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

A.  Ibrahim; D.W.L. Sprung; G.V. Morozov

doi:10.1364/JOSAB.35.001223

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

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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 language	English
Pages (from-to)	1223-1232
Number of pages	10
Journal	Journal of the Optical Society of America B
Volume	35
Issue number	6
DOIs	https://doi.org/10.1364/JOSAB.35.001223
Publication status	Published - 2 May 2018

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2018 04 04 Ibrahim et al Floquet-BlochAccepted author manuscript, 2.62 MBLicence: CC BY-NC

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title = "Construction and Floquet–Bloch analysis of analytically solvable Hill equations with smooth potentials",

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.",

author = "A. Ibrahim and D.W.L. Sprung and G.V. Morozov",

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T1 - Construction and Floquet–Bloch analysis of analytically solvable Hill equations with smooth potentials

AU - Ibrahim, A.

AU - Sprung, D.W.L.

AU - Morozov, G.V.

PY - 2018/5/2

Y1 - 2018/5/2

N2 - 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.

AB - 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.

U2 - 10.1364/JOSAB.35.001223

DO - 10.1364/JOSAB.35.001223

M3 - Article

SN - 0740-3224

VL - 35

SP - 1223

EP - 1232

JO - Journal of the Optical Society of America B

JF - Journal of the Optical Society of America B

IS - 6

ER -

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

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