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Scientific Reports

Observation of positive–negative sub-wavelength interference without intensity correlation calculation

Ling-Yu Dou, De-Zhong Cao, De-Qin Xu, An‐Ning Zhang, Xin-Bing Song

Published Jan 28, 2021• 2 citations
Publisher

Abstract

We report an experimental demonstration of positive-negative sub-wavelength interference without correlation. Typically, people can achieve sub-wavelength effects with correlation measurement no matter by using bi-photon or thermal light sources. In this paper, we adopt a thermal light source, and we count the realizations in which the intensities of the definite symmetric points are above or below a certain threshold. The distribution of numbers of these realizations which meet the restriction will show a sub-wavelength effect. With proper constrictions, positive and negative interference patterns are demonstrated.

DOI
10.1038/s41598-021-82030-9

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We report an experimental demonstration of positive-negative sub-wavelength interference without correlation. Typically, people can achieve sub-wavelength effects with correlation measurement no matter by using bi-photon or thermal light sources. In this paper, we adopt a thermal light source, and we count the realizations in which the intensities of the definite symmetric points are above or below a certain threshold. The distribution of numbers of these realizations which meet the restriction will show a sub-wavelength effect. With proper constrictions, positive and negative interference patterns are demonstrated.
We report an experimental demonstration of sub-wavelength interference without correlation. Typically, people can achieve sub-wavelength effect with correlation measurement no matter by using bi-photon or thermal light sources. Here we adopt a thermal light source. And we count the realizations in which the intensities of the definite symmetric points are above or below a certain threshold. The distribution of numbers of these realizations who satisfy the restriction will show a sub-wavelength effect. With proper constrictions, positive and negative interference patterns are demonstrated.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.
The high-order intensity correlation function of NNN-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the NthN\mathrm{th}Nth-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as NNN increases in the incoherent case.
We examine thermal light diffracted through a double slit using photon-number-resolved detection to directly measure high-order spatial correlations, and we see sinusoidal modulations of those correlations. The fringe width can, in principal, be made arbitrarily small, and we have experimentally obtained fringe widths as small as 30 nm with 800 nm wavelength light. This extreme sub-wavelength resolution, along with this direct detection technique, offers potential for high precision measurement applications.