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arXiv:1011.3593 · Journal of Modern Optics

Quantum theory of light diffraction

Xiang-Yao Wu, Baijun Zhang, Jinghai Yang, Li-Xin Chi, Xiao-Jing Liu, Yiheng Wu, Qingcai Wang, Yan Wang, Jing-Wu Li, Yi-Qing Guo

Published Oct 15, 2010• 12 citations
arXivHTMLPDF

Abstract

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.

DOI
10.1080/09500340.2010.521593

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At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.
In this paper,the light double-slit diffraction with quantum theory approach is studied.Firstly,the light wave function in slits is calculated,and the diffraction wave function is obtained with Kirchhoff’s law.The diffraction intensity is proportional to the diffraction wave function da party.Futhermore,the intensity formula of light double-slit diffraction is obtained;by comparing the quantum theory calculation results and classical electromagnetic theory calculation results and the experimental date,it is found that the calculate result of quantum theory is in accordance with the experment data,but the classical electromagnetic theory calculation result with the experiment date has certain deviation.So,the quantum theory can explain the light diffraction more precisely.The proposed method can also further study the light of the single slit,many slits and grating diffraction experiment phenomena.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study electronic double-slit diffraction with a quantum mechanical approach and obtain the following results: (1) When the ratio of ( d + a )/ a = n ( n = 1,2,3,…), orders n ,2 n ,3 n ,… are missing in diffraction pattern. (2) When the ratio of ( d + a )/ a ≠ n ( n = 1,2,3,…), there is not missing order in diffraction pattern. (3) The slit thickness c has a large affect on the electronic diffraction pattern, which is a new quantum effect. We believe that all the predictions in our work can be tested by the electronic double slit diffraction experiment.
In this paper, we study the light double-slit diffraction experiment with quantum theory approach. Firstly, we calculate the light wave function in slits by quantum theory of photon. Secondly, we calculate the diffraction wave function with Kirchhoff's law. Thirdly, we give the diffraction intensity of light double-slit diffraction, which is proportional to the square of diffraction wave function. Finally, we compare calculation result of quantum theory and classical electromagnetic theory with the experimental data. We find the quantum calculate result is accordance with the experiment data, and the classical calculation result with certain deviation. So, the quantum theory is more accurately approach for studying light diffraction.
We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.
The phenomena of electron,neutron,atomic and molecular diffraction were researched by many experiments in recent year and these experiments were explained by various theory.In this paper,we study the double-slit diffraction of neutron with an approach of quantum mechanics at frist.We find some new results: When slit width a and slit distance d is the ratio of(a+d)/a=n(n=1,2,3,…),order n,2n,3n,… are missing in diffraction pattern;When the ratio of(a+d)/a≠n(n=1,2,3,…),there isn't missing order in diffraction pattern;The length of slit b only affects the diffraction intensity while the thickness c not only affects the intensity,but also changes the missing order in diffraction patterns.