Abstract

The continuous increase of the average laser power of ultrafast lasers is a challenge with respect to the thermal load of the processing optics. The power which is absorbed in an optical element leads to a temperature increase, temperature gradients, changing refractive index and shape, and finally causes distortions of the transmitted beam. In a first-order approximation this results in a change of the focal position, which may lead to an uncon-trolled change of the laser machining process. The present study reports on investigations on the focal shift induced in thin plano-convex lenses by a high-power ultra-short pulsed laser with an average laser power of up to 525 W. The focal shift was determined for lenses made of different materials (N-BK7, fused silica) and with different coatings (un-coated, broadband coating, specific wavelength coating).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” in, SPIE Proceedings (SPIE, 2006), 62732K.
    [Crossref]
  2. P.-E. Dupouy, M. Büchner, P. Paquier, G. Trénec, and J. Vigué, “Interferometric measurement of the temperature dependence of an index of refraction: application to fused silica,” Appl. Opt. 49(4), 678–682 (2010).
    [Crossref] [PubMed]
  3. R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
    [Crossref]
  4. A. Forbes, Laser Beam Propagation. Generation and Propagation of Customized Light (Taylor and Francis, 2014).
  5. B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
    [Crossref]
  6. B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
    [Crossref]
  7. R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014).
    [Crossref] [PubMed]
  8. R. Weber, T. Graf, C. Freitag, A. Feuer, T. Kononenko, and V. I. Konov, “Processing constraints resulting from heat accumulation during pulsed and repetitive laser materials processing,” Opt. Express 25(4), 3966–3979 (2017).
    [Crossref] [PubMed]
  9. S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
    [Crossref]
  10. C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
    [Crossref]
  11. C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
    [Crossref]
  12. J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013).
    [Crossref] [PubMed]
  13. J.-P. Negel, A. Loescher, D. Bauer, D. Sutter, A. Killi, M. Abdou Ahmed, and T. Graf, “Second Generation Thin-Disk Multipass Amplifier Delivering Picosecond Pulses with 2 kW of Average Output Power,” in Applications of Lasers for Sensing and Free Space Communications. Part of Lasers: 30 October-3 November 2016, Boston, Massachusetts, United States, OSA technical digest (online) (OSA - The Optical Society, 2016), ATu4A.5.
    [Crossref]
  14. T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
    [Crossref]
  15. W. Koechner, Solid-State Laser Engineering (Springer, 2006).
  16. T. Graf, Laser. Grundlagen der Laserstrahlerzeugung, 2., überarbeitete und erweiterte Auflage (Springer Vieweg, 2015).
  17. H. Hügel and T. Graf, Laser in der Fertigung. Strahlquellen, Systeme, Fertigungsverfahren, 3., überarb. und erw. Aufl. (Springer Fachmedien Wiesbaden GmbH, 2014).
  18. B. E. A. Saleh, M. C. Teich, and J. W. Goodman, Fundamentals of Photonics (John Wiley & Sons, Inc, 1991).

2018 (1)

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

2017 (1)

2015 (1)

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

2014 (1)

2013 (2)

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013).
[Crossref] [PubMed]

2011 (1)

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

2010 (1)

2009 (1)

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

1999 (1)

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
[Crossref]

1997 (1)

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Abdou Ahmed, M.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013).
[Crossref] [PubMed]

Balmer, J. E.

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Bauer, D.

Berger, P.

Bielke, U.

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

Büchner, M.

Cai, L.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Dupouy, P.-E.

Faas, S.

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

Feuer, A.

Freitag, C.

Graf, T.

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

R. Weber, T. Graf, C. Freitag, A. Feuer, T. Kononenko, and V. I. Konov, “Processing constraints resulting from heat accumulation during pulsed and repetitive laser materials processing,” Opt. Express 25(4), 3966–3979 (2017).
[Crossref] [PubMed]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014).
[Crossref] [PubMed]

J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013).
[Crossref] [PubMed]

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Hunziker, U.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

Jaeggi, B.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

Johannsen, J.

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

Killi, A.

Kononenko, T.

Konov, V. I.

Li, G.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Li, J.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Loescher, A.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

Muralt, M.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

Negel, J.-P.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013).
[Crossref] [PubMed]

Neuenschwander, B.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
[Crossref]

Onuseit, V.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014).
[Crossref] [PubMed]

Paquier, P.

Schmid, M.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

Sutter, D.

Thiel, C.

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

Trénec, G.

Vigué, J.

Voss, A.

Weber, H. P.

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
[Crossref]

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Weber, R.

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

R. Weber, T. Graf, C. Freitag, A. Feuer, T. Kononenko, and V. I. Konov, “Processing constraints resulting from heat accumulation during pulsed and repetitive laser materials processing,” Opt. Express 25(4), 3966–3979 (2017).
[Crossref] [PubMed]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014).
[Crossref] [PubMed]

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
[Crossref]

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Wiedenmann, M.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014).
[Crossref] [PubMed]

Wu, B.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Ye, X.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Zhou, M.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Zuercher, J.

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys., A Mater. Sci. Process. (2)

S. Faas, U. Bielke, R. Weber, and T. Graf, “Prediction of the surface structures resulting from heat accumulation during processing with picosecond laser pulses at the average power of 420 W,” Appl. Phys., A Mater. Sci. Process. 124(9), 612 (2018).
[Crossref]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

Appl. Surf. Sci. (1)

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256(1), 61–66 (2009).
[Crossref]

Opt. Commun. (1)

T. Graf, J. E. Balmer, R. Weber, and H. P. Weber, “Multi-Nd. YAG-rod variable-configuration resonator (VCR) end pumped by multiple diode-laser bars,” Opt. Commun. 135(1-3), 171–178 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. (1)

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999).
[Crossref]

Phys. Procedia (2)

B. Jaeggi, B. Neuenschwander, M. Schmid, M. Muralt, J. Zuercher, and U. Hunziker, “Influence of the Pulse Duration in the ps-Regime on the Ablation Efficiency of Metals,” Phys. Procedia 12, 164–171 (2011).
[Crossref]

C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a Laser Welding Process Against Focal Shift Effects using Beam Manipulation,” Phys. Procedia 41, 209–215 (2013).
[Crossref]

Other (7)

D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” in, SPIE Proceedings (SPIE, 2006), 62732K.
[Crossref]

A. Forbes, Laser Beam Propagation. Generation and Propagation of Customized Light (Taylor and Francis, 2014).

J.-P. Negel, A. Loescher, D. Bauer, D. Sutter, A. Killi, M. Abdou Ahmed, and T. Graf, “Second Generation Thin-Disk Multipass Amplifier Delivering Picosecond Pulses with 2 kW of Average Output Power,” in Applications of Lasers for Sensing and Free Space Communications. Part of Lasers: 30 October-3 November 2016, Boston, Massachusetts, United States, OSA technical digest (online) (OSA - The Optical Society, 2016), ATu4A.5.
[Crossref]

W. Koechner, Solid-State Laser Engineering (Springer, 2006).

T. Graf, Laser. Grundlagen der Laserstrahlerzeugung, 2., überarbeitete und erweiterte Auflage (Springer Vieweg, 2015).

H. Hügel and T. Graf, Laser in der Fertigung. Strahlquellen, Systeme, Fertigungsverfahren, 3., überarb. und erw. Aufl. (Springer Fachmedien Wiesbaden GmbH, 2014).

B. E. A. Saleh, M. C. Teich, and J. W. Goodman, Fundamentals of Photonics (John Wiley & Sons, Inc, 1991).

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Figures (5)

Fig. 1
Fig. 1 Experimental setup for the measurement of the thermally induced shift of the focal position of thin lenses. A neutral-density filter (NDF) attenuates the beam reflected by the AR-coated wedge to avoid damages of the CCD chip of the camera.
Fig. 2
Fig. 2 Measured thermally induced total focal shift with lens no. 2 in the testing setup (square points). The red curve is given by Eq. (8) which was fitted to the measured data. The least-square fit led to D * =0.77 10 6  mm/W. Laser parameters: λ = 1030 nm, M2 = 1.2, f = 300 kHz.
Fig. 3
Fig. 3 Extrapolation of the thermally induced focal shift of thin lenses made of fused silica (a) and N-BK7 (b) with different coating types to average laser powers of up to 1000 W. The calculations are based on the experimentally determined thermal dioptric powers of the various lenses. The orange dashed line illustrates a focal shift of one Rayleigh-length zR. Laser parameters: λ = 1030 nm, wcb = 2.5 mm, M2 = 1.2.
Fig. 4
Fig. 4 Experimental setup for the measurement of the thermally induced focal shift of the NDF. A neutral-density filter (NDF) attenuates the beam reflected by the AR-coated wedge to avoid damages of the CCD chip of the camera.
Fig. 5
Fig. 5 Measured thermally induced focal shift caused by the NDF as a function of the incident average intensity (square data points). The red curve is a fit of Eq. (13) to the measured data. Laser parameters: λ = 1030 nm, wcb = 2.5 mm, M2 = 1.2, f = 300 kHz.

Tables (1)

Tables Icon

Table 1 Experimentally determined thermal refractive power (column 7) and specifications (column 1-6) of the tested plano-convex lenses. The substrate of the lenses is either fused silica (FS) or N-BK7. The lenses are either uncoated (UC) or coated with a specific wavelength coating (WLC) or a broadband coating (BBC).

Equations (14)

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

1 f tot = 1 f 0 + 1 f th = 1 f 0 + D * × P i π× w i 2 = 1 f 0 + D * × I i = 1+ f 0 D * I i f 0 ,
Δf z R = f tot - f 0 z R = 1 z R ( f 0 1+ f 0 D * I i - f 0 )=- f 0 2 D * I i z R ×( 1+ f 0 D * I i ) .
Δf z R - f 0 2 D * I i z R =- f 0 2 D * P i z R π w i 2 .
w 0 =- f 0 λ M 2 π w i
z R =- π w 0 2 λ M 2 ,
Δf z R - D * λ M 2 P i
Δ f tot z R f 0 2 D * I i + f 0 2 D NDF * R I i 1 d f 0 d f 0 D NDF * R I i 1 d f 0 d f 0 2 D * I i D NDF * R I i 1 d f 0 z R ( 1+ f 0 D NDF * R I i 1 d f 0 d D NDF * R I i 1 d f 0 ) .
Δ f tot z R f 0 2 D * I i + f 0 2 D NDF * R I i 1 d f 0 d f 0 D NDF * R I i 1 d f 0 d f 0 2 D * I i D NDF * R I i 1 d f 0 z R ( 1+ f 0 D NDF * R I i 1 d f 0 d D NDF * R I i 1 d f 0 ) +Δ f 0 ,
M=( A B C D )=( 1 0 - 1 f th,NDF 1 )( 1 d 0 1 )( 1 0 - 1 f th 1 )( 1 0 - 1 f 0 1 ) =( 1- d f th - d f 0 d - 1 f 0 - 1 f th - 1 f th,NDF + d f 0 f th,NDF + d f th f th,NDF 1- d f th,NDF ),
1 f tot = 1+ f 0 D * I i + f 0 D NDF * I NDF -d D NDF * I NDF -d f 0 D * I i D NDF * I NDF f 0 ,
Δ f tot z R = f 0 2 D * I i + f 0 2 D NDF * R I i 1 d f 0 d f 0 D NDF * R I i 1 d f 0 d f 0 2 D * I i D NDF * R I i 1 d f 0 z R ( 1+ f 0 D * I i + f 0 D NDF * R I i 1 d f 0 d D NDF * R I i 1 d f 0 d f 0 D * I i D NDF * R I i 1 d f 0 ) .
Δ f tot z R f 0 2 D * I i + f 0 2 D NDF * R I i 1 d f 0 d f 0 D NDF * R I i 1 d f 0 d f 0 2 D * I i D NDF * R I i 1 d f 0 z R ( 1+ f 0 D NDF * R I i 1 d f 0 d D NDF * R I i 1 d f 0 ) .
Δ f NDF z R = f 0 2 D NDF * I i z R ( 1+ f 0 D NDF * I i ) +Δ f 0 .
D NDF * =3.32 10 4 mm W

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