In nonlinear optics, B-Integral is a measure of the nonlinear optics phase shift of light. It calculates the exponential growth of the least stable spatial frequency in a laser beam, and is the numerical equivalent of the nonlinear phase shift along the laser system's optical axis.
In a multipass laser system as a cumulative measure of the nonlinear interaction,[1] this integral is given by:
where is the optical intensity along the beam axis, the position in beam direction, and the nonlinear index quantifying the Kerr nonlinearity. As is the nonlinear change in the refractive index, one easily recognizes the B integral to be the total on-axis nonlinear phase shift accumulated in a passage through the device.
The B integral is frequently used in the context of ultrafast amplifiers, e.g. for optical components such as the Pockels cell of a regenerative amplifier.
^"B Integral". Encyclopedia of Laser Physics and Technology.
In nonlinear optics, B-Integral is a measure of the nonlinear optics phase shift of light. It calculates the exponential growth of the least stable spatial...
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process...
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...
improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context...
calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integral of the form ∫ a ( x ) b ( x ) f ( x , t ) d...
an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over A. If A, B are fields,...
mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear...
as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It...
In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, an equality ab = ac implies b = c. "Integral domain"...
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that...
Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function...
several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of...
calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of...
antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative...
integral version of the product rule of differentiation; it is indeed derived using the product rule. The integration by parts formula states: ∫ a b u...
The integral symbol: ∫ (Unicode), ∫ {\displaystyle \displaystyle \int } (LaTeX) is used to denote integrals and antiderivatives in mathematics, especially...
mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an...
mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may...
to compute an approximate solution to a definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} to a given degree of accuracy. If f(x)...
Integral theory as developed by Ken Wilber is a synthetic metatheory aiming to unify a broad spectrum of Western theories and models and Eastern meditative...
complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related...
the limit of integrals of simple functions. Let ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} be a measure space, and B {\displaystyle B} be a Banach...
(Darboux) integrals, which exist for any bounded real-valued function f {\displaystyle f} on the interval [ a , b ] . {\displaystyle [a,b].} The Darboux...
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...
classical Riemann integral of a function f : [ a , b ] → R {\displaystyle f:[a,b]\to \mathbb {R} } can be defined by the relation ∫ a b f ( x ) d x = lim...
Z+Z+Z/2Z if b=0, and Z+Z if b=1. They are homeomorphic to the Klein bottle bundles {b; (o2, 1);}. {b; (n2, 1); (2, 1), (2, 1)} (bintegral) For b=−1 this...
calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the...
Global Information
