Efficient method to calculate the optical quantities of
multi-layer systems with randomly rough boundaries using the
Rayleigh Rice theory

J 2019

Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory

VOHÁNKA, Jiří, Martin ČERMÁK, Daniel FRANTA and Ivan OHLÍDAL

Basic information

Original name

Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory

Authors

VOHÁNKA, Jiří (203 Czech Republic, guarantor, belonging to the institution), Martin ČERMÁK (203 Czech Republic, belonging to the institution), Daniel FRANTA (203 Czech Republic, belonging to the institution) and Ivan OHLÍDAL (203 Czech Republic, belonging to the institution)

Edition

Physica Scripta, Bristol, IOP Publishing Ltd. 2019, 0031-8949

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10306 Optics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.985

RIV identification code

RIV/00216224:14310/19:00109310

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1088/1402-4896/aafbc1

UT WoS

000457287900001

Keywords in English

optical quantities; Rayleigh-Rice theory; multi-layer systems; random boundary roughness

Abstract

V originále

An efficient and numerically stable method for calculating the optical quantities of multi-layer systems with slightly rough boundaries using the second order Rayleigh–Rice theory is developed. It is assumed that the mean planes of the boundaries are parallel and all the media forming the system are nonmagnetic, isotropic and homogeneous. The perturbation series is formulated using the four-dimensional formalism inspired by the Yeh matrix formalism, but the final result is written using the two-dimensional formalism which is more efficient for the numerical calculations. The final formulae, which are expressed using an arbitrary power spectral density function (PSDF), include the mixing between the p and s polarizations occurring for anisotropic roughness. Although in the general case the calculation of optical quantities requires evaluation of double integrals, it is shown that for the PSDF given by the isotropic Gaussian function some integrals can be calculated analytically and only single integrals have to be evaluated numerically. The random roughness of boundaries is a defect that occurs frequently in practice, and it must be taken into account in the optical characterization and synthesis of thin film systems exhibiting this defect. The presented method is suitable for these purposes, since both of the mentioned applications require methods that are very fast.

Links

LO1411, research and development project

Name: Rozvoj centra pro nízkonákladové plazmové a nanotechnologické povrchové úpravy (Acronym: CEPLANT plus)

Investor: Ministry of Education, Youth and Sports of the CR

Citovat

VOHÁNKA, Jiří, Martin ČERMÁK, Daniel FRANTA and Ivan OHLÍDAL. Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory. Physica Scripta. Bristol: IOP Publishing Ltd., 2019, vol. 94, No 4, p. 1-22. ISSN 0031-8949. Available from: https://dx.doi.org/10.1088/1402-4896/aafbc1.

@article{1507078,
   author = {Vohánka, Jiří and Čermák, Martin and Franta, Daniel and Ohlídal, Ivan},
   article_location = {Bristol},
   article_number = {4},
   doi = {http://dx.doi.org/10.1088/1402-4896/aafbc1},
   keywords = {optical quantities; Rayleigh-Rice theory; multi-layer systems; random boundary roughness},
   language = {eng},
   issn = {0031-8949},
   journal = {Physica Scripta},
   title = {Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory},
   url = {https://iopscience.iop.org/article/10.1088/1402-4896/aafbc1},
   volume = {94},
   year = {2019}
}

TY  - JOUR
ID  - 1507078
AU  - Vohánka, Jiří - Čermák, Martin - Franta, Daniel - Ohlídal, Ivan
PY  - 2019
TI  - Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory
JF  - Physica Scripta
VL  - 94
IS  - 4
SP  - 1-22
EP  - 1-22
PB  - IOP Publishing Ltd.
SN  - 00318949
KW  - optical quantities
KW  - Rayleigh-Rice theory
KW  - multi-layer systems
KW  - random boundary roughness
UR  - https://iopscience.iop.org/article/10.1088/1402-4896/aafbc1
L2  - https://iopscience.iop.org/article/10.1088/1402-4896/aafbc1
N2  - An efficient and numerically stable method for calculating the optical quantities of multi-layer systems with slightly rough boundaries using the second order Rayleigh–Rice theory is developed. It is assumed that the mean planes of the boundaries are parallel and all the media forming the system are nonmagnetic, isotropic and homogeneous. The perturbation series is formulated using the four-dimensional formalism inspired by the Yeh matrix formalism, but the final result is written using the two-dimensional formalism which is more efficient for the numerical calculations. The final formulae, which are expressed using an arbitrary power spectral density function (PSDF), include the mixing between the p and s polarizations occurring for anisotropic roughness. Although in the general case the calculation of optical quantities requires evaluation of double integrals, it is shown that for the PSDF given by the isotropic Gaussian function some integrals can be calculated analytically and only single integrals have to be evaluated numerically. The random roughness of boundaries is a defect that occurs frequently in practice, and it must be taken into account in the optical characterization and synthesis of thin film systems exhibiting this defect. The presented method is suitable for these purposes, since both of the mentioned applications require methods that are very fast.
ER  -

VOHÁNKA, Jiří, Martin ČERMÁK, Daniel FRANTA and Ivan OHLÍDAL. Efficient method to calculate the optical quantities of multi-layer systems with randomly rough boundaries using the Rayleigh Rice theory. \textit{Physica Scripta}. Bristol: IOP Publishing Ltd., 2019, vol.~94, No~4, p.~1-22. ISSN~0031-8949. Available from: https://dx.doi.org/10.1088/1402-4896/aafbc1.

Detailed Information on Publication Record