Talbot effect
At smaller regular fractions of the Talbot length, sub-images can also be observed.
At one quarter of the Talbot length, the self-image is halved in size, and appears with half the period of the grating (thus twice as many images are seen).
At one eighth of the Talbot length, the period and size of the images is halved again, and so forth creating a fractal pattern of sub images with ever-decreasing size, often referred to as a Talbot carpet.
[2] Talbot cavities are used for coherent beam combination of laser sets.
[4] In this case the exact expression derived by Lord Rayleigh should be used: The number of Fresnel zones
[5] This result is obtained via exact evaluation of Fresnel-Kirchhoff integral in the near field at distance
[6] Due to the quantum mechanical wave nature of particles, diffraction effects have also been observed with atoms—effects which are similar to those in the case of light.
Chapman et al. carried out an experiment in which a collimated beam of sodium atoms was passed through two diffraction gratings (the second used as a mask) to observe the Talbot effect and measure the Talbot length.
[7] The beam had a mean velocity of 1000 m/s corresponding to a de Broglie wavelength of
Their experiment was performed with 200 and 300 nm gratings which yielded Talbot lengths of 4.7 and 10.6 mm respectively.
The nonlinear Talbot effect results from self-imaging of the generated periodic intensity pattern at the output surface of the periodically poled LiTaO3 crystal.
Both integer and fractional nonlinear Talbot effects were investigated.
, nonlinear Talbot effect of rogue waves is observed numerically.
In the experiment, the group observed that higher frequency periodic patterns at the fractional Talbot distance disappear.
Further increase in the wave steepness lead to deviations from the established nonlinear theory, unlike in the periodic revival that occurs in the linear and nonlinear regime, in highly nonlinear regimes the wave crests exhibit self acceleration, followed by self deceleration at half the Talbot distance, thus completing a smooth transition of the periodic pulse train by half a period.
[10] The optical Talbot effect can be used in imaging applications to overcome the diffraction limit (e.g. in structured illumination fluorescence microscopy).
[11] Moreover, its capacity to generate very fine patterns is also a powerful tool in Talbot lithography.
[13] In experimental fluid dynamics, the Talbot effect has been implemented in Talbot interferometry to measure displacements [14][15] and temperature,[16][17] and deployed with laser-induced fluorescence to reconstruct free surfaces in 3D,[18] and measure velocity.
