Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00112014" target="_blank" >RIV/00216224:14310/19:00112014 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1116/1.5122276" target="_blank" >https://doi.org/10.1116/1.5122276</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1116/1.5122276" target="_blank" >10.1116/1.5122276</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions

Popis výsledku v původním jazyce

The broadening of a sharp (unbroadened) dielectric function is a fruitful approach to the construction of models of dielectric response of materials. It naturally includes structural disorder or finite state lifetime and allows parameterization of such effects. The unbroadened function is often taken as a piecewise polynomial. Broadening it with the Lorentzian then leads to relatively simple analytical formulae. The Gaussian broadening, however, requires evaluation of several special functions, including the antiderivative of the Dawson function which is not generally available in mathematical libraries. Recently, the authors described the simple recurrent formulae for the construction of a Gaussian-broadened piecewise polynomial model of a complex dielectric function using three special functions, the error function, the Dawson function, and its antiderivative. In this paper, for the Dawson function and its antiderivative an efficient evaluation method is developed enabling the utilization of this model in optical spectra fitting. The effectiveness of this approach is illustrated using elementary and real-world examples of complex dielectric function models.

Název v anglickém jazyce

Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions

Popis výsledku anglicky

The broadening of a sharp (unbroadened) dielectric function is a fruitful approach to the construction of models of dielectric response of materials. It naturally includes structural disorder or finite state lifetime and allows parameterization of such effects. The unbroadened function is often taken as a piecewise polynomial. Broadening it with the Lorentzian then leads to relatively simple analytical formulae. The Gaussian broadening, however, requires evaluation of several special functions, including the antiderivative of the Dawson function which is not generally available in mathematical libraries. Recently, the authors described the simple recurrent formulae for the construction of a Gaussian-broadened piecewise polynomial model of a complex dielectric function using three special functions, the error function, the Dawson function, and its antiderivative. In this paper, for the Dawson function and its antiderivative an efficient evaluation method is developed enabling the utilization of this model in optical spectra fitting. The effectiveness of this approach is illustrated using elementary and real-world examples of complex dielectric function models.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Vacuum Science & Technology B

ISSN

2166-2746

e-ISSN

2166-2754

Svazek periodika

37

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

„062909-1“-„062909-7“

Kód UT WoS článku

000522021700060

EID výsledku v databázi Scopus

2-s2.0-85073624942