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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References

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  1. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 82, 172–175 (1909).
    [CrossRef]
  2. W. Liu and J. Talghader, “Thermally invariant dielectric coatings for micromirrors,” Appl. Opt. 41, 3285–3293 (2002).
    [CrossRef]
  3. J. Klemberg-Sapieha, J. Oberste-Berghaus, L. Martinu, R. Blacker, I. Stevenson, G. Sadkhin, D. Morton, S. McEldowney, R. Klinger, P. Martin, N. Court, S. Dligatch, M. Gross, and R. Netterfield, “Mechanical characteristics of optical coatings prepared by various techniques: a comparative study,” Appl. Opt. 43, 2670–2679 (2004).
    [CrossRef]
  4. J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
    [CrossRef]
  5. R. Thielsch, A. Gatto, and N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
    [CrossRef]
  6. H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34, 667–675 (1995).
    [CrossRef]
  7. J. Mouchart, “Thin film optical coatings. 5: buffer layer theory,” Appl. Opt. 17, 72–75 (1978).
    [CrossRef]
  8. P. Baumeister, Optical Coating Technology (SPIE, 2004), pp. 2–70.
  9. Z. Knittl, “Control of polarization effects by internal antireflection,” Appl. Opt. 20, 105–110 (1981).
    [CrossRef]
  10. F. Lemarquis and E. Pelletier, “Buffer layers for the design of broadband optical filters,” Appl. Opt. 34, 5665–5672 (1995).
    [CrossRef]
  11. L. Li, J. Dobrowolski, J. Sankey, and J. Wimperis, “Antireflection coatings for both visible and far-infrared spectral regions,” Appl. Opt. 31, 6150–6156 (1992).
    [CrossRef]
  12. L. Li and J. Dobrowolski, “Design of optical coatings for two widely separated spectral regions,” Appl. Opt. 32, 2969–2975 (1993).
    [CrossRef]
  13. “OIC 2013 Design Problems,” http://www.osa.org/osaorg/media/osa.media/Meetings/PDFSupportingDoc/2013-OIC-Design-Problems.pdf .
  14. M. Ohring, Material Science of Thin Films (Academic, 1992), pp. 416–420.
  15. A. Macleod, Thin Film Optical Filters, 2nd ed. (Adam Hilger, 1986), p. 54.
  16. W. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A 8, 549–553 (1991).
    [CrossRef]

2004 (1)

2002 (2)

1999 (1)

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

1995 (2)

1993 (1)

1992 (1)

1991 (1)

1981 (1)

1978 (1)

1909 (1)

G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 82, 172–175 (1909).
[CrossRef]

Baumeister, P.

P. Baumeister, Optical Coating Technology (SPIE, 2004), pp. 2–70.

Blacker, R.

Court, N.

Dligatch, S.

Dobrowolski, J.

Dognin, L.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Ganau, P.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Gatto, A.

Gross, M.

Kaiser, N.

Klemberg-Sapieha, J.

Klinger, R.

Knittl, Z.

Lagrange, B.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Lemarquis, F.

Li, L.

Liu, W.

Mackowski, J. M.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Macleod, A.

A. Macleod, Thin Film Optical Filters, 2nd ed. (Adam Hilger, 1986), p. 54.

Martin, P.

Martinu, L.

McEldowney, S.

Michel, C.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Morgue, M.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Morton, D.

Mouchart, J.

Netterfield, R.

Oberste-Berghaus, J.

Ohring, M.

M. Ohring, Material Science of Thin Films (Academic, 1992), pp. 416–420.

Pelletier, E.

Pinard, L.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Sadkhin, G.

Sankey, J.

Southwell, W.

Stevenson, I.

Stoney, G.

G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 82, 172–175 (1909).
[CrossRef]

Takashashi, H.

Talghader, J.

Thielsch, R.

Wimperis, J.

Appl. Opt. (9)

J. Mouchart, “Thin film optical coatings. 5: buffer layer theory,” Appl. Opt. 17, 72–75 (1978).
[CrossRef]

Z. Knittl, “Control of polarization effects by internal antireflection,” Appl. Opt. 20, 105–110 (1981).
[CrossRef]

L. Li and J. Dobrowolski, “Design of optical coatings for two widely separated spectral regions,” Appl. Opt. 32, 2969–2975 (1993).
[CrossRef]

H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34, 667–675 (1995).
[CrossRef]

F. Lemarquis and E. Pelletier, “Buffer layers for the design of broadband optical filters,” Appl. Opt. 34, 5665–5672 (1995).
[CrossRef]

W. Liu and J. Talghader, “Thermally invariant dielectric coatings for micromirrors,” Appl. Opt. 41, 3285–3293 (2002).
[CrossRef]

R. Thielsch, A. Gatto, and N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
[CrossRef]

L. Li, J. Dobrowolski, J. Sankey, and J. Wimperis, “Antireflection coatings for both visible and far-infrared spectral regions,” Appl. Opt. 31, 6150–6156 (1992).
[CrossRef]

J. Klemberg-Sapieha, J. Oberste-Berghaus, L. Martinu, R. Blacker, I. Stevenson, G. Sadkhin, D. Morton, S. McEldowney, R. Klinger, P. Martin, N. Court, S. Dligatch, M. Gross, and R. Netterfield, “Mechanical characteristics of optical coatings prepared by various techniques: a comparative study,” Appl. Opt. 43, 2670–2679 (2004).
[CrossRef]

Appl. Surf. Sci. (1)

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, and M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the Virgo gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (1)

G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 82, 172–175 (1909).
[CrossRef]

Other (4)

P. Baumeister, Optical Coating Technology (SPIE, 2004), pp. 2–70.

“OIC 2013 Design Problems,” http://www.osa.org/osaorg/media/osa.media/Meetings/PDFSupportingDoc/2013-OIC-Design-Problems.pdf .

M. Ohring, Material Science of Thin Films (Academic, 1992), pp. 416–420.

A. Macleod, Thin Film Optical Filters, 2nd ed. (Adam Hilger, 1986), p. 54.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic representation of an optical coating split into two halves.

Fig. 2.
Fig. 2.

Schematic representation of two design structures containing two iso-admittance layers. The internal antireflection (AR) structures needed to define the iso-admittance layers are assumed to be optimized for the same spectral region as that for which the optical stack provides various specified optical properties. The thicknesses of the iso-admittance layers then have no influence in this region and can be used freely to adjust the optical design in other regions of the spectrum or for mechanical purposes.

Fig. 3.
Fig. 3.

Reflectance profile (average polarization 45° angle of incidence in air) of the beam-splitter design provided in Table 2.

Fig. 4.
Fig. 4.

Reflectance profiles (average polarization, 45° angle of incidence in air) corresponding to the backside antireflection coating provided in Table 2. The thick line corresponds to the optical stack, the thin line to the whole coating, and the dashed line to the internal antireflection structure (right vertical scale).

Fig. 5.
Fig. 5.

Schematic representation of the self-compensated design structure corresponding to the initial design (beam splitter or backside antireflection coating), to which a Z iso-admittance layer is added, together with the two required internal antireflection structures.

Fig. 6.
Fig. 6.

Reflectance profile (average polarization, 45° angle of incidence in air) of the self-compensated beam splitter (thick line). The thin line indicates the difference between this profile and the initial profile shown in Fig. 3 (right vertical scale).

Fig. 7.
Fig. 7.

Reflectance profiles (average polarization, 45° angle of incidence in air) of the self-compensated backside antireflection coating (thick line) and of the internal antireflection structure used to insert the Z iso-admittance layer (thin line, right vertical scale).

Tables (3)

Tables Icon

Table 1. List of Material Indices and Stress Values Authorized for the 2013 OIC Design Contest, Problem B

Tables Icon

Table 2. Initial Designs Proposed for the Beam Splitter (First Column) and Backside Antireflection (AR) Coating (Split into Four Substructures Corresponding to the Last Four Columns)a

Tables Icon

Table 3. Design Formula for the Internal Antireflection Structure with Which It Is Proposed to Insert a Z Iso-admittance Layer for the Self-Compensating Designsa

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

1R=6·(1νs)Es·ds2·σ·df,
1R=i1Ri=6·(1νs)Es·ds2·iσi·di.
(layerσi·di)front face=(layerσi·di)rear face.
(materialσi·Di)front face=(materialσi·Di)rear face.
σ=σint+σtherm=σint+(E1ν)film(αsubαfilm)(TTd).
material[(E1ν)i(αsubαi)·(TTdi)·(DifrontDirear)]+material[σinti(DifrontDirear)]=0.
Difront=Direar.
T=TaTb(1RaRb)2·[1+4RaRb(1RaRb)2sin2(ϕa+ϕb22πndλ)]1.

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