Performance Analysis of a Prime-Parameterized Fibonacci Spiral-Based Optical Phased Array

TL;DR

This work addresses scalable, non-redundant beam-steering for optical phased arrays by introducing a Fibonacci spiral layout with prime-number parameterization and an angular control parameter $α$. The authors derive a general near-field to far-field framework and implement a Fibonacci-prime geometry where antenna positions follow a radius $r \approx a_p \phi^{2\theta_p/\pi}$ with a prime-based angular schedule, enabling two configurable regimes that trade off side-lobe suppression and the number of resolvable points. Simulation results show that with 93 antennas, Config.1 ($α=0.45$) achieves $N_o \approx 14{,}086$ and strong SLSR with modest FWHM, while Config.2 ($α=0.75$) dramatically increases $N_o$ to ≈56,562 at the cost of SLSR in one axis, all within FoV limits of ~11.9°. The study also demonstrates robustness to fabrication-like positional disturbances (\sigma = 0.04), with moderate tolerances that preserve beam quality, and discusses scalability and a comparison with Costas arrays, indicating a favorable FoV for the Fibonacci-prime approach. The proposed method is compatible with mainstream PIC platforms and offers practical tunability for LiDAR, FSOC, and related applications.

Abstract

Optical phased arrays (OPAs) are a promising technology for realizing fast and on-chip non-mechanical beam steering. In this work, we propose and analyze the performance of a non-uniformly spaced antenna arrangement based on the Fibonacci Spiral. A unique prime-number-based parameterization for antenna positioning and a tunable positional-control parameter ($α$) are introduced. We show that, depending on the intended application of the OPA, by adjusting $α$, we can achieve $\approx$ 56,562 resolvable points with 93 antennas arranged according to the prime-parametrization. To the best of our knowledge, this result exceeds the reported values in existing literature for comparable non-redundant array configurations. We analyze the robustness of this design by evaluating the sensitivities of the three key performance metrics of an OPA: side-lobe suppression ratio (SLSR), field of view (FoV), and the far-field full width at half-maximum (FWHM), to the random disturbances in antenna positions that may occur for practical implementation on a photonic chip.

Figures (11)

• Figure 1: Schematic of the proposed Fibonacci-prime spiral-based optical phased array (OPA), illustrating five phase shifters for simplicity. The background Fibonacci spiral(yellow region) represents the bio-inspired geometric foundation of the antenna arrangement.
• Figure 2: Arrangement for 93 antennas in (a) configuration 1 ($\alpha ~=~ 0.45$) (b) configuration 2 ($\alpha ~=~ 0.75$) (c) a configuration with $\alpha ~=~ 0$. The coordinate axes represent antenna positions in the x-y plane.
• Figure 3: Simulated far-field radiation pattern for (a) uniform arrangement of 100 antennas. (b) an arrangement of 93 antennas in Fibonacci-prime layout with $\alpha ~=~ 0$.
• Figure 4: Simulated two-dimensional far-field pattern for the Fibonacci-prime array with 93 antennas: (a) configuration 1 ($\alpha ~=~ 0.45$) (b) configuration 2 ($\alpha ~=~ 0.75$). Color scale indicates normalized intensity in the $\theta-\psi$ plane. Insets display magnified views around the main lobe region to highlight beam confinement. White dashed contour in the insets mark the regions of FWHM
• Figure 5: Simulated one-dimensional far-field patterns for the Fibonacci-prime array with 93 antennas in configuration 1: (a) $\theta$-direction (b) $\psi$-direction. Red and green markers indicate the main lobe and the strongest side lobe, respectively. Insets present zoomed views around the strongest side lobe in a logarithmic (dB) scale