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Optical Cavities: Free-Space Laser Resonators
Published in Chunlei Guo, Subhash Chandra Singh, Handbook of Laser Technology and Applications, 2021
The Rayleigh length is the distance necessary to travel from the beam waist for the spot size to increase by a factor of 2. The confocal parameter b of a Gaussian beam, a commonly used parameter, is twice the Rayleigh range: b=kω02=2πnω02/λ0.
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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
ray tracing amplitude varies slowly compared to the wavelength. ray tracing (1) a high-frequency electromagnetic analysis technique in which the propagation path is modeled by flux lines or "rays." The ray density is proportional to the power density, and frequently, bundles of these rays are called ray tubes. (2) a rendering technique in which the paths of light rays reaching the viewpoint are computed to obtain realistic images. Given a 3-D description of a scene as a collection of surfaces characterized by different optical properties, rays are traced backward from the viewpoint through the image plane until they hit one of the surfaces or go off to infinity. ray transfer matrix real two-by-two matrix governing the transformation of the ray displacement and slope with respect to a fixed axis. Rayleigh criterion a method of distinguishing between rough and smooth surfaces in order to determine whether specular reflection will occur. A surface is considered smooth if the phase difference between waves reflected from the surface is less than ninety degrees. Rayleigh distribution the probability distribution of the magnitude of a complex quantity whose real and imaginary parts are independent Gaussian random variables with zero mean. Frequently used to approximate multipath fading statistics in non-line-of-sight mobile radio systems. Rayleigh length distance over which the spot size of a Gaussian beam increases from its value at the beam waist to a value 2.5 larger; a measure of the waist size of a Gaussian beam, times waist spot size squared divided by wavelength; half of the confocal parameter. Rayleigh noise the envelope of a zero mean, wide-sense stationary, narrowband Gaussian noise process. The probability density function of a sinusoid in narrowband noise is a generalized Rayleigh 2 2 distribution, p(z) = z e-z 2 , z 0. Also known as a Rician distribution. Rayleigh scattering (1) theory for the interaction between light and a medium composed of particles whose size is much smaller than the wavelength. According to it, the scattering cross section is proportional to the fourth power of the wavelength of the scattered light. This explains both the red and blue colors of the sky. (2) an intrinsic effect of glass that contributes to attenuation of the guided optical wave. The effect is due to random localized variations in the molecular structure of the glass which acts as scattering centers. Rayleigh-Ritz procedure a procedure for solving functional equations. See also moment method. Rayleigh-wing scattering of light the scattering of light with no change in central frequency, and with moderate (of the order of 101 1 Hz) broadening of spectrum of the light. Rayleigh-wing scattering occurs when light scatters from anisotropic molecules. RBC See radiation boundary condition.
Lateral shifts and angular deviations of Gaussian optical beams reflected by and transmitted through dielectric blocks: a tutorial review
Published in Journal of Modern Optics, 2019
Stefano De Leo, Gabriel G. Maia
Let us consider a Gaussian beam hitting the left face of the optical system discussed in Section 3. Its electric field is given by where is the electric field's amplitude in the centre of the beam, and is the Gaussian angular distribution, given by In the expression above, is the distribution's waist and the position of its centre, which is the incidence angle of the beam. Note that as becomes greater, the Gaussian function becomes more strongly centred around , taking the beam to the plane wave limit. In order for our analysis of beam shifts to be more approachable, we will consider the paraxial limit, which lies on the path to the plane wave limit, without being as drastic. The paraxial limit considers strongly collimated beams, with , which in turn allows the expansion of the trigonometric functions in the phase of the electric field given by Equation (31) up to second order around : By defining a coordinate system , see Figure 6(b),which is parallel to the incidence direction of the beam, we have that and we can then write Equation (31) as where we have used the paraxial approximation to make the integration limits infinite. This integral is integrable, returning where , being the Rayleigh length, which gives the distance from the point of minimum waist to where the area of the cross section of the beam doubles. Besides, is the Gouy's phase, which describes the phase change of the beam after the point of minimal beam waist, that is, , and defines the diameter of the Gaussian beam, giving the radius where the electric field intensity falls to of its peak value [55].