Extraordinary light transmission through subwavelength apertures: Convergence of the simulations to very low levels of numerical error is demonstrated. This allows to reach excellent agreement to experimental results from the literature.  

Experiments by Lezec et al (Science 297, 820) investigating light transmission through circular subwavelength apertures in metallic films with surrounding nanostructures have revealed surprising effects of enhanced transmission and a collimated beam of transmitted light.

Fig 1: x-y-cross section through the layout of a single hole with surrounding grooves in a thin silver film. The layout is symmetric under rotation around the y-axis.

For a fully quantitative understanding and from the point of view of optics design, accurate numerical simulations of Maxwell's equations for the 3D, cylindrically symmetric problem are desired.
JCMsuite is used for the simulation task at hand. With this, accurately converged results can be obtained in relatively short computation times. The experimental setup has been simulated, and the simulation results agree very well with the results of the experiment.

Fig. 2: Near field in a plane 1nm above the silver film in a pseudo-color representation.

Figure 1 schematically shows the geometrical setup of Lezec et al: a thin silver sheet is perforated with a single hole which is surrounded by circular grooves at the upper and at the lower side of the silver sheet. Hole diameter, groove spacing and depth are in the range of a few hundred nanometers, well below the wavelength of light. The setup is illuminated by an optical plane wave under perpendicular incidence.

JCMsuite's 3D FEM scattering solver with the option for cylindrically symmetric 3D problems has been used. With this the 3D problem is decomposed to a series of 2D problems in cylindrical coordinates. This decomposition works automatically and is error-controlled.

Fig. 3: Numerical convergence of transmission through the nanoaperture. (Relative error in dependence on number of unknowns of the FEM problem.)

Figure 2 shows a cross-section 1nm above the silver sheet through the computed 3D field distribution. Figure 3 shows how the numerical error of the observable (transmitted light intensity detected at a specific detection angle) converges towards zero. The convergence plot shows that for achieving a relative error of, e.g., one percent a moderate number of unknowns of about N = 100,000 is needed, corresponding to computation times well below one minute on a standard personal computer (PC). Figure 4 shows a typical transmission spectrum, which exhibits excellent agreement with experimental results of Lezec et al.

Fig. 4: Transmission spectrum: transmission to a detection angle of zero degree in dependence of the wavelength of the illuminating light.

Lezec et al.: Beaming Light from a Subwavelength Aperture - Experimental results.

Finite-element simulations of light propagation through circular subwavelength apertures - Numerical results.