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Abstract
Optical phased arrays (OPAs), the optical counterpart of phased arrays at radio frequencies, can electronically steer an optical beam without any moving parts. To achieve a 180° field of view (FOV), the array emitters should be spaced a half-wavelength apart or less. However, a conventional OPA based on a waveguide grating array suffers from strong cross talk between adjacent waveguides when the pitch is a half-wavelength or less. Here, we theoretically describe and experimentally demonstrate a two-dimensional aliasing-free beam steering regime for an integrated OPA with the entire 180° FOV. We achieve this by using a half-wavelength-pitch waveguide array combined with a trapezoidal slab grating as a single emitter. Our OPA also features a low sidelobe level of ${\lt}{-}19\;{\rm dB}$ while the beam is steered from ${-}{40}^\circ$ to ${+}{40}^\circ$, breaking the trade-off between FOV and beam quality. The chip-based OPA with a large beam steering range and high beam quality provides a promising route for a compact, solid-state, cost-effective, and high-performance light detection and ranging system, enabling a wide range of classical and quantum applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
The radio frequency (RF) phased array was first proposed more than a century ago and has been widely used for radar and wireless communications [1]. Infrared and visible light, the electromagnetic waves at optical frequencies, have a wavelength of 3 to 5 orders of magnitude shorter than that of the radio wave; therefore, the optical phased array (OPA) could offer much higher precision than the RF phased array. The OPA can quickly and precisely steer light in a non-mechanical way [2–12], thus representing a new enabling technology for compact solid-state two-dimensional (2D) beam steering as an alternative to traditional mechanical beam steering including microelectromechanical systems [13].
The chip-scale OPA opens a promising path for a solid-state light detection and ranging system, which has a wide range of applications such as autonomous vehicles, holography, augmented and virtual reality, biological imaging, and free-space optical communications [8,14–19]. The aliasing-free 2D beam steering with a large field of view (FOV) and high beam quality is of crucial importance for an OPA. However, current OPAs remain limited in FOV and beam quality due to unwanted grating lobes and sidelobes [2,3,5–7,20,21]. A conventional phased array consists of arrays of coherent emitters, and a desired far-field radiation pattern can be formed and steered through the interference of the emissions by controlling the phase of each emitter. If the emitter spacing is a half-wavelength or less, aliasing-free 180° FOV can be achieved and grating lobes can be avoided. While if the emitter spacing is larger than a half-wavelength, strong constructive interference occurs at multiple far-field angles and grating lobes are generated, which causes aliasing and limits the FOV.
Half-wavelength spacing has been achieved in RF phased arrays due to strong confinement in metals, but metals are extremely lossy for optical frequencies. Dielectric waveguides are usually used to confine light in OPAs, but waveguide array emitters cannot be spaced a half-wavelength or less since this causes uncontrollable strong evanescent coupling between adjacent waveguides. The OPAs based on an edge-emitting (end-fire) array, where light emits into free space at the edge of the device, have achieved half-wavelength spacing and a large FOV [10,11]. However, the beam of the end-fire OPAs is a stripe rather than a spot, which can only be steered in one dimension. A non-uniform spacing between adjacent emitters can avoid constructive interference and suppress grating lobes [9]. However, this approach does not increase the power in the main beam and only redistributes the power of grating lobes into a wider range of angles, resulting in increased background noise.
Here, we present an OPA that can simultaneously achieve aliasing-free beam steering over the entire 180° FOV and a high-quality beam with a low sidelobe level (SLL). Fundamentally different from the conventional OPA based on waveguide grating arrays as emitters, we use fast-converged waveguide superlattices followed by a trapezoidal slab grating as a single emitter, which avoids uncontrolled coupling and achieves half-wavelength spacing. On the other hand, the conventional OPA with uniform emission results in a ${{\rm sinc}^2}$ pattern in the far field with a theoretical minimum SLL of ${-}{13.26}\;{\rm dB}$. We apply a Gaussian amplitude distribution (GAD) for the emitter [14], which can suppress sidelobes but at the cost of a reduced effective emitting area. An SLL of ${\lt}- {19}\;{\rm dB}$ over the entire 180° FOV is achieved while the beam is steered from ${-}{40}^\circ$ to ${+}{40}^\circ$, which is the lowest SLL demonstrated to date. Our OPA is fabricated on a silicon on insulator wafer using the silicon photonic process, which is complementary metal–oxide–semiconductor (CMOS) compatible and allows for mass production at a low cost.
Fig. 1. Chip-based optical phased array. (a) Schematic illustration of the OPA chip. The light from an optical fiber is distributed to 64 channels with a Gaussian amplitude distribution through a grating coupler and a star coupler. Then the light in the 64 channels is converged to a half-wavelength-spacing waveguide array and emitted to far field through a trapezoidal slab grating. The inset shows the direction of the spherical coordinator system. (b) The half-wavelength-spacing waveguide array followed by the slab grating; inset is the scanning electron microscope (SEM) image of the zoom-in part. (c) The cross talk between adjacent waveguides with varying widths.
2. RESULTS AND DISCUSSION
Figure 1(a) shows the schematic of the chip-based OPA, which mainly consists of a star coupler, phase shifter array, half-wavelength-spacing waveguide superlattices, and a trapezoidal slab grating. A near-infrared light around 1550 nm is coupled into the device with the transverse electric mode through an apodized grating coupler [22]. The 1-to-64 star coupler splits the light into 64 channels and generates the GAD for these channels. The center-to-edge GAD ratio is 7.5 dB so the SLL can achieve ${-}{30}\;{\rm dB}$ in theory (Supplement 1, Fig. S4). Each channel passes through a thermo-optical phase shifter [23], which has folded waveguides with varying waveguide widths and 1.2 µm pitch (Supplement 1, Fig. S3). Each phase shifter is individually controlled by a digital-to-analog converter allowing arbitrary phase control from 0 to ${2}\pi$; therefore, arbitrary beam pattern forming and dynamic beam steering can be realized in the far field. At the output of the phase shifter array, the waveguides are bended and tightly squeezed down to half-wavelength spacing (775 nm). The bending radii are optimized in order to minimize the coupling between adjacent waveguides. Waveguide superlattices [24] with the widths of 560, 400, 580, and 380 nm are used to further reduce cross talk, as shown in Fig. 1(b). The four different widths are chosen based on the cross-talk map [Fig. 1(c)] between waveguides with different widths. The cross talk is calculated by simulating the coupling power between two waveguides with different widths, of which the space is tapered from 2 µm to 0.775 µm within a fixed length of 100 µm. The waveguide supperlattices are tapered to the same width of 450 nm to avoid periodical amplitude fluctuation of each channel. At the end of the waveguide array, light from each waveguide freely propagates into the emitter, which is a 4 mm long trapezoidal slab grating with a shallow etch depth of 10 nm and a pitch of 560 nm. By combining the half-wavelength-spacing waveguide array and the trapezoidal slab grating, the aliasing-free beam steering over the entire 180° FOV is achieved. In addition, the shallow-etched long grating ensures good directionality of the beam and a small spot size in the vertical direction.
Unlike the conventional waveguide array grating as emitters [6,9,20], we use a trapezoidal slab grating as a single emitter. If the phases of light at the end of the waveguide array are aligned, the light propagating in the slab grating can be described as a quasi-plane wave, which is diffracted by the weak-coupled grating teeth. The ${k_{\textit{ux}}} = k{\sin}{\theta _x}$ and ${k_{\textit{uy}}} = k{\sin}{\theta _y}$ characterize the directions of the wave vector of the diffracted field and can be written as [25]
where $k$ is the wavenumber in air, and ${n_0}$ is the effective refractive index of the slab grating. ${\phi _0}$ is the propagating angle of the quasi-plane wave in the near field [Fig. 1(a)], and $\Lambda$ and $m$ are the pitch and grating order of the slab grating, respectively. It can be seen from these equations that the far-field pattern is an arc centered at $({2{ m\pi}/{\Lambda},0})$. The angle ${\phi _0}$ is determined by the interference of light from the waveguide array, which can be described by the near-field grating equation:Fig. 2. Imaging system for measuring the emission of the OPA chip. (a) The imaging system consisting of an infrared camera and lenses is used to measure far-field and near-field emissions of the OPA chip. The lens (${\rm NA} = {0.42}$) with the back focal plane on the infrared camera sensor is used to obtain the far-field image and a telecentric lens assembly is used to obtain the near-field image. The imaging system is rotated along a circle rail in order to measure the entire 180° FOV. (b) The image of the OPA chip that is wire-bonded to a PCB. (c) Schematic of the imaging system.
In order to achieve aliasing-free beam steering with 180° FOV in the horizontal direction of the far field, the condition of ${n_0}{\sin}{\phi _0} \gt 1$ needs to be satisfied according to Eq. (2). Applying this condition to Eq. (4), we can derive the aliasing-free condition of $\Delta d \lt \lambda /2$, same as the conventional OPAs based on the waveguide grating array.
Fig. 3. Characterization of far-field and near-field emissions. (a) The spliced image of the far-field radiation pattern when the beam is steered from ${-}{70}^\circ$ to 70° in the horizontal direction. The trajectory is a curve since the imaging system rotates along a circular rail. The inset is the zoomed-in image of the beam steered to 0°. (b) Measured average far-field optical power along the horizontal direction over the entire 180° FOV, demonstrating aliasing-free beam steering in this direction. (c) Measured SLL and spot size of the far-field beam in the horizontal direction. (d) The near-field emission of the OPA when the beam is steered to 0° and 40° in the far field, respectively.
The tuning efficiency of each phase shifter and the amplitude distribution of all the channels are measured from the far-field image captured by the setup shown in Fig. 2(a), and Fig. 2(b) shows the packaged OPA chip mounted on a printed circuit board (PCB). Figure 2(c) shows the simplified illustration of the imaging system. The tuning efficiencies of the phase shifters are measured to be around $7\;{\rm mW/}\pi$ and can be further improved [14,23]. In order to compensate for phase misalignment of the 64 channels, a gradient descending algorithm is used to calibrate the initial phases and form the main beam in the far field. The GAD of the 64 channels is also measured by tracking far-field intensity variations (Supplement 1, Fig. S4). The amplitude ratio from the center to the edge of the GAD is measured to be around 7 dB, which is in good agreement with the star coupler design and a trade-off between the SLL and the far-field spot size. Although a higher amplitude ratio can further lower the SLL, it also reduces the effective emitting area due to low amplitude at the edge.
Fig. 4. Far-field radiation pattern. (a) The spliced image of the far-field radiation pattern when the beam is steered from 1.4° to 14.9° in the vertical direction, by tuning the wavelength from 1480 nm to 1580 nm. (b)–(d) The formed 2D image of three letters (“D,” “T,” “U”) centered at the angles of ${-}{60}^\circ$, 0°, and 60° in the horizontal direction, respectively, by tuning both wavelengths and phase shifters.
We experimentally achieve aliasing-free beam steering over the entire 180° FOV and the beam can be steered from ${-}{70}^\circ$ to 70° at a fixed wavelength (1550 nm), as shown in Figs. 3(a) and 3(b). The far-field patterns at different angles form a curved trajectory since the imaging system rotates along a circular rail in order to measure the entire 180° FOV [Fig. 2(a)] and Eqs. (1) and (2) also indicated a curved pattern of the far field. The SLL and spot size of the far-field beam steered to different angles ranging from ${-}{70}^\circ$ to 70° are also characterized [Fig. 3(c)]. The SLL is ${\lt}- {19}\;{\rm dB}$ when the beam is steered within $\pm {40}^\circ$ range and ${\lt}- {13.2}\;{\rm dB}$ within $\pm {70}^\circ$ range, indicating successful suppression of sidelobes by the GAD in the waveguide array. The beam width is 2.1° at the angle of 0°, which is mainly limited by the aperture size of 49.6 µm (${64} \times {0.775}\;{\unicode{x00B5}{\rm m}}$) in the horizontal direction. In addition, the GAD reduces the effective aperture size and results in relatively large beam width. One effective way to narrow down the beam size is by adding more channels. It is worth mentioning that the beam can also be steered beyond $\pm {70}^\circ$ but with low SLL and broadened the main beam since the grazing angle reduces effective aperture size.
We capture the near-field image of OPA emission [Fig. 3(d)], when the beam is steered to 0° and 40° in the horizontal direction, respectively. At the emitting angle of 0°, only zeroth-order radiation of the near field described by Eq. (3) is observed, and higher-order radiations are filtered out by the trapezoidal shape of the grating. At the emitting angle of 40°, zeroth-order radiation of the near field is steered to 13° in the slab plane, which matches well with the prediction by Eq. (2). First-order radiation of these two angles only appears in the near field but turns into the evanescent field and does not emit to the far field. The near-field beams in these three angles show good lateral confinement, which validates our approximation of the near field as a quasi-plane wave.
We also characterize the beam steering in the vertical direction by tuning the wavelength from 1480 to 1580 nm [Fig. 4(a)]. A 13.5° tuning range is achieved in the vertical direction, corresponding to a 0.135°/nm tuning efficiency. The beam width is measured to be around 0.08°, which is much smaller than that in the horizontal direction due to a much larger aperture size (4 mm) in the vertical direction. The measured beam width is larger than the calculated beam width (0.02°) of a uniform 4 mm long emitting aperture. It is mainly due to the limited resolution of our measurement setup and also the amplitude drop along the emitting grating, which can be observed from the near field in Fig. 3(d). Besides beam steering, the chip-based OPA can also form an arbitrary pattern based on the Gerchberg–Saxton algorithm [26], as long as each phase shifter can be controlled independently. Even though phase tuning can only be achieved in one dimension, we can use the wavelength to slice the 2D pattern and assemble the sliced images afterward. Figures 4(b)–4(d) show the formed 2D pattern by multiple wavelengths ranging from 1480 to 1580 nm. At each wavelength, phase shifters are tuned to form the corresponding sliced image. Thus, three images showing three letters of “D,” “T,” and “U” are produced at angles of ${-}{60}^\circ$, 0°, and 60°, respectively. These images were captured using the same setup as the far-field measurement.
3. CONCLUSIONS
We have demonstrated a chip-based OPA, which overcomes the long-lasting issues of OPAs and simultaneously achieves aliasing-free 2D beam steering over the entire 180° FOV and high beam quality with a low SLL. The OPA chip is fabricated on a silicon photonic platform and can be produced at high volume in CMOS foundries at a low cost. Our demonstration may be transformative for a wide range of applications including autonomous vehicles, free-space optical communications, 3D holography, biomedical sensing, and virtual reality.
Funding
Innovationsfonden (1048-00030B); Villum Fonden (15401).
Disclosures
YL, HH (P).
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.
Supplemental document
See Supplement 1 for supporting content.
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