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Download as PDF; Printable version; ... This article summarizes equations used in optics, including geometric optics, physical optics, ... Springer. pp. 12 ...
Fourier optics begins with the homogeneous, scalar wave equation (valid in source-free regions): (,) = where is the speed of light and u(r,t) is a real-valued Cartesian component of an electromagnetic wave propagating through a free space (e.g., u(r, t) = E i (r, t) for i = x, y, or z where E i is the i-axis component of an electric field E in the Cartesian coordinate system).
To constrain the solution to a set of unique values, a technique involving multi-spectral analysis can be used. In the simplest case, this entails depositing the film on two different substrates and then simultaneously analyzing the results using the Forouhi–Bloomer dispersion equations.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
The two-dimensional analogue of the vibrating string is the vibrating membrane, with the edges clamped to be motionless. The Helmholtz equation was solved for many basic shapes in the 19th century: the rectangular membrane by Siméon Denis Poisson in 1829, the equilateral triangle by Gabriel Lamé in 1852, and the circular membrane by Alfred Clebsch in 1862.
Rejecting Descartes' solution, Pierre de Fermat arrived at the same solution based solely on his principle of least time. Descartes assumed the speed of light was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of ...
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum.Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light guides, and liquid waveguides.
This is the Fresnel diffraction integral; it means that, if the Fresnel approximation is valid, the propagating field is a spherical wave, originating at the aperture and moving along z. The integral modulates the amplitude and phase of the spherical wave. Analytical solution of this expression is still only possible in rare cases.