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Calculation of the diffracted light field: Regarding Fresnel near-field diffraction, how should the field distribution be calculated after a plane wave encounters a metasurface and experiences a phase jump?

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A friend wanted to see the article before.Matlab optical Fresnel diffraction, dynamic visualization of Matlab curves and graphics.The source code is in this article.

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If the questioner wants to see the field distribution of metasurfaces or 'very close' fields, I think directly solving the full wave to see the field distribution in two dimensions would be sufficient. The computational load should not be very large.

If the questioner wants to see the field distribution at a farther position, full wave calculations can be used to obtain the field distribution near the metasurface, extract the field data, and analyze the far-field electromagnetic field propagation behavior using angular spectrum or other methods.

Moreover, the questioner mentioned Fresnel near-field diffraction, which also has certain conditions. You can refer to a previous article:Knowledge Notes | Multi-slit Diffraction..

To see the Fresnel diffraction situation of diffraction patterns (light fields carrying specific phase information or light fields passing through specific devices), you can first look at the basic formulas of Fresnel diffraction.

Through the above formula, we can understand that under the conditions of Fresnel diffraction, the field distribution at our observation position can be seen as the incident field superimposed with the modulated phase of the diffraction pattern (here it can also be considered as the phase jump provided by the metasurface) synthesized from the Fourier transform of the incident information field.This analysis is often applicable at not very far distances and within a small vertical axis range. Whether using the above method or angular spectrum, implementing it in Matlab is quite simple, mainly thanks to the fast Fourier transform functions fft and fft2 in Matlab. Below is a simple way to observe the propagation behavior of light fields through a focusing lens.

In fact, in diffraction optics or when studying DOE, approximate models can be used to estimate the diffraction field. What is crucial is how to sample and understand the changes in physical dimensions during the transmission process.

It is often the case that the observation plane takes the same pixels as the diffraction plane. The pixel size of the observation screen is.During the fft process, there are also some 'zero-padding' operations, which allow for calculations at greater distances and improve computational accuracy.

When the Fourier transform becomes the above discrete Fourier transform, there exists a.relationship, which helps to understand the above description and the actual effects brought by increased sampling.