Abstract
With sub-wavelength scaled structures in a large system, the conventional finite-difference time-domain method can consume much computational resources since it includes both the spatial and temporal dimension in the scheme. In order to reduce the computational cost, we combine the novel methodology “transformation optics” in the simulation to map a physical coordinate with designated non-uniform grids to a uniform numerical coordinate. For a demonstration, the transmission spectrum through a sub-wavelength metallic aperture with one-dimensional and two-dimensional coordinate transformation is simulated, and compared with uniform-grid cases. We show that the proposed method is accurate, and the computational cost can be reduced remarkably to at most 5.31%, in comparison with the simulation of the finest uniform grids demonstrated. We are confident that it should be helpful to the simulation study in sub-wavelength optics due to its verified accuracy and efficiency.
Highlights
Since the extraordinary enhanced optical transmission through a metallic sub-wavelength hole array was discovered two decades ago [1], plasmonics has become an active research area.The academic interest is in the anomalous optical phenomena when light propagates through sub-wavelength structures perforated in metallic film [2,3]
We are confident that the method should be helpful to the finite-difference time-domain (FDTD) simulation study in sub-wavelength optics due to its verified accuracy and efficiency
We have shown the capability of the FDTD simulation with transformation optics” (TO) for non-uniform grids to enhance efficiency
Summary
Since the extraordinary enhanced optical transmission through a metallic sub-wavelength hole array was discovered two decades ago [1], plasmonics has become an active research area. Non-uniform cell algorithms that have been developed for decades, such as the sub-gridding approach [10,11], might be applied to lower the computational requirement; but, the implementation of the source codes is usually not simple. A procedure for structured nonorthogonal discretization grids implemented in FDTD with the reconsideration of the EM field updating scheme is proposed [30]; the methodology is employed to generate non-uniform grids around the interfaces and openings of a metallic slit in a finite-difference frequency-domain scheme [31]; an additional cylindrical coordinate for the local mesh refinement is introduced in the Cartesian-coordinate-based FDTD simulation [32].
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