Abstract

We have developed and tested an antireflection (AR) coating method for silicon lenses used at cryogenic temperatures and millimeter wavelengths. Our particular application is a measurement of the cosmic microwave background. The coating consists of machined pieces of Cirlex glued to the silicon. The measured reflection from an AR-coated flat piece is less than 1.5% at the design wavelength. The coating has been applied to flats and lenses and has survived multiple thermal cycles from 300 to 4  K. We present the manufacturing method, the material properties, the tests performed, and estimates of the loss that can be achieved in practical lenses.

© 2006 Optical Society of America

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References

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  1. J. W. Lamb, "Miscellaneous data on materials for millimeter and submillimeter optics," Int. J. Infrared Millim. Waves 17, 1997-2034, (1996).
    [CrossRef]
  2. G. H. Sherman and P. D. Coleman, "Antireflection coatings for silicon in the 2.5-50 μm region," Appl. Opt. 10, 2675-2678 (1971).
    [CrossRef] [PubMed]
  3. S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
    [CrossRef]
  4. N. G. Ugras, J. Zmuidzinas, and H. G. LeDuc, "Quasioptical SIS Mixer with a Silicon Lens for Submillimeter Astronomy," in Proceedings of the 5th International Symposium Space Terahertz Technology (1994), p. 125.
  5. A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
    [CrossRef]
  6. J. W. Fowler, "The Atacama Cosmology Telescope Project," in Millimeter and Submillimeter Detectors for Astronomy II, J. Zmuidzinas, W.S. Holland, and S. Withington, eds., Proc. SPIE 5498, 1-10 (2004).
    [CrossRef]
  7. Fralock, Division of Lockwood Industries, Inc., 21054 Osborne Street, Canoga Park, Calif. 91304.
  8. Stycast 1266, Emerson and Cuming, 869 Washington Street, Canton, Mass. 02021.
  9. Chemlok AP-134, Lord Corporation, 111 Lord Drive, P.O. Box 8012, Cary, N.C. 27512.
  10. E.I. du Pont de Nemours and Company, 1007 Market Street, Wilmington, Del. 19898.
  11. W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
    [CrossRef]
  12. J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
    [CrossRef]
  13. V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
    [CrossRef]
  14. T. H. K. Barron and G. K. White, Heat Capacity and Thermal Expansion at Low Temperatures (Kluwer Academic, 1999).
    [CrossRef]
  15. G. W. Swift and R. E. Packard, "Thermal contraction of Vespel SP-22 and Stycast 1266 from 300 K to 4 K," Cryogenics 19, 362-363 (1979).
    [CrossRef]
  16. Diamond-MM-32-AT PC/104 board, Diamond Systems Corporation, 8430-D Central Avenue, Newark, Calif. 94560.
  17. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

2004 (1)

J. W. Fowler, "The Atacama Cosmology Telescope Project," in Millimeter and Submillimeter Detectors for Astronomy II, J. Zmuidzinas, W.S. Holland, and S. Withington, eds., Proc. SPIE 5498, 1-10 (2004).
[CrossRef]

2000 (1)

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

1996 (1)

J. W. Lamb, "Miscellaneous data on materials for millimeter and submillimeter optics," Int. J. Infrared Millim. Waves 17, 1997-2034, (1996).
[CrossRef]

1995 (1)

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

1990 (1)

J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
[CrossRef]

1979 (1)

G. W. Swift and R. E. Packard, "Thermal contraction of Vespel SP-22 and Stycast 1266 from 300 K to 4 K," Cryogenics 19, 362-363 (1979).
[CrossRef]

1974 (1)

W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

1971 (1)

Andreev, B. A.

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

Baker-Jarvis, J.

J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
[CrossRef]

Barron, T. H. K.

T. H. K. Barron and G. K. White, Heat Capacity and Thermal Expansion at Low Temperatures (Kluwer Academic, 1999).
[CrossRef]

Biber, S.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Coleman, P. D.

du Pont de Nemours, E. I.

E.I. du Pont de Nemours and Company, 1007 Market Street, Wilmington, Del. 19898.

Fowler, J. W.

J. W. Fowler, "The Atacama Cosmology Telescope Project," in Millimeter and Submillimeter Detectors for Astronomy II, J. Zmuidzinas, W.S. Holland, and S. Withington, eds., Proc. SPIE 5498, 1-10 (2004).
[CrossRef]

Gatesman, A. J.

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

Gusev, A. V.

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

Heidinger, R.

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

Ji, M.

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

Kissick, W. A.

J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
[CrossRef]

Lamb, J. W.

J. W. Lamb, "Miscellaneous data on materials for millimeter and submillimeter optics," Int. J. Infrared Millim. Waves 17, 1997-2034, (1996).
[CrossRef]

LeDuc, H. G.

N. G. Ugras, J. Zmuidzinas, and H. G. LeDuc, "Quasioptical SIS Mixer with a Silicon Lens for Submillimeter Astronomy," in Proceedings of the 5th International Symposium Space Terahertz Technology (1994), p. 125.

Martius, S.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
[CrossRef]

Musante, C.

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

Packard, R. E.

G. W. Swift and R. E. Packard, "Thermal contraction of Vespel SP-22 and Stycast 1266 from 300 K to 4 K," Cryogenics 19, 362-363 (1979).
[CrossRef]

Parshin, V. V.

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

Richter, J.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
[CrossRef]

Schmidt, L.-P.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
[CrossRef]

Sherman, G. H.

Shmagin, V. B.

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

Swift, G. W.

G. W. Swift and R. E. Packard, "Thermal contraction of Vespel SP-22 and Stycast 1266 from 300 K to 4 K," Cryogenics 19, 362-363 (1979).
[CrossRef]

Ugras, N. G.

N. G. Ugras, J. Zmuidzinas, and H. G. LeDuc, "Quasioptical SIS Mixer with a Silicon Lens for Submillimeter Astronomy," in Proceedings of the 5th International Symposium Space Terahertz Technology (1994), p. 125.

Vanzura, E. J.

J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
[CrossRef]

Waldman, J.

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

Weir, W. B.

W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

White, G. K.

T. H. K. Barron and G. K. White, Heat Capacity and Thermal Expansion at Low Temperatures (Kluwer Academic, 1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Yngvesson, S.

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

Zmuidzinas, J.

N. G. Ugras, J. Zmuidzinas, and H. G. LeDuc, "Quasioptical SIS Mixer with a Silicon Lens for Submillimeter Astronomy," in Proceedings of the 5th International Symposium Space Terahertz Technology (1994), p. 125.

Appl. Opt. (1)

Cryogenics (1)

G. W. Swift and R. E. Packard, "Thermal contraction of Vespel SP-22 and Stycast 1266 from 300 K to 4 K," Cryogenics 19, 362-363 (1979).
[CrossRef]

IEEE Microwave Guid. Wave Lett. (1)

A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guid. Wave Lett. 10, 264-266 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech. 38, 1096-1103 (1990).
[CrossRef]

Int. J. Infrared Millim. Waves (2)

V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin, "Silicon as an advanced window material for high power gyrotrons," Int. J. Infrared Millim. Waves 16, 863-877 (1995).
[CrossRef]

J. W. Lamb, "Miscellaneous data on materials for millimeter and submillimeter optics," Int. J. Infrared Millim. Waves 17, 1997-2034, (1996).
[CrossRef]

Proc. IEEE (1)

W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

Proc. SPIE (1)

J. W. Fowler, "The Atacama Cosmology Telescope Project," in Millimeter and Submillimeter Detectors for Astronomy II, J. Zmuidzinas, W.S. Holland, and S. Withington, eds., Proc. SPIE 5498, 1-10 (2004).
[CrossRef]

Other (9)

Fralock, Division of Lockwood Industries, Inc., 21054 Osborne Street, Canoga Park, Calif. 91304.

Stycast 1266, Emerson and Cuming, 869 Washington Street, Canton, Mass. 02021.

Chemlok AP-134, Lord Corporation, 111 Lord Drive, P.O. Box 8012, Cary, N.C. 27512.

E.I. du Pont de Nemours and Company, 1007 Market Street, Wilmington, Del. 19898.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, "Design of artificial dielectrics for anti-reflection-coatings," in Proceedings of the 33rd European Microwave Conference, Munich (2003), pp. 1115-1118.
[CrossRef]

N. G. Ugras, J. Zmuidzinas, and H. G. LeDuc, "Quasioptical SIS Mixer with a Silicon Lens for Submillimeter Astronomy," in Proceedings of the 5th International Symposium Space Terahertz Technology (1994), p. 125.

T. H. K. Barron and G. K. White, Heat Capacity and Thermal Expansion at Low Temperatures (Kluwer Academic, 1999).
[CrossRef]

Diamond-MM-32-AT PC/104 board, Diamond Systems Corporation, 8430-D Central Avenue, Newark, Calif. 94560.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (4)

Fig. 1
Fig. 1

Schematic (a) top and (b) side view of the reflectometer. The axes in (a) correspond to the phase of rotation (x axis) in Fig. 2. The plate rotates via a motor and belt at ω = 7.5 rad∕s under a fixed source and receiver. Five samples can be viewed in one revolution.

Fig. 2
Fig. 2

Four overlaid reflection plots from the reflectometer. Two samples are shown both before and after (denoted by primes) applying AR coating. The reflectometer measures aluminum in regions labeled “a”, and Eccosorb or a mounted sample at positions b1–b5. In the above plot, only b2 has a sample mounted. The stability of the measurement from one sample to another is good, as shown by the almost perfect overlap of the data.

Fig. 3
Fig. 3

Room-temperature transmission T of the coated 4 mm thick silicon flat (Flat 7), both modeled (black) and measured on the FTS (gray). The measurement is the ratio of a sample to a reference spectrum. The lower curve shows that the difference (measurement minus model) is within 5% of zero through the well-measured range. The high transmission near 133 and 400 GHz is due to the AR coating being λ0∕4 and 3λ0∕4 thick. The slow reduction in T with increasing frequency is due to increasing loss in the coating and glue. This sample was made before precise values of the index of Cirlex and Stycast 1266 were known. Thus, the center of the passband window, 133 GHz, is 12 GHz below our target frequency.

Fig. 4
Fig. 4

Absorption and reflection loss modeled in two notional lenses, 5 and 20 mm thick. Each lens is assumed to be coated with tg = 20 μm of glue and enough Cirlex so that (ngtg + nctc ) equals one quarter of the vacuum wavelength. Solid curves indicate normal incidence; dashed curves are for 40° incident angle. The curves labeled A5 and A20 show the absorption loss. The R20 curves give the reflection from the 20 mm lens; the results are not visibly different for reflection from the 5 mm lens. Absorption increases for oblique angles and at higher frequencies. We show the expected loss at room temperature in 5000 Ω cm silicon. Cryogenically, absorption loss should be reduced.

Tables (2)

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Table 1 Dielectric Properties of the Materials for AR Coating

Tables Icon

Table 2 Reflection of Silicon Before and After AR Coating

Equations (3)

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

tan   δ Im ( ϵ ˜ ) Re ( ϵ ˜ ) = 0.027 3.37 = 0.008.
ϵ ˜ ( ν ) = Re ( ϵ ˜ ) + i 2 π ν ϵ o ρ
n c t c + n g t g = λ 0 / 4 .

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