Abstract

We propose a new family of achromatic phase shifters for infrared nulling interferometry. These key optical components can be seen as optimized Fresnel rhombs, using the total internal reflection phenomenon, modulated or not. The total internal reflection indeed comes with a phase shift between the polarization components of the incident light. We propose a solution to implement this vectorial phase shift between interferometer arms to provide the destructive interference process needed to disentangle highly contrasted objects from one another. We also show that, modulating the index transition at the total internal reflection interface allows compensating for the intrinsic material dispersion in order to make the subsequent phase shift achromatic over especially broad bands. The modulation can be induced by a thin film of a well-chosen material or a subwavelength grating whose structural parameters are thoroughly optimized. We present results from theoretical simulations together with preliminary fabrication outcomes and measurements for a prototype in Zinc Selenide.

© 2007 Optical Society of America

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References

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  1. R.N. Bracewell, "Detecting Non Solar Planets by Spinning Infrared Interferometer," Nature 274, 780-781 (1978).
    [CrossRef]
  2. A. Leger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, "Could We Search for Primitive Life on Extrasolar Planets in the Near Future," Icarus 123, 249-255 (1996).
    [CrossRef]
  3. A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
    [CrossRef]
  4. J. Gay and Y. Rabbia, "Principe d’un coronographe interf’erentiel," C. R. Acad. Sci. Paris 322, 265-271 (1996).Q1
  5. E. Serabyn and M. M. Colavita, "Fully Symmetric Nulling Beam Combiners," Appl. Opt. 40, 1668-1671 (2001).
    [CrossRef]
  6. B. Chazelas, F. Brachet, P. Borde, B. Mennesson, M. Ollivier, O. Absil, A. Labeque, C. Valette, A. LegerA., "Instrumental stability requirements for exoplanet detection with a nulling interferometer: variability noise as a central issue," Appl. Opt. 45, 984-992 (2006).
    [CrossRef] [PubMed]
  7. F. Henault, "Design of achromatic phase shifters for spaceborne nulling interferometry," Opt. Lett. 31, 3635- 3637 (2006).
    [CrossRef] [PubMed]
  8. C. Hanot, et al., Proc. SPIE 6693-62, in press (2007).
  9. A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
    [CrossRef]
  10. D. Mawet, C. Lenaerts, P. Riaud, J. Surdej, S. Habraken, D. Vandormael, "Use of subwavelength gratings in TIR incidence as achromatic phase shifters," Opt. Express 13, 8686-8691 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. M. Born & E. Wolf, "Reflection and refraction of a plane wave," in Principles of Optics eds. (Cambridge University press, seventh edition, 1997), 49-53.
  13. K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, "Design and performance of a stable linear retarder," Appl. Opt. 36, 6458-6465 (1997).
    [CrossRef]
  14. R. Anderson, "Quarterwaveplate and Fresnel rhomb compared in the 10-Mum CO2 laser emission region," Appl. Opt. 27, 2746-2747 (1988).
    [CrossRef] [PubMed]
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  16. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
    [CrossRef]
  17. Gary J. Hawkins, Spectral Characterisation of Infrared Optical Materials and Filters (PhD Thesis - The University of Reading UK, 1998).
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    [CrossRef]
  19. W. J. Tropf, "Temperature-dependent refractive index models for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS and ZnSe," Opt. Eng. 34, 1369-1373 (1995).
    [CrossRef]
  20. W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
    [CrossRef]
  21. A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
    [CrossRef]
  22. P. Lalanne, P. Pichon, P. Chavel, E. Cambril, H. Launois, "Interferometric Characterization of Subwavelength Lamellar Gratings," Appl. Opt. 38, 4980-4984 (1999).
    [CrossRef]
  23. W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
    [CrossRef]
  24. K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).
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    [CrossRef] [PubMed]
  26. C. Yang and P. Yeh, "Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings," J. Appl. Phys. 81, 23-29 (1997).
    [CrossRef]

2006 (2)

2005 (1)

2004 (2)

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

2002 (1)

K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).

2001 (1)

2000 (2)

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
[CrossRef]

1999 (1)

1998 (2)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
[CrossRef]

1997 (2)

C. Yang and P. Yeh, "Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings," J. Appl. Phys. 81, 23-29 (1997).
[CrossRef]

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, "Design and performance of a stable linear retarder," Appl. Opt. 36, 6458-6465 (1997).
[CrossRef]

1996 (2)

J. Gay and Y. Rabbia, "Principe d’un coronographe interf’erentiel," C. R. Acad. Sci. Paris 322, 265-271 (1996).Q1

A. Leger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, "Could We Search for Primitive Life on Extrasolar Planets in the Near Future," Icarus 123, 249-255 (1996).
[CrossRef]

1995 (1)

W. J. Tropf, "Temperature-dependent refractive index models for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS and ZnSe," Opt. Eng. 34, 1369-1373 (1995).
[CrossRef]

1988 (1)

1981 (2)

1978 (1)

R.N. Bracewell, "Detecting Non Solar Planets by Spinning Infrared Interferometer," Nature 274, 780-781 (1978).
[CrossRef]

1969 (1)

1923 (1)

F. Peter, Z Phys 15, 358-368 (1923).
[CrossRef]

Absil, O.

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

Anderson, R.

Blache, P.

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

Bokhove, H.

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

Braat, J.J.

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

Bracewell, R.N.

R.N. Bracewell, "Detecting Non Solar Planets by Spinning Infrared Interferometer," Nature 274, 780-781 (1978).
[CrossRef]

Brachet, F.

B. Chazelas, F. Brachet, P. Borde, B. Mennesson, M. Ollivier, O. Absil, A. Labeque, C. Valette, A. LegerA., "Instrumental stability requirements for exoplanet detection with a nulling interferometer: variability noise as a central issue," Appl. Opt. 45, 984-992 (2006).
[CrossRef] [PubMed]

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

Cambril, E.

Chang, S. J.

W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
[CrossRef]

Chavel, P.

Chazelas, B.

B. Chazelas, F. Brachet, P. Borde, B. Mennesson, M. Ollivier, O. Absil, A. Labeque, C. Valette, A. LegerA., "Instrumental stability requirements for exoplanet detection with a nulling interferometer: variability noise as a central issue," Appl. Opt. 45, 984-992 (2006).
[CrossRef] [PubMed]

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

Chen, W. R.

W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
[CrossRef]

Clapham, P.

Clarke, I. G.

Colavita, M.M.

Commeaux, C.

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

Day, G. W.

Downs, M.

Fuse, K.

K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).

Gay, J.

J. Gay and Y. Rabbia, "Principe d’un coronographe interf’erentiel," C. R. Acad. Sci. Paris 322, 265-271 (1996).Q1

Gaylord, T.K

Habraken, S.

Hale, P. D.

Hirai, T.

K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).

Karlsson, A.L.

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

King, R.

Kurisu, K.

K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).

Lab`eque, A.

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

Lagarias, J.C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

Lalanne, P.

Launois, H.

Lenaerts, C.

Linevsky, M.J.

W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
[CrossRef]

Mariner, G.R.

Mawet, D.

Mieremet, A.L.

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

Moharam, M.G.

Perdigues Armengol, J.M.

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

Peter, F.

F. Peter, Z Phys 15, 358-368 (1923).
[CrossRef]

Pichon, P.

Rabbia, Y.

J. Gay and Y. Rabbia, "Principe d’un coronographe interf’erentiel," C. R. Acad. Sci. Paris 322, 265-271 (1996).Q1

Ravel, K.

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

Riaud, P.

Rochford, K. B.

Rose, A. H.

Serabyn, E.

Su, Y. K.

W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
[CrossRef]

Surdej, J.

Thomas, M.E.

W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
[CrossRef]

Tropf, W. J.

W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
[CrossRef]

W. J. Tropf, "Temperature-dependent refractive index models for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS and ZnSe," Opt. Eng. 34, 1369-1373 (1995).
[CrossRef]

Vandormael, D.

Vedam, K.

Wallner, O.

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

Wang, C. M.

Williams, P. A.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

Yang, C.

C. Yang and P. Yeh, "Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings," J. Appl. Phys. 81, 23-29 (1997).
[CrossRef]

Yeh, P.

C. Yang and P. Yeh, "Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings," J. Appl. Phys. 81, 23-29 (1997).
[CrossRef]

Appl. Opt. (7)

C. R. Acad. Sci. Paris (1)

J. Gay and Y. Rabbia, "Principe d’un coronographe interf’erentiel," C. R. Acad. Sci. Paris 322, 265-271 (1996).Q1

Icarus (1)

A. Leger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, "Could We Search for Primitive Life on Extrasolar Planets in the Near Future," Icarus 123, 249-255 (1996).
[CrossRef]

J. Appl. Phys. (1)

C. Yang and P. Yeh, "Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings," J. Appl. Phys. 81, 23-29 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

W. R. Chen, S. J. Chang, Y. K. Su et al., "Refractive Ion Etching of ZnSe, ZnSSe, ZnCdSe and ZnMgSSe by H2/Ar and CH4/H2/AR," Jpn. J. Appl. Phys. 39, 3308-3313 (2000).
[CrossRef]

Nature (1)

R.N. Bracewell, "Detecting Non Solar Planets by Spinning Infrared Interferometer," Nature 274, 780-781 (1978).
[CrossRef]

Opt. Eng. (1)

W. J. Tropf, "Temperature-dependent refractive index models for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS and ZnSe," Opt. Eng. 34, 1369-1373 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (4)

A. L. Mieremet, J. J. Braat, H. Bokhove, K. Ravel, "Achromatic phase shifting using adjustable dispersive elements," Proc. SPIE 4006, 1035-1041 (2000).
[CrossRef]

A. L. Karlsson, O. Wallner, J. M. Perdigues Armengol, and O. Absil,"Three telescope nuller based on multibeam injection into single-mode waveguide," Proc. SPIE 5491, 831-841 (2004).
[CrossRef]

W. J. Tropf, M. E. Thomas, M. J. Linevsky, "Infrared refractive indices and thermo-optic coefficients for several materials," Proc. SPIE 3425, 160-171 (1998).
[CrossRef]

A. Labeque, B. Chazelas, F. Brachet, C. Commeaux, P. Blache, A. Leger, M. Ollivier, T. Lepine, C. Valette, "The Nulltimate project: building and testing, at low temperature, achromatic phase shifters to prepare the Darwin mission," Proc. SPIE 5491, 999-1010 (2004).
[CrossRef]

SEI Technical Review (1)

K. Kurisu, T. Hirai, K. Fuse, et al., "Development of a Diffractive Optical Element for Laser Processing," SEI Technical Review 53, 86-91 (2002).

SIAM Journal of Optimization (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization 9, 112-147 (1998).
[CrossRef]

Z Phys (1)

F. Peter, Z Phys 15, 358-368 (1923).
[CrossRef]

Other (3)

Gary J. Hawkins, Spectral Characterisation of Infrared Optical Materials and Filters (PhD Thesis - The University of Reading UK, 1998).

M. Born & E. Wolf, "Reflection and refraction of a plane wave," in Principles of Optics eds. (Cambridge University press, seventh edition, 1997), 49-53.

C. Hanot, et al., Proc. SPIE 6693-62, in press (2007).

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Figures (14)

Fig. 1.
Fig. 1.

This scheme shows the double-rhomb configuration. θ 1 (resp. θ 2) is the angle of incidence upon the TIR interfaces of the first (resp. second) rhomb.

Fig. 2.
Fig. 2.

The double-rhomb geometry allows incidence-angle variations δθ to be compensated by the angle complementarity between the two rhombs and the linearity of the phase shift with respect to the rhomb angle. The linearity is present in the bare Fresnel rhomb or the TIR modulated one.

Fig. 3.
Fig. 3.

Implementation of a vectorial phase shifter (retarder) in a two-telescope nulling interferometer (Bracewell). The π retardance between the orthogonal polarizations s and p induced by the light differential optical delay between the slow (s) and fast axis (f) of the vectorial phase shifters 1 and 2 (φ s1o - φ p1o = φ p2o - φ p2o = π) can be spatially distributed between the interferometer arms. Indeed, a rotation of 90° of the retarders around the optical axis permutes the role of the polarizations so that at the output, the potentially interfering polarization states, i.e. the parallel ones are in phase opposition, φ s1o - φ s2o = φ p1o - φ p2o = ±π

Fig. 4.
Fig. 4.

ZnSe double-rhomb APS: comparison between Fresnel Rhomb (FR) with non-treated TIR interfaces, TIR thin film (TIRTF) and TIR grating (TIRG). More than substantially improving the global (mean) null depth over the considered wavelength range, the TIRTF and the TIRG solutions significantly decrease the strong leakage at its edges, inevitable with the FR solution.

Fig. 5.
Fig. 5.

Schematic of a subwavelength grating. The structure parameters are: the grating vector ∣ K ∣ = 2π/Λ, perpendicular to the grating lines, with Λ the spatial period, the thickness h and the filling factor f, such that fΛ is the feature line. TE and TM are the orthogonal polarization components of the θ-incident light. ni and nt are the refractive indices of the incident and emergent (transmitting) media, respectively. n 1 and n 2 are the refractive indices of the grating itself (in this case, n 2 = ni and n 1 = nt ).

Fig. 6.
Fig. 6.

6 – 14 μm ZnSe double rhomb APS with 900 nm period. Top left: optimized null depth vs feature line. Top right: thickness adjustment (optimized) vs feature line. Middle left: angle optimized null depth vs thickness for a fixed feature line of 250 nm. Middle right: corresponding angle adjustment (optimized) vs thickness. Bottom: two-dimensional maps of the null depth (log scale, 10-α ) according to the variables “thickness of the layer” and “incidence angle”. Left: ZnSe TIRTF APS coated with Diamond for the 6 to 14 micron band. Right: CdTe TIRTF APS coated with Diamond for the 6 to 18 micron band.

Fig. 7.
Fig. 7.

Trapezoidal profile likely to emerge from the plasma-etching process. The new parameter to be taken into account is the grating slope angle α.

Fig. 8.
Fig. 8.

Double-rhomb geometrical scheme and definition of the wedge angle w.

Fig. 9.
Fig. 9.

ZEMAX ray-tracing analysis of a ZnSe double wedged (1°) rhomb.

Fig. 10.
Fig. 10.

a. Picture of a ZnSe Fresnel rhomb. b. ZYGO interferograms. c. WYKO profiles.

Fig. 11.
Fig. 11.

Left: principle of holographic lithography (Lloyd mirror mounting). The grating period is inversely proportional to the angle between the two interferometer beams. Right: Micro-pattern on photoresist to be transferred by reactive plasma beam etching into the ZnSe substrate. The period and filling factor correspond to the design specifications.

Fig. 12.
Fig. 12.

Design of the ZnSe double Fresnel rhomb APS mechanical mounts. Right illustrates the practical implementation of the components in the interferometer at 45° from the test bench table, rotated of 90? from each other.

Fig. 13.
Fig. 13.

Optical setup used to perform the ZnSe rhomb retardance measurement. Linearly polarized light (P1) is incident upon the rhomb, and the light emerges with an elliptical polarization. The intensities of the two orthogonal polarization states are measured by rotating the output polarizer (P2). s and f are respectively the slow and fast rhomb axis.

Fig. 14.
Fig. 14.

ZnSe single rhomb retardance measurement. In blue: limits of the expected re-tardance vs polarizer inclinations. In red: fitted curve corresponding to a retardance of 88.8°±1.5°. The RMS error of the fit is 0.05616 and corresponds to a phase error of 1.5°, which is fully compliant with our setup precision.

Tables (1)

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Table 1. Average null depths for the optimized Fresnel double rhomb, TIRG, TIRTF configurations for the selected infrared materials. D stands for Diamond (CVD).

Equations (3)

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N ( λ ) = 10 5 ( λ 7 μm ) 3.37
Δ φ s p = 2 arctan [ sin 2 θ n ti 2 n ti 2 cos θ ] 2 arctan [ sin 2 θ n ti 2 cos θ ]
I 0 I π 2 = sin 2 2 α sin 2 ( Γ 2 ) 1 sin 2 2 α sin 2 ( Γ 2 )

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