Spin-orbit coupling modification of photons to ray equation in inhomogeneous medium

Based on the principle of general relativity,geometrization of interaction,the interaction of the inhomogeneous isotropic medium to light can be equated to a non-Euclidean geometry field just like the situation of gravity,i.e.,light travels in the null geodesic in the non-Euclidean curved space-time,which is equivalent to the Fermat principle for the inhomogeneous media.In this paper,the propagation of light in an inhomogeneous media is studied by means of the effective metric theory.The modification to the classical ray equation of photons is derived from the geodesic equation of photon by considering the spin effect of photons,which is induced via the spin-orbit coupling of photons,and the corresponding Hamiltonian of photonis proposed.Based on the spin-orbit coupling of photon,a light splitting phenomenon emerges in the inhomogeneous media,which is the spin hall effect of photon.

Ray equation migration of wide-angle reflections in Dabie orogenic zone

ay equation migration of wide-angle reflections in 2-D medium is one kind of Kirchhoff prestack depth migration method. Based on ray theory, this method can be used extensively in 2-D inhomogeneous medium, and shows its advantage in wide-angle reflection study. After calculating ray fields, we can get the wave fields of sources and receivers by interpolation, and the intensity (or amplitude) AP corresponding to the depth point P at travel-time tP=tSP+tPR can be found in seismograms. Ray equation migration is completed by transforming AP according to the specific relation, migrating it to the depth point, then calculating the ray fields of lots of sources and receivers in the same way and finally stacking the outcomes. Numerical calculation has yielded satisfactory results. Data processing of the Zhuangmu-Yuexi-Huangmei-Zhanggongdu profile passing through the Dabie orogenic zone provides a structural form of M-discontinuity along the profile. The result shows that the high pressure metamorphic rock zone of South Dabie rock mass is related to the uplifting of M-discontinuity here. 'Mountain root' exists under North Dabie rock mass, which conforms with gravity isostasy theory. The Xiaotian-Mozitan fault is a suture zone as a result of the collision of North China plate with Yangtze plate, and extends through M-discontinuity. The abyssal fault near Liu'an is the extended eastern section of the Luonan-Minggang fault, which is also confirmed here.

A Comparison of the Radar Ray Path Equations and Approximations for Use in Radar Data Assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction （NWP）. They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth＇s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.

Measurement and verification of concentration-dependent diffusion coefficient:Ray tracing imagery of diffusion process

Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens(LCL),which has dual functions of diffusion cell and image formation.The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations,the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution.Guided by the calculation conditions,the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper.The spatial and temporal concentration profile Ce(z,t)of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL;Then,the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D0×(1+α1C+α2C2+α3C3+…).The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z,t).The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z,t)with Ce(z,t).Finally,the obtained polynomial D(C)is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL.Based on the ray propagation law in inhomogeneous media and the calculated n(z,t),the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C).The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.