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In an optical fiber, the material dispersion coefficient, M(λ), characterizes the amount of pulse broadening by material dispersion per unit length of fiber and per unit of spectral width. It is usually expressed in picoseconds per ( nanometre · kilometre ).
In a dispersive prism, material dispersion (a wavelength-dependent refractive index) causes different colors to refract at different angles, splitting white light into a spectrum. A compact fluorescent lamp seen through an Amici prism. Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. [1]
A dispersion is a system in which distributed particles of one material are dispersed in a continuous phase of another material. The two phases may be in the same or different states of matter . Dispersions are classified in a number of different ways, including how large the particles are in relation to the particles of the continuous phase ...
A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.
The dispersion relation of phonons is also non-trivial and important, being directly related to the acoustic and thermal properties of a material. For most systems, the phonons can be categorized into two main types: those whose bands become zero at the center of the Brillouin zone are called acoustic phonons , since they correspond to ...
If the matrix of diffusion coefficients is diagonal, then this system of equations is just a collection of decoupled Fick's equations for various components. Assume that diffusion is non-diagonal, for example, D 12 ≠ 0 {\displaystyle D_{12}\neq 0} , and consider the state with c 2 = ⋯ = c n = 0 {\displaystyle c_{2}=\cdots =c_{n}=0} .
In optics and lens design, the Abbe number, also known as the Vd-number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of Vd indicating low dispersion.