating couplers or waveguide grating antennas (WGAs) [7–9]. In contrast with 1D “end-fire” waveguide facet arrays [6], WGAs hold great potential for 2D beam forming and steering [7]. Desired features of these antennas include good directionality, high efficiency, wide field of view (FOV), and flat-top far-field pattern [21]. It is known for a WGA that part of optical power radiates to the substrate [22], with a decreased radiation efficiency. Then, the downward radiation may be reflected back, which leads to beam interference and power fluctuation or even blind spots on the far-field pattern. Since small fluctuation and blind spots are very important for precise steering and imaging [8,23], it is desirable to enhance upward transmission.
Many efforts have been made so far to reduce downward radiation. Metal mirrors or Bragg reflectors used as a reflector increase upward transmission and improve directionality in grating antennas [24], while overlayered or slanted structures also help [24]. Recently, a dual-layer Si3N4 waveguide antenna has been proposed for unidirectional emission and produces an efficiency of 93% at a wavelength of 1.55 µm with the elimination of blind spots [23]. Some dual-layer WGAs [25,26] have been proposed to achieve efficient emission for a wideband spectrum. In addition, a unidirectional broadband nano-patch antenna has been proposed to improve emission directionality, which features emission directionality up to 12.91 dBc over a wide operating bandwidth of >400 nm [27].
Another highly desirable feature of an antenna is a wide FOV, which is critical in determining the number of OPAs required to cover the whole 360° range. For example, a Vernier OPA transceiver has been proposed to widen steering angles and suppress grating lobes in [28]. OPAs based on superlattice structures formed by waveguides with different widths can overcome conventional crosstalk problem and have wide steering angles [29,30]. The steering range of the antenna proposed in [29] reaches 106°, and it becomes 130° in [30]. There are also some aperiodic OPAs to realize wide steering angles without sidelobes [9,31]. Some OPAs have recently proposed towards a steering angle of 180° [32].
In principle, far-field patterns of OPAs are calculated as the multiplication of the far field of an individual antenna and an array factor [7,33,34]. To achieve a wide steering angle of OPAs, there are twofold efforts to be made. First, grating lobes need to be suppressed by aperiodic arrays [35]. Second, the steering angle should be extended by increasing the FOV of individual antennas. However, this is challenging because, as mentioned above, it is hard to realize WGAs with an FOV of nearly 180°. Moreover, it is difficult to eliminate downward radiation for high emission efficiencies. Therefore, it has been almost impossible to achieve both simultaneously.
In this paper, we propose a bidirectional wide-angle WGA for OPAs. Instead of aiming at the elimination of downward radiation to improve efficiencies, we in turn utilize downward radiation and equalize the radiated powers and FOVs in both directions in order to double the range of beam steering. For both upward and downward emission, the FOVs, at the full width at half maximum (FWHM) of radiation intensity in the polar direction, are more than 90°, and thus the total FOV of the proposed bidirectional antenna is wider than 180°, which shows promising capability for wide-angle OPAs. In addition to widened FOVs, the steered beams in two directions come from a common set of power splitters, phase shifters and antennas, which greatly reduces chip complexity and power consumption, especially for large-scale OPAs. Moreover, we obtain that the intensity remains almost unchanged with a variation of less than 10% from -39° to 39° for the upward radiation and from -42° to 42° for the downward radiation. The greatly improved flatness of the far-field radiation pattern is favorable to achieve precise beam steering.
2. Device configuration and principle
An array of bidirectional wide-angle WGAs is shown in Fig. 1(a). In this scheme, incident light S0 at a wavelength of 1.55 µm propagates through 3-dB splitters and is turned by sharply bent waveguides [36] or Bragg mirrors to perform as the two inputs to the proposed WGA, S1 and S2.
Fig. 1. (a) The conceptual structure of a wide-angle optical phased array (without up layers). (b) Schematic and (c) cross section of a wide field of view waveguide grating antenna. θ is the incident angle and φ is the angle of refraction. Dimensions are not to scale.
The proposed bidirectional wide-angle WGA is presented in Figs. 1(b) and 1(c). Two layers near the silicon (Si) substrate are a silicon nitride (Si3N4) layer and a silicon dioxide (SiO2) layer. The Si3N4 layer has a half-wavelength thickness and the SiO2 layer is a quarter-wavelength film. In principle, the two layers of Si3N4 and SiO2 function as a hybrid antireflection coating (AC) to improve the downward transmissivity. A lithium niobate (LiNbO3) layer is on the top of the SiO2 layer. An amorphous Si waveguide is formed on the LiNbO3 layer and has a Si3N4 cladding. The refractive index of amorphous Si is 3.48 at a wavelength of 1.55 µm [37]. The refractive indices of the two cladding layers are approximate (n = 2.211 for LiNbO3 and n = 1.996 for Si3N4) at a wavelength of 1.55 µm.
The TE mode is used here. Note that four trenches are in the center of the Si waveguide and symmetric about the y-z plane. In addition, the LiNbO3 layer can also be used as high-performance phase shifters owing to its good electro-optical property. Meanwhile, a SiO2/Si3N4 hybrid layer on the mentioned Si3N4 cladding layer functions as another AC and increases the upward transmissivity. Deep trenches can be formed on the backside of the wafer underneath the grating, reaching the SiO2 layer [38], and then Si3N4 is deposited on the backside to eliminate the distortion of the radiated pattern downward caused by the Si substrate. In this way, the WGA has similar emission in both the upward and downward directions. We utilize the finite-difference time-domain method to obtain field distribution.
Typically, ACs work well at near-normal incidences, and their performance is usually sensitive to incident angles [39]. Here, we need to carefully examine the sensitivity of the ACs at a large angle for both the upward and downward radiation. We use a structure with a plane wave propagating from the Si layer to the ACs with an incidence angle, θ, as shown in Fig. 1(c), in the case with no trenches on the Si waveguide.
Incidence angle dependences of transmissivity and angle of refraction are presented in Fig. 2. As mentioned above, the Si3N4 layer has a half-wavelength thickness, and the SiO2 layer is a quarter-wavelength film. For the upper hybrid AC, the transmissivity remains high within 10° and becomes decreasing when the incident angle is larger. For the lower AC layer, similar variations are shown when the incident angles are smaller and larger than 14°, respectively. Total internal reflection in both upward and downward directions happens on the interfaces between the outermost Si3N4 layers and air when the incidence angle θ is 16.7°. The incidence angle dependence of the angle of refraction, φ, is the same for the two directions, as shown in Fig. 2.
3. Performance optimization
Radiation from WGAs can be regarded as a combination of radiations at various angles, with its far-field pattern evaluated in a multi-objective optimization. First, high efficiency is aimed in both upward and downward directions. Second, a plateau in the far-field pattern and an FOV of nearly 90° are highly desirable for practical applications of OPAs [21]. Third, the above performance can be obtained for both upward and downward radiations. The particle swarm optimization is used, and we first conduct a two-dimensional (2D) optimization in z = 0 plane, followed by three-dimensional (3D) simulation, to save computation time. Equation (1) sets up the optimization goal
In 2D design, the optimized structural parameters of the bidirectional WGA are listed in the No. 0 line in Table 1. Normalized far-field radiation intensity versus radiation angle is shown in Fig. 3, which remains quite high (>0.9) and almost unchanged from -39° to 39° for the upward radiation and from -42° to 42° for the downward radiation, with a variation of less than 10%. In this way, the bidirectional WGA can handle beam steering of 180° in total.
Table 1. Structural parameters after optimization and values of structural parameters randomly changed within a range of ±2% for 10 times (unit: µm)
Over the angle range of interest from -45° to 45°, the normalized intensity of the two directions is greater than 0.6. Besides, the transmissivities of the upward and downward radiations are 0.33 and 0.36, respectively. Outside the angle range of -45° to 45°, the far-field radiation is mostly suppressed. One can see that the nearly identical results are produced in the two directions.
Then, in 3D simulations, we consider the effect of the WGA width on the far-field patterns of the upward and downward radiations, as shown in Figs. 4 and 5, respectively, where the widths are varied to be 2, 4, 5, and 10 µm, respectively. In the polar direction, the radiation mainly concentrates in the range from -45° to 45°, for all the widths under consideration. In contrast, the radiation in the azimuthal direction becomes narrower as width increases, as shown in Figs. 4 and 5. We note that the far-field pattern becomes quite diverged in the azimuthal direction with a 2-µm waveguide width, because the TE mode is sensitive to the width, and mode confinement becomes weaker as width decreases.
Fig. 4. Normalized upward far-field patterns of 3D WGAs, for width of (a) 2 µm, (b) 4 µm, (c) 5 µm, and (d) 10 µm.
Fig. 5. Normalized downward far-field patterns of 3D WGAs, for width of (a) 2 µm, (b) 4 µm, (c) 5 µm, and (d) 10 µm.
Compared with the 2D results, the normalized far-field intensity of 3D-designed WGAs in the z = 0 plane, as shown in Fig. 6, has small variations for the widths of 4, 5, and 10 µm. For a 10-µm-wide WGA that is wide enough to mimic the 2D one, the normalized intensity remains almost unchanged and has a variation of 10% from -39° to 39° for the upward radiation and from -42° to 42° for the downward. For the 5-µm WGA, the upward intensity has the almost same variation, and a variation of 8% from -42° to 42° is shown in the downward direction. The smaller variation of downward radiation is due to a slight increase in intensity near ±42°. When the WGA is further narrowed from 4 µm down to 3 and 2 µm, the radiation becomes a saddle shape with a dip in the middle, because the 3D structure cannot be mimicked in a 2D optimization.
Fig. 6. Normalized far-field patterns for a varied width for (a) upward and (b) downward directions.
To quantify the divergence of radiated beams, the FWHM of a WGA in the polar (FWHMp) and azimuthal direction (FWHMa) versus width is shown in Fig. 7. With the increase of the width from 2 to 5 µm, the polar FWHM becomes larger. When the width is larger than 5 µm, the polar FWHM remains unchanged. In contrast, the azimuthal FWHMs decreases. The reason is that the TE mode and the far-field pattern is sensitive to the waveguide width, as mentioned above. In addition, the FWHMp is larger than 90° in both directions, and the total polar FOV of the proposed WGA is thus larger than 180°.
Considering that a large waveguide width in a WGA may require a taper to connect the WGA and wiring waveguides, we believe that a width of 5 µm would be preferred to balance the trade-off between far-field patterns and footprints. The FOVs are found to be 93° × 20° and 99° × 21° for the upward and downward radiations, respectively. The transmissivities in the two directions are 0.32 and 0.36, respectively, which are almost equal to the 2D results.
Photonic devices are usually sensitive to fabrication errors. In order to examine the fabrication tolerance of the proposed WGA, we randomly change the structural parameters in the 2D WGA design within a range of ±2%, which is repeated for 10 times. The structural parameters are listed in the lines from No.1 to No. 10 in Table I. It is noted that the LiNbO3 layer is chemically inert and difficult to be etched, and thus hetch is set to be equal to h4 if the randomly generated hetch is larger than the height of the Si waveguide.
The curves of No. 0 in Fig. 8 are the far-field patterns of the optimized 2D WGA. The polar FWHM has a negligible change for all 10 cases, from No. 1 to No. 10. It is quite tolerant to the dimensional variations in fabrication. In contrast to the FOV, the far-field intensity may vary, but the normalized intensity is always greater than 0.64, which is believed to be acceptable for wide-angle OPAs.
Fig. 8. Far-field patterns of the optimized 2D WGA, No. 0, and with structural parameters randomly changed within a range of ±2% for 10 times, from No. 1 to No. 10, to mimic the influence of fabrication errors for (a) upward and (b) downward direction.
Far-field patterns of the 2D WGA with phase differences are presented in Fig. 9. It is noteworthy that the phase difference of 30° corresponds to a length of ∼44 nm. The WGA is quite tolerant to the phase differences produced by asymmetry in fabrication. Furthermore, a post-fabrication trimming of germanium implantation [40] and thermo-optic phase tuners can be implemented to correct phase errors caused by fabrication variations.
Fig. 9. Far-field patterns of the 2D WGA with phase differences for (a) upward and (b) downward direction.
4. Conclusion
We propose a bidirectional wide-angle WGA featured by a flat pattern in normalized far-field radiation intensity. Its FOVs are more than 90° for both upward and downward radiation. In this way, the bidirectional WGA can handle beam steering of 180° in total. The normalized intensity remains almost the same with a small variation of 10% from -39° to 39° for the upward emission and from -42° to 42° for the downward emission. In addition, specially designed AC layers help significantly increase radiation efficiency. This holds great potential to achieve wide-angle OPAs.
Funding
National Natural Science Foundation of China (62005195).
Acknowledgments
We acknowledge support by the Advanced Integrated Optoelectronics Facility at the Tianjin University.
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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