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2016-01-07
Optimized Superconducting Nanowire Single Photon Detectors to Maximize Absorptance
By
Progress In Electromagnetics Research B, Vol. 65, 81-108, 2016
Abstract
Dispersion characteristics of four types of superconducting nanowire single photon detectors, nano-cavity-array- (NCA-), nano-cavity-deflector-array- (NCDA-), nano-cavity-double-deflector-array- (NCDDA-) and nano-cavity-trench-array- (NCTA-) integrated (I-A-SNSPDs) devices was optimized in three periodicity intervals commensurate with half-, three-quarter- and one SPP wavelength. The optimal con gurations capable of maximizing NbN absorptance correspond to periodicity-dependent tilting in S-orientation (90˚ azimuthal orientation). In NCAI-A-SNSPDs absorptance maxima are reached at the plasmonic Brewster angle (PBA) due to light tunneling. The absorptance maximum is attained in a wide plasmonic-pass-band in NCDAI1/2*λ-A, inside a flat-plasmonic-pass-band in NCDAI3/4*λ-A and inside a narrow plasmonic-band in NCDAIλ-A. In NCDDAI1/2*λ-A bands of strongly coupled cavity and plasmonic modes cross, in NCDDAI3/4*λ-A an inverted-plasmonic-band-gap develops, while in NCDDAIλ-A a narrow plasmonic-pass-band appears inside an inverted-minigap. The absorptance maximum is achieved in NCTAI1/2*λ-A inside a plasmonic-pass-band, in NCTAI3/4*λ-A at inverted-plasmonic-band-gap center, while in NCTAIλ-A inside an inverted-minigap. The highest 95.05% absorptance is attained at perpendicular incidence onto NCTAIλ-A. Quarter-wavelength type cavity modes contribute to the near-field enhancement around NbN segments except in NCDAIλ-A and NCDDAI3/4*λ-A. The polarization contrast is moderate in NCAIA-SNSPDs (~102). NCDAI- and NCDDAI-A-SNSPDs make possible to attain considerably large polarization contrast (~102-103 and ~103~104), while NCTAI-A-SNSPDs exhibit a weak polarization selectivity (~10-102).
Citation
Maria Csete, Gabor Szekeres, Andras Szenes, Balazs Banhelyi, Tibor Csendes, and Gabor Szabo, "Optimized Superconducting Nanowire Single Photon Detectors to Maximize Absorptance," Progress In Electromagnetics Research B, Vol. 65, 81-108, 2016.
doi:10.2528/PIERB15090904
References

1. Hadfield, R. H., J. L. Habif, J. Schlafer, R. E. Schwall, and S. W. Nam, "Quantum key distribution at with twin superconducting single-photon detectors," Applied Physics Letters, Vol. 89, 241129, 2006.
doi:10.1063/1.2405870

2. Takesue, H., S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting photon-detectors," Nature Photonics, Vol. 1, 343, 2007.
doi:10.1038/nphoton.2007.75

3. Honjo, T., S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, "Long-distance etanglement-based quantum key distribution over optical fiber," Optics Express, Vol. 16, 19118, 2008.
doi:10.1364/OE.16.019118

4. Hadfield, R. H., "Single-photon detectors for optical quantum information applications," Nature Photonics, Vol. 3, 696, 2009.
doi:10.1038/nphoton.2009.230

5. Eisaman, M. D., J. Fan, A. Migdall, and S. V. Polyakov, "Invited review article: Single-photon sources and detectors," Review of Scientific Instruments, Vol. 82, 071101, 2011.
doi:10.1063/1.3610677

6. Natarajan, C. M., M. G. Tanner, and R. H. Hadfield, "Superconducting nanowire single-photon detectors: Physics and applications," Superconductor Science and Technology, Vol. 25, 063001, 2012.
doi:10.1088/0953-2048/25/6/063001

7. Bonneau, D., M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. Obrien, "Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices," Physical Review Letters, Vol. 108, 053601, 2012.
doi:10.1103/PhysRevLett.108.053601

8. Najafi, F., J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, "On-chip detection of non-classical light by scalable integration of integration of single-photon detectors," Nature Communications, Vol. 6, 5873, 2014.
doi:10.1038/ncomms6873

9. Kerman, A. J., E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Goltsman, and B. Voronov, "Kinetic-inductance-limited reset time of superconducting nanowire photon counters," Applied Physics Letters, Vol. 88, 111116, 2006.
doi:10.1063/1.2183810

10. Rosfjord, K. M., J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Goltsman, and K. K. Berggren, "Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating," Optics Express, Vol. 14, 527, 2006.
doi:10.1364/OPEX.14.000527

11. Robinson, B. S., A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, and K. K. Berggren, "781 Mbit/s photon-counting optical communications using a superconducting nanowire detector," Optics Letters, Vol. 31/4, 444, 2006.
doi:10.1364/OL.31.000444

12. Robinson, B. S., A. J. Kerman, J. K. W. Yang, K. M. Rosfjord, V. Anant, B. Voronov, G. Gol'tsman, and K. K. Berggren, "Multi-element superconducting nanowire single-photon detector," IEEE Transactions on Applied Superconductivity, Vol. 17, 279, 2007.
doi:10.1109/TASC.2007.898720

13. Anant, V., A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M. Rosfjord, and K. K. Berggren, "Optical properties of superconducting nanowire single-photon detectors," Optics Express, Vol. 16, 10750, 2008.
doi:10.1364/OE.16.010750

14. Dorenbos, S. N., E. M. Reiger, N. Akopian, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, "Low noise superconducting single photon detectors on silicon," Applied Physics Letters, Vol. 93, 161102, 2008.
doi:10.1063/1.3003579

15. Divochiy, A., F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol'tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, "Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths," Nature Photonics, Vol. 2, 302, 2008.
doi:10.1038/nphoton.2008.51

16. Dauler, E. A., A. J. Kerman, B. S. Robinson, J. K. W. Yang, B. Voronov, G. Goltsman, S. A. Hamilton, and K. K. Berggren, "Photon-number resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors," Journal of Modern Optics, Vol. 56, 364, 2009.
doi:10.1080/09500340802411989

17. Marsili, F., D. Bitauld, A. Fiore, A. Gaggero, R. Leoni, F. Mattioli, A. Divochiy, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, and G. Goltsman, "Superconducting parallel nanowire detector with photon number resolving functionality," Journal of Modern Optics, Vol. 56, 334, 2009.
doi:10.1080/09500340802220729

18. Miki, S., M. Takeda, M. Fujiwara, M. Sasaki, and Z. Wang, "Compactly packaged superconducting nanowire single-photon detector with an optical cavity for multichannel system," Optics Express, Vol. 17, 23557, 2009.
doi:10.1364/OE.17.023557

19. Baek, B., J. A. Stern, and S. W. Nam, "Superconducting nanowire single-photon detector in an optical cavity for front-side illumination," Applied Physics Letters, Vol. 95, 191110, 2009.
doi:10.1063/1.3263715

20. Bitauld, D., F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, "Nanoscale optical detector with single-photon and multiphoton sensitivity," Nano Letters, Vol. 10, 2977, 2010.
doi:10.1021/nl101411h

21. Gaggero, A., S. J. Nejad, F. Marsili, F. Mattioli, R. Leoni, D. Bitauld, D. Sahin, G. J. Hamhuis, R. Nötzel, R. Sanjines, and A. Fiore, "Nanowire superconducting single-photon detectors and GaAs for integrated quantum photonic applications," Applied Physics Letters, Vol. 97, 151108, 2009.
doi:10.1063/1.3496457

22. Marsili, F., F. Najafi, E. Dauler, F. Bellei, X. Hu, M. Csete, R. J. Molnar, and K. K. Berggren, "Single-photon detectors based on ultra-narrow superconducting nanowires," Nano Letters, Vol. 11, 2048, 2011.
doi:10.1021/nl2005143

23. Csete, M., Á. Sipos, F. Najafi, X. Hu, and K. K. Berggren, "Numerical method to optimize the polar-azimuthal orientation of infrared superconducting nanowire single-photon detectors," Applied Optics, Vol. 50/31, 5949, 2011.
doi:10.1364/AO.50.005949

24. Hu, X., E. A. Dauler, R. J. Molnar, and K. K. Berggren, "Superconducting nanowire single-photon detectors integrated with optical nano-antennae," Optics Express, Vol. 19, 17, 2011.
doi:10.1364/OE.19.000017

25. Csete, M., Á. Sipos, F. Najafi, and K. K. Berggren, "Optimized polar-azimuthal orientations for polarized light illumination of different superconducting nanowire single-photon detector designs," Journal of Nanophotonics, Vol. 6/1, 063523, 2012.
doi:10.1117/1.JNP.6.063523

26. Csete, M., A. Szalai, Á. Sipos, and G. Szabó, "Impact of polar-azimuthal illumination angles on efficiency of nano-cavity-array integrated single-photon detectors," Optics Express, Vol. 20/15, 17065, 2012.
doi:10.1364/OE.20.017065

27. Akhlaghi, M. K., H. Atikian, A. Eftekharian, M. Loncar, and A. H. Majedi, "Reduced dark counts in optimized geometries for superconducting nanowire single photon detectors," Optics Express, Vol. 20/21, 23610, 2012.
doi:10.1364/OE.20.023610

28. Verma, V. B., F. Marsili, S. Harrington, A. E. Lita, R. P. Mirin, and S. W. Nam, "A three-dimensional, polarization-insensitive superconducting nanowire avalanche photodetector," Applied Physics Letters, Vol. 101, 251114, 2012.
doi:10.1063/1.4768788

29. Marsili, F., V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, "Detecting single infrared photons with 93% system efficiency," Nature Photonics, Vol. 7, 210, 2013.
doi:10.1038/nphoton.2013.13

30. Eftekharian, A., H. Atikian, and A. H. Majedi, "Plasmonic superconducting nanowire single photon detector," Optics Express, Vol. 21/3, 3043, 2013.
doi:10.1364/OE.21.003043

31. Csete, M., Á. Sipos, A. Szalai, F. Najafi, G. Szabó, and K. K. Berggren, "Improvement of infrared single-photon detectors absorptance by integrated plasmonic structures," Scientific Reports, Vol. 3, 2406, 2013.
doi:10.1038/srep02406

32. Heath, R. M., M. G. Tanner, T. D. Drysdale, S. Miki, V. Giannini, S. A. Maier, and R. H. Hadfield, "Nano-antenna enhancement for telecom-wavelength superconducting single photon detectors," Nano Letters, Vol. 15/2, 819, 2014.

33. Csete, M., G. Szekeres, A. Szenes, A. Szalai, and G. Szabó, "Plasmonic structure integrated single-photon detector configurations to improve absorptance and polarization contrast," Sensors, Vol. 15, No. 2, 3513, 2015.
doi:10.3390/s150203513

34. Bennett, C. and G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, 175-179, 1984.

35. Pryde, G. J., J. L. Obrien, A. G. White, S. D. Bartlett, and T. C. Ralph, "Measuring a photonic qubit without destroying it," Physical Review Letters, Vol. 92, 190402, 2004.
doi:10.1103/PhysRevLett.92.190402

36. Knill, E., R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature, Vol. 409, 46, 2001.
doi:10.1038/35051009

37. Ladd, T. D., F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. Obrien, "Quantum computers," Nature, Vol. 464, 45, 2010.
doi:10.1038/nature08812

38. Sánchez-Gil, J. A., "Surface defect scattering of surface plasmon polaritons: Mirrors and light emitters," Applied Physics Letters, Vol. 73/24, 3509, 1998.
doi:10.1063/1.122820

39. Csendes, T., L. Pál, J. O. H. Sendín, and J. R. Banga, "The GLOBAL optimization method revisited," Optimization Letters, Vol. 2, 445, 2008.
doi:10.1007/s11590-007-0072-3

40. Bánhelyi, B., T. Csendes, B.M. Garay, and L. Hatvani, "A computer-assisted proof for Sigma_3-chaos in the forced damped pendulum equation," SIAM Journal on Applied Dinamical Systems, Vol. 7, 843, 2008.
doi:10.1137/070695599

41. Bánhelyi, B., T. Csendes, T. Krisztin, and A. Neumaier, "Global attractivity of the zero solution for Wright's equation," SIAM Journal on Applied Dinamical Systems, Vol. 13, 537, 2014.
doi:10.1137/120904226

42. Al, A., G. Daguanno, N. Mattiucci, and M. J. Bloemer, "Plasmonic Brewster angle: Broadband extraordinary transmission though optical gratings," Physical Review Letters, Vol. 106, 123902, 2011.
doi:10.1103/PhysRevLett.106.123902

43. Aközbek, N., N. Mattiucci, D. de Ceglia, R. Trimm, A. Al, G. Daguanno, M. A. Vincenti, M. Scalora, and M. J. Bloemer, "Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave," Physical Review B, Vol. 85, 205430, 2012.
doi:10.1103/PhysRevB.85.205430

44. Argyropoulos, C., G. Daguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Al, "Matching and funneling light at the plasmonic Brewster angle," Physical Review B, Vol. 85, 024304, 2012.
doi:10.1103/PhysRevB.85.024304

45. Sobnack, M. B., W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, "Stationary surface plasmons on a zero-order metal grating," Physical Review Letters, Vol. 80/25, 5667, 1998.
doi:10.1103/PhysRevLett.80.5667

46. Tan, W.-C., T. W. Preist, J. R. Sambles, and N. P. Wanstall, "Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings," Physical Review B, Vol. 59/19, 12661, 1999.
doi:10.1103/PhysRevB.59.12661

47. Hooper, I. R. and J. R. Sambles, "Dispersion of surface plasmon polaritons on short-pitch metal gratings," Physical Review B, Vol. 65, 165432, 2002.
doi:10.1103/PhysRevB.65.165432

48. Hooper, I. R. and J. R. Sambles, "Surface plasmon polaritons on narrow-ridged short-pitch metal gratings," Physical Review B, Vol. 66, 205408, 2002.
doi:10.1103/PhysRevB.66.205408

49. Chen, Y. J., E. S. Koteles, R. J. Seymour, G. J. Sonek, and J. M. Ballantyne, "Surface plasmon on gratings: Coupling in the minigap regions," Solid State Communications, Vol. 46/2, 95, 1983.
doi:10.1016/0038-1098(83)90586-0

50. Garcia-Vidal, F. J., J. Sanchez-Dehesa, A. Dechelette, E. Bustarret, T. Lopez-Rios, T. Fournier, and B. Pannetier, "Localized surface plasmons in lamellar metallic gratings," Journal of Lightwave Technology, Vol. 17/11, 2191, 1999.
doi:10.1109/50.803010

51. Marquier, F., J.- J. Greffet, S. Collin, F. Pardo, and J. L. Pelouard, "Resonant transmission through a metallic film due to coupled modes," Optics Express, Vol. 13/1, 70, 2004.

52. de Ceglia, D., M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, "Plasmonic band edge effects on the transmission properties of metal gratings," AIP Advances, Vol. 1, 032151, 2011.
doi:10.1063/1.3638161

53. Collin, S., "Nanostructure arrays in free-space: Optical properties and applications," Reports on Progress in Physics, Vol. 77, 126402, 2014.
doi:10.1088/0034-4885/77/12/126402

54. Wood, R. W., "Anomalous diffraction gratings," Physical Review, Vol. 15, 928, 1935.
doi:10.1103/PhysRev.48.928

55. Hessel, A. and A. A. Oliner, "A new theory of Wood's anomalies on optical gratings," Applied Optics, Vol. 4/10, 1275-1297, 1965.
doi:10.1364/AO.4.001275

56. Sarrazin, M., J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Physical Review B, Vol. 67, 085415, 2003.
doi:10.1103/PhysRevB.67.085415

57. Philpot, M. R. and J. D. Swalen, "Exciton surface polaritons on organic crystals," The Journal of Chemical Physics, Vol. 69, No. 6, 2912, 1978.
doi:10.1063/1.436890

58. Welford, K. R., "Surface plasmon-polaritons," IOP Short Meeting Series, Vol. 9, 25, 1988.

59. Yang, F., J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Physical Review B, Vol. 44, 5855, 1991.
doi:10.1103/PhysRevB.44.5855

60. Sarrazin, M. and J.-P. Vigneron, "Light transmission assisted by Brewster-Zennek modes in chromium films carrying a subwavelength hole array," Physical Review, Vol. 71, 075404, 2005.
doi:10.1103/PhysRevB.71.075404

61. Weiner, J., "The physics of light transmission through subwavelength apertures and aperture arrays," Reports on Progress in Physics, Vol. 72, 064401, 2009.
doi:10.1088/0034-4885/72/6/064401

62. Torma, P. and W. L. Barnes, "Strong coupling between surface plasmon polaritons and emitters: A review," Reports on Progress in Physics, Vol. 78, 013901, 2015.
doi:10.1088/0034-4885/78/1/013901

63. Fan, R.-H., R.-W. Peng, X.-R. Huang, J. Li, Y. Liu, Q. Hu, M. Wang, and X. Zhang, "Transparent metals for ultrabroadband electromagnetic waves," Advanced Materials, Vol. 24, 1980, 2012.
doi:10.1002/adma.201104483

64. Sakat, E., G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Hadar, and J.-L. Pelouard, "Free-standing guided-mode resonance band-pass filters: From 1D to 2D structures," Optics Express, Vol. 20/12, 13082, 2012.
doi:10.1364/OE.20.013082

65. Shen, H. and B. Maes, "Enhanced optical transmission through tapered metallic gratings," Applied Physics Letters, Vol. 100, 241104, 2012.
doi:10.1063/1.4729005

66. Barbara, A., P. Quémerais, E. Bustarret, T. López-Rios, and T. Fournier, "Electromagnetic resonances of subwavelength rectangular metallic gratings," The European Physical Journal D, Vol. 23, 143, 2003.
doi:10.1140/epjd/e2003-00025-9

67. Tan, W.-C., J. R. Sambles, and T. W. Preist, "Double-period zero-order metal gratings as effective selective absorbers," Physical Review B, Vol. 61/19, 13177, 2000.
doi:10.1103/PhysRevB.61.13177

68. Chan, H. B., Z. Marcet, Kwangje Woo, D. B. Tanner, D. W. Carr, J. E. Bower, R. A. Cirelli, E. Ferry, F. Klemens, J. Miner, C. S. Pai, and J. A. Taylor, "Optical transmission through double-layer metallic subwavelength slit arrays," Optics Letters, Vol. 31/4, 516, 2006.
doi:10.1364/OL.31.000516

69. Cheng, C., J. Chen, D.-J. Shi, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, J. Ding, and H.-T. Wang, "Physical mechanism of extraordinary electromagnetic transmission in dual-metallic grating structures," Physics Review B, Vol. 78, 075406, 2008.
doi:10.1103/PhysRevB.78.075406

70. Barbara, A., S. Collin, Ch. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, "Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating," Optics Express, Vol. 18/14, 14913, 2010.
doi:10.1364/OE.18.014913

71. Skigin, D. C. and R. A. Depine, "Narrow gaps of transmission through metallic structured gratings with subwavelength slits," Physics Review E, Vol. 74, 046606, 2006.
doi:10.1103/PhysRevE.74.046606

72. Csendes, T., B. M. Garay, and B. Bánhelyi, "A verified optimization technique to locate chaotic regions of a Hénon system," Journal of Global Optimization, Vol. 35, 145, 2006.
doi:10.1007/s10898-005-1509-9