Abstract

We demonstrate that high-quality interference filters for the wavelength range 1300–1600 nm can be holographically fabricated in DuPont HRF-800X001 photopolymer material by use of visible laser illumination. We also summarize a chain-matrix technique, which we call thin-film decomposition, that is useful for modeling multilayer films with an arbitrary index profile n(z). We use the thin-film-decomposition technique to create design curves that allow one to choose the proper exposure angle and film thickness with which to fabricate a holographic interference filter with a desired transmission efficiency and bandwidth at a particular wavelength. These curves are of general utility and are not confined to any particular holographic recording medium. Excellent agreement between theory and experiment is found.

© 2003 Optical Society of America

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References

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  1. T. W. Stone, B. J. Thompson, eds., Selected Papers on Holographic and Diffractive Lenses and Mirrors, Vol. MS 34 of SPIE Milestones Series (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
  2. S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
    [CrossRef]
  3. T. Stone, N. George, B. D. Guenther, “Index variation and scattering in a holographic medium,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. SPIE1136, 35–44 (1989).
    [CrossRef]
  4. R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Vol. 5, Chap. 5, pp. 247–286.
    [CrossRef]
  5. D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
    [CrossRef]
  6. R. T. Ingwall, H. L. Fielding, “Hologram recording with a new photopolymer system,” Opt. Eng. 24, 808–811 (1985).
    [CrossRef]
  7. W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).
  8. J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1555, 268–278 (1991).
    [CrossRef]
  9. L. T. Blair, L. Solymar, “Grating profiles in dichromated gelatin,” Opt. Commun. 77, 365–367 (1990).
    [CrossRef]
  10. T. J. Trout, W. J. Gambogi, S. H. Stevenson, “Photopolymer materials for color holography,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 94–105 (1995).
    [CrossRef]
  11. K. W. Steijn, “Multicolor holographic recording in DuPont holographic recording film: determination of exposure conditions for color balance,” in Holographic Materials II, T. J. Trout, ed., Proc. SPIE2688, 123–134 (1996).
    [CrossRef]
  12. S. H. Stevenson, K. W. Steijn, “A method for characterization of film thickness and refractive index in volume holographic materials,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 88–97 (1995).
    [CrossRef]
  13. H. J. Zhou, V. Morozov, J. Neff, “Characterization of DuPont photopolymers in infrared light for free-space optical interconnects,” Appl. Opt. 34, 7457–7459 (1995).
    [CrossRef] [PubMed]
  14. A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
    [CrossRef]
  15. K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, “Accurate optical frequency atlas of the 1.5-μm bands of acetylene,” J. Opt. Soc. Am. B 13, 2708–2714 (1996).
    [CrossRef]
  16. M. G. Moharam, T. K. Gaylord, “Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings,” J. Opt. Soc. Am. 72, 187–190 (1982).
    [CrossRef]
  17. X. Ning, “Analysis of multiplexed-reflection holographic gratings,” J. Opt. Soc. Am. A 7, 1436–1440 (1990).
    [CrossRef]
  18. R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
    [CrossRef]
  19. R. Alferness, “Analysis of propagation at the second-order Bragg angle of a thick holographic grating,” J. Opt. Soc. Am. 66, 353–362 (1976).
    [CrossRef]
  20. T. W. Stone, “Holographic optical elements,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1986).
  21. T. Stone, N. George, “Wavelength performance of holographic optical elements,” Appl. Opt. 24, 3797–3810 (1985).
    [CrossRef] [PubMed]
  22. P. F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans le milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 12, 596–640, 706–784 (1950).
  23. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1989).
  24. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, 1999).
    [CrossRef]

1996 (1)

1995 (1)

1990 (2)

X. Ning, “Analysis of multiplexed-reflection holographic gratings,” J. Opt. Soc. Am. A 7, 1436–1440 (1990).
[CrossRef]

L. T. Blair, L. Solymar, “Grating profiles in dichromated gelatin,” Opt. Commun. 77, 365–367 (1990).
[CrossRef]

1985 (3)

S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
[CrossRef]

T. Stone, N. George, “Wavelength performance of holographic optical elements,” Appl. Opt. 24, 3797–3810 (1985).
[CrossRef] [PubMed]

R. T. Ingwall, H. L. Fielding, “Hologram recording with a new photopolymer system,” Opt. Eng. 24, 808–811 (1985).
[CrossRef]

1982 (1)

1976 (1)

1975 (1)

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

1969 (1)

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

1950 (1)

P. F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans le milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 12, 596–640, 706–784 (1950).

Abeles, P. F.

P. F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans le milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 12, 596–640, 706–784 (1950).

Alferness, R.

R. Alferness, “Analysis of propagation at the second-order Bragg angle of a thick holographic grating,” J. Opt. Soc. Am. 66, 353–362 (1976).
[CrossRef]

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Awaji, Y.

Blair, L. T.

L. T. Blair, L. Solymar, “Grating profiles in dichromated gelatin,” Opt. Commun. 77, 365–367 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

Brault, R. G.

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

Chen, A.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Close, D. H.

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

de Labachelerie, M.

Duncan, S. S.

S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
[CrossRef]

Fan, R.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Felder, T. C.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Fielding, H. L.

R. T. Ingwall, H. L. Fielding, “Hologram recording with a new photopolymer system,” Opt. Eng. 24, 808–811 (1985).
[CrossRef]

Gambogi, W. J.

T. J. Trout, W. J. Gambogi, S. H. Stevenson, “Photopolymer materials for color holography,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 94–105 (1995).
[CrossRef]

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Gao, Q.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Gaylord, T. K.

George, N.

T. Stone, N. George, “Wavelength performance of holographic optical elements,” Appl. Opt. 24, 3797–3810 (1985).
[CrossRef] [PubMed]

T. Stone, N. George, B. D. Guenther, “Index variation and scattering in a holographic medium,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. SPIE1136, 35–44 (1989).
[CrossRef]

Guenther, B. D.

T. Stone, N. George, B. D. Guenther, “Index variation and scattering in a holographic medium,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. SPIE1136, 35–44 (1989).
[CrossRef]

Harton, A.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Ingwall, R. T.

R. T. Ingwall, H. L. Fielding, “Hologram recording with a new photopolymer system,” Opt. Eng. 24, 808–811 (1985).
[CrossRef]

Jacobson, A. D.

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

Jacobsson, R.

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Vol. 5, Chap. 5, pp. 247–286.
[CrossRef]

Kourogi, M.

Loeffler, M. F.

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1555, 268–278 (1991).
[CrossRef]

Mackara, S. R.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1989).

Margerum, J. D.

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

McCartney, D. J.

S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
[CrossRef]

McClung, F. J.

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

McQuoid, J. A.

S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
[CrossRef]

Mikish, D. J.

W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).

Moharam, M. G.

Morozov, V.

Nakagawa, K.

Neff, J.

Ning, X.

Salter, J. L.

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1555, 268–278 (1991).
[CrossRef]

Smothers, W. K.

W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).

Solymar, L.

L. T. Blair, L. Solymar, “Grating profiles in dichromated gelatin,” Opt. Commun. 77, 365–367 (1990).
[CrossRef]

Steijn, K. W.

K. W. Steijn, “Multicolor holographic recording in DuPont holographic recording film: determination of exposure conditions for color balance,” in Holographic Materials II, T. J. Trout, ed., Proc. SPIE2688, 123–134 (1996).
[CrossRef]

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

S. H. Stevenson, K. W. Steijn, “A method for characterization of film thickness and refractive index in volume holographic materials,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 88–97 (1995).
[CrossRef]

Stevenson, S. H.

T. J. Trout, W. J. Gambogi, S. H. Stevenson, “Photopolymer materials for color holography,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 94–105 (1995).
[CrossRef]

S. H. Stevenson, K. W. Steijn, “A method for characterization of film thickness and refractive index in volume holographic materials,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 88–97 (1995).
[CrossRef]

Stone, T.

T. Stone, N. George, “Wavelength performance of holographic optical elements,” Appl. Opt. 24, 3797–3810 (1985).
[CrossRef] [PubMed]

T. Stone, N. George, B. D. Guenther, “Index variation and scattering in a holographic medium,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. SPIE1136, 35–44 (1989).
[CrossRef]

Stone, T. W.

T. W. Stone, “Holographic optical elements,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1986).

Trout, T. J.

T. J. Trout, W. J. Gambogi, S. H. Stevenson, “Photopolymer materials for color holography,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 94–105 (1995).
[CrossRef]

W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Weber, A. M.

W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

Wyatt, K.

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

Zhou, H. J.

Ann. Phys. (Paris) (1)

P. F. Abeles, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans le milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 12, 596–640, 706–784 (1950).

Appl. Opt. (2)

Appl. Phys. (1)

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Appl. Phys. Lett. (1)

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, F. J. McClung, “Hologram recording on photopolymer materials,” Appl. Phys. Lett. 14, 159–160 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

Opt. Commun. (1)

L. T. Blair, L. Solymar, “Grating profiles in dichromated gelatin,” Opt. Commun. 77, 365–367 (1990).
[CrossRef]

Opt. Eng. (2)

R. T. Ingwall, H. L. Fielding, “Hologram recording with a new photopolymer system,” Opt. Eng. 24, 808–811 (1985).
[CrossRef]

S. S. Duncan, J. A. McQuoid, D. J. McCartney, “Holographic filters in dichromated gelatin position tuned over the near-infrared region,” Opt. Eng. 24, 781–785 (1985).
[CrossRef]

Other (12)

T. Stone, N. George, B. D. Guenther, “Index variation and scattering in a holographic medium,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. SPIE1136, 35–44 (1989).
[CrossRef]

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Vol. 5, Chap. 5, pp. 247–286.
[CrossRef]

T. W. Stone, “Holographic optical elements,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1986).

T. W. Stone, B. J. Thompson, eds., Selected Papers on Holographic and Diffractive Lenses and Mirrors, Vol. MS 34 of SPIE Milestones Series (SPIE Optical Engineering Press, Bellingham, Wash., 1991).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1989).

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

W. K. Smothers, T. J. Trout, A. M. Weber, D. J. Mikish, “Hologram recording in DuPont’s new photopolymer materials,” in Second International Conference on Holographic Systems, Components and Applications, IEE Conf. Pub.311, 184–189 (1989).

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1555, 268–278 (1991).
[CrossRef]

T. J. Trout, W. J. Gambogi, S. H. Stevenson, “Photopolymer materials for color holography,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 94–105 (1995).
[CrossRef]

K. W. Steijn, “Multicolor holographic recording in DuPont holographic recording film: determination of exposure conditions for color balance,” in Holographic Materials II, T. J. Trout, ed., Proc. SPIE2688, 123–134 (1996).
[CrossRef]

S. H. Stevenson, K. W. Steijn, “A method for characterization of film thickness and refractive index in volume holographic materials,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 88–97 (1995).
[CrossRef]

A. Chen, Q. Gao, R. Fan, A. Harton, K. Wyatt, T. C. Felder, W. J. Gambogi, S. R. Mackara, K. W. Steijn, T. J. Trout, “Enhanced reflective liquid crystal displays using DuPont holographic recording films,” in Holographic Materials IV, T. J. Trout, ed., Proc. SPIE3294, 201–206 (1998).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Setup for holographic fabrication of infrared multilayer mirrors, showing the path of a ray through the prism-film assembly: F, film; P, 45° roof prism; G, black glass; E, electric field vector polarized perpendicular to the plane of incidence. Light is s polarized with respect to the prism face.

Fig. 2
Fig. 2

Comparison of the transmission spectra through DuPont HRF-800X001-15 photopolymer film. Solid curve, before exposure; dashed curve, after polymerization.

Fig. 3
Fig. 3

Overlay of the transmission spectra of four holograms, showing reflection peaks at 1311, 1391, 1473, and 1541 nm.

Fig. 4
Fig. 4

Experimental data for the average index of refraction, n f ′, of DuPont HRF-800X001 photopolymer after exposure and processing. Dashed line, mean value.

Fig. 5
Fig. 5

Tunable infrared laser spectrophotometer system: C, controller for the diode laser; DL, tunable diode laser; BS, beam splitter; D1, D2, InGaAs photodetectors; O, digital oscilloscope; PC, digital computer with GPIB interface.

Fig. 6
Fig. 6

Design curve relating exposure angle θ i to peak reflected wavelength λ p . Solid curve, plot of Eq. (4). The circles (filled and open) represent two sets of experimental data.

Fig. 7
Fig. 7

Design curve plotting minimum transmission T p ) versus dimensionless parameter (L/Λ) × (Δn/ n f ′) for a cosinusoidal index variation. We calculated the curve by using thin-film decomposition.

Fig. 8
Fig. 8

Design curves for Δλ/λ p versus L/Λ, calculated by use of thin-film decomposition for a cosinusoidal index modulation and a range of index modulations characterized by (Δn/ n f ′).

Equations (12)

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

Λ=S λ02nfλ0cos θf,
λp=2nfλpΛ cos θf,
np sin θ1=n0 sin θi, θ2=45°-θ1, nf sin θf=np sin θ2.
λ=λ0S nfnf1-12npnf2+sin θinf2×np2-sin2 θi1/2-1/2.
EaHa=cos δi sin δ/ηiη sin δcos δEsHs,
BC=cos δi sin δ/nin sin δcos δ1ns,
nz=nf+Δn cos2πΛ z,
m=m11m12m21m22,
mN=m11UN-1a-UN-2am12UN-1am21UN-1am22UN-1a-UN-2a,
a=½ m11+m22
UNa=sinN+1cos-1 a1-a1/2.
Tλ=4n0Rensn0B+Cn0B+C*,

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