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Phase detection of coherence singularities and determination of the topological charge of a partially coherent vortex beam

We propose and experimentally demonstrate a noniterative diffractive imaging method for reconstructing the complex-valued transmission function of an object illuminated by spatially partially coherent light from the far-field diffraction pattern. Our method is based on a pinhole array mask, which is specially designed such that the correlation function in the mask plane can be obtained directly by inverse Fourier transforming the diffraction pattern. Compared to the traditional iterative diffractive imaging methods using spatially partially coherent illumination, our method is noniterative and robust to the degradation of the spatial coherence of the illumination. In addition to diffractive imaging, the proposed method can also be applied to spatial coherence property characterization, e.g., free-space optical communication and optical coherence singularity measurement.

We introduce an optimal metagrating design for transverse-position metrology in presence of photon shot noise. The proposed working principle is closely related to the formation of a phase vortex in the diffraction orders in the parameter space. Using the topological robustness, we optimize the design and compress all the transverse-position information around a certain point into a small number of detected photons, saturating the shot-noise limit had all the photons used for probing the position been detected. The current scheme avoids the problem of detector saturation in the presence of high probe power while maintaining all the information detected, allowing one to make full use of the high power that is available. Besides, the direct link between the resonant property in the unit cell and the conditions to achieve the bound is given: one with the zeroth dipole resonance and the other one with the anapole condition of the first dipole. The connection between the metagrating design and the optimization using topological robustness along with the fundamental precision limit using classical light gives new insights in all of these fields.

Abstract:In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM). 145-148 (1965). 6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento 9, 426-438 (1952). 7. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). 8. C. J. R. Sheppard, "Synthesis of filters for specified axial properties," J. Mod. Opt. 43, 525-536 (1996)