OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 36 — Dec. 20, 2013
  • pp: 8747–8758

Large-aperture wide-bandwidth antireflection-coated silicon lenses for millimeter wavelengths

R. Datta, C. D. Munson, M. D. Niemack, J. J. McMahon, J. Britton, E. J. Wollack, J. Beall, M. J. Devlin, J. Fowler, P. Gallardo, J. Hubmayr, K. Irwin, L. Newburgh, J. P. Nibarger, L. Page, M. A. Quijada, B. L. Schmitt, S. T. Staggs, R. Thornton, and L. Zhang  »View Author Affiliations


Applied Optics, Vol. 52, Issue 36, pp. 8747-8758 (2013)
http://dx.doi.org/10.1364/AO.52.008747


View Full Text Article

Enhanced HTML    Acrobat PDF (1191 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

OCIS Codes
(000.2190) General : Experimental physics
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.3630) Optical design and fabrication : Lenses
(310.1210) Thin films : Antireflection coatings
(160.1245) Materials : Artificially engineered materials
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Thin Films

History
Original Manuscript: July 26, 2013
Revised Manuscript: October 24, 2013
Manuscript Accepted: October 25, 2013
Published: December 16, 2013

Citation
R. Datta, C. D. Munson, M. D. Niemack, J. J. McMahon, J. Britton, E. J. Wollack, J. Beall, M. J. Devlin, J. Fowler, P. Gallardo, J. Hubmayr, K. Irwin, L. Newburgh, J. P. Nibarger, L. Page, M. A. Quijada, B. L. Schmitt, S. T. Staggs, R. Thornton, and L. Zhang, "Large-aperture wide-bandwidth antireflection-coated silicon lenses for millimeter wavelengths," Appl. Opt. 52, 8747-8758 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-36-8747


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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]
  2. 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]
  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]
  4. S. Hanany, M. D. Niemack, and L. Page, “CMB telescopes and optical systems,” arXiv:1206.2402 (2012).
  5. J. C. Thompson and B. A. Younglove, “Thermal conductivity of silicon at low temperatures,” J. Phys. Chem. Solids 20, 146–149 (1961). [CrossRef]
  6. S. W. Va Sciver, Helium Cryogenics, International Cryogenics Monograph Series (Springer Science+Business Media, 2012), Chap. 2.
  7. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1990), pp. 749–786.
  8. 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]
  9. 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]
  10. S. B. Cohn, Lens Type Radiators: Antenna Engineering Handbook (McGraw-Hill, 1961).
  11. 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]
  12. 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).
  13. P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by ‘moth eye’ principle,” Nature 244, 281–282 (1973). [CrossRef]
  14. B. S. Thornton, “Limit of the moth’s eye principle and other impedance-matching corrugations for solar-absorber design,” J. Opt. Soc. Am. 65, 267–270 (1975). [CrossRef]
  15. M. E. Motamedi, W. H. Southwell, and W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992). [CrossRef]
  16. 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]
  17. 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.
  18. 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]
  19. 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).
  20. 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]
  21. 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]
  22. 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).
  23. 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]
  24. S. Rytov, “The electromagnetic properties of finely layered medium,” Sov. Phys. JETP 2, 466–475 (1956).
  25. S. Biber, J. Richter, S. Martius, and L. P. Schmidt, “Design of artificial dielectrics for anti-reflection-coatings,” 33rd European Microwave Conference, Munich, 2003.
  26. 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]
  27. T. K. Gaylord, W. E. Baird, and M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986). [CrossRef]
  28. D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982). [CrossRef]
  29. 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]
  30. W. G. Egan and D. E. Aspnes, “Finite-wavelength effects in composite media,” Phys. Rev. B 26, 5313–5321 (1982). [CrossRef]
  31. A. Wagner-Gentner, U. U. Graf, D. Rabanus, and K. Jacobs, “Low loss THz window,” Infrared Phys. Technol. 48, 249–253 (2006). [CrossRef]
  32. G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks and Coupling Structures (McGraw-Hill, 1964), pp. 300–304.
  33. D. H. Raguin and G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surfaces profiles,” Appl. Opt. 32, 2582–2598 (1993). [CrossRef]
  34. J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
  35. “Ansoft High Frequency Structure Simulator (HFSS) software package,” http://www.ansys.com/Products/Simulation+Technology/Electromagnetics/High-Performance+Electronic+Design/ANSYS+HFSS .
  36. T. Duffar, Crystal Growth Processes Based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques (Wiley, 2010).
  37. 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]
  38. 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).
  39. 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]
  40. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  41. F. Gervais, “High-temperature infrared reflectivity spectroscopy by scanning interferometry,” in Electromagnetic Waves in Matter, K. J. Button, ed., Part I, Vol. 8 of Infrared, and Millimeter Waves (Academic, 1983), pp. 284–287.
  42. 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]
  43. 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]
  44. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer, 1984), Chap. 4.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited