Microwave Realization of the Hofstadter Butterfly

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Abstract
The transmission of microwaves through an array of 100 scatterers inserted into a waveguide is studied. The length of each scatterer could be varied individually, thus allowing the realization of arbitrary scattering arrangements. For periodic sequences with varying period length the found transmission bands reproduced the Hofstadter butterfly, originally predicted for the spectra of conduction electrons in strong magnetic fields. In the experiment it was used that the same transfer matrix formalism is applicable to both the microwave and the electronic systems.