Generalized Spatial Differentiation from the Spin Hall Effect of Light and Its Application in Image Processing of Edge Detection

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Generalized Spatial Differentiation from the Spin Hall Effect of Light and Its Application in Image Processing of Edge Detection

Tengfeng Zhu, Yijie Lou, Yihan Zhou, Jiahao Zhang, Junyi Huang, Yan Li, Hailu Luo, Shuangchun Wen, Shiyao Zhu, Qihuang Gong, Min Qiu, and Zhichao Ruan

Phys. Rev. Applied 11, 034043 – Published 18 March 2019

Abstract

Optics naturally provides us with some powerful mathematical operations. Here, we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorial-field computation and perform edge detection for ultrafast image processing.

Received 23 July 2018
Revised 25 November 2018

DOI:https://doi.org/10.1103/PhysRevApplied.11.034043

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Angular momentum of light Classical optics Polarization of light Refraction Spin Hall effect

Imaging & optical processing Weak measurements

Atomic, Molecular & Optical

Authors & Affiliations

Tengfeng Zhu^1,‡, Yijie Lou^1,†, Yihan Zhou¹, Jiahao Zhang¹, Junyi Huang¹, Yan Li³, Hailu Luo⁴, Shuangchun Wen⁴, Shiyao Zhu^1,2, Qihuang Gong³, Min Qiu^2,*, and Zhichao Ruan^1,2,†

¹Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
²State Key Laboratory of Modern Optical Instrumentation and College of Optical Engineering, Zhejiang University, Hangzhou 310027, China
³State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China
⁴Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China

^*minqiu@zju.edu.cn
^†zc.ruan@gmail.com
^‡These authors contributed equally to this work.

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Issue

Vol. 11, Iss. 3 — March 2019

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Images

Figure 1
Schematic of spatial differentiation from the SHE of light on an optical planar interface between two isotropic materials, e.g., an air-glass interface. The two polarizers (dark gray) are oriented at the angles indicated with double-head arrows: (a) preparing along $x$ and analyzing along $y$ and (b) vice versa. As a result, when an obliquely incident paraxial beam has an electric field distribution of $f (x, y)$ , the output field distribution corresponds to $\partial f / \partial y$ . Here, $x$ and $y$ are the beam profile coordinates for the incident and reflected light, which are perpendicular to the beam propagation direction as the wavevectors $k$ and share the same origin on the interface, and $x$ is in the incident plane.
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Figure 2
Measurement of the spatial spectral transfer function on an air-glass interface. (a) Experimental setup: glass slab (material BK7); precision rotator R; polarizers P1 and P2; lenses L1 and L2 with focal lengths 50 and 30 mm, respectively; collimator C; and beam profiler BP (Ophir SP620). The light source is a green laser (wavelength $λ_{0} = 532$ nm) and it is connected to the collimator through a fiber with a polarization controller. (b) Measured spatial transfer function spectra with an incident angle $θ_{0} = 45^{\circ}$ . (c) Theoretical results of numerical simulations. (d) Experimental (dotted line) and theoretical (dashed lines) spatial spectral transfer function for $k_{x} = 0$ , and the ideal one (solid lines) based on the first-order differentiation of Eq. (4). The inset corresponds to a wide range from $k_{y} = - 0.5 k_{0}$ to $k_{y} = 0.5 k_{0}$ .
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Figure 3
Experimental setup for spatial differentiation under Gaussian beam illumination. Components include glass slab (material BK7), precision rotator R, polarizers P, lens L, collimator C; and beam profiler BP (Ophir SP620). The light source is a green laser (wavelength $λ_{0} = 532$ nm) and it is connected to the collimator through a fiber with a polarization controller.
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Figure 4
Spatial differentiation demonstration for a Gaussian illumination with an incident angle $θ_{0} = 45^{\circ}$ . (a),(b) Measured intensity profiles of the incident and reflected beams, respectively. (c),(d) Numerical Gaussian fitting (c) to the incident beam with a waist radius $w_{0} = 44.2 λ_{0}$ , and the ideal spatial differentiation results (d) corresponding to $y$ -direction differentiation of (c). (e),(f) Normalized intensities of the incident and reflected fields at $x = 0.0 λ_{0}$ , $16.54 λ_{0}$ , and $33.08 λ_{0}$ , as indicated by the right arrows in (c),(d), where the dotted and solid lines correspond to the intensities of the experimental and ideal results, respectively.
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Figure 5
Edge detection for different images stored in $E_{x}^{in}$ and $E_{y}^{in}$ , respectively, with either amplitude or phase modulation. (a) Incident image consisting of the Chinese character for “light” with amplitude modulation on $E_{x}^{in}$ . (b) Reflected intensity image corresponding to (a) by measuring $E_{y}^{out}$ . (c) Incident image consisting of the LIGHT letters generated with phase modulation on $E_{y}^{in}$ , where the inside and the outside of the letters have different phases but the same intensity. (d) Reflected intensity image corresponding to (c) by measuring $E_{x}^{out}$ . The white bars correspond to the length of $50 μ m$ . (e) Slot test patterns on the SLM with the different phases for the black and the white areas. The widths of the slots are listed below in micrometers. (f) Measured reflected intensity image corresponding to (e).
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Figure 6
Edge detection demonstration on different material interfaces and for a variety of incident angles. (a)–(f) The weak reflection case on the air-glass interface. (g)–(l) The total reflection case with a planar interface on a 210-nm-thick gold layer. (a) and (g) are the schematics of the light reflection for two cases, respectively. The spatial differentiation results are shown for the incident images with (b)–(f) the Chinese character for “light” and (h)–(l) the letters LIGHT. Here, the field intensities are normalized with each maximum. The incident angle for each column is listed below.
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