We explore the physical origin of Brewster angle in the external and internal reflections associated with an anisotropic material. We obtain the expressions of the reflected fields and the existence condition of Brewster angle by using the extinction theorem. It is found that the Brewster angle will occur if the total contribution of the anisotropic material's electric and magnetic dipoles to the reflection field becomes zero. In internal reflection, the requirements on the material parameters ε and µ for Brewster angle are the same as those in external reflection, and the Brewster angle is just the refraction angle in external reflection at the incidence of external Brewster angle. In contrast to the conventional isotropic medium, an anisotropic material can exhibit Brewster angle for both TE and TM waves due to its anisotropy. The results of the present paper are applicable to anisotropic dielectric and magnetic materials, including metamaterials.
We present and demonstrate an approach for femtosecond laser processing by using patterned vector optical fields (PVOFs) composed of multiple individual vector optical fields. The PVOFs can be flexibly engineered due to the diversity of individual vector optical fields in spatial arrangement and distribution of states of polarization, and it is easily created with the aid of a spatial light modulator. The focused PVOFs will certainly result in various interference patterns, which are then used to fabricate multi-microholes with various patterns on silicon. The present approach can be expanded to fabricate three-dimensional microstructures based on two-photon polymerization.
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrarily tunable OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrarily tunable OAM we presented has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrarily tunable OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.
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