Abstract

The increasing scale of cryogenic detector arrays for submillimeter and millimeter wavelength astrophysics has led to the need for large aperture, high index of refraction, low loss, cryogenic refracting optics. Silicon with n=3.4, low loss, and high thermal conductivity is a nearly optimal material for these purposes but requires an antireflection (AR) coating with broad bandwidth, low loss, low reflectance, and a matched coefficient of thermal expansion. We present an AR coating for curved silicon optics comprised of subwavelength features cut into the lens surface with a custom three-axis silicon dicing saw. These features constitute a metamaterial that behaves as a simple dielectric coating. We have fabricated silicon lenses as large as 33.4 cm in diameter with micromachined layers optimized for use between 125 and 165 GHz. Our design reduces average reflections to a few tenths of a percent for angles of incidence up to 30° with low cross polarization. We describe the design, tolerance, manufacture, and measurements of these coatings and present measurements of the optical properties of silicon at millimeter wavelengths at cryogenic and room temperatures. This coating and lens fabrication approach is applicable from centimeter to submillimeter wavelengths and can be used to fabricate coatings with greater than octave bandwidth.

© 2013 Optical Society of America

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2012 (2)

D. Bintley, M. MacIntosh, W. Holland, J. Dempsey, P. Friberg, H. Thomas, P. Ade, R. Sudiwala, K. Irwin, G. Hilton, M. Niemack, M. Amiri, E. Chapin, and M. Halpern, “Commissioning SCUBA-2 at JCMT and optimising the performance of the superconducting TES arrays,” J. Low Temp. Phys. 167, 152–160 (2012).
[CrossRef]

J. J. McMahon, J. Beall, D. Becker, H. M. Cho, R. Datta, A. Fox, N. Halverson, J. Hubmayr, K. Irwin, J. Nibarger, M. Niemack, and H. Smith, “Multi-chroic feed-horn coupled TES polarimeters,” J. Low Temp. Phys. 167, 879–884 (2012).
[CrossRef]

2010 (1)

P. Han, Y. W. Chen, and X.-C. Zhang, “Application of silicon micropyramid structures for antireflection of terahertz waves,” IEEE J. Sel. Top. Quantum Electron. 16, 338–343 (2010).
[CrossRef]

2009 (1)

2008 (3)

S. Padin, Z. Staniszewski, R. Keisler, M. Joy, A. A. Stark, P. A. R. Ade, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, T. M. Crawford, A. T. Crites, M. A. Dobbs, N. W. Halverson, S. Heimsath, R. E. Hills, W. L. Holzapfel, C. Lawrie, A. T. Lee, E. M. Leitch, J. Leong, W. Lu, M. Lueker, J. J. McMahon, S. S. Meyer, J. J. Mohr, T. E. Montroy, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, E. Shirokoff, H. G. Spieler, and J. D. Vieira, “South Pole Telescope optics,” Appl. Opt. 47, 4418–4428 (2008).
[CrossRef]

M. Shimon, B. Keating, N. Ponthieu, and E. Hivon, “CMB polarization systematics due to beam asymmetry: impact on inflationary science,” Phys. Rev. D77, 083003 (2008).

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

2007 (1)

2006 (4)

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging (invited paper),” J. Opt. Soc. Am. B 23, 391–403 (2006).
[CrossRef]

J. Lau, J. Fowler, T. Marriage, L. Page, J. Leong, E. Wishnow, R. Henry, E. Wollack, M. Halpern, D. Marsden, and G. Marsden, “Millimeter-wave antireflection coating for cryogenic silicon lenses,” Appl. Opt. 45, 3746–3751 (2006).
[CrossRef]

A. Wagner-Gentner, U. U. Graf, D. Rabanus, and K. Jacobs, “Low loss THz window,” Infrared Phys. Technol. 48, 249–253 (2006).
[CrossRef]

J. Krupka, J. Breeze, A. Centeno, N. Alford, T. Claussen, and L. Jensen, “Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies,” IEEE Trans. Microwave Theor. Tech. 54, 3995–4000 (2006).
[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]

1994 (2)

M. N. Afsar and H. Chi, “Millimeter wave complex refractive index, complex dielectric constant, and loss tangent of extra high purity and compensated silicon,” Int. J. Infrared Millim. Waves 15,  1181–1188 (1994).

D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef]

1993 (1)

1992 (1)

1990 (1)

M. Van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2  THz,” Appl. Phys. Lett. 56, 1694–1696 (1990).
[CrossRef]

1989 (1)

A. MacKay, “Proof of polarization independence and nonexistence of crosspolar terms for targets presenting n-fold (n>2) rotational symmetry with special reference to frequency-selective surfaces,” Electron. Lett. 25, 1624–1625 (1989).
[CrossRef]

1986 (1)

1984 (2)

Y. Okada and Y. Tokumaru, “Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500  K,” J. Appl. Phys. 56, 314–320 (1984).
[CrossRef]

P.-S. Kildal, K. Jakobsen, and K. Sudhakar Rao, “Meniscus-lens-corrected corrugated horn: a compact feed for a Cassegrain antenna,” IEE Proc. H Microwaves Opt. Antennas 131, 390–394 (1984).
[CrossRef]

1982 (3)

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

D. E. Aspnes, “Bounds on allowed values of the effective dielectric function of two-component composites at finite frequencies,” Phys. Rev. B 25, 1358–1361 (1982).
[CrossRef]

W. G. Egan and D. E. Aspnes, “Finite-wavelength effects in composite media,” Phys. Rev. B 26, 5313–5321 (1982).
[CrossRef]

1975 (1)

1973 (1)

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by ‘moth eye’ principle,” Nature 244, 281–282 (1973).
[CrossRef]

1961 (1)

J. C. Thompson and B. A. Younglove, “Thermal conductivity of silicon at low temperatures,” J. Phys. Chem. Solids 20, 146–149 (1961).
[CrossRef]

1956 (1)

S. Rytov, “The electromagnetic properties of finely layered medium,” Sov. Phys. JETP 2, 466–475 (1956).

Aboobaker, A. M.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
[CrossRef]

Ade, P.

D. Bintley, M. MacIntosh, W. Holland, J. Dempsey, P. Friberg, H. Thomas, P. Ade, R. Sudiwala, K. Irwin, G. Hilton, M. Niemack, M. Amiri, E. Chapin, and M. Halpern, “Commissioning SCUBA-2 at JCMT and optimising the performance of the superconducting TES arrays,” J. Low Temp. Phys. 167, 152–160 (2012).
[CrossRef]

Ade, P. A. R.

J. Zhang, P. A. R. Ade, P. Mauskopf, L. Moncelsi, G. Savini, and N. Whitehouse, “New artificial dielectric metamaterial and its application as a terahertz antireflection coating,” Appl. Opt. 48, 6635–6642 (2009).
[CrossRef]

S. Padin, Z. Staniszewski, R. Keisler, M. Joy, A. A. Stark, P. A. R. Ade, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, T. M. Crawford, A. T. Crites, M. A. Dobbs, N. W. Halverson, S. Heimsath, R. E. Hills, W. L. Holzapfel, C. Lawrie, A. T. Lee, E. M. Leitch, J. Leong, W. Lu, M. Lueker, J. J. McMahon, S. S. Meyer, J. J. Mohr, T. E. Montroy, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, E. Shirokoff, H. G. Spieler, and J. D. Vieira, “South Pole Telescope optics,” Appl. Opt. 47, 4418–4428 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
[CrossRef]

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Afsar, M. N.

M. N. Afsar and H. Chi, “Millimeter wave complex refractive index, complex dielectric constant, and loss tangent of extra high purity and compensated silicon,” Int. J. Infrared Millim. Waves 15,  1181–1188 (1994).

Aguirre, J.

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Aird, K. A.

Alford, N.

J. Krupka, J. Breeze, A. Centeno, N. Alford, T. Claussen, and L. Jensen, “Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies,” IEEE Trans. Microwave Theor. Tech. 54, 3995–4000 (2006).
[CrossRef]

Allen, C.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

Amiri, M.

D. Bintley, M. MacIntosh, W. Holland, J. Dempsey, P. Friberg, H. Thomas, P. Ade, R. Sudiwala, K. Irwin, G. Hilton, M. Niemack, M. Amiri, E. Chapin, and M. Halpern, “Commissioning SCUBA-2 at JCMT and optimising the performance of the superconducting TES arrays,” J. Low Temp. Phys. 167, 152–160 (2012).
[CrossRef]

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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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J. J. McMahon, J. Beall, D. Becker, H. M. Cho, R. Datta, A. Fox, N. Halverson, J. Hubmayr, K. Irwin, J. Nibarger, M. Niemack, and H. Smith, “Multi-chroic feed-horn coupled TES polarimeters,” J. Low Temp. Phys. 167, 879–884 (2012).
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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
[CrossRef]

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Dicker, S. R.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
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Doriese, W. B.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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P.-S. Kildal, K. Jakobsen, and K. Sudhakar Rao, “Meniscus-lens-corrected corrugated horn: a compact feed for a Cassegrain antenna,” IEE Proc. H Microwaves Opt. Antennas 131, 390–394 (1984).
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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
[CrossRef]

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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K. F. Schuster, N. Krebs, Y. Guillaud, F. Mattiocco, M. Kornberg, and A. Poglitsch, “Micro-machined quasi-optical elements for THz applications,” Sixteenth International Symposium on Space Terahertz Technology, Chalmers University of Technology, Gšteborg, Sweden, May2–4, 2005, pp. 524–528.

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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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D. Rosen, A. Suzuki, B. Keating, W. Krantz, A. T. Lee, E. Quealy, P. L. Richards, P. Siritanasak, and W. Walker, “Epoxy-based broadband anti-reflection coating for millimeter-wave optics,” arXiv:1307.7827 (2013).

Krebs, N.

K. F. Schuster, N. Krebs, Y. Guillaud, F. Mattiocco, M. Kornberg, and A. Poglitsch, “Micro-machined quasi-optical elements for THz applications,” Sixteenth International Symposium on Space Terahertz Technology, Chalmers University of Technology, Gšteborg, Sweden, May2–4, 2005, pp. 524–528.

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J. Krupka, J. Breeze, A. Centeno, N. Alford, T. Claussen, and L. Jensen, “Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies,” IEEE Trans. Microwave Theor. Tech. 54, 3995–4000 (2006).
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Lau, J. M.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
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Lawrie, C.

Lee, A. T.

Leitch, E. M.

Leong, J.

Limon, M.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
[CrossRef]

J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
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D. Bintley, M. MacIntosh, W. Holland, J. Dempsey, P. Friberg, H. Thomas, P. Ade, R. Sudiwala, K. Irwin, G. Hilton, M. Niemack, M. Amiri, E. Chapin, and M. Halpern, “Commissioning SCUBA-2 at JCMT and optimising the performance of the superconducting TES arrays,” J. Low Temp. Phys. 167, 152–160 (2012).
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M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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Marsden, G.

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K. F. Schuster, N. Krebs, Y. Guillaud, F. Mattiocco, M. Kornberg, and A. Poglitsch, “Micro-machined quasi-optical elements for THz applications,” Sixteenth International Symposium on Space Terahertz Technology, Chalmers University of Technology, Gšteborg, Sweden, May2–4, 2005, pp. 524–528.

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Mauskopf, P. D.

McMahon, J.

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

McMahon, J. J.

Menanteau, F.

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Meyer, S. S.

Moharam, M. G.

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Moodley, K.

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Morris, G. M.

Moseley, H.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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Nibarger, J.

J. J. McMahon, J. Beall, D. Becker, H. M. Cho, R. Datta, A. Fox, N. Halverson, J. Hubmayr, K. Irwin, J. Nibarger, M. Niemack, and H. Smith, “Multi-chroic feed-horn coupled TES polarimeters,” J. Low Temp. Phys. 167, 879–884 (2012).
[CrossRef]

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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

Niemack, M.

J. J. McMahon, J. Beall, D. Becker, H. M. Cho, R. Datta, A. Fox, N. Halverson, J. Hubmayr, K. Irwin, J. Nibarger, M. Niemack, and H. Smith, “Multi-chroic feed-horn coupled TES polarimeters,” J. Low Temp. Phys. 167, 879–884 (2012).
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D. Bintley, M. MacIntosh, W. Holland, J. Dempsey, P. Friberg, H. Thomas, P. Ade, R. Sudiwala, K. Irwin, G. Hilton, M. Niemack, M. Amiri, E. Chapin, and M. Halpern, “Commissioning SCUBA-2 at JCMT and optimising the performance of the superconducting TES arrays,” J. Low Temp. Phys. 167, 152–160 (2012).
[CrossRef]

Niemack, M. D.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
[CrossRef]

M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

S. Hanany, M. D. Niemack, and L. Page, “CMB telescopes and optical systems,” arXiv:1206.2402 (2012).

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M. D. Niemack, P. A. R. Ade, J. Aguirre, F. Barrientos, J. A. Beall, J. R. Bond, J. Britton, H. M. Cho, S. Das, M. J. Devlin, S. Dicker, J. Dunkley, R. Dunner, J. W. Fowler, A. Hajian, M. Halpern, M. Hasselfield, G. C. Hilton, M. Hilton, J. Hubmayr, J. P. Hughes, L. Infante, K. D. Irwin, N. Jarosik, J. Klein, A. Kosowsky, T. A. Marriage, J. McMahon, F. Menanteau, K. Moodley, J. P. Nibarger, M. R. Nolta, L. A. Page, B. Partridge, E. D. Reese, J. Sievers, D. N. Spergel, S. T. Staggs, R. Thornton, C. Tucker, E. Wollack, and K. W. Yoon, “ACTPol: a polarization sensitive receiver for the Atacama Cosmology Telescope,” Proc. SPIE7741, 77411S (2010).

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Page, L.

M. D. Niemack, Y. Zhao, E. Wollack, R. Thornton, E. R. Switzer, D. S. Swetz, S. T. Staggs, L. Page, O. Stryzak, H. Moseley, T. A. Marriage, M. Limon, J. M. Lau, J. Klein, M. Kaul, N. Jarosik, K. D. Irwin, A. D. Hincks, G. C. Hilton, M. Halpern, J. W. Fowler, R. P. Fisher, R. Dunner, W. B. Doriese, S. R. Dicker, M. J. Devlin, J. Chervenak, B. Burger, E. S. Battistelli, J. Appel, M. Amiri, C. Allen, and A. M. Aboobaker, “A kilopixel array of TES bolometers for ACT: development, testing, and first light,” J. Low Temp. Phys. 151, 690–696 (2008).
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J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, “Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera,” Appl. Opt. 46, 3444–3454 (2007).
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J. Lau, J. Fowler, T. Marriage, L. Page, J. Leong, E. Wishnow, R. Henry, E. Wollack, M. Halpern, D. Marsden, and G. Marsden, “Millimeter-wave antireflection coating for cryogenic silicon lenses,” Appl. Opt. 45, 3746–3751 (2006).
[CrossRef]

S. Hanany, M. D. Niemack, and L. Page, “CMB telescopes and optical systems,” arXiv:1206.2402 (2012).

Page, L. A.

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D. Rosen, A. Suzuki, B. Keating, W. Krantz, A. T. Lee, E. Quealy, P. L. Richards, P. Siritanasak, and W. Walker, “Epoxy-based broadband anti-reflection coating for millimeter-wave optics,” arXiv:1307.7827 (2013).

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Siritanasak, P.

D. Rosen, A. Suzuki, B. Keating, W. Krantz, A. T. Lee, E. Quealy, P. L. Richards, P. Siritanasak, and W. Walker, “Epoxy-based broadband anti-reflection coating for millimeter-wave optics,” arXiv:1307.7827 (2013).

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Figures (14)

Fig. 1.
Fig. 1.

Left: Ray diagram of one set of ACTPol reimaging optics, which includes three silicon lenses feeding a detector array. Right: Histogram of the angles of incidence of rays at the surfaces of these three silicon lenses.

Fig. 2.
Fig. 2.

Geometry of the two-layer metamaterial AR coating. The left side shows a cross section through the center of the pillars indicating the design parameters discussed in the text. The right side shows an isometric view of the structure resulting from making cuts along two perpendicular directions.

Fig. 3.
Fig. 3.

Comparison of the reflectance calculated from an HFSS numerical simulation of a pillar geometry to fits based on a model of a simple dielectric layer. The geometry is specified in the inset in the top. In the simulated geometry, p = 400 μm , t phys = 220 μm , k = 40 μm , and n Si = 3.38 . A comparison between fits where only the index n is free and where both the index n and thickness t are varied is shown. The HFSS simulation and the best fit curve differ by 5% at 220 GHz (1.36 mm) for the analytic fit varying n and t and at 180 GHz (1.67 mm) for the analytic fit varying only n . This corresponds to the minimum wavelength, λ 5 % , (and a corresponding maximum frequency f 5 % ) for the specified pitch, p , below (above) which the layer no longer behaves as a simple dielectric layer.

Fig. 4.
Fig. 4.

Summary of results from HFSS simulations of single layers of pillars with varying geometry. Left: Minimum wavelength λ 5 % for which the single pillar layer is fit by an analytic model to 5% accuracy as a function of pitch p at normal incidence. Center: effective index of refraction n eff as a function of the volume fill factor v f obtained by fitting the simulated reflectances up to the minimum wavelength λ 5 % = 1360 μm for a pitch p = 400 μm , 40 μm. The line labeled “Biber model” is a prediction from the analytic Biber model [25], which corresponds to the quasi-static circuit approximation for the media. Right: Thickness t eff for a slab dielectric quarter-wave layer divided by the thickness t phys of pillars forming an effective quarter-wave coating as a function of p / λ . The index of the simulated dielectric layer was held fixed at n Si for these simulations. A quadratic fit is plotted to guide the eye.

Fig. 5.
Fig. 5.

Left: Simulation of the performance of the ACTPol coating at a range of angles of incidence. Right: Unit cell geometry (based on measured cut profiles) modeled using HFSS.

Fig. 6.
Fig. 6.

Cross section of the perimeter of the ACTPol lens 2, which is designed to enable machining of the AR layers and clamping the lens without damaging the AR coatings.

Fig. 7.
Fig. 7.

Measured silicon transmission at room temperature (upper panels) and 4.5 K (lower panels). The left and right columns in the panel are for samples specified as 1 < ρ < 5 Ω - cm and ρ > 500 Ω - cm , respectively; the sample thickness is 180 μm . The figure contains the measured FTS data (red), model (dashed blue), and residual (green).

Fig. 8.
Fig. 8.

The custom, micrometer accurate, three axis silicon dicing system used to fabricate AR coatings on the lenses. The labels identify the key components and axes described in Section 6.

Fig. 9.
Fig. 9.

Left: Photograph of the curved front surface of an AR coated ACTPol silicon lens (lens 2) with zoomed view of a small patch. Right: Photographs taken with side-looking metrology microscope of a reference wafer taken prior to and after cutting the coatings on a lens.

Fig. 10.
Fig. 10.

Comparison between simulations and measurements of the fabricated lens. The two-sided simulations model the AR coatings on both sides of a flat silicon sample of thickness equal to that of the lens at its center. The single-sided simulations model the AR coatings on only one side of a flat silicon sample.

Fig. 11.
Fig. 11.

This figure shows the families of machining errors considered in the tolerance analysis and described in the text. The dashed lines show the target shape for the grooves and that for the pillars while the white space in the gray represents the material as actually cut. Therefore difference between the dashed region and the white region represent machining errors. For the asymmetric depth and damaged row errors the sketches show the geometry of the errors.

Fig. 12.
Fig. 12.

Band averaged reflectance at a 15° angle of incidence as a function of changes in the pitch. The gray region shows range for which the performance is within 3 dB of the fiducial design.

Fig. 13.
Fig. 13.

This figure shows the impact of errors in the kerf, slopes in the sidewalls, overall depth errors, and asymmetric differences in depth between the two orthogonal cuts. The color scale presents the degradation in reflection at 15° incidence compared to the simulations in Fig. 5. The fiducial design is at the coordinate (0, 0) in all the plots as highlighted by a “+” or arrow. The outer edge of the light blue contour (see label) represents 3 dB degradation. The horizontal (vertical) axis represents errors in the inner (outer) layer for the labeled parameters.

Fig. 14.
Fig. 14.

Left: Simulated impact of having the surface of the lens tilted by 10°. Right: Simulated impact of variation in the refractive index of the silicon substrate.

Tables (3)

Tables Icon

Table 1. Parameters for the ACTPol Metamaterial Coating

Tables Icon

Table 2. Silicon Drude Model Fit Parameters

Tables Icon

Table 3. Summary of the 3 dB Sensitivities for All Parameters Described in the Text

Equations (2)

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p < λ ( n s + n i sin θ i ) ,
ε r * ( ω ) = ε * ω p 2 ω · ( ω + i Γ ) ,

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