Abstract

Large heterodyne receiver arrays (~100 pixel) allow astronomical instrumentations to map more area within limited space mission lifetime. One challenge is to generate multiple local oscillator (LO) beams. Here, we succeeded in generating 81 beams at 3.86 THz by combining a reflective, metallic Fourier grating with an unidirectional antenna coupled 3rd-order distributed feedback (DFB) quantum cascade laser (QCL). We have measured the diffracted 81 beams by scanning a single pyroelectric detector at a plane, which is in the far field for the diffraction beams. The measured output beam pattern agrees well with a simulated result from COMSOL Multiphysics, with respect to the angular distribution and power distribution among the 81 beams. We also derived the diffraction efficiency to be 94 ± 3%, which is very close to what was simulated for a manufactured Fourier grating (97%). For an array of equal superconducting hot electron bolometer mixers, 64 out of 81 beams can pump the HEB mixers with similar power, resulting in receiver sensitivities within 10%. Such a combination of a Fourier grating and a QCL can create an LO with 100 beams or more, enabling a new generation of large heterodyne arrays for astronomical instrumentation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  15. T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), 257 (2015).
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    [Crossref] [PubMed]
  19. Y. Nakata, K. Osawa, and N. Miyanaga, “Utilization of the high spatial-frequency component in adaptive beam shaping by using a virtual diagonal phase grating,” Sci. Rep. 9(1), 4640 (2019).
    [Crossref] [PubMed]
  20. H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
    [Crossref]
  21. G. Schmahl, “Holographically made diffraction gratings for the visible, UV and soft X-ray region,” J. Spectrosc. Soc. Jpn. 23, 3–11 (1974).
  22. P. Bliek, R. Deleuil, M. Breidne, and D. Maystre, “Microwave verification of a numerical optimization of fourier gratings,” Appl. Phys. (Berl.) 24(2), 147–150 (1981).
    [Crossref]
  23. N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
    [Crossref]
  24. W. Lanigan, N. Trappe, J. A. Murphy, R. Colgan, C. O’Sullivan, and S. Withington, “Quasi-optical multiplexing using reflection phase gratings,” in 11th International Symposium on Space Terahertz Technology (ISSTT, 2000), pp. 616–625.
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    [Crossref]
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    [Crossref]
  27. B. Mirzaei, J. R. G. Silva, Y. C. Luo, X. X. Liu, L. Wei, D. J. Hayton, J. R. Gao, and C. Groppi, “Efficiency of multi-beam Fourier phase gratings at 1.4 THz,” Opt. Express 25(6), 6581–6588 (2017).
    [Crossref] [PubMed]
  28. J. R. G. Silva, B. Mirzaei, W. Laauwen, N. More, A. Young, C. Kulesa, C. Walker, A. Khalatpour, Q. Hu, C. Groppi, and J. R. Gao, “4×2 HEB receiver at 4.7 THz for GUSTO,” Proc. SPIE 10708, 107080Z (2018).
    [Crossref]
  29. H. Dammann and E. Klotz, “Coherent Optical Generation and Inspection of Two-dimensional Periodic Structures,” Opt. Acta (Lond.) 24(4), 505–515 (1977).
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  30. A. Khalatpour, J. L. Reno, N. P. Kherani, and Q. Hu, “Unidirectional photonic wire laser,” Nat. Photonics 11(9), 555–559 (2017).
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  31. J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1968).
  32. C O M S O L. Multiphysics, https://www.comsol.com/rf-module .
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    [Crossref]
  34. P. Khosropanah, J. R. Gao, W. M. Laauwen, and M. Hajeniusb, “Low noise NbN hot electron bolometer mixer at 4.3 THz,” Appl. Phys. Lett. 91(22), 221111 (2007).
    [Crossref]
  35. H. Ekström, B. S. Karasik, E. L. Kollberg, and K. S. Yngvesson, “Conversion gain and noise of niobium superconducting hot-electron-mixers,” IEEE Trans. Microw. Theory Tech. 43(4), 938–947 (1995).
    [Crossref]
  36. The isothermal technique is based on the assumption that the mixer has the same response to LO power and DC power, we can estimate the absorbed LO power in a mixer from the pumped current-voltage curves. In [34] P. Khosropanah, et al measured a set of current-voltage curves of a similar HEB mixer pumped with different LO power operated at 4.3 THz, and from the data when the LO power varies within ~40% the change in HEB mixer’s bias current is ~37%, which responds to ~10% changes in the noise temperature.
  37. U. U. Graf, “Enhanced diffraction efficiency of two-dimensional phase gratings,” Opt. Express 26(25), 32739–32742 (2018).
    [Crossref] [PubMed]

2019 (3)

C. Pabst, R. Higgins, J. R. Goicoechea, D. Teyssier, O. Berne, E. Chambers, M. Wolfire, S. T. Suri, R. Guesten, J. Stutzki, U. U. Graf, C. Risacher, and A. G. G. M. Tielens, “Disruption of the Orion molecular core 1 by wind from the massive star θ1 Orionis C,” Nature 565(7741), 618–621 (2019).
[Crossref] [PubMed]

Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
[Crossref]

Y. Nakata, K. Osawa, and N. Miyanaga, “Utilization of the high spatial-frequency component in adaptive beam shaping by using a virtual diagonal phase grating,” Sci. Rep. 9(1), 4640 (2019).
[Crossref] [PubMed]

2018 (3)

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
[Crossref]

J. R. G. Silva, B. Mirzaei, W. Laauwen, N. More, A. Young, C. Kulesa, C. Walker, A. Khalatpour, Q. Hu, C. Groppi, and J. R. Gao, “4×2 HEB receiver at 4.7 THz for GUSTO,” Proc. SPIE 10708, 107080Z (2018).
[Crossref]

U. U. Graf, “Enhanced diffraction efficiency of two-dimensional phase gratings,” Opt. Express 26(25), 32739–32742 (2018).
[Crossref] [PubMed]

2017 (4)

2016 (2)

Q.-K. Li, Q.-D. Chen, L.-G. Niu, Y.-H. Yu, L. Wang, Y.-L. Sun, and H.-B. Sun, “Sapphire-Based Dammann Gratings for UV Beam Splitting,” IEEE Photonics J. 8(6), 2500208 (2016).
[Crossref]

P. Garbacz, “Terahertz imaging – principles, techniques, benefits, and limitations,” Problemy Eksploatacji - Maintenance Problems 1, 81–92 (2016).

2015 (3)

U. U. Graf, C. E. Honingh, K. Jacobs, and J. Stutzki, “Terahertz Heterodyne Array Receivers for Astronomy,” J. Infrared Millim. Terahertz Waves 36(10), 896–921 (2015).
[Crossref]

M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
[Crossref] [PubMed]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), 257 (2015).
[Crossref]

2014 (2)

A. M. Korolev, V. M. Shulga, and S. I. Tarapov, “Extra-low power consumption amplifier based on HEMT in unsaturated mode for use at subkelvin ambient temperatures,” Cryogenics 60, 76–79 (2014).
[Crossref]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

2011 (2)

C. E. Groppi and J. H. Kawamura, “Coherent Detector Arrays for Terahertz Astrophysics Applications,” IEEE Trans. Terahertz Sci. Technol. 1(1), 85–96 (2011).
[Crossref]

S. Kumar, “Recent Progress in Terahertz Quantum Cascade Lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 38–47 (2011).
[Crossref]

2008 (1)

E. Gerecht, D. Gu, L. You, and K. Sigfrid Yngvesson, “A Passive Heterodyne Hot Electron Bolometer Imager Operating at 850 GHz,” IEEE Trans. Microw. Theory Tech. 56(5), 1083–1091 (2008).
[Crossref]

2007 (2)

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
[Crossref] [PubMed]

P. Khosropanah, J. R. Gao, W. M. Laauwen, and M. Hajeniusb, “Low noise NbN hot electron bolometer mixer at 4.3 THz,” Appl. Phys. Lett. 91(22), 221111 (2007).
[Crossref]

2006 (1)

P. H. Siegel and R. J. Dengler, “Terahertz Heterodyne Imaging Part II: Instruments,” J. Infrared Millim. Terahertz Waves 27(5), 631–655 (2006).
[Crossref]

2003 (1)

C. E. Groppi, C. K. Walker, C. Kulesa, D. Golish, A. Hedden, P. Gensheimer, G. Narayanan, A. W. Lichtenberger, U. U. Graf, and S. Heyminck, “Desert STAR: A 7 pixel 345 GHz heterodyne array receiver for the Heinrich Hertz Telescope,” Proc. SPIE 4855, 330–337 (2003).
[Crossref]

2001 (1)

U. U. Garf and S. Heyminck, “Fourier grating as submillimeter beam splitter,” IEEE Trans. Antenn. Propag. 49(4), 542–543 (2001).
[Crossref]

1999 (1)

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, and S. Withington, “Modal Analysis of the Quasi-Optical Performance of Phase Gratings,” J. Infrared Millim. Terahertz Waves 20(8), 1469–1486 (1999).
[Crossref]

1995 (1)

H. Ekström, B. S. Karasik, E. L. Kollberg, and K. S. Yngvesson, “Conversion gain and noise of niobium superconducting hot-electron-mixers,” IEEE Trans. Microw. Theory Tech. 43(4), 938–947 (1995).
[Crossref]

1981 (1)

P. Bliek, R. Deleuil, M. Breidne, and D. Maystre, “Microwave verification of a numerical optimization of fourier gratings,” Appl. Phys. (Berl.) 24(2), 147–150 (1981).
[Crossref]

1977 (1)

H. Dammann and E. Klotz, “Coherent Optical Generation and Inspection of Two-dimensional Periodic Structures,” Opt. Acta (Lond.) 24(4), 505–515 (1977).
[Crossref]

1974 (1)

G. Schmahl, “Holographically made diffraction gratings for the visible, UV and soft X-ray region,” J. Spectrosc. Soc. Jpn. 23, 3–11 (1974).

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Aladro, R.

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
[Crossref]

Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Bell, A.

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
[Crossref]

Bernasconi, P. N.

Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
[Crossref]

Berne, O.

C. Pabst, R. Higgins, J. R. Goicoechea, D. Teyssier, O. Berne, E. Chambers, M. Wolfire, S. T. Suri, R. Guesten, J. Stutzki, U. U. Graf, C. Risacher, and A. G. G. M. Tielens, “Disruption of the Orion molecular core 1 by wind from the massive star θ1 Orionis C,” Nature 565(7741), 618–621 (2019).
[Crossref] [PubMed]

Bliek, P.

P. Bliek, R. Deleuil, M. Breidne, and D. Maystre, “Microwave verification of a numerical optimization of fourier gratings,” Appl. Phys. (Berl.) 24(2), 147–150 (1981).
[Crossref]

Breidne, M.

P. Bliek, R. Deleuil, M. Breidne, and D. Maystre, “Microwave verification of a numerical optimization of fourier gratings,” Appl. Phys. (Berl.) 24(2), 147–150 (1981).
[Crossref]

Bruneau, P.

J. V. Siles, R. H. Lin, C. Lee, E. Schlecht, A. Maestrini, P. Bruneau, A. Peralta, J. Kloosterman, J. Kawamura, and I. Mehdi, “Development of high-power multi-pixel LO sources at 1.47 THz and 1.9 THz for astrophysics: present and future,” 26th International Symposium on Space Terahertz Technology (ISSTT 2015), pp. 40–42.

Buchbender, C.

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
[Crossref]

Büchel, D.

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
[Crossref]

Burton, M. G.

Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
[Crossref]

Chambers, E.

C. Pabst, R. Higgins, J. R. Goicoechea, D. Teyssier, O. Berne, E. Chambers, M. Wolfire, S. T. Suri, R. Guesten, J. Stutzki, U. U. Graf, C. Risacher, and A. G. G. M. Tielens, “Disruption of the Orion molecular core 1 by wind from the massive star θ1 Orionis C,” Nature 565(7741), 618–621 (2019).
[Crossref] [PubMed]

Chang, M.-C. F.

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C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, R. Aladro, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, C. Duran, U. U. Graf, R. D. Higgins, C. E. Honingh, K. Jacobs, M. Justen, B. Klein, M. Mertens, Y. Okada, A. Parikka, P. Pütz, N. Reyes, H. Richter, O. Ricken, D. Riquelme, N. Rothbart, N. Schneider, R. Simon, M. Wienold, H. Wiesemeyer, M. Ziebart, P. Fusco, S. Rosner, and B. Wohler, “The upGREAT dual frequency heterodyne arrays for SOFIA,” J. Astron. Instrum. 7(04), 1840014 (2018).
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A. M. Korolev, V. M. Shulga, and S. I. Tarapov, “Extra-low power consumption amplifier based on HEMT in unsaturated mode for use at subkelvin ambient temperatures,” Cryogenics 60, 76–79 (2014).
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Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
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Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
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Y. M. Seo, P. F. Goldsmith, C. Walker, D. J. Hollenbach, M. G. Wolfire, C. Kulesa, V. Tolls, P. N. Bernasconi, Ü. Kavak, F. F. S. van der Tak, R. Shipman, R. G. Jian, A. Tielens, M. G. Burton, H. Yorke, E. Young, W. L. Peters, A. Young, C. Groppi, K. Davis, J. L. Pineda, W. D. Langer, J. H. Kawamura, A. Stark, G. Melnick, D. Rebolledo, G. F. Wong, S. Horiuchi, and T. B. Kuiper, “Probing ISM Structure in Trumpler 14 & Carina I Using The Stratospheric Terahertz Observatory 2,” Astrophys. J. 878(2), 2 (2019).
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C O M S O L. Multiphysics, https://www.comsol.com/rf-module .

The isothermal technique is based on the assumption that the mixer has the same response to LO power and DC power, we can estimate the absorbed LO power in a mixer from the pumped current-voltage curves. In [34] P. Khosropanah, et al measured a set of current-voltage curves of a similar HEB mixer pumped with different LO power operated at 4.3 THz, and from the data when the LO power varies within ~40% the change in HEB mixer’s bias current is ~37%, which responds to ~10% changes in the noise temperature.

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Figures (5)

Fig. 1
Fig. 1 (a) 81 pixel Fourier grating machined on a 5 mm thick aluminum plate. Gating contains 16 × 16 unit cells, each of them is 1.2 mm × 1.2 mm in size, thus the entire grating is 2 cm × 2 cm. (b) The surface topology of the 81 pixel grating taken by a 3D optical microscope. The color indicates the height. (c), (d) The comparison between the designed profile in red (dashed) and the manufactured profile in blue.
Fig. 2
Fig. 2 (a) The SEM of the 3rd-order DFB QCL [30]. (b) Array of DFB lasers gold-wire bonded to an electronic chip [30]. (c) Beam pattern of the QCL measured at a distance ~3.5 cm from the laser. It deviates from Gaussian profile and has large divergence angles in both vertical and horizontal directions. (d) Pattern of the QCL beam collimated by a lens and filtered by an iris aperture, measured after reflection from a flat gold-coated mirror in place of the grating in the setup.
Fig. 3
Fig. 3 Schematic diagram of the measurement setup to test the performance of the grating. The QCL is cooled to ~10 K by a pulse tube cooler and its bias voltage is modulated by a sinusoidal function at 70 Hz using an arbitrary waveform generator. The QCL beam is first collimated by a high-density polyethylene lens and filtered by an iris aperture, then reflected by an aluminum mirror to illuminate the grating plane. A pyro-electric detector mounted on a 2D scanner stage is used to map the beam pattern. The received signal is read out by a lock-in amplifier with a 70 Hz sinusoidal function reference. The computer controls the stage and reads out the signal received from the lock-in amplifier.
Fig. 4
Fig. 4 (a) Measured beam pattern. (b) 3D beam profile of the image beam pattern. (c) Image beam pattern after calibrated the effect of the coupling with detector and removed the noise floor. (d) Simulated far field beam pattern of the designed grating.
Fig. 5
Fig. 5 (a) The power distribution of the measured image beams distributed in different columns. (b) The power distribution of the image beams from the simulation using a designed surface structure.

Tables (1)

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Table 1 The diffraction efficiency and minimum radius of curvature of gratings with different number of beams.*

Equations (1)

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U(x,y)= e jλz jλz e j k 2z ( x 2 + y 2 ) {U(ξ,η) e j k 2z ( ξ 2 + η 2 ) } e j 2π λz (xξ+yη) dξdη

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