11/7/2023 0 Comments Metal reflection graphIn short, the wider the computational domain relative to the wavelengths in the materials above and below, the more diffraction orders can be present (the number of diffraction orders varies with the incident angle). The conditions under which higher-order diffraction appears and the appropriate modeling procedure is presented in depth in the example of a plasmonic wire grating, so let’s not go into it at length here. There can be multiple diffraction orders present, depending on the ratio of wavelength to domain width, refractive index, and incident angles. If we are studying a range of incident angles, we must make sure to compute all of the diffraction orders present at the limits of the angular sweep. The software computes the appropriate number of ports based on the domain width, material properties, and specified incident angle. To properly compute the reflection and transmission, we need to add several diffraction order ports. In other words, light can be reflected and transmitted into several different directions. However, if spacing is large enough, then we can have higher-order diffraction. We can still apply the same domain properties and all of the same boundary conditions. Clearly, we now need to consider a larger unit cell that considers a single ripple.Ī surface with periodic variations reflects and transmits light into several different diffraction orders. Let’s now make things a little bit more complicated and introduce a periodic structural variation: a sinusoidal ripple. Adding Complexity: A Surface with Periodic Variations The transmittance, reflectance, and absorbance of 550-nm light at various angles of incidence. The transmittance, reflectance, and absorbance of light normally incident on a flat glass surface with a metal coating as a function of wavelength. If these do not add up to one, then we must carefully check our model setup. The sample results below show the transmitted, reflected, and absorbed light as well as their total - which should always add up to one. A simple rule of thumb is to place the Port boundary conditions at least half a wavelength away from the material interfaces and to check if making the domain larger alters the results. In the most general cases, it is difficult to determine how far the evanescent field extends. Any evanescent component of the field that reaches the Port boundary condition is artificially reflected, so we must place the port boundary far enough away from the material interfaces. The reason for this has to do with the Port boundary conditions, which can only consider the propagating component of the electromagnetic field. This distance must be large enough such that any evanescent field drops off to approximately zero within the modeling domain. If we are interested in computing incident light at off-normal incident angles, then we also have to concern ourselves with the height of the modeling domain - the distance between the material interfaces and the Port boundary conditions. The computational model that calculates the optical properties of a metal film on glass. We can integrate the losses within the metal layer to compute the absorbance within the gold layer. The Port boundary condition at the top launches a plane wave at a specified angle of incidence and computes the reflected light, while the one at the bottom calculates the transmitted light. The model includes Floquet periodic boundary conditions on the left and right sides of the modeling domain and a Port boundary condition at the top and bottom. Light incident on a metal coating on top of a glass substrate is reflected, transmitted, and absorbed. This type of index requires that we manually adjust the mesh size based on the minimum wavelength in each material as well as the skin depth, as described in a previous blog post. This computational model is based on the Fresnel equation example, one of the verification models in the Application Gallery, but is modified to include a layer of gold with a wavelength-dependent refractive index. In addition, it can be modeled quite simply in the COMSOL Multiphysics® software by considering a small two-dimensional unit cell that has a width much smaller than the wavelength. Such a model exhibits negligible structural variation in the plane of glass. Starting Simple: An Optically Flat Surfaceīefore we get to the rough surface, let’s start with something simple: a thin uniform layer of gold coating on top of optically flat glass, as shown in the image below. In this blog post, we will introduce and develop a computational model for this situation. The dielectric surface and the metal coating also often have some random variations in height and thickness. Sometimes, we add a metal coating, such as gold, which alters the transmittance and reflectance as well as leads to some absorption of light. Whenever light is incident on a dielectric material, like glass, part of the light is transmitted while another part is reflected.
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