Abstract

Phase dispersion induced by coatings can be a critical phenomenon in interferometry. We are interested in special mirrors intended for a Fabry–Perot interferometer with a high reflectance region and a low reflectance region in which phase dispersion on reflection must be avoided. We describe how a classical approach that uses the concepts of admittance and symmetrical multilayers allows the design of simple solutions.

© 1996 Optical Society of America

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References

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  1. P. Connes, “Development of absolute accelerometry,” Astrophys. Space Sci. 212, 357–367 (1994).
    [CrossRef]
  2. W. H. Southwell, “Multilayer coating design achieving a broadband 90° phase shift,” Appl. Opt. 19, 2688–2692 (1980).
    [CrossRef] [PubMed]
  3. J. H. Apfel, “Graphical method to design multilayer phase retarders,” Appl. Opt. 20, 1024–1029 (1981); “Phase retardance of periodic multilayer mirrors,” Appl. Opt. 21, 733–738 (1982).
    [CrossRef] [PubMed]
  4. S. H. C. Piotrowski McCall, J. A. Dobrowolski, G. G. Shepherd, “Phase shifting thin film multilayer for Michelson interferometers,” Appl. Opt. 28, 2854–2859 (1989).
    [CrossRef]
  5. F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter and compensating plate coatings in a Michelson type interferometer,” Pure Appl. Opt.4, 185–198 (1995); F. Lemarquis, E. Pelletier, “Compensation of phase dispersion in Michelson type interferometer,” in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 354–356.
    [CrossRef]
  6. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Hilger, Bristol, 1986), Chap. 2, p. 11.
  7. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 3, p. 41.

1994 (1)

P. Connes, “Development of absolute accelerometry,” Astrophys. Space Sci. 212, 357–367 (1994).
[CrossRef]

1989 (1)

1981 (1)

1980 (1)

Apfel, J. H.

Connes, P.

P. Connes, “Development of absolute accelerometry,” Astrophys. Space Sci. 212, 357–367 (1994).
[CrossRef]

Dobrowolski, J. A.

Fornier, A.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter and compensating plate coatings in a Michelson type interferometer,” Pure Appl. Opt.4, 185–198 (1995); F. Lemarquis, E. Pelletier, “Compensation of phase dispersion in Michelson type interferometer,” in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 354–356.
[CrossRef]

Lemarquis, F.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter and compensating plate coatings in a Michelson type interferometer,” Pure Appl. Opt.4, 185–198 (1995); F. Lemarquis, E. Pelletier, “Compensation of phase dispersion in Michelson type interferometer,” in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 354–356.
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Hilger, Bristol, 1986), Chap. 2, p. 11.

Pelletier, E.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter and compensating plate coatings in a Michelson type interferometer,” Pure Appl. Opt.4, 185–198 (1995); F. Lemarquis, E. Pelletier, “Compensation of phase dispersion in Michelson type interferometer,” in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 354–356.
[CrossRef]

Piotrowski McCall, S. H. C.

Shepherd, G. G.

Southwell, W. H.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 3, p. 41.

Appl. Opt. (3)

Astrophys. Space Sci. (1)

P. Connes, “Development of absolute accelerometry,” Astrophys. Space Sci. 212, 357–367 (1994).
[CrossRef]

Other (3)

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter and compensating plate coatings in a Michelson type interferometer,” Pure Appl. Opt.4, 185–198 (1995); F. Lemarquis, E. Pelletier, “Compensation of phase dispersion in Michelson type interferometer,” in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 354–356.
[CrossRef]

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Hilger, Bristol, 1986), Chap. 2, p. 11.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), Chap. 3, p. 41.

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Figures (11)

Fig. 1
Fig. 1

Block diagram of the Absolute Astronomical Accelerometry experiment developed by Connes.1 FP, Fabry–Perot interferometer; Dich., dichroic filter.

Fig. 2
Fig. 2

Typical reflectance profile required for Fabry–Perot mirrors. Phase retardation should be constant in the low reflectance spectral region. In the case studied in this paper, λ1 = 430 nm, λ2 = 630 nm, and λ3 = 780 nm.

Fig. 3
Fig. 3

Schematic representation of a multilayer.

Fig. 4
Fig. 4

Evolution of the admittance versus wavelength for a coating that gives constant reflectance. The parameters of the cylinder are given in the text. Most often, the admittance wraps around the cylinder (dashed curve) and this gives phase dispersion on reflection. To avoid phase dispersion, the admittance should remain constant over the spectrum, whatever its value (long–short dashed line). The easiest cases correspond to the two real values the admittance can take, Y 2 = 0.25 and Y 1 = 4 for 36% reflectance in the air (solid curves). Solutions are given that correspond to the last value (see text).

Fig. 5
Fig. 5

Reflectance of the design, glass (n = 1.52)/2L H/n ext, with n ext = 1 (solid curve) and n ext = 4 (dashed curve). n L = 1.3, n H = 2.4, λ0 = 520 nm.

Fig. 6
Fig. 6

Reflectance of the designs, n ext = 0.8/(L 2H L)3/n ext =0.8 (solid curve) and glass (n = 1.52)/L M 2H L/n ext = 0.8 (dashed curve). n L = 1.3, n M = 1.45, n H = 2.4, λ0 = 520 nm.

Fig. 7
Fig. 7

Reflectance of the mirror, glass (n = 1.52)/L M 2H L (L 2H L)3 L 2H M L 2L H/air. n L = 1.3, n M = 1.45, n H = 2.4, λ0 = 520 nm.

Fig. 8
Fig. 8

Phase retardation on reflection of the mirror, glass (n = 1.52)/L M 2H L (L 2H L)3 L 2H M L 2L H/air. n L = 1.3, n M = 1.45, n H = 2.4, λ0 = 520 nm.

Fig. 9
Fig. 9

Reflectance of the design, n ext = 4/(H 4L H)4/n ext =4. n L = 1.3, n H = 2.4, λ0 = 520 nm.

Fig. 10
Fig. 10

Reflectance of the mirror, glass (n = 1.52)/2L H (H 4L H)4/air. n L = 1.3, n H = 2.4, λ0 = 520 nm.

Fig. 11
Fig. 11

Phase retardation on reflection of the mirror, glass (n = 1.52)/2L H (H 4L H)4/air. n L = 1.3, n H = 2.4, λ0 = 520 nm.

Tables (1)

Tables Icon

Table 1 Description of the Three Solutions that Permit the Completion of the Initial Coating, Glass/2L H/Air, while Preserving 36% Reflectance from 430 to 630 nma

Equations (13)

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Y = C / B ,
( B C ) = i = 1 p [ cos δ i j n i sin δ i j n i sin δ i cos δ i ] ( 1 n s ) , δ i = 2 π n i e i λ ,             j 2 = - 1 ,
R = ( n 0 - Y n 0 + Y ) ( n 0 - Y n 0 + Y ) * ,
Φ R = arg ( n 0 - Y n 0 + Y ) .
( n 0 1 + R 0 1 - R 0 , 0 )
n 0 [ ( 1 + R 0 1 - R 0 ) 2 - 1 ] 1 / 2 .
glass / 2 L H / n ext ,             λ 0 = 520 nm .
n ext = 0.8 / ( L 4 H L ) 3 / n ext = 0.8 ,             λ 0 = 520 nm .
glass / L M 2 H L / n ext = 0.8 ,             λ 0 = 520 nm ,
glass / L M 2 H L ( L 4 H L ) 3 L 2 H M L 2 L H / air , λ 0 = 520 nm .
n ext = 4 / ( H 4 L H ) 4 / n ext = 4 ,             λ 0 = 520 nm .
glass / 2 L H ( H 4 L H ) 4 / air ,             λ 0 = 520 nm .
glass / ( 2 L 2 H 2 L ) 4 2 L H / air ,             λ 0 = 520 nm .

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