# Integrated Optical Phased Arrays for Beam Forming and Steering
## 7 Performances
### FOV, Beamwidth, and Sidelobe Suppression  
Integrated OPAs enable beam steering with no moving parts. Aliasing-free [12; 59] OPAs with wide FOVs [94; 114], narrow beamwidths [12; 65], and plateau envelopes [59; 113; 118] are highly desirable. As a fundamental evaluator of OPAs, FOVs, also named steering angles, steering ranges, steering abilities, and addressability, determine the range of beam forming and steering. The beamwidths, also termed beam divergences, spot sizes, and divergence angles, are the sizes of transmitted or received spots of OPAs. FOVs and beamwidths are  
Figure 13: Some typical thermal crosstalk-suppressed structures for OPAs. (**a**) An OPA with a fan-in/fan-out section for thermal crosstalk suppression. Reprinted with permission from [41] © The Optical Society. (**b**) Cross-section of a TO phase shifter with deeply etched trenches. Reproduced from [72] published by IEEE, 2019. (**c**) An OPA with both a fan-in/fan-out section and deeply etched isolation trenches. Reproduced from [75] published by The Royal Society of Chemistry, 2018.  
typically described in degrees. The ratio between an FOV and a beamwidth is the number of resolvable points, which determines the maximum theoretically resolvable directions during steering. Resolvable points of an OPA are the multiplication of the number of resolvable points along two steering axes [12]. OPAs suffer from a trade-off between FOVs and beamwidths [109], which can be mitigated by metasurface-based OPAs [136]. These OPAs achieve wide FOVs and narrow beamwidths simultaneously [131]. Efficient radiation with a narrow beamwidth is essential for OPA-based applications over long distances. Considering the diffraction nature of light, a large-scale OPA is required [15]. Based on the phased array principle, the lateral FOV, \(\varphi\), [7] is given by  
\[\sin\varphi=\frac{\lambda\Delta\varphi}{2\pi d} \tag{7}\]  
where \(\Delta\varphi\) is the uniform phase difference between the WGAs with a spacing, \(d\). The beamwidth is proportional to the ratio of wavelength to the multiplication of the aperture size of the \(N\)-element OPA and the cosine of the steering angle \(\varphi\)[7], as  
\[\Delta\varphi_{FWHM}\approx\frac{0.886\lambda}{Nd\cos\varphi} \tag{8}\]  
FOVs are limited by grating lobes, when the pitch is larger than half wavelength [18; 59]. For an OPA with a fixed number of emitters, the FOV can be widened by decreasing the spacing. However, the resolution of the OPA is unchanged for the increased main lobe beamwidth [12; 117]. As described above, element pitches cannot be too small to avoid on-chip coupling between adjacent elements [12; 60; 117]. An off-chip divergence lens can widen FOVs, in which the resolution is unchanged for the expanded beamwidth [12]. Aperiodic arrays solve the issues of strong optical coupling between adjacent waveguides and fabrication difficulties in forming small pitches simultaneously [6]. Wide FOVs and high SMSRs can be simultaneously achieved by well-designed aperiodic OPAs [41; 59; 60; 107; 114; 137] at the cost of decreased main lobe efficiencies and signal-to-noise ratios [59; 107; 114; 137]. As the aperture is the same, the main lobe width is preserved by the sparse aperiodic arrays with a simplified control circuit [114]. Additionally, sidelobes of WGA superlattices are strongly suppressed by misaligning steering angles of sidelobes in different sub-arrays [60]. Aperiodic large-scale OPAs require complex design, increased fabrication complexity, and cost [60]. A 128-channel aperiodic OPA exhibited an impressively high-performance steerability with over 60,000 resolvable spots, where a wide FOV of 80\({}^{\circ}\)\(\times\) 17\({}^{\circ}\) and a narrow beamwidth of 0.14\({}^{\circ}\)\(\times\) 0.14\({}^{\circ}\) were achieved simultaneously [12]. Furthermore, multi-beam steering can also widen FOVs. Multiple-beam scanning can be realized in an OPA with a large element spacing by utilizing higher-order grating lobes [113].