Synthesis of gradient-index profiles corresponding to spectral reflectance derived by inverse Fourier transform

Boivin, Germain; St.-Germain, Daniel

doi:10.1364/ao.26.004209

Cited by 35 publications

(11 citation statements)

References 9 publications

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“…Other periodic profiles [4,5] for " r (z) can also be accommodated by the procedure described in this section. A plane wave is obliquely incident on the interface z ¼ 0 from the vacuous half space.…”

Section: Theorymentioning

confidence: 99%

Reflection from a semi-infinite rugate filter

Lakhtakia

2011

Journal of Modern Optics

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A theoretical approach was applied to compute the reflectance spectrums of semi-infinite rugate filters with a sinusoidal refractive-index profile. Regardless of the linear polarization state of the incident plane wave, the reflectance spectrum of a sufficiently thick rugate filter contains a top-hat feature -indicative of the Bragg regime -with ripples on both flanks. The corresponding reflectance spectrum of a semi-infinite rugate filter also contains the top-hat feature, but is devoid of ripples.

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Section: Theorymentioning

confidence: 99%

Reflection from a semi-infinite rugate filter

Lakhtakia

2011

Journal of Modern Optics

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“…In other words, functions of single variable describe courses of the refractive index and extinction coefficient from the lower to upper boundaries of these inhomogeneous thin films (single variable corresponds to axis perpendicular to parallel boundaries of these films). As for optics of inhomogeneous thin films one can recommend, for example, these papers [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Within the last three decades an interest concerning optics of inhomogeneous thin films was intensified.…”

Section: Introductionmentioning

confidence: 99%

Approximate methods for the optical characterization of inhomogeneous thin films: Applications to silicon nitride films

Ohlı́dal

Vohánka

Franta

et al. 2019

Journal of Electrical Engineering

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In this paper the overview of the most important approximate methods for the optical characterization of inhomogeneous thin films is presented. The following approximate methods are introduced: Wentzel–Kramers–Brillouin–Jeffreys approximation, method based on substituting inhomogeneous thin films by multilayer systems, method based on modifying recursive approach and method utilizing multiple-beam interference model. Principles and mathematical formulations of these methods are described. A comparison of these methods is carried out from the practical point of view, ie advantages and disadvantages of individual methods are discussed. Examples of the optical characterization of three inhomogeneous thin films consisting of non-stoichiometric silicon nitride are introduced in order to illustrate efficiency and practical meaning of the presented approximate methods.

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“…Within the optical characterization and optical synthesis of thin films, inhomogeneous layers play an important role. While there are many works devoted to methods usable in optical characterization and optical synthesis of homogeneous thin films (see, eg, previous studies , less attention has been devoted to the methods enabling us to characterize or perform optical synthesis of inhomogeneous thin films exhibiting refractive index profiles. Therefore, it is necessary to develop new procedures usable in the optics of inhomogeneous layers.…”

Section: Introductionmentioning

confidence: 99%

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization

Vohánka

Ohlı́dal

Ženíšek

et al. 2018

Surface & Interface Analysis

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A new approach to calculation of optical quantities of inhomogeneous layers is presented. In this approach, the Richardson extrapolation is used to improve the accuracy of the method, in which the inhomogeneous layer is approximated by a stack of thin homogeneous layers. The results presented in this paper are based on the assumption that the media are isotropic and the inhomogeneity is along the axis normal to the boundary. The results obtained by the new method are compared with those obtained without the Richardson extrapolation. The Richardson extrapolation brings significant improvement in accuracy, especially if the number of approximating layers is large. Moreover, the method using the Richardson extrapolation proceeds in steps with an error estimate available in each step; thus, the calculation can be stopped when the desired accuracy is reached. The use of the method is illustrated by means of the optical characterization of strongly inhomogeneous film of non-stoichiometric silicon nitride. KEYWORDS ellipsometry, inhomogeneous layers, optical characterization, silicon nitride 1 INTRODUCTION Within the optical characterization and optical synthesis of thin films, inhomogeneous layers play an important role. While there are many works devoted to methods usable in optical characterization and optical synthesis of homogeneous thin films (see, eg, previous studies 1-18 ), less attention has been devoted to the methods enabling us to characterize or perform optical synthesis of inhomogeneous thin films exhibiting refractive index profiles. Therefore, it is necessary to develop new procedures usable in the optics of inhomogeneous layers.In the literature, many procedures for calculating of the optical quantities of inhomogeneous layers have been published, eg, previous studies. 11,[19][20][21][22][23][24][25][26][27][28][29][30] The theoretical procedures can be divided into those providing the exact solution and those providing approximate solution.The exact solution is known only for few special refractive index profiles (eg, linear profile and exponential profile 24 ); thus, the approximate methods are usually used in practice. As more and more sophisticated methods of the optical characterization and optical synthesis are developed, the approximate methods with increased precision and reduced calculation time are required.The general approximate method enabling us to calculate the optical quantities of inhomogeneous layers with arbitrary refractive index profile is based on dividing these layers into a stack of thin homogeneous layers. 19,20,22,24 We will refer to this method as to homogeneous layers approximation (HLA). Unfortunately, to calculate the optical quantities with high accuracy, a very large number of approximating layers is required in this method. In this paper, we will show that the Richardson extrapolation (RE) can be used to increase the accuracy of this method. The RE 31,32 is a mathematical method that can be used to increase the rate of convergence of a series, provided certain criteria ...

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Synthesis of gradient-index profiles corresponding to spectral reflectance derived by inverse Fourier transform

Cited by 35 publications

References 9 publications

Reflection from a semi-infinite rugate filter

Reflection from a semi-infinite rugate filter

Approximate methods for the optical characterization of inhomogeneous thin films: Applications to silicon nitride films

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization

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