Construction and Floquet–Bloch analysis of analytically solvable Hill equations with smooth potentials

A. Ibrahim, D.W.L. Sprung, G.V. Morozov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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 languageEnglish
Pages (from-to)1223-1232
Number of pages10
JournalJournal of the Optical Society of America B
Volume35
Issue number6
DOIs
Publication statusPublished - 2 May 2018

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