Phase calibration for optical phased arrays enabled by ambiguity-free neural networks

Integrated optical phased arrays (OPAs) have attracted research attention for potential applications in image projection, light detection and ranging (LiDAR), and wireless optical communication. This can be attributed to their ability to control light propagation behaviors without requiring bulky mechanical components. The advances in complementary metal-oxide-semiconductor (CMOS) technologies have enabled the formation of compact phased array systems by on-chip integration of many components. As the optical paths of integrated OPA components are designed using silicon waveguides with the high index contrast, fabrication process variations of waveguides often leads to random phase errors in the waveguide paths. These errors can induce distorted far-field patterns, which are not the same as the ideal state of an optical phased array.

These phase deviation errors can be compensated by adding extra phase shifts through phase calibration for OPAs. There are several calibration approaches based on optimal searching methods like genetic algorithm, gradient descent, and swarm optimization algorithms. Although these optimization-based calibration methods can align the wavefront to the original state to achieve moderately good results, several issues limit their practical applications. For example, these iterative processes are time-consuming. Furthermore, the calibration results are not always accurate—due to the so-called “local optimum” issue associated with these methods. Despite the efforts devoted to modifying the algorithms to improve the calibration efficiency and accuracy, they are still based on iterative search for optimum, which is not only time-consuming but also costly, especially for a large number of OPAs.

The key difficulty in overcoming these limitations is to inversely solve the complex nonlinear relationship between the near-field phase distribution and far-field beam pattern to accurately determine the phase error distribution of the OPA elements. With the increasing popularity and success of deep-learning-based technologies in different fields, it has been identified as a promising solution for solving the complex inverse problem of OPA calibration.

Inspired by previous work in related fields, a student team composed of Lemeng Leng, Zhaobang Zeng, Guihan Wu, Zhongzhi Lin, Xiang Ji, and Zhiyuan Shi led by Professor Wei Jiang from Nanjing University developed an artificial neural network (ANN)-assisted method for accurate calibration of OPA and identification of phase error distribution among the OPA components. The devices calibrated in this study were designed and fabricated on silicon-on-insulator wafers. The accuracy and efficacy of the ANN-assisted methods for improving phase calibration of OPA systems were evaluated and discussed. Their research work is currently published in the journal, Photonics Research.

The research team showed that while the ANN-assisted method was generally effective, its efficiency and accuracy for the OPA system were significantly affected by the phase ambiguities such as periodic and conjugate ambiguities. By using device-physics-based analysis, the authors identified the cause of the phase ambiguities and potential strategies for overcoming the ambiguity-induced problems. These ambiguities were effectively resolved by creating a tailored ANN with phase-masked far-field patterns in conjugate pairs and constructing a loss function to preserve continuity. This approach allowed the extraction of the phase error distribution, and rapid, noniterative calibration of the device from the measured far-field patterns. The approach was verified experimentally and pure main-beam profiles with >12 dB sidelobe suppressions ratios were observed. Co-author Lemeng Leng commented, “Phase calibration for an OPA was a pain. The old iterative method was tedious and sometimes might fall into the trap of ‘local optimum’. Now with this new approach, we are relieved.”

In summary, Nanjing University scientists developed a new noniterative and efficient phase calibration method based on ANN for calibrating integrated OPAs. The introduction of the device-physics-based analysis played an important role in solving ambiguity and related problems. The trained ANN-based model successfully identified the phase error distributions and retrieved the original working state of the OPA by only two measurements of the far-field patterns. Compared with the existing iterative-based calibration methods, the present method is noniterative, highly efficient and suitable for calibrating a wide range of devices. In a statement to Advances in Engineering, Professor Wei Jiang said the new findings could advance the calibration of OPA devices for widespread applications.