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Talbot-effect

The Talbot-effect is a near field 'self-imaging' effect generic for certain wave equations like the paraxial wave equation and the Schrödinger equation. Any spatial modulation of period  of a plane carrier wave is reproduced after the Talbot-length  zR = 22/.


 


Moreover, starting with a pure phase modulation in a certain plane, after a distance of  zT /4 and 3zT /4 there are planes, in which the field has a pure amplitude modulation in first order.

Therefore, the resulting amplitude grating will be

  • in phase with the original refractive index grating after a propagation by  zT /4 . The resulting wavelength of the pattern in a focusing nonlinear medium is foc = sqrt(4d) .
  • in anti-phase with the original refractive index grating after a propagation by  3zT /4 . The resulting wavelength of the pattern in a defocusing nonlinear medium is def = sqrt(3/4d)
It should be cautioned that the real experimental system has two additional characteristic length scales in addition to the diffractive one given by the Talbot-effect. One is the diffusion length of the atomic motion. This will tend to suppress the instability for small wavelengths. The other is the overal size of the experimental system with is given by the diameter of the input beam.

Literatur:


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