Abstract

We construct analytically solvable Hill equations with smooth potentials and smooth solutions using a method of Wu and Shih. We then use Floquet–Bloch theory to analyze the band structure and find the Floquet–Bloch fundamental system of solutions of the resulting differential equation. Three examples of constructed potentials and their corresponding solutions are worked out.

© 2018 Optical Society of America

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Corrections

8 May 2018: A typographical correction was made to Eq. (6).


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Equations (68)

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