Quasi-optimal synthesis for antireflection coatings: a new method

Tikhonravov, Alexander V.; Dobrowolski, J. A.

doi:10.1364/ao.32.004265

Cited by 53 publications

(29 citation statements)

References 7 publications

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“…[11] that the optimization of AR designs with respect to the thicknesses of design layers is an optimization problem that is close to the optimization of convex functions. This is an important fact because any convex function has a single minimum that can be reliably found using various optimization methods.…”

Section: Numerical Study Of Sequences Of Optimal Antireflection Designsmentioning

confidence: 99%

Estimation of the average residual reflectance of broadband antireflection coatings

et al. 2007

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Estimation of the average residual reflectance of broadband antireflection coatingsWe deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high-and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.

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Section: Numerical Study Of Sequences Of Optimal Antireflection Designsmentioning

confidence: 99%

Estimation of the average residual reflectance of broadband antireflection coatings

et al. 2007

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“…The reflectance of the systems (3a) and (c) obtained at that point is respectable, even compared to that of the final, refined quasi-optimal multilayers described in Ref. (8). The reflectance of such multilayers is represented by a dotted line in the figures.…”

Section: Discussionmentioning

confidence: 58%

“…(4a) and (6a) of Ref. (8). This is all the more interesting since it was not clear at first that a design method assimple as this frequency filtering process would work at all.…”

Section: Discussionmentioning

confidence: 98%

“…In Refs (8)(9), this is done systematically by minimizing Eq. (3) with a sophisticated quadratic programming method.…”

Section: Discussionmentioning

confidence: 99%

“…(8)(9), the integral JQ2()d (3) is minimized in the AR region by using a powerful quadratic programming optimization method. The solutions are called quasioptimal in the sense that the global minimum of Eq.…”

Section: Introductionmentioning

confidence: 99%

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Fourier transform technique with frequency filtering for antireflection coating design

Verly

1994

Optical Interference Coatings

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A new, very simple AR coating synthesis method is further developed and compared to a recent "quasi-optimal" technique. A remarkable resemblance is found in the results. The reason for this similarity is given and the performance of both approaches is discussed. INTRODUCTIONFourier transfcwm techniques are well suited to the synthesis of dielectric optical coatings with either gradual M stepped variations in the refractive index. Such techniques have been used in the solution of difficult thin film problems, and resulted in designs -sometimes complex -whichhave been successfully fabricated.There is a close connection between the Fourier transform of a refractive index variation versus optical thickness on one hand, and the reflectance variation versus inverse wavelength on the other hand (see Sect. 3). Since Fourier transforms are linear, it is possible to decompose a refractive index profile into elementary subsystems which make distinct contributions to the optical peiformance. For example, multiline rugate filters can be obtained from the superposition of two or mxe single line rugates.3'4 Southwell proposed a modification of this approach based on the combination of apodized rugates or "wavelets".5 A number of years ago, Dobrowolski demonstrated a related multilayer design technique using minus filters -or apodized quarter wave stacksinstead of wavelets.6In the three approaches mentioned above, an increasing number of subsystems is combined until the desired spectral performance is achieved. Spatial frequency components are thus progressively added to the Fourier spectrum of the refractive index profile. Interesting results are also obtained when such spatial frequencies are removed.7 This operation is called frequency filtering. Fx example, the elimination of the high spatial frequencies of existing graded index profiles, with values outside a spectral region of interest, yields simplified (smoothed) solutions. After reoptimization, these often have a similar if not improved optical performance in the region of interest. Moreover, preliminary results presented in Ref. (7) suggested that AR coatings can be synthesized by suppressing the spatial frequencies of a starting design in the AR region.7The present work is a further discussion of this new and very simple AR coating design technique. A comparison with the "quasi-optimal" synthesis method recently proposed by Tikhonravov and Dobrowoiski is also ded8'9 A remarkable resemblance is found in the results. The reason for this similarity is given and the performance of both methods is discussed. BACKGROUND.Only a brief summary of the Fourier transform method is given below. Additional details can be found elsewhere.1 Under suitable conditions, a simple a Fourier transform (VF) relationshipL) a exists, within a multiplicative constant, between a refractive index profile n(x) and a complex function of the reflectance R(a) and inverse wavelength a=1IX. The variable x is twice the centered optical thickness, with the origin set at the center of the coating (see Fi...

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Global Optimization of Planar Multilayered Dielectric Structures

Adjiman¹,

Oulton²

2008

Encyclopedia of Optimization

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Quasi-optimal synthesis for antireflection coatings: a new method

Cited by 53 publications

References 7 publications

Estimation of the average residual reflectance of broadband antireflection coatings

Estimation of the average residual reflectance of broadband antireflection coatings

Fourier transform technique with frequency filtering for antireflection coating design

Global Optimization of Planar Multilayered Dielectric Structures

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