|
Rayleigh Length
In optics and especially laser science, the Rayleigh length or Rayleigh range, z_\mathrm, is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. A related parameter is the confocal parameter, ''b'', which is twice the Rayleigh length. The Rayleigh length is particularly important when beams are modeled as Gaussian beams. Explanation For a Gaussian beam propagating in free space along the \hat axis with wave number k = 2\pi/\lambda, the Rayleigh length is given by :z_\mathrm = \frac = \frac k w_0^2 where \lambda is the wavelength (the vacuum wavelength divided by n, the index of refraction) and w_0 is the beam waist, the radial size of the beam at its narrowest point. This equation and those that follow assume that the waist is not extraordinarily small; w_0 \ge 2\lambda/\pi. The radius of the beam at a distance z from the waist is :w(z) = w_0 \, \sqrt . The minimum value of w(z) occurs at w(0) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Diameter
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in common use: D4σ, 10/90 or 20/80 knife-edge, 1/e2, FWHM, and D86. The beam width can be measured in units of length at a particular plane perpendicular to the beam axis, but it can also refer to the angular width, which is the angle subtended by the beam at the source. The angular width is also called the beam divergence. Beam diameter is usually used to characterize electromagnetic beams in the optical regime, and occasionally in the microwave regime, that is, cases in which the aperture from which the beam emerges is very large with respect to the wavelength. Beam diameter usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Strutt, 4th Baron Rayleigh
Robert John Strutt, 4th Baron Rayleigh (28 August 1875 – 13 December 1947) was a British peer and physicist. He discovered "active nitrogen" and was the first to distinguish the glow of the night sky. Early life and education Strutt was born at Terling Place, the family home near Witham, Essex, the eldest son of John William Strutt, 3rd Baron Rayleigh and his wife Evelyn Georgiana Mary (). He was thus a nephew of Arthur Balfour and of Eleanor Mildred Sidgwick. He was educated at Eton College and Trinity College, Cambridge, where he initially read mathematics, but changed after two terms to Natural Sciences.A. C. Egerton, 'Strutt, Robert John, fourth Baron Rayleigh (1875–1947)', rev. Isobel Falconer He became a research student in physics at the Cavendish Laboratory under J. J. Thomson, whose biography he subsequently wrote. His work at this time was on discharge of electricity through gases, including early work on x-rays and electrons. He wrote one of the first books o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Strutt, 3rd Baron Rayleigh
John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Among many honors, he received the 1904 Nobel Prize in Physics "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies." He served as president of the Royal Society from 1905 to 1908 and as chancellor of the University of Cambridge from 1908 to 1919. Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as " Rayleigh scattering", which notably explains why the sky is blue. He studied and described transverse surface waves in solids, now known as " Rayleigh waves". He contributed extensively to fluid dynamics, with concepts such as the Rayleigh number (a dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Wave Equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field or the magnetic field , takes the form: \begin \left(v_^2\nabla^2 - \frac \right) \mathbf &= \mathbf \\ \left(v_^2\nabla^2 - \frac \right) \mathbf &= \mathbf \end where v_ = \frac is the speed of light (i.e. phase velocity) in a medium with permeability , and permittivity , and is the Laplace operator. In a vacuum, , a fundamental physical constant. The electromagnetic wave equation derives from Maxwell's equations. In most older literature, is called the ''magnetic flux density'' or ''magnetic induction''. The following equations\begin \nabla \cdot \mathbf &= 0\\ \nabla \cdot \mathbf &= 0 \endpredicate that any electromagnetic wave must be a transverse wave, whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric " bell curve" shape. The parameter is the height of the curve's peak, is the position of the center of the peak, and (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value and variance . In this case, the Gaussian is of the form g(x) = \frac \exp\left( -\frac \frac \right). Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Parameter Product
In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist). The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot. A Gaussian beam has the lowest possible BPP, \lambda/\pi, where \lambda is the wavelength of the light. The ratio of the BPP of an actual beam to that of an ideal Gaussian beam at the same wavelength is denoted M2 ("M squared"). This parameter is a wavelength-independent measure of beam quality. The quality of a beam is important for many applications. In fiber-optic communications beams with an M2 close to 1 are required for coupling to single-mode optical fiber. Laser machine shops care a lot about the M2 parameter of their lasers because the beams will focus to an area that is M4 times larger than that of a Gaussian beam with the same wavelength and D4σ waist width; in other words, the fluence scales as 1/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Divergence
In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Practically speaking, however, the far field can commence physically close to the radiating aperture, depending on aperture diameter and the operating wavelength. Beam divergence is often used to characterize electromagnetic beams in the optical regime, for cases in which the aperture from which the beam emerges is very large with respect to the wavelength. However, it is also used in the radio frequency (RF) band for cases in which the antenna is very large relative to a wavelength. Beam divergence usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam divergence must be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Optics
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory. Principle ''Physical optics'' is also the name of an approximation commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray optics and not that it is an exact physical theory. This approximation consists of using ray optics to estimate the field on a surface and then integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born approxima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraxial Approximation
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). A paraxial ray is a ray which makes a small angle (''θ'') to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for ''θ'' in radians) for calculation of the ray's path, namely: : \sin \theta \approx \theta,\quad \tan \theta \approx \theta \quad \text\quad\cos \theta \approx 1. The paraxial approximation is used in Gaussian optics and ''first-order'' ray tracing. Ray transfer matrix analysis is one method that uses the approximation. In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is : \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
