By investigating the surface wave of photonic crystal, we put forward two sets of rules: the right-handed screw rule, judging the transverse spin angular momentum (SAM) directions according to the propagation direction of the surface wave; and the left-handed rule, judging the excitation direction of the surface wave in accordance to the SAM direction of incident circularly polarized light and the relative position of the dipole-like scatterer with respect to the interface where the surface wave propagates. Both right- and left-handed rules apply to the interface consisting of opposite-sign-permittivity materials. With the help of these two sets of rules, it is convenient to judge the direction of the transverse SAM and the excited surface wave, which facilitate the application involving transverse SAM of the surface wave.

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By eliminating the spherical aberrations of microsphere we derived a simple but useful formula on the focusing of dielectric microsphere. On basis of this formula, not only can researchers determine the parameters of an optical microsphere system with super-resolution, but they can also perform parameter transformation. In order to facilitate the application, the principle of parameter transformation was summarized into three kinds of case listed in Table 1, which were all demonstrated numerically with concrete examples by finite-difference time-domain method. This formula will be conducive to the development of applications based on microsphere, such as photonic nano-jet lithography, microsphere nano-scope.