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This equation, Bragg's law, describes the condition on θ for constructive interference. [12] A map of the intensities of the scattered waves as a function of their angle is called a diffraction pattern. Strong intensities known as Bragg peaks are obtained in the diffraction pattern when the scattering angles satisfy Bragg condition.
Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil.
The dynamical theory of diffraction considers the wave field in the periodic potential of the crystal and takes into account all multiple scattering effects. Unlike the kinematic theory of diffraction which describes the approximate position of Bragg or Laue diffraction peaks in reciprocal space , dynamical theory corrects for refraction, shape ...
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions , =, …,.Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction).
When the incident light beam is at Bragg angle, a diffraction pattern emerges where an order of diffracted beam occurs at each angle θ that satisfies: [3] = Here, m = ..., −2, −1, 0, +1, +2, ... is the order of diffraction, λ is the wavelength of light in vacuum, and Λ is the wavelength of the sound. [4]
A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror .
Multiple-scattering effects of light scattering by particles are treated by radiative transfer techniques (see, e.g. atmospheric radiative transfer codes). The relative size of a scattering particle is defined by its size parameter x, which is the ratio of its characteristic dimension to its wavelength:
As opposed to crystallographic scattering experiments, where the scatterer or "target" has very distinct order, which leads to well defined patterns (presenting Bragg peaks for example), the stochastic nature of polymer configurations and deformations (especially in a solution), gives rise to quite different results.