Sparsity-based super-resolution and phase-retrieval in waveguide arrays.

Area of Science:

• Photonics and Waveguide Technology
• Information Theory
• Computational Physics

Background:

• Waveguide arrays are crucial for optical signal processing.
• Recovering complex input fields from partial intensity measurements is challenging due to ill-posed inversion problems.
• Input field sparsity is a known property in certain optical systems.

Purpose of the Study:

• To develop a method for reconstructing complex input fields in waveguide arrays.
• To demonstrate that prior knowledge of input sparsity can improve reconstruction accuracy.
• To validate the method through experimental and simulation studies.

Main Methods:

• Utilizing partial output intensity measurements from a waveguide array.
• Leveraging the GESPAR (Generalized Sparse Phase Retrieval) algorithm.
• Employing prior knowledge of input field sparsity to regularize the reconstruction.

Main Results:

• Successful recovery of complex input fields was achieved even with partial measurements.
• The prior knowledge of sparsity significantly improved reconstruction accuracy compared to non-sparse methods.
• Experimental and simulation results confirmed the effectiveness of the proposed scheme.

Conclusions:

• Sparsity is a powerful prior for solving ill-conditioned phase retrieval problems in waveguide arrays.
• The GESPAR-based method offers a robust solution for optical signal reconstruction.
• The approach has potential applications in optical interconnects, quantum state tomography, and MIMO communication systems.