Abstract

The absorption of light in transmissive optics cause a thermally induced effect known as thermal lensing. This effect provokes an often undesired change of a laser beam transmitted by the optic. In this paper we present a measurement method that allows us to determine thermal lensing in commonly used optical components. The beam influenced by the thermal lens is expanded into the eigenmodes of an optical cavity, and its modal content is analyzed in the eigenbasis of the cavity. The measured quantity depends neither on beam parameters nor on the position of the optical component under investigation. This method allows, to our knowledge, for the first time the direct measurement of the mode conversion coefficient |ε2| of the thermal lens.

© 2015 Optical Society of America

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    [Crossref]
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2012 (1)

2011 (1)

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

2010 (2)

N. Lastzka, J. Steinlechner, S. Steinlechner, and R. Schnabel, “Measuring small absorptions by exploiting photothermal self-phase modulation,” Appl. Opt. 49, 5391–5398 (2010).
[Crossref] [PubMed]

G. M. Harry and the LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[Crossref]

2009 (1)

2008 (2)

2007 (1)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[Crossref] [PubMed]

2006 (4)

2004 (1)

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

2003 (1)

2001 (1)

1999 (1)

1992 (1)

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

1991 (1)

W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[Crossref] [PubMed]

1990 (1)

P. Hello and J.-Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).
[Crossref]

1984 (1)

1968 (1)

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “Holographic storage in lithium niobate,” Appl. Phys. Lett. 13, 223–225 (1968).
[Crossref]

1966 (2)

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[Crossref] [PubMed]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

1964 (1)

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of the thermal lens effect using an He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[Crossref]

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Amin, R.

Anderson, D. Z.

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Ballmer, S.

Baptista, M. S.

Beausoleil, R. G.

Betzwieser, J.

Blair, D.

Bogan, C.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

C. Bogan, “Stabilized high power lasers and spatial mode conversion,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2013).

Bourgoin, J.-P.

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Brooks, A. F.

Byer, R. L.

Cabrera, H.

Camp, J.

Catunda, T.

Chen, F. S.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “Holographic storage in lithium niobate,” Appl. Phys. Lett. 13, 223–225 (1968).
[Crossref]

Chen, S.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Chen, Y.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Clubley, D.

Cruz, R. A.

D’Ambrosio, E.

Danzmann, K.

Degallaix, J.

Deng, H.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Deveaux, M.

Dias, L. G.

Doiron, S.

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Fan, Y.

Fejer, M. M.

Franzen, K. Y.

Fraser, D. B.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “Holographic storage in lithium niobate,” Appl. Phys. Lett. 13, 223–225 (1968).
[Crossref]

Frede, M.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Fritschel, P.

P. Fritschel, “Advanced LIGO Systems Design,” Technical Report LIGO-T010075-v2, LIGO Scientific Collaboration (2008).

Gleason, J.

Grote, H.

Guerra, M.

Gugliotti, M.

Gürsel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Gustafson, E. K.

Haché, A.

Harry, G. M.

G. M. Harry and the LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[Crossref]

Hello, P.

P. Hello and J.-Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).
[Crossref]

Hennawi, J.

Hewitson, M.

Hild, S.

Hosken, D.

Hough, J.

Jacinto, C.

Ju, L.

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Kells, W.

Kim, H.

King, P.

Kluzik, R.

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Kogelnik, H.

Kong, Y.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Kracht, D.

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Kwee, P.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

P. Kwee and B. Willke, “Automatic laser beam characterization of monolithic Nd:YAG nonplanar ring lasers,” Appl. Opt. 47, 6022–6032 (2008).
[Crossref] [PubMed]

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[Crossref] [PubMed]

LaMacchia, J. T.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “Holographic storage in lithium niobate,” Appl. Phys. Lett. 13, 223–225 (1968).
[Crossref]

Lastzka, N.

Lee, J.

Leidel, C.

Leite, R. C. C.

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of the thermal lens effect using an He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[Crossref]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Li, T.

Lück, H.

Malec, M.

Mansell, J. D.

Marcano, A.

Moore, R. S.

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of the thermal lens effect using an He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[Crossref]

Mueller, G.

Munch, J.

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Neumann, J.

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Ottaway, D.

Poeld, J.

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Pöld, J.

Politi, M. J.

Puncken, O.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Quetschke, V.

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Rakhmanov, M.

Reitze, D. H.

Rüdiger, A.

W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[Crossref] [PubMed]

Savage, R. L.

Schilling, R.

W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[Crossref] [PubMed]

Schnabel, R.

Seifert, F.

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Slagmolen, B.

Smith, J.

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Steinlechner, J.

Steinlechner, S.

Strain, K.

Tanner, D. B.

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Veitch, P. J.

Veltkamp, C.

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Vinet, J.-Y.

P. Hello and J.-Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).
[Crossref]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Waldman, S.

Weiss, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Wessels, P.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Whinnery, J. R.

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of the thermal lens effect using an He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[Crossref]

Whitcomb, S. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Willems, P.

Willke, B.

Winkelmann, L.

P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, “Stabilized high-power laser system for the gravitational wave detector advanced LIGO,” Opt. Express 20, 10617–10634 (2012).
[Crossref] [PubMed]

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Winkler, W.

S. Hild, H. Lück, W. Winkler, K. Strain, H. Grote, J. Smith, M. Malec, M. Hewitson, B. Willke, J. Hough, and K. Danzmann, “Measurement of a low-absorption sample of OH-reduced fused silica,” Appl. Opt. 45, 7269–7272 (2006).
[Crossref] [PubMed]

W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
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Xu, J.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Yan, B.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Yan, Z.

Yao, J.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Yoshida, S.

Zhang, G.

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Zhang, L.

Zhao, C.

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Appl. Opt. (9)

S. Hild, H. Lück, W. Winkler, K. Strain, H. Grote, J. Smith, M. Malec, M. Hewitson, B. Willke, J. Hough, and K. Danzmann, “Measurement of a low-absorption sample of OH-reduced fused silica,” Appl. Opt. 45, 7269–7272 (2006).
[Crossref] [PubMed]

A. F. Brooks, D. Hosken, J. Munch, P. J. Veitch, Z. Yan, C. Zhao, Y. Fan, L. Ju, D. Blair, P. Willems, B. Slagmolen, and J. Degallaix, “Direct measurement of absorption-induced wavefront distortion in high optical power systems,” Appl. Opt. 48, 355–364 (2009).
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J. D. Mansell, J. Hennawi, E. K. Gustafson, M. M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a shack-hartmann wavefront sensor,” Appl. Opt. 40, 366–374 (2001).
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M. Gugliotti, M. S. Baptista, L. G. Dias, and M. J. Politi, “Single-beam interface thermal lensing,” Appl. Opt. 38, 1213–1215 (1999).
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J.-P. Bourgoin, S. Doiron, M. Deveaux, and A. Haché, “Single laser beam measurement of thermal diffusivity,” Appl. Opt. 47, 6530–6534 (2008).
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N. Lastzka, J. Steinlechner, S. Steinlechner, and R. Schnabel, “Measuring small absorptions by exploiting photothermal self-phase modulation,” Appl. Opt. 49, 5391–5398 (2010).
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H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
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P. Kwee and B. Willke, “Automatic laser beam characterization of monolithic Nd:YAG nonplanar ring lasers,” Appl. Opt. 47, 6022–6032 (2008).
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Appl. Phys. B (1)

L. Winkelmann, O. Puncken, R. Kluzik, C. Veltkamp, P. Kwee, J. Poeld, C. Bogan, B. Willke, M. Frede, J. Neumann, P. Wessels, and D. Kracht, “Injection-locked single-frequency laser with an output power of 220 W,” Appl. Phys. B 102, 529–538 (2011).
[Crossref]

Appl. Phys. Lett. (3)

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “Holographic storage in lithium niobate,” Appl. Phys. Lett. 13, 223–225 (1968).
[Crossref]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of the thermal lens effect using an He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[Crossref]

Class. Quantum Grav. (1)

G. M. Harry and the LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. France (1)

P. Hello and J.-Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[Crossref] [PubMed]

Physica B (1)

J. Yao, Y. Chen, B. Yan, H. Deng, Y. Kong, S. Chen, J. Xu, and G. Zhang, “Characteristics of domain inversion in magnesium-oxide-doped lithium niobate,” Physica B 352, 294–298 (2004).
[Crossref]

Rev. Sci. Instrum. (1)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[Crossref] [PubMed]

Science (1)

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[Crossref] [PubMed]

Other (5)

P. Fritschel, “Advanced LIGO Systems Design,” Technical Report LIGO-T010075-v2, LIGO Scientific Collaboration (2008).

Northrup Gruman Space Technology, Synoptics document, “Terbium Gallium Garnet–TGG,” http://www.optoscience.com/maker/northrop/pdf/TGG.pdf .

C. Bogan, “Stabilized high power lasers and spatial mode conversion,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2013).

For mirrors with high reflectance only a small fraction of the light passes the substrate such that the situation might be different.

For BK7 the thermal expansion α is approximately three times larger than the temperature dependence of the refractive index β (dn/ dT). As the two effects act on the beam in the same way the two effects add up linearly.

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Figures (4)

Fig. 1
Fig. 1 Experimental setup to measure the thermal lens of a test substrate. DAQ + Control, Data-Acquisition and Control system; PD, photo detector; CCD, camera with high dynamic range; PZT, mirror with piezoelectric element; QPD, quadrant photo diode, TFP, thin-film polarizer.
Fig. 2
Fig. 2 Cavity scan at a power level of 1 W between the two attenuation units. The positions of the five lowest-order modes are marked according to the free spectral range. A back-ground measurement was performed without a test substrate. A measurement with an additional optical lens in the beam path agrees well with prediction (see Eqs. (9) and (13)).
Fig. 3
Fig. 3 Power of the thermal lens of a N-BK7 window measured at position x = 5.03. The measurement of the relative beam size change was performed with the WinCam. The amount of power in the LG10 mode was measured with the cavity and the thermal lens calculated. Both measurements agree within their errors, which are shown shaded.
Fig. 4
Fig. 4 Thermal lens of a polarizing beam splitter cube made of flint glass: The relative mode content of the two first-order HG modes and the two second-order LG modes is shown as function of the power that was transmitted through the substrate. For comparison a measurement with no test substrate placed in the beam path is shown (background measurement).

Tables (1)

Tables Icon

Table 1 Parameter and results of thermal lens measurements of different substrates. The quantity |ε2| = a2 · P was shown to depend exclusively on material parameters (see Eq. (12)).

Equations (16)

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δ S = 1.3 β p a d 4 π κ P ,
f thermal = w 2 2 δ S = 2 π κ 1.3 p a β d w 2 P ,
Φ thermal = m 0 P w 2 .
q = q 1 1 Φ q q + Φ q 2 with q : = i z 0 z ,
w 0 ( q ) = ( q ) λ π , z ( q ) = ( q ) ,
ε 2 : = δ w w 0 + i δ z 2 z 0 ,
δ w w 0 = w 0 ( q ) w 0 ( q ) w 0 ( q ) = 1 1 2 z Φ z Φ
δ z z 0 = z ( q ) z ( q ) z 0 = z 0 Φ + z 2 z 0 Φ
ε 2 z Φ i 2 ( z 0 Φ z 2 Φ z 0 ) = z 0 Φ γ ( z / z 0 )
with γ ( x ) : = x i 2 ( 1 x 2 )
and | γ ( x ) | = 1 + x 2 2 .
| ε 2 | = 1 + x 2 2 z 0 m 0 P w 2 = π 2 λ m 0 P = 2.6 β p a d 8 κ λ P .
P LG 10 P tot = | ε 2 | 2 .
P 2 ( P ) P tot = | ε s + ε 2 | 2 + P LG 02 P tot = | ε s | 2 + P LG 02 P tot + z 0 m 0 w 2 ( ε s γ + ε s γ ) P + π 2 4 λ 2 m 0 2 P 2 ,
P 2 ( P ) P tot = a 0 + a 1 P + a 2 2 P 2 = a 0 + a 1 P + | ε 2 | 2 .
p a = 4 κ λ a 2 1.3 β d = 0.00131 cm 1 ,

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