Band structure analysis of an analytically solvable Hill equation with continuous potential

G. V. Morozov, D. W. L. Sprung

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This paper concerns analytically solvable cases of Hill's equation containing a continuously differentiable periodic potential. We outline a procedure for constructing the Floquet-Bloch fundamental system, and analyze the band structure of the system. The similarities to, and differences from, the cases of a piecewise constant periodic potential and the Mathieu potential, are illuminated.
Original languageEnglish
Article number035607
Number of pages8
JournalJournal of Optics
Volume17
Issue number3
DOIs
Publication statusPublished - 13 Feb 2015

Keywords

  • Hill equation
  • Floquet-Bloch waves
  • band structure

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