The Optimal Weak Measurements Of Photonic Spin Hall Effect

The photonic spin Hall effect we study in this text is a phenomenon in which the photons undergo a spin-dependent shift perpendicular to the refractive index gradient due to the spin-orbital interaction when the linearly polarized beam passing through the inhomogeneous medium. Photonic spin Hall effect is a potential tool in precision metrology, so it is significant to charact erize the parameters of nanostructures. Note that the spin-dependent shift is sensitive to the thickness of the nanometal film, so in this text we establish a three-dimensional propagation model which is based on the weak measurements of the photonic spin Hall effect for describing Gaussian beam reflection from a planar air-prism interface. After analyzing optimal weak measurements of photonic spin Hall effect for measuring nanometal film, we propose using optimal weak measurements to measure the parameters of nanostructures. Besides, the theoretical research of the optimal weak measurements for observing photonic spin Hall effect in total internal reflection is studied. The paper is organized as follows:Firstly, the optimal weak measurements point in weak measurements of photonic spin Hall effect in nanometal film is studied. Establishing propagation models of vertically polarized Gaussian beam reflection on the interface of nanometal film, we reveal that the amplified transverse shifts of the photonic SHE in nanometal film not only relate to the incident angle and the thickness of the nanometal film, but also the amplification angle. It is founded that when the amplification angle is chosen as a special value(the optimal value) in the weak measurement, the amplified transverse shifts of the photonic SHE in nanometal film can reach the maximum value, and the measured values of transverse shift can also be more accurate to calculate the thickness of the nanometal film. With the help of the optimal weak measurements, we can greatly improve the precision of the detection of the photonic SHE. These findings provide the possibility for improving the precision of weak measurements and thereby have possible application for accurately characterizing the parameters of the nanostructures.Secondly, the optimal weak measurements in weak measurements for observing photonic spin Hall effect in total internal reflection is studied. Establishing a three-dimensional propagation model on an interface of air-prism, we obtain the relationships of incident angle, the amplification angle and amplified transverse shifts of the photonic SHE in total internal reflection. We find that there still exist the optimal weak measurements point in weak measurements. In such case the amplified transverse shifts of the photonic SHE in total internal reflection can reach maximum value. As a result, we can greatly improve the precision of the detection of the photonic SHE and characterize the parameter by the measurements. This research provides not only a new thinking to explore the physical phenomenon in total internal reflection, but also the possibility for developing the new Nano optical devices.