Ex) Article Title, Author, Keywords
New Phys.: Sae Mulli 2023; 73: 413-420
Published online May 31, 2023 https://doi.org/10.3938/NPSM.73.413
Copyright © New Physics: Sae Mulli.
Young Chul Kim*
Department of Optometry, Eulji University, Seongnam 461-713, Korea
Correspondence to:*E-mail: firstname.lastname@example.org
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We conducted a study using 3D simulation with the The finite-difference time-domain (FDTD) method to investigate the transmitted light distribution for the sub-skin-depth metal array medium. We confirmed the negative refraction phenomenon in the metal plate structure reported in an earlier study. Furthermore, we analyzed the intensity distribution of light passing through the metal cylinder array structure with the results of the layered metal plate structure. Our findings showed that the cylindical metal array medium exhibited a beam splitting phenomenon, which was not observed in the metal plate medium. We determined that this phenomenon was due to multiple interactions of the light beam with the metal arrays arranged in open space.
Keywords: Skin-depth, Negative refraction, Focusing, Surface plasmon, 3D simulation
When polarized light passes through a sub-skin-depth metal, a nonclassical phenomenon is observed at the metal-dielectric interface, such as a metal exposed to air or a metal thin film coated on a dielectric. Surface plasmons are generated by the redistribution of free electrons in the metal by an external field at the metal-dielectric interface. As a result, the field distribution in the metal changes, leading to increased light transmittance and a beaming effect[1-9].
Active research has been conducted on metalenses for use as verstile multifunctional photonic components and the design of metasurfaces for ultrathin, ultralight, and planar multifunction, including high-quality imaging by overcoming the diffraction limit and correcting aberrations. Furthermore, on genetic algorithms to automate the metasurfaces design for absorption bandwidth broadening, and the application of metasurfaces to electromagnetics has been reported. When light passes through a medium composed of a metal array of sub-skin-depth size, more complex effects appear. In a medium composed of metal plates, fields induced on the metal surface get coupled[15-17]. Additionally, in the metal array structure, multiple interactions occur between the light scattered in the process of passing through the medium and the induced fields around the metal. Interactions between gold nanoparticles and quantification of the interactions between metal particles have been published in previous studies.
This study investigates the optical properties in a medium composed of sub-skin-depth metal arrays through three-dimensional (3D) simulation. We analyzed the light intensity distribution in the metal plate medium with a thickness less than the skin depth. In addition, the characteristics of light passing through the metal cylinder array medium were comparatively analyzed with those of the metal plate. The validity of the simulation results was confirmed by comparing them with the results of previous studies that analyzed space and mesh size for the plate structure. Furthermore, in this study, we analyzed the beam characteristics in a cylindrical metal array structure, which is a two-dimensional isotropic medium structure (with respect to two mutually perpendicular axes). We also discuss the results for the spherical metal array, which is a three-dimensional isotropic structure.
The metal plate and cylinder analyzed in this study were made of Au. The skin depth of Au is 25 nm, and the relative permittivity is
The simulation analysis area and mesh size are directly related to the computation time. The computation time decreases as the mesh size increases. However, if the mesh size is larger than the appropriate size, the nano effect may not be included in the calculation result. Therefore, determining the optimum mesh size at an appropriate level is very important in nano-optical research. In this study, considering the analysis time, the simulation space was set to 1.0 μm × 1.0 μm × 2.2 μm, and the FDTD simulation mesh spacing was set to 5 nm in order to include the nanostructure effect in the simulation results. In addition, boundary conditions were set such that all electric and magnetic fields reaching the simulation interface were absorbed. Even when light propagates through empty space, it diverges and the intensity is reduced. In the simulation, absorption at domain boundaries reduces the intensity measured by the detector.
The graph in Fig. 1 shows the intensity measured at the output plane
The thickness of the nano-sized metal platesand the gap between them were 20 nm and 30 nm, respectively. The medium consists of 21 metal plates aligned in the
Figure 2 illustrates the simulated intensity distribution in the
The field intensity distribution in the
Figure 4 shows the
Also, upon comparing the input and output distributions, i.e., the black dotted line and the green solid line, it can be observed that the widths of the two distributions are similar. Considering that light spreads as it passes through empty space, as shown in Fig. 1, it can be inferred that there is almost no beam spread even after the beam passes through the medium. This is because, as demonstrated in Fig. 2, the spread is minimal due to the focusing phenomenon, in which light is collected while passing through the metal plate medium, was minimal. By utilizing the focusing phenomenon, the diffraction of light, which is responsible for the image blur in imaging optical systems, can be controlled. The resolution of an image is limited by the diffraction of the optical system, which is commonly known as the diffraction limit. However, if this limit can be overcome, it has the potential to significantly improve image resolution and play a crucial role in microstructure analysis.
Let us consider a case where light is incident at +45 degrees with respect to the horizontal direction. Refracted light at the interface between the metal plate and the air must travel upwards above the horizontal line after being refracted according to Snell's law. However, as shown in Fig. 5, it proceeds below the horizontal line after refraction. That is, it was negatively refracted as it passed through the metal plate. The focusing phenomenon in Fig. 2 is explained by negative refraction, i.e., light traveling upward is refracted downward at the air-medium interface. On the other hand, light traveling downward is refracted upward and focused with in the medium.
The amplitude of field
In this model, the field induced on each metal plate interacts only with the field of its adjacent plate, and the coupling coefficient is
The cylinder-shaped array elements (Au) analyzed in this study are lined up along the
Figure 7 shows the distribution of the Pointing
In Fig. 8(a), the electric field intensity distribution in the
As compared to a medium with a plate structure, light propagates differently in a cylinder-shaped medium. Figure 8(b) and (c) show the cross-sectional structures of the metal plate medium and the metal cylinder medium, respectively. The metal plate medium in Fig. 8(b) has a structure in which metal plates and air layers of a certain thickness are alternately arranged periodically. Since it is a closed structure in the longitudinal direction, only interaction with adjacent plates is possible. On the other hand, the cylinder medium has a periodic structure in both the lateral and longitudinal directions as shown in Fig. 8(c), and there is no blockage. Therefore, multiple interactions are possible in the lateral, longitudinal, and diagonal directions in the cylinder structure. This difference in structure causes a difference in the light intensity distribution between the plate and cylinder structures.
The amplitude of field
The second term in the equation above consists of nine items. The coefficient
Figure 9(a) shows the distribution of the
The birefringence observed in previous studies[20, 21, 22] is due to phase retardation caused by asymmetric structures. However, the beam splitting observed in this study is believed to be a multiple interference phenomenon resulting from the interaction between nano structures. This phenomenon does not occur in plate structures, where the space is closed and multiple interactions are subtracted. On the other hand, the light distribution for the spherical 3D array medium capable of multiple interactions was found to be very similar to that of the cylinder medium.
In this study, 3D simulations were used to investigate the light intensity distribution in sub-skin-depth metal arrays, optical properties of metal plate and cylinder array mediawere analyzed. Light incident perpendicular to the medium boundary was focused in all media, with light transmittance of 0.197 and 0.292 for plate and cylinder media, respectively. The light transmittance, ratio of output intensity to input, of the cylinder medium was 48.0% higher than that of the plate medium. The cylinder structure showed diffraction, similar to a diffraction grating, but without a decrease in transmittance due to the narrow tunnel. Further research is needed to understand the role of multiple interactions in increasing light transmittance. In all media analyzed, negative refraction occurred when light was incident obliquely on the interface. The cylinder medium also showed beam splitting due to multiple interactions of the metal structures. The optical characteristics on the
Optical isotropy is a crucial property that widens the usability of a medium by giving the same optical result regardless of the incident angle of light. Negative refraction, which was earlier observed in plates, formed a one-dimensional interaction barrier. In contrast, the cylinder structure analyzed in this study provides a two-dimensional isotropic medium with respect to two mutually perpendicular axes, while the spherical metal array structure can ensure 3D optical isotropy. Complete 3D optical isotropy would require random spacing of the materials constituting the medium.