We propose and experimentally demonstrate a broadband and high efficient circularly polarizing dichroism using a simple single-cycle and single-helical plasmonic surface array arranged in square lattice. Two types of helical surface structures (partially or completely covered with a gold film) are investigated. It is shown that the circular polarization dichroism in the mid-IR range (3µm - 5µm) can reach 80% (when the surface is partially covered with gold) or 65% (when the surface is completely covered with gold) with a single-cycle and single-helical surface. Experimental fabrications of the proposed helical plasmonic surface are implemented with direct 3D laser writing followed by electron beam evaporation deposition of gold. The experimental evaluations of the circular polarization dichroism are in excellent agreement with the simulation. The proposed helical surface structure is of advantages of easy-fabrication, high-dichroism and scalable to other frequencies as a high efficient broadband circular polarizer.
Abstract. We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in application oriented fields. In this paper we provide a rigorous analysis of the method that covers systems of equations with unbounded coefficients. Working in a natural space for densities, L 1 , we obtain stability, consistency, and new convergence results for the method, new well-posedness and semigroup generation results for the related Fokker-Planck-Kolmogorov equation, and a new and rigorous connection to the corresponding probability density functions for both the approximate and the exact problems. To prove the results we combine semigroup and PDE arguments in a new way that should be of independent interest.
Abstract. The Sandwich Pair theorems have presented very efficient ways to determine existence of critical points or critical sequences for nonlinear differentiable functionals. In this paper, under rather weak hypotheses new relationships are established between sign-changing critical points and Sandwich Pairs or Linking Sandwich Pairs. The abstract results are demonstrated by applications on semi-linear elliptic equations.
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