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.
Original language | English |
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Pages (from-to) | 1223-1232 |
Number of pages | 10 |
Journal | Journal of the Optical Society of America B |
Volume | 35 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2 May 2018 |