- Wedge Mode Propagation Characteristics of Triangular–shaped Surface Plasmon Waveguide. - Abstract: In this paper, we investigate wedge mode propagation characteristics of a triangular- shaped surface plasmon waveguide. - This structure consists of a thin metal layer deposited onto the surface of a triangular–shaped silicon waveguide which could be fabricated on a silicon–on–. - These elements are embedded in a dielectric medium (such as air) to form metal–dielectric interface and the surface plasmon wave propagates at the wedge of metal layer. - The influence of structural parameters such as metal layer, height of silicon waveguide and effect of fabrication on the wedge mode propagation characteristics of the waveguide is analyzed by using numerical simulation.. - Keywords: V–shaped waveguide, Surface plasmon polariton, plasmonic waveguide.. - Surface Plasmon Polariton (SPP) is surface electromagnetic wave which propagates at the metal–. - It is the result of the strong coupling between light and collective oscillation of free electron at a metal surface. - In recent decades, the study on the theories and applications of SPP is growing fast and separated in a new field – Plasmonics. - As a surface wave, the propagation of SPP is highly sensitive to the roughness and the electromagnetic field is confined in the space near the interface of the medium. - Therefore, the propagation characteristics of SPP will be changed. - The former two nanophotonic waveguides, which utilize nano- structures with ultra-high index contrast, are limited due to the classical optical diffraction phenomena.. - Among these, the wedge plasmon polariton (WPP) waveguides are the most prominent about the possibility of electromagnetic field confinement. - Model of the surface plasmon polariton waveguide. - Structure of surface plasmon polariton waveguide is shown in Fig. - A noble metal layer is deposited onto the surface of the waveguide to form metal–dielectric interface. - The silicon waveguide forms a mold to deposit a metal layer in an inverted V-like shape. - The interface between the V-shaped metal layer and air medium is used for guiding surface plasmon wave. - The surface plasmon polariton (WPP) mode propagates on the top wedge of structure. - We will evaluate the dependence of propagation characteristics on the change of structural parameters such as deposited metal layer and dimensions of silicon waveguide.. - Schematic of triangular-shaped plasmonic waveguide used for simulation: (a) a 3D view of the waveguide and (b) cross-section of the waveguide.. - (1) with the effective refractive index and skin depth. - On a metal tip, WPP is the coupling mode formed by two SPP waves propagating toward the tip on the two opposite faces of the wedge [14]. - h 1 µm Height of waveguide. - n Si 3.4757 Refractive index of silicon. - n SiO2 1.4957 Refractive index of silicon dioxide layer n Ag i Complex refractive index of Silver n Au i Complex refractive index of Gold. - t nm Thickness of metal layer. - By finite element method, we can find the propagation constant of WPP mode, that satisfies eigenvalue equations. - The model is three – dimension with the calculation size is 4x4x10 µm 3 . - Two boundary ports are applied on the back and front face of the waveguide to analyze modes that can propagate in structure. - Firstly, we investigate the influence of metal layer on the propagation of plasmon wave on the waveguide. - The metal layer can be deposited onto triangular silicon waveguide by sputtering technique. - The thickness is studied in each step of 10 nm in the range from 10nm to 200 nm. - To ensure that the thickness of metal film is the same throughout the structure, the wedge of metal is filleted with a radius equal to the thickness of the metal layer.. - Distribution of normalized electric field in the cross-section of waveguide at various thicknesses of silver and gold layer: (a)-(b) for Ag with the thicknesses of 10 nm and 200nm respectively and (c)-(d) for Au with the thicknesses of 10 nm and 200nm respectively. - For both metals, the maximum electric field values are almost the same. - When the thickness of metal layer increases, the maximum electric field values also increase. - The electric field distributes in air medium, and concentrates mainly on the area round the wedge of the waveguide. - This electric field reaches the maximum value at metal surface and declines rapidly when it is away from the surface. - Figure 2 (e) describes more clearly about the sharp decline of the field along (BB’) cutline (shown in Fig. - The field falls off exponentially in air, the intersection of these curves with 1/e line giving a quantitative estimation of the confinement of electromagnetic energy. - In the case of very thin metal layer (10nm), the field falls off to 1/e at a distance of only a few tens of nanometers. - Otherwise, in the case of thick metal film (200nm), the mode size increases to about 500 nm. - Thus, the confinement of waveguide mode does not depend on the nature of metal, but depends strongly on the thickness of metal layer.. - The propagation characteristics of the waveguide at various metal thicknesses are shown in Fig. - When the metal thickness increases, the effective mode index decreases and the propagation length increases. - Both these quantities tend asymptotically to a value corresponding to the infinite thickness.. - The mode area of gold and silver are almost the same and increase strongly with the thickness. - With the same structural parameters, the attenuation using gold is stronger than using silver about two times, while other characteristics are almost the same. - 3 (b), at the thickness t = 20 nm, the propagation length has a minimum value. - It might be due to the coupling of WPP with a high order mode in silicon waveguide. - Increasing the thickness of metal layer, the coupling decreases and will be negligible at thickness larger than 150nm.. - Propagation characteristics of WPP mode at various thicknesses of metal (a)-(c) and the shape of mode area (d).. - (a)-(c) are distributions of electric field, when we fillet the top corner of silicon waveguide. - (d)-(f) are propagation chracteristics of waveguide at various thicknesses of metal, in which R = t (blue line) and R = 200 nm (red line) are for the plasmonic waveguide with and without the silicon waveguide filleted at the top wedge. - In the above study, we have filleted the wedge of metal layer with radius equal the value of metal thickness. - It leads to the changing of wedge mode area that concentrates the electromagnetic energy, thus the propagation of WPP mode is changed. - To keep the wedge radius of metal constant, we have to fillet the top wedge corner of silicon waveguide with the appropriate value of radius. - Figure 4 shows the simulation results with the radius of metal wedge is always 200nm. - For the homogenization of metal layer on the entire structure, we set the filleted radius of silicon waveguide is (200 – t) nm with respective to the thickness of metal layer t. - If we increase the thickness of metal, the maximum value of field will be increased, which is the same as the wedge of silicon waveguide not filled. - However, the propagation properties in this case are slightly different (Figs.4 (d)-(f. - For comparison, the propagation mode characteristics of the silicon waveguide without filleting the top wedge corner are also shown in Figs. - The propagation length is no longer a minimum value at 20nm and reaches a maximum value at. - Electromagnetic field of WPP mode distributes on the wedge of waveguide at different heights in two cases t = 60nm (a)-(c) and 200nm (d)-(f).. - the thickness of 60nm. - With the same thickness, the attenuation in structure with the filleted top wedge corner of silicon waveguide is smaller than in the remaining structure. - It may be due to the decreasing of confinement of WPP mode. - This investigation on the filleting effect is a guideline for predicting the operation characteristics of the waveguide when there is variation in fabrication condition.. - The dependence of WPP mode on the height h of triangular cross–section of the waveguide is studied in next section. - In the fabrication using wet–bulk micromachining on SOI wafer, the height of waveguide approximates the thickness of device layer. - So, by choosing SOI wafers having different device layer thicknesses, we can change the height of the waveguide. - Figure 5 displays the distribution of electromagnetic field at various values of h in which the thicknesses of metal layer are 60nm for Figs. - In waveguides with large height (h = 5μm), electromagnetic field concentrates mainly on the wedge of the waveguide. - In waveguides with low height (h ≤ 0.5μm), the field not only distributes on the wedge but also spreads over the surface of substrate.. - The propagation characteristics of waveguide are investigated as a function of h when t = 60nm (red line) and 200nm (blue line).. - The propagation characteristics depending on the height of the waveguide are shown in Fig. - In the case of large metal thickness, when the height increases, the wavenumber (n eff ) and the attenuation (1/L wpp ) increase and they approach to special values when h is more than 2μm. - In the case that the thickness is 60nm, the coupling with high order mode in the silicon waveguide makes the curve fluctuate, but the shape is the same. - Approximately, we can explain that phenomena as follow: the WPP mode is the result of coupling between two SPPs waves that propagate on two sidewalls of the waveguide. - This coupling is like the coupling in a thin metal film with the variation of thickness. - When the height is more than 2μm, the film becomes so thick that the coupling is negligible and only the part nears the wedge contributing to the coupling. - This causes the saturation of wavenumber and propagation length of WPP mode in the waveguide. - When h is too small, the coupling becomes weak and the effective mode index of WPP mode approximates the mode index of SPPs (n spp = 1.0038).. - We have investigated in detail propagation characteristics of the wedge surface plasmon waveguide depending on geometrical parameters and deposited metal. - The investigated results show that the mode confinement and propagation length strongly depend on the thickness of metal layer.. - The mode confinement decreases when the thickness of metal layer increases. - When the height of the waveguide increases, the mode size and propagation length decrease.. - [4] Han, Z., Bozhevolnyi, S.I.: Radiation guiding with surface plasmon polaritons
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