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Resonant Waveguide Grating Structures

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Optical Characterization of Thin Solid Films

Part of the book series: Springer Series in Surface Sciences ((SSSUR,volume 64))

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Abstract

Resonant waveguide gratings are subwavelength structures that possess the ability to selectively reflect or transmit light in terms of wavelength, incidence angle and polarization state. They are of interest in a large variety of optical sensors and optoelectronic devices. Resonant waveguide gratings have also emerged as low-noise optical components in high-precision metrology, for example frequency stabilized laser systems for the realization of optical clocks or gravitational wave detectors. In these applications, Brownian thermal noise of optical coatings, sets a severe limitation to the feasible sensitivity. In this chapter, we will discuss the relevance of the mechanical loss of optical thin film coatings for Brownian thermal noise. We will present monolithic resonant waveguide gratings to circumvent the use of amorphous coatings to reduce thermal noise. First, we will introduce a method to characterize the mechanical loss of optical coatings and discuss its implications for high-precision metrology. Afterwards we will explain the working principle of resonant waveguide gratings. Then, several characterization techniques for the dimensional and optical characterization will be discussed and experimental results for monolithic waveguide gratings with one-dimensional and two-dimensional periodicity will be presented.

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Notes

  1. 1.

    The reader may be familiar with this relationship from the Johnson-Nyquist noise of electric resistors. Here thermal noise is also proportional to the electric resistance, i.e. the dissipation [42, 43].

References

  1. L. Mashev, E. Popov, Zero order anomaly of dielectric coated gratings. Opt. Commun. 55, 377–380 (1985)

    Google Scholar 

  2. A. Sharon, D. Rosenblatt, A.A. Friesem, Narrow spectral bandwidths with grating waveguide structures. Appl. Phys. Lett. 69, 4154 (1997)

    Google Scholar 

  3. D.L. Brundrett, E.N. Glytsis, T.K. Gaylord, Normal-incidence guided-mode resonant grating filters: design and experimental demonstration. Opt. Lett. 23, 700–702 (1998)

    Article  ADS  Google Scholar 

  4. Y. Wang, Y. Kanamori, J. Ye, H. Sameshima, K. Hane, Fabrication and characterization of nanoscale resonant gratings on thin silicon membrane. Opt. Express 17, 4938–4943 (2009)

    Article  ADS  Google Scholar 

  5. F. Brückner, S. Kroker, D. Friedrich, E.-B. Kley, A. Tünnermann, Widely tunable monolithic narrowband grating filter for near-infrared radiation. Opt. Lett. 36, 436–438 (2011)

    Article  ADS  Google Scholar 

  6. Y. Ding, R. Magnusson, Doubly resonant single-layer bandpass optical filters. Opt. Lett. 29 1135–1137 (2004)

    Google Scholar 

  7. S. Steiner, S. Kroker, T. Käsebier, E.-B. Kley, A. Tünnermann, Angular bandpass filters based on dielectric resonant waveguide gratings. Opt. Express 20, 22555–22562 (2012)

    Article  ADS  Google Scholar 

  8. M.C.Y. Huang, Y. Zhou, J. Chang-Hasnain, A surface-emitting laser incorporating a high-index-contrast subwavelength grating. Nat. Photonics 1, 119–122 (2007)

    Article  ADS  Google Scholar 

  9. Y. Fang, A.M. Ferrie, N.H. Fontaine, J. Mauro, J. Balakrishnan, Resonant Waveguide Grating Biosensor for Living Cell Sensing. Biophys. J. 91, 1925–1940 (2006)

    Article  ADS  Google Scholar 

  10. H.N. Daghestani, B.W. Day, Theory and applications of surface plasmon resonance, resonant mirror, in Resonant Waveguide Grating, and Dual Polarization Interferometry Biosensors. Sensors, vol. 10, pp. 9630–9646 (2010)

    Google Scholar 

  11. I.-S. Chunga, Jesper Mørk, Silicon-photonics light source realized by III–V/Si-grating-mirror laser. Appl. Phys. Lett. 97, 151113 (2010)

    Article  ADS  Google Scholar 

  12. M. Siltanena, S. Leivo, P. Voima, M. Kauranen, Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating. Appl. Phys. Lett. 91, 111109 (2007)

    Article  ADS  Google Scholar 

  13. A. Saari, G. Genty, M. Siltanen, P. Karvinen, P. Vahimaa, M. Kuittinen, M. Kauranen, Giant enhancement of second-harmonic generation in multiple diffraction orders from sub-wavelength resonant waveguide grating. Opt. Lett. 18, 12298–12303 (2010)

    Google Scholar 

  14. R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P.S. Priambodo, P.P. Young, A. Maldonado, Photonic devices enabled by waveguide-mode resonance effects in periodically modulated films, in Nano- and Micro-Optics for Information Systems. Proceedings of SPIE, vol. 5225, pp. 20–34 (2003)

    Google Scholar 

  15. C.F.R. Mateus, M.C.Y. Huang, Y. Deng, A.R. Neureuther, C.J. Chang-Hasnain, Ultrabroadband mirror using low-index cladded subwavelength grating. IEEE Photonics Technol. Lett. 16, 518–520 (2004)

    Article  ADS  Google Scholar 

  16. K.J. Lee, J. Curzan, M. Shokooh-Saremi, R. Magnusson, Resonant wideband polarizer with single silicon layer. Appl. Phys. Lett. 98, 211112 (2011)

    Google Scholar 

  17. S. Kroker, T. Käsebier, E.-B. Kley, A. Tünnermann, Coupled grating reflectors with highly angular tolerant reflectance. Opt. Lett. 38, 3336–3339 (2013)

    Article  ADS  Google Scholar 

  18. S. Peng, G.M. Morris, Experimental demonstration of resonant anomalies in diffraction from twodimensional gratings. Opt. Lett. 21, 549–551 (1996)

    Article  ADS  Google Scholar 

  19. S. Kroker, T. Käsebier, S. Steiner, E.-B. Kley, A. Tünnermann, High efficiency two-dimensional grating reflectors with angularly tunable polarization efficiency. Appl. Phys. Lett. 102, 161111 (2013)

    Google Scholar 

  20. Y. Ding, R. Magnusson, Resonant leaky-mode spectral-band engineering and device applications. Opt. Express 12, 5661–5674 (2004)

    Google Scholar 

  21. R. Magnusson, M. Shokooh-Saremi, Physical basis for wideband resonant reflectors. Opt. Express 16, 3456–3462 (2008)

    Google Scholar 

  22. Y. Ding, R. Magnusson, Use of nondegenerate resonant leaky modes to fashion diverse optical spectra. Opt. Express 12, 1885–1891 (2004)

    Google Scholar 

  23. A. Bunkowski, O. Burmeister, D.Friedrich, K. Danzmann, R. Schnabel, High reflectivity grating waveguide coatings for 1064 nm. Class. Quant. Gravity 23, 7279–7303 (2006)

    Google Scholar 

  24. F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E.-B. Kley, A. Tünnermann, R. Schnabel, Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal. Phys. Rev. Lett. 104, 163903 (2010)

    Google Scholar 

  25. D. Friedrich, et al., Waveguide grating mirror in a fully suspended 10 meter Fabry-Perot cavity. Class. Quant. Gravity 19, 14955–14963 (2011)

    Google Scholar 

  26. Y. Levin, Internal thermal noise in the LIGO test masses: a direct approach. Phys. Rev. D 57, 659 (1998)

    Google Scholar 

  27. K. Numata, A. Kemery, J. Camp, Thermal-noise limit in the frequency stabilization of lasers with rigid cavities. Phys. Rev. Lett. 93, 250602 (2004)

    Google Scholar 

  28. T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M.J. Martin, L. Che, J. Ye, A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nat. Photonics 6, 687–692 (2012)

    Google Scholar 

  29. K. Jacobs, I. Tittonen, H.M. Wiseman, S. Schiller, Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion. Phys. Rev. A 60, 538 (1999)

    Google Scholar 

  30. G.M. Harry, et al., Thermal noise from optical coatings in gravitational wave detectors. Appl. Opt. 45, 1569–1574 (2006)

    Google Scholar 

  31. B.P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)

    Google Scholar 

  32. W.A. Edelstein, J. Hough, J.R. Pugh, W. Martin, Limits to the measurement of displacement in an interferometric gravitational radiation detector. J. Phys. E: Sci. Instrum. 11, 710 (1978)

    Google Scholar 

  33. G.M. Harry. (for the LIGO Scientific Collaboration), Advanced LIGO: the next generation of gravitational wave detectors. Class. Quant Gravity 27, 084006 (2010)

    Google Scholar 

  34. A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik. 7, 769–822 (1916)

    Article  MATH  Google Scholar 

  35. B. Sathyaprakash, et al., Scientific objectives of Einstein telescope. Class. Quant. Gravity 29, 124013 (2012)

    Google Scholar 

  36. M. Punturo, et al., The Einstein Telescope: a third-generation gravitational wave observatory. Class. Quant. Gravity 27, 194002 (2010)

    Google Scholar 

  37. The Einstein Telescope Science Team, Einstein gravitational wave Telescope conceptual de-sign study, ET-0106C-10, http://www.et-gw.eu/etdsdocument, 2011

  38. R. Nawrodt, S. Rowan, J. Hough, M. Punturo, F. Ricci, J.-Y. Vinet, Challenges in thermal noise for 3rd generation of gravitational wave detectors. Gen. Relat. Gravity 43, 593–622 (2011)

    Google Scholar 

  39. L. Pinard, C. Michel, B. Sassolas, L. Balzarini, J. Degallaix, V. Dolique, R. Flaminio, D. Forest, M. Granata, B. Lagrange, N. Straniero, J. Teillon, G. Cagnoli, Mirrors used in the LIGO interferometers for first detection of gravitational waves. Appl. Opt. 56, C11–C15 (2016)

    Google Scholar 

  40. G.E. Uhlenbeck, L.S. Ornstein, On the theory of the Brownian Motion. Phys. Rev. 36, 823 (1930)

    Google Scholar 

  41. H.B. Callen, T.A. Welton, Irreversibility and generalized noise. Phys. Rev. 83,34 (1951)

    Google Scholar 

  42. J.B. Johnson, Thermal agitation of electricity in conductors. Phys. Rev. 32, 97 (1928)

    Article  ADS  Google Scholar 

  43. H. Nyquist, Thermal agitation of electric charge in conductors. Phys. Rev. 32, 100 (1928)

    Article  ADS  Google Scholar 

  44. C. Zener, Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev. 53, 90 (1938)

    Article  ADS  MATH  Google Scholar 

  45. D. Heinert, A. Grib, K. Haughian, J. Hough, S. Kroker, P. Murray, R. Nawrodt, S. Rowan, C. Schwarz, P. Seidel, A. Tünnermann, Potential mechanical loss mechanisms in bulk materials for future gravitational wave detectors. J. Phys: Conf. Ser. 228, 012032 (2010)

    Google Scholar 

  46. C. Schwarz, Private Communication

    Google Scholar 

  47. M. Granata, E. Saracco, N. Morgado, A. Cajgfinger, G. Cagnoli, J. Degallaix, V. Dolique, D. Forest, J. Franc, C. Michel, L. Pinard, R. Flaminio, Mechanical loss in state-of-the-art amorphous optical coatings. Phys. Rev. D 93, 012007 (2017)

    Article  ADS  Google Scholar 

  48. M. Principe, I.M. Pinto, V. Pierro, R. DeSalvo, I. Taurasi, A.E. Villar, E.D. Black, K.G. Libbrecht, C. Michel, N. Morgado, L. Pinard, Material loss angles from direct measurements of broadband thermal noise. Phys. Rev. D 91, 022005 (2015)

    Google Scholar 

  49. S. Gras, H. Yu, W. Yam, D. Martynov, M. Evans, Audio-band coating thermal noise measurement for advanced LIGO with a multi-mode optical resonator. Phys. Rev. D 95, 022001 (2017)

    Article  ADS  Google Scholar 

  50. I.W. Martin et al., Comparison of the temperature dependence of the mechanical dissipation in thin films of Ta2O5 and Ta2O5 doped with TiO2. Class. Quant. Gravity 26, 155012 (2009)

    Google Scholar 

  51. R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, B. Sassolas, A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors. Class. Quant. Gravity 27, 084030 (2010)

    Google Scholar 

  52. G.D. Cole, W. Zhang, M.J. Martin, J. Ye, M. Aspelmeyer, Tenfold reduction of Brownian noise in high-reflectivity optical coatings. Nat. Photonics 7, 644–650 (2013)

    Google Scholar 

  53. A. Sharon, D. Rosenblatt, A.A. Friesem, Resonant grating-waveguide structures for visible and near-infrared radiation. J. Opt. Soc. Am. A 14, 2985–2993 (1997)

    Google Scholar 

  54. O. Stenzel, S. Wilbrandt, X. Chen, R. Schlegel, L. Coriand, A. Duparré, U. Zeitner, T. Benkenstein, C. Wächter, Observation of the waveguide resonance in a periodically patterned high refractive index broadband antireflection coating. Appl. Opt. 53, 3147–3156 (2014)

    Article  ADS  Google Scholar 

  55. F. Brückner, T. Clausnitzer, O. Burmeister, D.Friedrich, E.-B. Kley, K. Danzmann, A. Tünnermann, R. Schnabel, Monolithic dielectric surfaces as new low-loss light–matter interfaces. Opt. Lett. 33 264–266 (2008)

    Google Scholar 

  56. P. Lalanne, J.P. Hugonin, P. Chavel, Optical properties of deep lamellar gratings: a Bloch mode insight. J. Lightwave Technol. 24, 2442–2449 (2006)

    Google Scholar 

  57. V. Karagodsky, C.J. Chang-Hasnain, Physics of near-wavelength high contrast gratings. Opt. Express 20, 10888–10895 (2012)

    Google Scholar 

  58. M.G. Moharam, T.K. Gaylord, Rigorous coupled-wave analysis of planar grating diffraction. J. Opt. Soc. Am. A 71, 811–818 (1981)

    Google Scholar 

  59. S. Schröder, T. Herffurth, H. Blaschke, A. Duparré, Angle-resolved scattering: an effective method for characterizing thin-film coatings. Appl. Opt. 50, C164–C171 (2011)

    Article  Google Scholar 

  60. H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, A. Rathsfeld, Mathematical modelling of indirect measurements in scatterometry. Measurement 39, 782–794 (2006)

    Article  Google Scholar 

  61. R.M.A. Azzam, N.M. Bashara, Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings. J. Opt. Soc. Am. 46, 1521–1523 (1972)

    Article  Google Scholar 

  62. www.perkinelmer.com

  63. http://www.ioffe.rssi.ru. Accessed 16 Jan 2017

  64. J. Komma, C. Schwarz, G. Hofmann, D. Heinert, R. Nawrodt, Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures. Appl. Phys. Lett. 101, 041905 (2012)

    Google Scholar 

  65. http://refractiveindex.info/. Accessed 16 Jan 2017

  66. H.Y. Fan, Temperature dependence of the energy gap in semiconductors. Phys. Rev. 82, 900 (1951)

    Google Scholar 

  67. D. Heinert, S. Kroker, D. Friedrich, S. Hild, E.-B. Kley, S. Leavey, I. W. Martin, R. Nawrodt, A. Tünnermann, S. P Vyatchanin, K. Yamamoto, Calculation of thermal noise in grating reflectors, Phy. Rev. D 88, 042001 (2013)

    Google Scholar 

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Acknowledgements

The sample preparation of the optical waveguide coatings for high-precision metrology was performed at the Institute of Applied Physics (Friedrich-Schiller University Jena). The support of T. Käsebier, M. Banasch, H. Schmidt, W. Gräf and W. Rockstroh in the sample preparation is acknowledged.

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Authors and Affiliations

  1. LENA Laboratory for Emerging Nanometrology, Technische Universität Braunschweig, Pockelsstraße 14, 38106, Braunschweig, Germany

    Stefanie Kroker

  2. Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116, Braunschweig, Germany

    Stefanie Kroker & Thomas Siefke

  3. Friedrich-Schiller-University Jena, Institute of Applied Physics, Albert-Einstein-Straße 15, 07745, Jena, Germany

    Thomas Siefke

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  1. Stefanie Kroker
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Correspondence to Stefanie Kroker .

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Editors and Affiliations

  1. Abbe School of Photonics, Friedrich-Schiller-University Jena, Jena, Thüringen, Germany

    Olaf Stenzel

  2. Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic

    Miloslav Ohlídal

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Kroker, S., Siefke, T. (2018). Resonant Waveguide Grating Structures. In: Stenzel, O., Ohlídal, M. (eds) Optical Characterization of Thin Solid Films. Springer Series in Surface Sciences, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-75325-6_12

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