Periodic solutions of Hill’s Equation in allowed bands

G. V. Morozov; A. Goussev

doi:10.1109/ICTON62926.2024.10647441

Periodic solutions of Hill’s Equation in allowed bands

G. V. Morozov
, A. Goussev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Abstract

A new set of periodic solutions of Hill’s equation is revealed for physical problems involving light propagation in photonic crystals and electron propagation in quantum periodic potentials. In contrast to the previously known cases of periodic solutions at the bandedges, these sets are located within the allowed bands of the corresponding potentials. Special emphasis is given to potentials that support periodic solutions in an exact analytical form.

Original language	English
Title of host publication	2024 24th International Conference on Transparent Optical Networks (ICTON)
Editors	Francesco Prudenzano, Marian Marciniak
Publisher	IEEE
Number of pages	4
ISBN (Electronic)	9798350377323
ISBN (Print)	9798350377330
DOIs	https://doi.org/10.1109/ICTON62926.2024.10647441
Publication status	Published - 2 Sept 2024

Keywords

Hill's equation
periodic solutions
band structure

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10.1109/ICTON62926.2024.10647441

2024 06 20 Morozov et al Periodic accepted - for PureAccepted author manuscript, 2.51 MBLicence: CC BY 4.0

Cite this

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AU - Goussev, A.

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N2 - A new set of periodic solutions of Hill’s equation is revealed for physical problems involving light propagation in photonic crystals and electron propagation in quantum periodic potentials. In contrast to the previously known cases of periodic solutions at the bandedges, these sets are located within the allowed bands of the corresponding potentials. Special emphasis is given to potentials that support periodic solutions in an exact analytical form.

AB - A new set of periodic solutions of Hill’s equation is revealed for physical problems involving light propagation in photonic crystals and electron propagation in quantum periodic potentials. In contrast to the previously known cases of periodic solutions at the bandedges, these sets are located within the allowed bands of the corresponding potentials. Special emphasis is given to potentials that support periodic solutions in an exact analytical form.

KW - Hill's equation

KW - periodic solutions

KW - band structure

U2 - 10.1109/ICTON62926.2024.10647441

DO - 10.1109/ICTON62926.2024.10647441

M3 - Conference contribution

SN - 9798350377330

BT - 2024 24th International Conference on Transparent Optical Networks (ICTON)

A2 - Prudenzano, Francesco

A2 - Marciniak, Marian

PB - IEEE

ER -

Periodic solutions of Hill’s Equation in allowed bands

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Keywords

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