Abstract

We report on a novel concept for reflective diffractive cavity couplers based on resonant waveguide gratings instead of multilayer coatings. The diffracting or rather beam splitting properties are induced to the subwavelength structures by a periodic parameter modulation of the ridges. Since such a perturbation of the highly reflective system also enhances transmission stacks of two and three reflectors are considered to retrieve transmittivities as low as possible. Our calculations show that transmissions of less than 10−4 are possible for different configurations based on silicon and silica. The results of first technological tests for the realization of stacked T-shape structures are presented. With a total effective layer thickness not exceeding 1.1 μm the discussed approaches are expected to remarkably reduce the urgent problem of coating thermal noise of conventional components for high-precision metrology.

© 2011 OSA

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2011 (3)

2010 (5)

S. Kroker, F. Brückner, E.-B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2010).
[CrossRef]

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

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
[CrossRef] [PubMed]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18, 12606–12614 (2010).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

2008 (2)

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

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

2006 (3)

A. Bunkowski, O. Burmeister, D. Friedrich, K. Danzmann, and R. Schnabel, “High reflectivity grating waveguide coatings for 1064 nm,” Class. Quantum Grav. 23, 7297–7303 (2006).
[CrossRef]

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

A. Bunkowski, O. Burmeister, T. Clausnitzer, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Optical characterization of ultrahigh diffraction efficiency gratings,” Appl. Opt. 45, 5795–5799 (2006).
[CrossRef] [PubMed]

2004 (1)

2002 (1)

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

2001 (1)

D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. 18, 2109–21120 (2001).
[CrossRef]

2000 (1)

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermo-refractive noise in gravitational-wave antennae,” Phys. Lett. A 271, 303–307 (2000).
[CrossRef]

1998 (1)

Y. Levin, “Internal thermal noise for LIGO test masses: a direct approach,” Phys. Rev. D 57, 659–663 (1998).
[CrossRef]

1997 (2)

K.-X. Sun and R. L. Byer, “All-reflective Michelson, Sagnac, and Fabry-Perot interferometers based on grating beams splitters,” Opt. Lett. 23, 567–569 (1997).
[CrossRef]

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

1995 (1)

R. W. P. Drever, “Concepts for extending the ultimate sensitivity of interferometric gravitational gravitational-wave detectors using non-transmissive optics with diffractive or holographic coupling,” in Proceedings of the seventh Marcel Grossman meeting on general relativity , M. Keiser and R. T. Jantzen (eds.), World ScientificSingapore (1995).

1994 (1)

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

1993 (1)

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

1992 (1)

1985 (1)

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1981 (2)

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled wave approach for planar diffraction gratings,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Beausoleil, R. G.

Z. Peng, D. A. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36, 1515–1517 (2011).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Beyersdorf, P.

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermo-refractive noise in gravitational-wave antennae,” Phys. Lett. A 271, 303–307 (2000).
[CrossRef]

Britzger, M.

M. Britzger, D. Friedrich, S. Kroker, F. Brückner, O. Burmeister, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Diffractively coupled Fabry-Perot resonator with power-recycling,” Opt. Express 19, 14964–14975 (2011).
[CrossRef] [PubMed]

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

Brückner, F.

Bunkowski, A.

Burmeister, O.

Byer, R. L.

Cagnoli, G.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Chang-Hasnain, C. J.

Chase, C.

Chen, J. M.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Clausnitzer, T.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Crandall, R. S.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Crooks, D. R. M.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Danzmann, K.

M. Britzger, D. Friedrich, S. Kroker, F. Brückner, O. Burmeister, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Diffractively coupled Fabry-Perot resonator with power-recycling,” Opt. Express 19, 14964–14975 (2011).
[CrossRef] [PubMed]

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

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

A. Bunkowski, O. Burmeister, T. Clausnitzer, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Optical characterization of ultrahigh diffraction efficiency gratings,” Appl. Opt. 45, 5795–5799 (2006).
[CrossRef] [PubMed]

A. Bunkowski, O. Burmeister, D. Friedrich, K. Danzmann, and R. Schnabel, “High reflectivity grating waveguide coatings for 1064 nm,” Class. Quantum Grav. 23, 7297–7303 (2006).
[CrossRef]

A. Bunkowski, O. Burmeister, P. Beyersdorf, K. Danzmann, R. Schnabel, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Low-loss grating for coupling to a high-finesse cavity,” Opt. Lett. 29, 2342–2344 (2004).
[CrossRef] [PubMed]

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, “Concepts for extending the ultimate sensitivity of interferometric gravitational gravitational-wave detectors using non-transmissive optics with diffractive or holographic coupling,” in Proceedings of the seventh Marcel Grossman meeting on general relativity , M. Keiser and R. T. Jantzen (eds.), World ScientificSingapore (1995).

Dunn, S. C.

D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. 18, 2109–21120 (2001).
[CrossRef]

Faraon, A.

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Fattal, D. A.

Fejer, M. M.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Fiorentino, M.

Z. Peng, D. A. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36, 1515–1517 (2011).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Friedrich, D.

Friesem, A. A.

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

Fritschel, P.

Gaylord, T. K.

Gorodetsky, M. L.

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermo-refractive noise in gravitational-wave antennae,” Phys. Lett. A 271, 303–307 (2000).
[CrossRef]

Gretarsson, A. M.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Harry, G. M.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Heinert, D.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Hough, J.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Hudl, M.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Jacob, D. K.

D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. 18, 2109–21120 (2001).
[CrossRef]

Karagodsky, V.

Kittelberger, S. E.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Kley, E.-B.

M. Britzger, D. Friedrich, S. Kroker, F. Brückner, O. Burmeister, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Diffractively coupled Fabry-Perot resonator with power-recycling,” Opt. Express 19, 14964–14975 (2011).
[CrossRef] [PubMed]

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

S. Kroker, F. Brückner, E.-B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2010).
[CrossRef]

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

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

A. Bunkowski, O. Burmeister, T. Clausnitzer, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Optical characterization of ultrahigh diffraction efficiency gratings,” Appl. Opt. 45, 5795–5799 (2006).
[CrossRef] [PubMed]

A. Bunkowski, O. Burmeister, P. Beyersdorf, K. Danzmann, R. Schnabel, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Low-loss grating for coupling to a high-finesse cavity,” Opt. Lett. 29, 2342–2344 (2004).
[CrossRef] [PubMed]

Koettig, T.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Kroker, S.

Levin, Y.

Y. Levin, “Internal thermal noise for LIGO test masses: a direct approach,” Phys. Rev. D 57, 659–663 (1998).
[CrossRef]

Li, J.

Z. Peng, D. A. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36, 1515–1517 (2011).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Liu, X.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Lu, F.

Mashev, L.

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

McPhredan, R. C.

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Merithew, R. D.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Mizuno, J.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Moharam, M. G.

D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. 18, 2109–21120 (2001).
[CrossRef]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled wave approach for planar diffraction gratings,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Nakagawa, N.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Nawrodt, R.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Nelson, B. P.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Nelson, P. G.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Neubert, R.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Nietzsche, S.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Peng, Z.

Z. Peng, D. A. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36, 1515–1517 (2011).
[CrossRef] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Penn, S. D.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Pohl, R. O.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Popov, E.

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Rosenblatt, D.

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

Rowan, S.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Rüdiger, A.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Saulson, P. R.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Schilling, R.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Schnabel, R.

Schnabel, Roman

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

Schwarz, C.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Sedgwick, F. G.

Seidel, P.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Sharon, A.

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

Shoemaker, D.

Spiel, C. L.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Startin, W. J.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

Strain, K. A.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Sun, K.-X.

Thürk, M.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Tünnermann, A.

M. Britzger, D. Friedrich, S. Kroker, F. Brückner, O. Burmeister, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Diffractively coupled Fabry-Perot resonator with power-recycling,” Opt. Express 19, 14964–14975 (2011).
[CrossRef] [PubMed]

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

S. Kroker, F. Brückner, E.-B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2010).
[CrossRef]

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

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

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

A. Bunkowski, O. Burmeister, T. Clausnitzer, E.-B. Kley, A. Tünnermann, K. Danzmann, and R. Schnabel, “Optical characterization of ultrahigh diffraction efficiency gratings,” Appl. Opt. 45, 5795–5799 (2006).
[CrossRef] [PubMed]

A. Bunkowski, O. Burmeister, P. Beyersdorf, K. Danzmann, R. Schnabel, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Low-loss grating for coupling to a high-finesse cavity,” Opt. Lett. 29, 2342–2344 (2004).
[CrossRef] [PubMed]

Vodel, W.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Vyatchanin, S. P.

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermo-refractive noise in gravitational-wave antennae,” Phys. Lett. A 271, 303–307 (2000).
[CrossRef]

Wang, Q.

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Weiss, R.

Winkler, W.

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Zimmer, A.

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Appl. Opt. (2)

Class. Quantum Grav. (2)

A. Bunkowski, O. Burmeister, D. Friedrich, K. Danzmann, and R. Schnabel, “High reflectivity grating waveguide coatings for 1064 nm,” Class. Quantum Grav. 23, 7297–7303 (2006).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002).
[CrossRef]

J. Opt. Soc. Am. (3)

D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. 18, 2109–21120 (2001).
[CrossRef]

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

M. G. Moharam and T. K. Gaylord, “Rigorous coupled wave approach for planar diffraction gratings,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

J. Phys. Conf. Ser. (1)

R. Nawrodt, A. Zimmer, T. Koettig, C. Schwarz, D. Heinert, M. Hudl, R. Neubert, M. Thürk, S. Nietzsche, W. Vodel, P. Seidel, and A. Tünnermann, “High mechanical Q-factor measurements on silicon bulk samples,” J. Phys. Conf. Ser. 122, 1–9 (2008).
[CrossRef]

Mat. Sci. Eng. A (1)

X. Liu, C. L. Spiel, R. D. Merithew, R. O. Pohl, B. P. Nelson, Q. Wang, and R. S. Crandall, “Internal friction of amorphous and nanocrystalline silicon at low temperatures,” Mat. Sci. Eng. A 442, 307–313 (2006)
[CrossRef]

Nat. Photonics (1)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Opt. Act. (1)

I. C. Botten, M. S. Craig, R. C. McPhredan, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Act. 122, 413–428 (1981).
[CrossRef]

Opt. Commun. (1)

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Opt. Express (3)

Opt. Lett. (6)

Phys. Lett. A (3)

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

K. A. Strain, K. Danzmann, J. Mizuno, P. G. Nelson, R. Schilling, and W. Winkler, “Thermal lensing in recycling interferometric gravitational-wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermo-refractive noise in gravitational-wave antennae,” Phys. Lett. A 271, 303–307 (2000).
[CrossRef]

Phys. Rev. D (1)

Y. Levin, “Internal thermal noise for LIGO test masses: a direct approach,” Phys. Rev. D 57, 659–663 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (3)

R. W. P. Drever, “Concepts for extending the ultimate sensitivity of interferometric gravitational gravitational-wave detectors using non-transmissive optics with diffractive or holographic coupling,” in Proceedings of the seventh Marcel Grossman meeting on general relativity , M. Keiser and R. T. Jantzen (eds.), World ScientificSingapore (1995).

http://ab-initio.mit.edu/wiki/index.php/NLopt .

R. Nawrodt, C. Schwarz, S. Kroker, I. W. Martin, F. Brückner, L. Cunningham, V. Große, A. Grib, D. Heinert, J. Hough, T. Käsebier, E.-B. Kley, R. Neubert, S. Reid, S. Rowan, P. Seidel, M. Thürk, and A. Tünnermann, “Investigation of mechanical losses of thin silicon flexures at low temperatures,” arXiv:1003.2893v1.

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Figures (10)

Fig. 1
Fig. 1

(Color online) (a) Sketch of a transmissively coupled cavity. Reflective cavity coupling by means of two-port (b) and a three-port grating coupler (c). The total transmission is the sum of all transmitted diffraction orders and should be minimized. (d) Example for the dependence of the reflectivity for a T-shaped RWG based on silicon and silica optimized for normal incidence and an angle of 45° and angular behavior of the reflectivity for a double T-shaped grating.

Fig. 2
Fig. 2

(a) Conventional configuration for a resonant waveguide grating. (b) T-shaped grating.

Fig. 3
Fig. 3

(a) Sketch of a depth modulated grating and (b) of a width modulated grating. The modulation also can be realized continuously with each ridge.

Fig. 4
Fig. 4

(Color online) (a) Geometrical grating parameters. (b) An example for the lateral field distribution of the magnetic field component Hy component for the first two grating modes excited by TM-polarized light at normal incidence. The grey bars represent the silicon grating ridges. (c) Illustration of the first two symmetric modes propagating through the grating. A phase difference of π between the modes at the bottom of the grating leads to minimum transmission of the zeroth diffraction order.

Fig. 5
Fig. 5

(Color online) Lower (black) and upper (blue and red) limits for the range of relevant grating periods in dependence of the duty cycles of the involved silicon and silica grating. The horizontal (dotted) grey lines mark the periods for the effective indices 1 and 3.8, respectively. Note that for the T-shape gratings the duty cycle of the silica grating is chosen lower than that of the silicon grating.

Fig. 6
Fig. 6

(Color online) Optimum geometric parameters for the grating illuminated at normal incidence. The silicon grating is made of amorphous silicon (n=3.8 at λ =1550 nm) whilst the substrate material is crystalline silicon (n=3.48).

Fig. 7
Fig. 7

(Color online) (a) Optimized grating parameters for a high-finesse cavity coupler with R 0 = 0.9995 and a total transmission of 5 × 10−6. (b) Optimized parameter set for R 0 = 0.9 and T = 10−5. For both cases the duty cycles with respect to p of the design in Fig. 6 were maintained. The sketches are not true to scale.

Fig. 8
Fig. 8

(Color online) (a) Optimized grating parameters for a high-finesse cavity coupler with R 0 = 0.9995 and a total transmission of 1 × 10−5. (b) Optimized parameter set for R 0 = 0.9 and T = 7 × 10−5. Again, the sketches are not true to scale. A restriction for the duty cycles due to fabrication is that f 3f 1 = f 4f 1 (see also Sec. 6). The labeled duty cycles are in relation to the period of the beam splitter pBS .

Fig. 9
Fig. 9

(Color online) Influence of the grating duty cycle variations on the total transmission T (a) and the reflectivity R 0 (b). The same deviations were added to all duty cycles of the design. Negative deviations represent duty cycles that are larger than the design values, positive deviations smaller ones.

Fig. 10
Fig. 10

(Color online) (a)–(d) Illustration of the fabrication process. (e) Scanning electron microscope (SEM) image of the fabricated double-T structures.

Tables (2)

Tables Icon

Table 1 Effective Indices for the Relevant Parameters of the Silicon Grating for TM-Polarization at Normal Incidence

Tables Icon

Table 2 Effective Layer Thicknesses heff for Beam Splitter Designs with Different Reflectivities R 0

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

λ p B S < 2 λ ,
λ n h p λ n l ,
cos ( β b ) cos ( γ c ) 1 2 ( n 2 2 β n 1 2 γ + n 1 2 γ n 2 2 β ) sin ( β b ) sin ( γ c ) = cos ( 2 π λ sin φ p ) ,
β = 2 π λ n 1 2 n eff 2 and , γ = 2 π λ n 2 2 n eff 2
s = λ 2 ( n eff 0 n eff 1 ) ( 2 m + 1 ) , m .
1550 nm 2 ( 3.62 0 ) < s < 1550 nm 2 ( 3.62 1.79 )
214 nm < s < 430 nm .

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