How is Huygen's Principle similar to Bragg's law of diffraction?
Huygen's principle states that the final wavefront pattern at a later time is the envelop of all the wavelets that passes through an opening. On the other hand, Bragg's law relates to constructive from planes of atoms. How do we relate them?
In the classical work D. Gabor and G. W. Stroke, “The theory of deep holograms,”Proc. R. Soc. London A 304, 275–289 (1968) https://dspace.sunyconnect.suny.edu/bitstream/handle/1951/37074/CEAS--93.pdf?sequence=1 the approach similar to the Huygens Principle is used to develop the theory of volume Bragg holograms. The Gabor-Stroke’s approach seems very powerful. We have used it for the different tasks in several our papers: https://www.researchgate.net/publication/234272572_X-ray_diffraction_on_a_multilayer_structure_modulated_by_surface_acoustic_waves https://www.researchgate.net/publication/320471999_On_Two_Image-Forming_Mechanisms https://www.researchgate.net/publication/238033164_Ultrashort_light_pulse_scattering_by_3D_interference_fringe_structure
Dear Rayshan,
my answer to your interesting question is very simple, since my choice could be reduced to an essential property. In both cases we are dealing with the interaction between a propagating tranversal wave (of a given wavelength ) and an obstacle (of a given size and periodicity). When waves and obstacles have a comparable size, their interference gives origin to a diffraction pattern. This means that a visible wavelength can be diffracted only by an optical grating having the periodicity of the order of 10-6 meters , while the same wavelength will be reflected or transmitted (without diffraction) by a crystal which shows the periodicity of the interatomic (intermolecular) distances (of the order of 10-10 meters). In the same way, a X-ray wavelength (of the order of 10-10 meters ) undergoes the diffraction with the crystal lattice where the planes spacing shows the same order of magnitude ( nanometer).
All the best !
Dino
Dear Dino
That is the most beautiful and elegant explanation! Thank you very much! Now I understand, that the wave and obstacle have to be comparable in size to give diffraction, instead of reflection or transmission.
When a radiation wavelength is much smaller than an obstacle the diffraction pattern can be seen if the distance is very big. Once, I watched the diffraction of sun light on the greate aeroplane during my flight above the land ice of Greenland.
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