Abstract

We report on the observation of high-efficiency frequency doubling of 1550nm continuous-wave laser light in a nonlinear cavity containing a periodically poled potassium titanyl phosphate crystal (PPKTP). The fundamental field had a power of 1.10W and was converted into 1.05W at 775nm, yielding a total external conversion efficiency of 95±1%. The latter value is based on the measured depletion of the fundamental field being consistent with the absolute values derived from numerical simulations. According to our model, the conversion efficiency achieved was limited by the nonperfect mode matching into the nonlinear cavity and by the nonperfect impedance matching for the maximum input power available. Our result shows that cavity-assisted frequency conversion based on PPKTP is well suited for low-decoherence frequency conversion of quantum states of light.

© 2011 Optical Society of America

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2010 (6)

2009 (1)

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

2008 (1)

2006 (2)

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

2005 (1)

R. Le Targat, J.-J. Zondy, and P. Lemonde, Opt. Commun. 247, 471 (2005).
[CrossRef]

2004 (1)

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

2002 (1)

1994 (1)

1992 (2)

1982 (1)

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Avtlokhin, A. V.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Bachor, H.-A.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Buchler, B. C.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Camargo, F. A.

Chen, C. K.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Cirac, J. I.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Danzmann, K.

Dong, H.

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

Dronov, A. G.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Eberle, T.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, Opt. Lett. 35, 1665 (2010).
[CrossRef] [PubMed]

Ehret, K.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Fejer, M. M.

Fiurasek, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Frede, M.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Gapontsev, V. P.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Ghazaryan, S.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Glöckl, O.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Hammerer, K.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

Händchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Heinz, T. F.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Henking, R.

Hétet, G.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Hildebrandt, M.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Hsu, M. T. L.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Huang, J.

J. Huang and P. Kumar, Phys. Rev. Lett. 68, 2153 (1992).
[CrossRef] [PubMed]

Julsgaard, B.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Kimble, H. J.

Knabbe, E.-A.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Kracht, D.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Krylov, A. A.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Kumar, P.

J. Huang and P. Kumar, Phys. Rev. Lett. 68, 2153 (1992).
[CrossRef] [PubMed]

Kurz, J. R.

Kürz, P.

Lam, P. K.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Lastzka, N.

N. Lastzka, J. Steinlechner, S. Steinlechner, and R. Schnabel, Appl. Opt. 49, 5391 (2010).
[CrossRef] [PubMed]

N. Lastzka, “Numerical modelling of classical and quantum effects in non-linear optical systems,” Ph.D. thesis (Gottfried Wilhelm Leibniz Universität Hannover, 2010).

Le Targat, R.

R. Le Targat, J.-J. Zondy, and P. Lemonde, Opt. Commun. 247, 471 (2005).
[CrossRef]

Lemonde, P.

R. Le Targat, J.-J. Zondy, and P. Lemonde, Opt. Commun. 247, 471 (2005).
[CrossRef]

Li, M.-J.

Lindner, A.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

List, J.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Longdell, J. J.

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

Lu, W.

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

Mehmet, M.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, Opt. Lett. 35, 1665 (2010).
[CrossRef] [PubMed]

Meier, T.

T. Meier, B. Willke, and K. Danzmann, Opt. Lett. 35, 3742 (2010).
[CrossRef] [PubMed]

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Meyer, N.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Mlynek, J.

Müller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Nolan, D. A.

Notz, D.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Ou, Z. Y.

Pan, H.

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

Parameswaran, K. R.

Paschotta, R.

Pereira, S. F.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Petrov, V.

Polzik, E. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, Opt. Lett. 17, 640 (1992).
[CrossRef] [PubMed]

Popov, S. V.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Redondo, J.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Ricard, D.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Ringwald, A.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Roussev, R. V.

Schiller, S.

Schnabel, R.

Shen, Y. R.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Sherson, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Sørensen, A. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

Steinlechner, J.

Steinlechner, S.

Taylor, J. R.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Vahlbruch, H.

M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, Opt. Lett. 35, 1665 (2010).
[CrossRef] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Vyatkin, M. Y.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Wetter, N. U.

Wiedemann, G.

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Willke, B.

T. Meier, B. Willke, and K. Danzmann, Opt. Lett. 35, 3742 (2010).
[CrossRef] [PubMed]

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Yagodkin, R. L.

M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

Zanon, T.

Zeng, H.

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

Zondy, J.-J.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Pan, H. Dong, H. Zeng, and W. Lu, Appl. Phys. Lett. 89, 191108 (2006).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature 432, 482 (2004).
[CrossRef] [PubMed]

Nucl. Instrum. Meth. Phys. Res. A (1)

K. Ehret, M. Frede, S. Ghazaryan, M. Hildebrandt, E.-A. Knabbe, D. Kracht, A. Lindner, J. List, T. Meier, N. Meyer, D. Notz, J. Redondo, A. Ringwald, G. Wiedemann, and B. Willke, Nucl. Instrum. Meth. Phys. Res. A 612, 83 (2009).
[CrossRef]

Opt. Commun. (1)

R. Le Targat, J.-J. Zondy, and P. Lemonde, Opt. Commun. 247, 471 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (5)

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

M. T. L. Hsu, G. Hétet, O. Glöckl, J. J. Longdell, B. C. Buchler, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 97, 183601 (2006).
[CrossRef] [PubMed]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

J. Huang and P. Kumar, Phys. Rev. Lett. 68, 2153 (1992).
[CrossRef] [PubMed]

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M. Y. Vyatkin, A. V. Avtlokhin, A. G. Dronov, A. A. Krylov, R. L. Yagodkin, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Multi-watt average power 388 nm UV generation through frequency quadrupling of Yb/Er fiber laser sources,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2004).

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Figures (3)

Fig. 1
Fig. 1

Schematic of experimental setup. SHG, second harmonic generation with nonlinear PPKTP crystal; DBS, dichroic beam splitter to separate 775 nm and 1550 nm light; PD_ input-monitor, photodetector monitoring power fluctuations of the 1550 nm pump field; PD-reflection, photodetector for relative measurement of the conversion efficiency; PD_locking, photodetector for the cavity length stabilization; EOM, electro-optic modulator producing sidebands of 138 MHz for the cavity length stabilization.

Fig. 2
Fig. 2

Depletion measurement for a fundamental input power of 1.1 W . Bottom trace (black), no light on PD_reflection refers to 100% conversion. Top trace (orange), SHG cavity off- resonant refers to 0% conversion. Trace at about 0.05 (green), SHG cavity is stabilized on maximum conversion. Peaked curve (blue), scan of the cavity length over an Airy peak of the TEM00 mode. The maximum conversion efficiency is 95%.

Fig. 3
Fig. 3

Conversion efficiency and harmonic power ( 775 nm ) versus fundamental input power ( 1550 nm ). Data with small error bars (black): pump depletion measurements. Data with large error bars (blue and green): absolute power measurements at both wavelengths. The dotted orange line and the solid red line show the full simulation of our system based on independently determined parameters and a fitted crystal nonlinearity of 7.3 pm / V .

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