Near-field optics

Number theoretic information in the Talbot-effect

During my Master’s thesis I dove into the connection of the Talbot effect and it’s description through Gauss Sums which are commonly used in number theory. It turns out that a clever measurement of the intensity in the “Talbot-carpet” along a certain line measures the Gauss-Sum directly and hence it can be used to “measure” prime number decompositions which we have shown experimentally in (Pelka et al., 2018)

Measurement of the Talbot Effect.

References

2018

Prime number decomposition using the Talbot effect

Karl Pelka, Jasmin Graf , Thomas Mehringer , and 1 more author

Optics Express, 2018

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@article{Pelka2018,
  title = {Prime number decomposition using the Talbot effect},
  author = {Pelka, Karl and Graf, Jasmin and Mehringer, Thomas and von Zanthier, Joachim},
  journal = {Optics Express},
  volume = {26},
  number = {12},
  pages = {15009--15014},
  year = {2018},
  publisher = {Optica Publishing Group},
}