<Dd> z T = λ 1 − 1 − λ 2 a 2 . (\ displaystyle z_ (T) = (\ frac (\ lambda) (1 - (\ sqrt (1 - (\ frac (\ lambda ^ (2)) (a ^ (2))))))).) </Dd> <P> 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 . The beam had a mean velocity of 1000 m / s corresponding to a de Broglie wavelength of λ d B (\ displaystyle \ lambda _ (dB)) = 0.017 nm . Their experiment was performed with 200 and 300 nm gratings which yielded Talbot lengths of 4.7 and 10.6 mm respectively . This showed that for an atomic beam of constant velocity, by using λ d B (\ displaystyle \ lambda _ (dB)), the atomic Talbot length can be found in the same manner . </P> <P> The nonlinear Talbot effect results from self - imaging of the generated periodic intensity pattern at the output surface of the periodically poled LiTaO crystal . Both integer and fractional nonlinear Talbot effects were investigated . </P> <P> In cubic nonlinear Schrödinger's equation i ∂ ψ ∂ z + 1 2 ∂ 2 ψ ∂ x 2 + ψ 2 ψ = 0 (\ displaystyle i (\ frac (\ partial \ psi) (\ partial z)) + (\ frac (1) (2)) (\ frac (\ partial ^ (2) \ psi) (\ partial x ^ (2))) + \ psi ^ (2) \ psi = 0), nonlinear Talbot effect of rogue waves is observed numerically . </P>

On copying diffraction gratings and on some phenomenon connected therewith