## Abstract

Mechanical stress in optical thin films can induce surface deflection of optical coatings. In the case of a substrate coated on both sides, a method is proposed which can provide perfect cancellation of this deflection, independently of the deposition process or any other external parameter, such as the temperature sensitivity of the mechanical stress. It is straightforward to implement this method, based on iso-admittance layers, since the thickness of such layers can be used to freely compensate for deflection effects only, without having any influence on the film’s optical properties. This method is illustrated by two possible solutions for the design problem B from the Optical Interference Coatings (OIC) 2013 meeting.

© 2014 Optical Society of America

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### Equations (8)

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(1)
$$\frac{1}{R}=\frac{6\xb7(1-{\nu}_{s})}{{E}_{s}\xb7{d}_{s}^{2}}\xb7\sigma \xb7{d}_{f},$$
(2)
$$\frac{1}{R}=\sum _{i}\frac{1}{{R}_{i}}=\frac{6\xb7(1-{\nu}_{s})}{{E}_{s}\xb7{d}_{s}^{2}}\xb7\sum _{i}{\sigma}_{i}\xb7{d}_{i}.$$
(3)
$${(\sum _{\text{layer}}{\sigma}_{i}\xb7{d}_{i})}_{\text{front face}}={(\sum _{\text{layer}}{\sigma}_{i}\xb7{d}_{i})}_{\text{rear face}}.$$
(4)
$${(\sum _{\text{material}}{\sigma}_{i}\xb7{D}_{i})}_{\text{front face}}={(\sum _{\text{material}}{\sigma}_{i}\xb7{D}_{i})}_{\text{rear face}}.$$
(5)
$$\sigma ={\sigma}_{\text{int}}+{\sigma}_{\text{therm}}={\sigma}_{\text{int}}+{\left(\frac{E}{1-\nu}\right)}_{\text{film}}({\alpha}_{\text{sub}}-{\alpha}_{\text{film}})(T-{T}_{d}).$$
(6)
$$\sum _{\text{material}}[{\left(\frac{E}{1-\nu}\right)}_{i}({\alpha}_{\text{sub}}-{\alpha}_{i})\xb7(T-{T}_{di})\xb7({D}_{i\text{front}}-{D}_{i\text{rear}})]+\sum _{\text{material}}[{\sigma}_{\text{int}i}({D}_{i\text{front}}-{D}_{i\text{rear}})]=0.$$
(7)
$${D}_{i\text{front}}={D}_{i\text{rear}}.$$
(8)
$$T=\frac{{T}_{a}{T}_{b}}{{(1-\sqrt{{R}_{a}{R}_{b}})}^{2}}\xb7{[1+\frac{4\sqrt{{R}_{a}{R}_{b}}}{{(1-\sqrt{{R}_{a}{R}_{b}})}^{2}}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}(\frac{{\varphi}_{a}+{\varphi}_{b}}{2}-\frac{2\pi nd}{\lambda})]}^{-1}.$$