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Upon reflection from the interface of two media, the light beam experiences two optical shifts: a longitudinal shift in the plane of incidence and a transverse shift normal to the plane, often referred to as Goos-Hänchen (GH) shift and Imbert-Fedorov (IF) shift . Simultaneously, the reflected light beam also experiences a small in-plane and out-of-plane angular deviation from the prediction of Snell’s law, i.e., the angular GH and IF shift, respectively. GH and IF shifts have attracted much attention in recent years due to their potential applications in many aspects, such as optical waveguide switch, integrated optics, and optical sensors. The GH and IF shifts have been widely investigated in various media and optical structures, such as dielectric slabs, metal surfaces, photonic crystal, and metasurfaces. The temperature-dependent GH shift has been investigated theoretically and experimentally, and proposed to detect the temperature variations. However, to the best of our knowledge, only the spatial GH shift was included in the reported temperature sensors based on GH shift, whereas the angular GH effect was neglected. In addition, IF shift based temperature sensor has not been addressed yet. In this work, we theoretically investigate the temperature-dependent spatial and angular GH and IF shifts of reflected light beam from the interface of air/gold film, and demonstrate a temperature sensor based on the GH (IF) shift.
The spatial GH shift for the s-polarized light with a wavelength of 633 nm is negative, while the p-polarized light exhibits a positive spatial GH shift with a significantly larger amplitude. The s-polarized light possesses a negative angular GH shift with its amplitude increases with the incident angle. For the p-polarized light, it exhibits positive and negative angular GH shifts, which depends on the incident angle. The s-polarized light exhibits a positive spatial IF shift. For the angular IF shift, it is negative for the s-polarized light, whereas the p-polarized light possesses a positive angular IF shift. The spatial and angular shift of the reflected beam can be combined into a total beam displacement when observed with a distance from the origin. For temperature sensing applications, the total beam displacement of the GH (IF) effect between the p- and s-polarized incident light was monitored. It is found that both the GH and IF shift based temperature sensor exhibit positive and negative sensitivities. The maximum sensitivity (amplitude) for the GH shift temperature sensor was obtained from 633 nm light beam incident onto the surface of gold film at almost grazing incidence (e.g., 0.3631 nm/K with the incident angle of 89 degrees). In contrast, a much smaller sensitivity of 0.01615 nm/K was obtained for temperature sensor based on the spatial GH shift. The maximum sensitivity is 0.09477 nm/K for the IF shift based temperature sensor, much smaller than that based on the GH shift. The sensitivity of the temperature sensor also depends on the wavelength of incident light. The maximum sensitivity for the GH shift temperature sensor increases with the wavelength, and the sensitivity of 6.337 nm/K was achieved using 3000 nm light at the almost grazing incidence. For the IF shift temperature sensor, the maximum sensitivity decreases with the wavelength of incident light. The findings will open up new opportunities for the development of GH and IF shift based highly sensitive optical thermometry.
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