hv photonics Article A Design Approach of Optical Phased Array with Low Side Lobe Level and Wide Angle Steering Range Xinyu He, Tao Dong *, Jingwen He and Yue Xu State Key Laboratory of Space-Ground Integrated Information Technology, Beijing Institute of Satellite Information Engineering, Beijing 100095, China; [email protected] (X.H.); [email protected] (J.H.); [email protected] (Y.X.) * Correspondence: [email protected] Abstract: In this paper, a new design approach of optical phased array (OPA) with low side lobe level (SLL) and wide angle steering range is proposed. This approach consists of two steps. Firstly, a nonuniform antenna array is designed by optimizing the antenna spacing distribution with particle swarm optimization (PSO). Secondly, on the basis of the optimized antenna spacing distribution, PSO is further used to optimize the phase distribution of the optical antennas when the beam steers for realizing lower SLL. Based on the approach we mentioned, we design a nonuniform OPA which has 1024 optical antennas to achieve the steering range of ±60◦. When the beam steering angle is 0◦, 20◦, 30◦, 45◦ and 60◦, the SLL obtained by optimizing phase distribution is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively. This kind of OPA with low SLL and wide angle steering range has broad application prospects in laser communication and lidar system. Keywords: optical phased array; antenna array; low side lobe; wide angle steering range 1. Introduction Citation: He, X.; Dong, T.; He, J.; Xu, Optical phased array (OPA) is an array operating at optical frequency that achieves Y. A Design Approach of Optical beam steering by controlling the phase distribution of the optical antennas. OPA has the Phased Array with Low Side Lobe abilities of fast beam steering and beam agility, and it has the advantages of small size, Level and Wide Angle Steering light weight, high resolution and good security. OPA has broad application prospects Range. Photonics 2021, 8, 63. https:// in laser communication, lidar and other fields [1–3]. At present, silicon-based OPA is a doi.org/10.3390/photonics8030063 common OPA design [4]. Arc dielectric grating antenna is mostly used in silicon-based OPA to realize light radiation. In order to realize effective radiation, the size of the arc Received: 28 January 2021 grating antenna is relatively large. In [5], the width of the arc grating antenna designed Accepted: 22 February 2021 µ µ Published: 25 February 2021 by Sun et al. is 2.8 m, which is much larger than the wavelength 1.55 m commonly used in optical communication. OPAs with equal antenna spacings and equal excitation amplitudes have been proposed and demonstrated many times [6–8]. Due to the large Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in size of the antenna, the antenna spacing between two adjacent antennas is larger than one published maps and institutional affil- wavelength. Therefore, there are grating lobes in the far field pattern of the OPA, which iations. results in a small beam steering range. The grating lobes cannot be effectively suppressed by weighting the amplitudes and the phases of the array excitation. A lot of research literatures have proved that the grating lobes can be suppressed by using nonuniform arrays [9–12]. In [12], a nonuniform OPA with 128 antennas is proposed and fabricated by CMOS (complex metal oxide semiconductor) technology compatible with silicon photonic Copyright: © 2021 by the authors. technology. The beam steering range of ±40◦ is achieved, and the side lobe level (SLL) is Licensee MDPI, Basel, Switzerland. − ◦ This article is an open access article 10 dB when the beam direction is 0 . However, in order to meet the wider application, distributed under the terms and we need to further suppress the SLL and achieve wider beam steering range. conditions of the Creative Commons In this paper, a design approach is proposed to realize the low SLL and wide angle Attribution (CC BY) license (https:// steering of OPA by optimizing the antenna spacing distribution and the antenna phase creativecommons.org/licenses/by/ distribution, respectively. Firstly, the particle swarm optimization (PSO) is used to optimize 4.0/). the antenna spacing distribution to achieve the grating lobes and side lobes suppression. Photonics 2021, 8, 63. https://doi.org/10.3390/photonics8030063 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 9 Photonics 2021, 8, 63 2 of 9 optimize the antenna spacing distribution to achieve the grating lobes and side lobes suppression. Secondly, after obtaining the antenna spacing distribution, we further Secondly, after obtaining the antenna spacing distribution, we further optimize the phase distributionoptimize the ofphase the distribution designed nonuniform of the designed antenna nonuniform array by antenna PSO under array different by PSO under beam steeringdifferent anglesbeam steering to suppress angles the to side suppress lobes inthe the side beam lobes steering in the beam state. steering After two state. steps After of optimization,two steps of optimization, the SLL lower the than SLL− lower17.91 dBthan under −17.91 the dB beam under steering the beam and steering a wide angleand a steeringwide angle range steering±60◦ rangeof the ±60° OPA of are the realized. OPA are realized. 2. Design A Approachpproach of Optical Phased Array Figure1 1 displays displays thethe schematicschematic diagramdiagram ofof OPA.OPA. Light Light from from a a tunable tunable laser laser is is fed fed into into the waveguide through a gratinggrating coupler, andand thenthen isis evenlyevenly distributeddistributed toto NN waveguideswaveguides through thethe opticaloptical distributiondistribution network.network. The phase of light in each waveguide isis controlledcontrolled by a tunable phase shifter. As shown in FigureFigure1 1,, the the waveguide waveguide arrayarray isis connected connected toto thethe grating antenna array, and the light light is is radiated radiated by by these these grating grating antennas. antennas. Figure 1. Schematic diagram of optical phased array (OPA).(OPA). The far fieldfield pattern of a nonuniformnonuniform arrayarray isis [[13]13]:: N−1N −1 2 2pjx(sin− sin ) j xn(sinnsq−sin qs) E(q) = Ane l (1) E() ∑= An e (1) = n 1n=1 n−1 n−1 xn = ∑ dk (2) xdnk=k=1 (2) k=1 where An is the excitation amplitude of the n-th optical antenna, N is the number of antennas,where An andis theλ, qexcitationand qs denote amplitude the operating of the n wavelength,-th optical antenna, the observation N is the direction number and of theantenna specifieds, and beam λ, θ and steering θs denote angle, the respectively. operating wavelength, In our design, the the observation excitation direction amplitude and is equal,the specified i.e., An beam= 1. The steering parameter angle,d respectivelyk is the distance. In our between design, the thek +excitation 1-th antenna amplitude and the is kequal,-th antenna, i.e., An and= 1. Thexn is parameter the position dk coordinateis the distance of the betweenn-th antenna. the k + 1-th antenna and the k- th antenna,The expression and xn is ofthe SLL position is: coordinate of the n-th antenna. E2 The expression of SLL is: SLL = max−sidelobe (3) E2 Emainlobe2 2 max− sidelobe 2 where E max−sidelobe is the intensity of theSLL maximum= 2 side lobes and E mainlobe is the intensity(3) of the main lobe. Emainlobe Due to the restriction of the optical antenna size, the antenna spacing of the OPA is where E2max−sidelobe is the intensity of the maximum side lobes and E2mainlobe is the intensity of difficultthe main to lobe be suppressed. to less than one wavelength. The grating lobes will appear in the far field pattern, which limits the steering range of the array. Therefore, the nonuniform arrangement of the antenna array is adopted to design the OPA. Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 Due to the restriction of the optical antenna size, the antenna spacing of the OPA is difficult to be suppressed to less than one wavelength. The grating lobes will appear in Photonics 2021, 8, 63 3 of 9 the far field pattern, which limits the steering range of the array. Therefore, the nonuniform arrangement of the antenna array is adopted to design the OPA. 2.1.2.1. Optimizing Optimizing the theSpacing Spacing Distri Distributionbution of the of theAntennas Antennas In Inorder order to to achieve achieve thethe gratinggrating lobes lobes and and side side lobes lobes suppression, suppression, the global the optimiza-global optimizationtion algorithm algorithm PSO [ 14PSO] is [14] used is to used find to the find optimal the optimal antenna antenna spacing spacing distribution. distribution. PSOPSO is a is bionic a bionic optimization optimization algorithm, algorithm, and and it is it a is stochastic a stochastic opt optimizationimization algorithm algorithm developeddeveloped by byimitating imitating the the foraging foraging behavior behavior of birds. of birds. In the In the algorithm, algorithm, each each of the of the birds birds is takenis taken as a as particle, a particle, and and it only it only has has two two attributes attributes of velocity of velocity and and position. position. PSO PSO has has been been widelywidely used used because because of its of itssimple, simple, less less constraints constraints and and strong strong global global optimization optimization ability. ability. TheThe flow flow chart chart of PSO of PSO algorithm algorithm is shown is shown in inFigure Figure 2. 2. FigureFigure 2. Flow 2. Flow chart chart of particle of particle swarm swarm optimization optimization (PSO (PSO)) algorithm algorithm.. TheThe steps steps involved involved in PSO in PSO are are as asfollows. follows.