Mechanism of Diffraction in Classical Physics

Mechanism of Diffraction in Classical Physics
Mechanism of Diffraction in Classical Physics - personal.math.ubc.c

Huygens-Fresnel and the principles of superposition of waves explain how waves propagate in classical physics and how diffraction develops as a result. To visualize how a wave propagates, consider each medium particle transmitted in a wavefront as a point source for a secondary spherical wave. The sum of these secondary waves determines the wave displacement at any subsequent location. Waves can have any amplitude between zero and the sum of their individual amplitudes, because when the waves come together, their sum is governed by both their individual amplitudes and their relative phases. For this reason, diffraction patterns typically consist of a series of maximums and minimums.

Each photon has a wave function, according to the current quantum mechanical understanding of the passage of light through a slit (or slits). The physical medium, including the slit shape, the screen distance, and the initial conditions at which the photon is produced, determines the wave function. The existence of the photon's wave function has been proven by important experiments (GI Taylor performed the first low-intensity double-slit experiment in 1909). The probability distribution is used to construct the diffraction pattern in the quantum technique, and the presence or absence of light and dark bands indicates that the photons are more or less likely to be detected in these regions.

The Huygens-Fresnel principle states that as light passes through slits and boundaries, secondary, point sources of light are formed near or along these obstacles, and the resulting diffraction pattern will be the intensity profile based on the collective interference of all these light sources with different optical paths. The quantum approach bears some striking similarities with this principle.

This is comparable to taking into account constrained regions around slits and boundaries where photons are more likely to originate when calculating the probability distribution in quantum formalism. According to traditional formalism, this distribution is exactly proportional to the density.

The Kirchhoff-Fresnel diffraction equation derived from the wave equation, the Fraunhofer diffraction approximation of the Kirchhoff equation valid for the far field, the Fresnel diffraction approach valid for the near field, and the Feynman path integral formulation are some of the analytical models that allow the calculation of the diffracted field. Most configurations cannot be solved analytically, but finite element and boundary element approaches can produce numerical solutions.

By analyzing how the relative phases of many secondary wave sources fluctuate, and especially where the phase difference is equal to half a cycle and the waves cancel each other out, it is possible to gain a qualitative insight into a large number of diffraction phenomena.

The simplest explanations for diffraction are those in which the problem is reduced to a two-dimensional problem. This is already true only for water waves moving along the ocean surface. If the refracting material lies in one direction for a much longer distance than the wavelength, we can often ignore that direction. In the case of light shining through small circular holes, we must take full account of the three-dimensional aspect of the problem.

Source: Wikipedia

Günceleme: 11/11/2022 14:17

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