Experimental demonstration of quantum-inspired optical symmetric hypothesis testing.

We use a phase-sensitive measurement to perform a binary hypothesis testing, i.e., distinguish between one on-axis and two symmetrically displaced Gaussian point spread functions. In the sub-Rayleigh regime, we measure a total error rate lower than allowed by direct imaging. Our results experimentally demonstrate that linear-optical spatial mode transformations can provide useful advantages for object detection compared with conventional measurements, even in the presence of realistic experimental cross talk, paving the way for meaningful improvements in identifying, detecting, and monitoring real-world, diffraction-limited scenes.

Quantum Fisher information for estimating N partially coherent point sources.

A partially coherent object's localization parameters are shown to be theoretically estimable with higher precision than those of an incoherent object, and the maximum number of independent parameters that have non-vanishing precision in the sub-Rayleigh regime is 3 (compared to 2 for an incoherent object). Normalization schemes, which are crucial in the proper interpretation of quantum Fisher information results in the presence of partial coherence, are introduced and detailed.

Experimental demonstration of superresolution of partially coherent light sources using parity sorting: erratum.

The authors include references that appeared on arXiv during the preparation of their paper [Opt. Express29, 22034 (2021)10.1364/OE.427734].

Propagation of Gaussian Schell-model beams in modulated graded-index media.

The evolution of partially coherent beams in longitudinally modulated graded-index media is studied. The special cases of Gaussian Schell-model beams and parametric modulation, when the modulation period is half the fiber self-imaging period, are examined in detail. We show that the widths of the intensity and coherence of Gaussian Schell-model beams undergo amplification in parametrically modulated parabolic graded-index media. The process is an analog of quantum mechanical parametric amplification and generation of squeezed states. Our work may find application in spatial and temporal imaging of partially coherent beams in fiber-based imaging systems.

Anomalous spatial coherence changes in radiation and scattering.

The superposition of two partially correlated waves is shown to produce fields with drastically altered coherence properties. It is demonstrated, both theoretically and experimentally, that two strongly correlated sources may generate a field with practically zero correlation between certain pairs of points. This anomalous change in coherence is a general phenomenon that takes place in all cases of wave superposition, including Mie scattering, as is shown. Our results are particularly relevant to applications in which it is assumed that highly coherent radiation maintains its spatial coherence on propagation, such as optical systems design and the imaging of extended sources.

Experimental demonstration of superresolution of partially coherent light sources using parity sorting.

Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced over direct imaging through the use of mode sorting. Here we theoretically and experimentally investigate the effect of partial coherence on the sub-diffraction limit localization of two sources based on parity sorting. With the prior information of a negative and real-valued degree of coherence, higher Fisher information is obtained than that for the incoherent case. Our results pave the way to clarifying the role of coherence in quantum-limited metrology.

Confocal super-resolution microscopy based on a spatial mode sorter.

Spatial resolution is one of the most important specifications of an imaging system. Recent results in the quantum parameter estimation theory reveal that an arbitrarily small distance between two incoherent point sources can always be efficiently determined through the use of a spatial mode sorter. However, extending this procedure to a general object consisting of many incoherent point sources remains challenging, due to the intrinsic complexity of multi-parameter estimation problems. Here, we generalize the Richardson-Lucy (RL) deconvolution algorithm to address this challenge. We simulate its application to an incoherent confocal microscope, with a Zernike spatial mode sorter replacing the pinhole used in a conventional confocal microscope. We test different spatially incoherent objects of arbitrary geometry, and we find that the resolution enhancement of sorter-based microscopy is on average over 30% higher than that of a conventional confocal microscope using the standard RL deconvolution algorithm. Our method could potentially be used in diverse applications such as fluorescence microscopy and astronomical imaging.

Modal Majorana Sphere and Hidden Symmetries of Structured-Gaussian Beams.

Structured-Gaussian beams are shown to be fully and uniquely represented by a collection of points (or a constellation) on the surface of the modal Majorana sphere, providing a complete generalization of the modal Poincaré sphere to higher-order modes. The symmetries of this Majorana constellation translate into invariances to astigmatic transformations, giving way to continuous or quantized geometric phases. The experimental amenability of this system is shown by verifying the existence of both these symmetries and geometric phases.