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Materials for Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
Surface plasmon waves are electromagnetic waves propagating at optical frequencies on an interface between a metal, typically gold or silver, and a dielectric. They are evanescent waves: their field intensity is concentrated in a very thin layer (a few tens of nanometers) across the interface. They are characterized by a propagation constant ksp. The propagation or wave vector of a wave is a vector quantity that defines the magnitude and direction of the wave; its magnitude is 2π/λ. For a flat interface, the propagation vector of surface plasmon waves is given by ksp=k0εmεdεm+εd
Basics of holography
Published in Tomoyoshi Shimobaba, Tomoyoshi Ito, Computer Holography, 2019
Tomoyoshi Shimobaba, Tomoyoshi Ito
where x=(x,y) represents the position vector, and k is the wave vector. The wave vector is a parameter that determines the propagation direction of the wave. The wave vector k is defined as () k=(kx,ky)=(kcosθ,ksinθ).
Light Propagation in Anisotropic Media
Published in Myeongkyu Lee, Optics for Materials Scientists, 2019
Here k is the magnitude of the wave vector k and kx, ky and kz are its components along the x, y, and z directions, respectively. For a given direction of propagation, two solutions exist. One is a sphere and the other, an ellipsoid of revolution. The intersection of the k-surfaces with the y–z plane is drawn in Figure 6.5a. The two surfaces touch at two points on the z axis, which is the only optic axis. We can assume that the k vector lies in the y–z plane without loss of generality due to symmetry about the z axis (optic axis). As ω/c is a common factor, Figure 6.5a is redrawn without it in Figure 6.5b. This construction, now representing n-surfaces, is more convenient for finding the indices of refraction. For a given k direction, the refractive index is determined by finding the intersection of k with the n-surfaces. In Figure 6.5b, the wave vector k intersects the n-surfaces at two points. The distances from the origin to these points are the refractive indices of the wave. If the wave is ordinarily polarized, it has a refractive index of no. When the wave is extraordinarily polarized, the refractive index n(θ) depends on θ, as given in eq 6.9. Although the indices of refraction in a uniaxial crystal can also be found by the procedure described previously (see Fig. 6.4), the construction shown in Figure 6.5b provides a more convenient method. If the wave propagates along the y direction, it has a refractive index of either no or ne, depending on its polarization direction. When the propagation direction is parallel to the optic axis, the wave has an index of no because its polarization directions are always perpendicular to the optic axis. In anisotropic media, the polarization direction of a wave is customarily defined by the direction of its displacement vector D because D is perpendicular to the wave vector k. Since D is always parallel to the electric field E in isotropic media, E is predominantly used to indicate the polarization state of light in air.
Investigation of photonic band gap properties of one-dimensional magnetized plasma spherical photonic crystals
Published in Waves in Random and Complex Media, 2023
Tian-Qi Zhu, Jia-Tao Zhang, Hai-Feng Zhang
Due to the special geometric properties of the sphere, inspired by the idea of the micro-element method and the definition of the incidence angle under the cylindrical photonic crystal [27], the TE waves and TM waves are defined by taking the profile of the spherical wave and 1-D MPSPCs parallel to the wave propagation direction, as shown in Figure 2. For this plane, the electric field E is perpendicular to the plane, the magnetic field H is parallel to the plane, and the wave vector k indicates the propagation direction. Therefore, the electric field E takes the form of in the TE waves and the magnetic field H takes the form of . By analogy, in the TM waves, the electric field E is denoted as and the magnetic field H is denoted as . 1-D MPSPCs and the spherical waves demonstrably have an intersection point. From the intersection point, the tangents to 1-D MPSPCs and the spherical waves are made respectively, and the angle between the two tangents is the angle of incidence, as shown in Figure 2. The electromagnetic wave propagates from the yoz plane at an angle of incidence α. It is prescribed that under the TE polarization the wave vector k is always perpendicular to the magnetic field H. Equally, under TM polarization the electric field E invariably remains perpendicular to the wave vector k.