Optical beamforming with tunable ring resonators

Abstract

Optical beamforming prevents beam-squint and imbalance loss effects, and enables wideband signal transmission/reception. There are different types of optical delay lines such as optical fiber delay lines, fiber Bragg grating delay lines, photonic crystal delay lines and coupled resonator optical waveguides. The crucial criterion to choose the proper delay line for beamforming is the tunability of the delay line. It is preferred to use a continuous delay line to steer the beam accurately to any direction within the coverage region and avoid complex lossy and bulky switching circuits. Among different delay lines, optical ring resonators are more promising for beamforming application shows an optical resonator delay line consisted of parallel rings coupled to a waveguide. The coupling factors, (kappa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , kappa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , ...kappa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> ), represent the amount of input power penetrating to each ring, and are adjusted with thermo-optic (TO) phase shifters. The change in refractive index due to temperature, dn/dT, can be significantly large for certain optical material (~ -5 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> )[2], however the reported rise times are not better than 1 ms [3]. Moreover, the coupling factors are adjusted manually [Zhuang, et al., 2005]. We propose a fast, robust and accurate algorithm to tune the coupling factors of parallel ring resonators to generate the required delay for beam steering of transmitter arrays. We show that this method provides a significant optical bandwidth, a high array gain and converges in a few iterations for most directions.