![]() SPP focusing at the desired focal spot ( f = 4λ SPP) calculated using eq 19 for the hole width d g =Ġ.0008 + 0.074i ( n s = 7.4 × 10 16 m –2) on both sides. (c) Surface plot of the intensity pattern on the 2D-sheet demonstrating The extractedįit parameter σ f in this case is 0.3791 + 2.7346i. Substrate (ε = 2.25) with vacuum on top λ 0 = 10 μm and λ SPP ≈ 227 nm. SurfaceĬonductivity on the two sides of the gap is assumed to be σ 0 = 0 + 0.074i for the model. The inset shows the model for calibration. (b) Calculated and fit curves of the reflection and transmissionĬoefficients of SPPs as a function of gap width ( d g). Fresnel Refraction and Diffraction of Surface Plasmon Polaritons in Two-Dimensional Conducting Sheets The propagation of surface plasmon polaritons (SPPs) along two-dimensional (2D) materials, such as graphene, is a complex phenomenon linking the microscale electronic properties to macroscale optical properties. (a) Schematic of the in-plane SPP diffraction setup using At the interface between two media, part of the light is reflected, and the other part passes through the interface with a modified propagation direction: this is called refraction. The presented formulation could facilitate the transfer of many existing plane wave based optical phenomenon to a surface wave based integrated optoelectronic devices. We present simple mathematical models to calculate the scattered electromagnetic fields of SPP waves based on Fresnel equations. We demonstrate that the propagation of surface waves can be manipulated in-plane using reflection, refraction, diffraction, and also generalized refraction laws analogous to plane waves. If the crest and trough are not of the same magnitude of displacement the destructive interference will not be total. Such a direct resemblance enables prediction, design, and calculation of SPP propagation through advanced geometries using fundamental laws of optics. Refraction, Di raction and Interference Interference Interference can be constructive or destructive - matching displacements are constructive, opposite are destructive. Here, we demonstrate that under a proper design of macroscopic conductivity profile, the propagation characteristics of SPPs in 2D materials can be made analogous to the propagation of plane waves in homogeneous layers with minimal out-of-plane scattering. Types of Refraction Diffuse refraction of light - It scatters light in a variety of directions. The formula is nc/v, where n is the index of refraction, c the vacuum velocity, and v the medium velocity. A screen at a given distance away will show the. The Index of Refraction describes how light in a medium is divided by light in a vacuum. Complex geometries increase the complexity of understanding the nature and performance of optoelectronic devices based on surface wave propagation. When light travels through a double slit, the waves diffract and start to interfere with each other. ![]() The propagation of surface plasmon polaritons (SPPs) along two-dimensional (2D) materials, such as graphene, is a complex phenomenon linking the microscale electronic properties to macroscale optical properties.
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