Abstract

This paper introduces a fast numerical method for the estimation of the fluorescence in an azimuthally symmetric cylindrical structure. The core technique of the approach is the expression of the volume fluorescence integral in terms of the absorption path integral parametrization variable. With the parametrization and cylindrical symmetry, the computationally intensive absorption path integrals need only be computed once. Volume integration is quickly performed using explicit elemental area expressions. Reflections from the ends of the cylindrical structure are included through integration over virtual volumes. A coarse quadrature truncation error estimate is provided. Finally, the utility of the algorithm is demonstrated for representative thin disk models. The algorithm was developed in MATLAB but also implemented in standard C to further reduce simulation run times.

© 2012 Optical Society of America

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References

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  2. M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
    [CrossRef]
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  4. A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
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2009 (3)

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

J. Speiser, “Scaling of thin-disk lasers—influence of amplified spontaneous emission,” J. Opt. Soc. Am. B 26, 26–35 (2009).
[CrossRef]

2008 (1)

J. Speiser and A. Giesen, “Scaling of thin disk pulse amplifiers,” Proc. SPIE 6871, 68710J (2008).
[CrossRef]

2007 (1)

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

2003 (1)

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

1999 (1)

S. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[CrossRef]

Amaro, F.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Antognini, A.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Bass, M.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Bigot, E.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Biraben, F.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Bowman, S.

S. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[CrossRef]

S. Bowman, “Fiber pumped radiation balanced laser,” presented at the Eighth Annual Directed Energy Symposium, Lihue, HI, 14–18Nov.2005.

Carson, T.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

Chen, B.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Chen, Y.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Davis, C.

C. Davis, Lasers and Electro-Optics: Fundamentals and Engineering (Cambridge University, 1996).

Dax, A.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Dong, J.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Giesen, A.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

J. Speiser and A. Giesen, “Scaling of thin disk pulse amplifiers,” Proc. SPIE 6871, 68710J (2008).
[CrossRef]

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

Golpaygani, A. H.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Graf, T.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Haensch, T.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Indelicato, P.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Julien, L.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Kandrot, E.

J. Sanders and E. Kandrot, CUDA By Example (Addison-Wesley, 2011).

Kao, C.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Kar, A.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Knowles, P.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Kottmann, F.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Latham, W. P.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

Liu, Y.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Lucas, T.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

Ludhova, L.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Moschuering, N.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Mulhauser, F.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Najafi, M.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Nebel, T.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Newell, T. C.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

Nez, F.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Patel, M.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

Peterson, P.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

Pohl, R.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Rabinowitz, P.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Sabbaghzadeh, J.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Sanders, J.

J. Sanders and E. Kandrot, CUDA By Example (Addison-Wesley, 2011).

Schlie, L.

L. Schlie, “Feasibility assessment for 25 kW thin disk laser with good BQ and efficiency—Scalability to 100 kilowatts,” AFRL Tech. Rep. (2006).

Schuhmann, K.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Schwob, C.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Sepehr, A.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Speiser, J.

J. Speiser, “Scaling of thin-disk lasers—influence of amplified spontaneous emission,” J. Opt. Soc. Am. B 26, 26–35 (2009).
[CrossRef]

J. Speiser and A. Giesen, “Scaling of thin disk pulse amplifiers,” Proc. SPIE 6871, 68710J (2008).
[CrossRef]

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

Taqqu, D.

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

Vretenar, N.

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

IEEE J. Quantum Electron. (2)

A. Antognini, K. Schuhmann, F. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. Haensch, P. Indelicato, L. Julien, C. Kao, P. Knowles, F. Kottmann, E. Bigot, Y. Liu, L. Ludhova, N. Moschuering, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[CrossRef]

S. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Proc. SPIE (2)

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1 (2003).
[CrossRef]

J. Speiser and A. Giesen, “Scaling of thin disk pulse amplifiers,” Proc. SPIE 6871, 68710J (2008).
[CrossRef]

Other (7)

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NVIDIA, “The CUDA compiler driver NVCC,” http://www.developer.nvidia.com .

S. Bowman, “Fiber pumped radiation balanced laser,” presented at the Eighth Annual Directed Energy Symposium, Lihue, HI, 14–18Nov.2005.

C. Davis, Lasers and Electro-Optics: Fundamentals and Engineering (Cambridge University, 1996).

L. Schlie, “Feasibility assessment for 25 kW thin disk laser with good BQ and efficiency—Scalability to 100 kilowatts,” AFRL Tech. Rep. (2006).

N. Vretenar, T. Carson, P. Peterson, T. Lucas, T. C. Newell, and W. P. Latham, “Thermal and stress characterization of various thin-disk laser configurations at room temperature,” AFRL Tech. Rep. (2011).

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Figures (10)

Fig. 1.
Fig. 1.

A view from the top of a cylindrical disk of the paths between the observation and fluorescence source points. Equivalently, a projection into a z=0 horizontal plane of the paths in the cylindrical structure. Thick lines are the original paths, while the thin lines are the same paths rotated to be horizontal to the x-axis.

Fig. 2.
Fig. 2.

The absorption integral path rotated to the horizontal line y=b. Note that for each observation point (circle) at radial distance R there are two source points at distance r (star). Two cases must also be distinguished: R<r (top) and rR (bottom).

Fig. 3.
Fig. 3.

The N=1 virtual volume. Only fluorescence from the active layer is included in the path integral. The inactive cap layer does not contribute.

Fig. 4.
Fig. 4.

The N=1 virtual volume. Only fluorescence from the active layer is included in the path integral. The inactive cap layer does not contribute.

Fig. 5.
Fig. 5.

The labeled fluorescence geometry with the path-parametrization variable b for the volume integration.

Fig. 6.
Fig. 6.

The geometry between the source (star) and observation (circle) points for the volume integration.

Fig. 7.
Fig. 7.

The FAZIMFLAL regions. The observation point lies on the x-axis. The lines indicate elemental area boundaries around the midpoints located at the symbols. Areas A+, B+, C+ correspond to the further source point or distance s and Jacobian M+. A, B, C correspond to the closer source point or distance s+ and Jacobian M. For each observation point at radius R, a different division of the semicircle occurs. The pathological case b=r forms the boundary between the C+ and C regions. The curve is defined through (xR/2)2+y2=(R/2)2. A+ and A regions are divided at b=R or the line x=R. The A and B regions are divided by r=R. A singularity occurs at b=r=R.

Fig. 8.
Fig. 8.

Passive case: direct integration and FAZIMFLAL solutions.

Fig. 9.
Fig. 9.

Passive case: actual and estimated relative errors scaled by the maximum value versus R for Nr=801.

Fig. 10.
Fig. 10.

Γ with 2–2 reflections for a 500 μm pump radius and ν=0.1.

Tables (7)

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Table 1. Explicit z-integration Exponential p Factors

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Table 2. FAZIMFLAL Regions Defined by the (r,b,s) Conditions (note that r, b, and R are discretized on the same grid (δr=δb))

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Table 3. FAZIMFLAL Path Integrals According to the Region of the Source Point (rj,bk,zm)

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Table 4. Area of the (j,k)-th Elemental Region

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Table 5. Area and Spectral Density Truncation Error in the (j,k)-th Elemental Region

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Table 6. Passive Illustration Physical Parameters

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Table 7. Passive dIdλ Case: Performance Summary Versus Nr (run times are for the MATLAB and C implementations of the grid area’s generation and the fluorescence/error estimate computation; the reported error is the maximum relative error over the R observation grid points)

Equations (57)

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Γ=λminλmaxαλdIdλdλ,
dIdλ(R,Θ,Z;λ)=02π0J(r,θ,z;λ)1s2(r,θ,z,R,Θ,Z)eα(r,θ,z;λ)dsrdrdθdz,
dIdλ(R,Z;λ)=VJ(r;λ)1s2eα(r;λ)dsrdrdθdz.
s(t)=(R2b2tr2b2(1t))x^+by^+((Zz)t+z)z^,s+(t)=(R2b2t+r2b2(1t))x^+by^+((Zz)t+z)z^.
s±2=(R2b2r2b2)2+(zZ)2.
s2=ξ2+(zZ)2,ds=1+(zZξ)2dxsec(ϕ)dx.
Cαds=sec(ϕ)xminxmaxα(x)dx.
P(xminxmax)=sg(xmax)0|xmax|α(x)dxsg(xmin)0|xmin|α(x)dx.
P(xrxR)=0xRα(x)dxsg(xr)0|xr|α(x)dx.
PjkL={q=k+1j1·(αqL+αq+1,L2)(xq,kxq1,k)bkrj,0otherwise.
P(x;b)c0(b)+c1(b)x+c2(b)x2+c3(b)x3+c4(b)x4.
dIdλ(R,Z;λ)=02π0ηD/2D/2J(r;λ)1s2eα(r;λ)dsdzrdrdθ
dIdλ|Total=NdIdλ|N(ρ[N]).
ρ[N]=ρT|N+12|ρB|N2|.
N>0,n=0,1,,N,zmin[n]=D2+nD+2L[n2],zmax[n]=D2+(n+1)D+2L[n2],{Zobzpathzmax[0]=D/2,n=0,zmin[N]zpathzso,n=N,zmin[n]zpathzmax[n],n=1,,N1,
N<0,n=N,N+1,,0zmin[n]=D2+nD+2Ln+12,zmax[n]=D2+(n+1)D+2Ln+12,{zmin[0]=D/2zpathzob,n=0,zsozpathzmax[N],n=N,zmin[n]zpathzmax[n],n=N+1,,1,
N>0,n=0,1,,N,{D/2zsozobzsot1,n=0,0tzmin[N]zsoZobzso,n=N,Zmax[N]zsozobzsotZmin[N]zsozobzso,n=1,,N1,
N<0,n=N,N+1,,0,{D/2zsozobzsot1,n=0,0tzmax[N]zsoZobzso,n=N,Zmin[N]zsozobzsotZmax[N]zsozobzso,n=N+1,,1.
dIdλ=AJ(r;λ)NzminNzmaxNρ[N]1s2exp[sec(ϕ)nNxmin[n]xmax[n]α(x)dx]dzdA.
Iz=zminNzmaxNρ[N]1s2exp[sec(ϕ)nNxmax[n]xmax[n]α(x)dx]dz.
Iz=1ξ(r,R,b)ϕ(tmin[N])ϕ(tmax[N])ρ[N](ϕ)exp[sec(ϕ)nNx(tmin[n];ϕ,b)x(tmax[n],ϕ,b)α(x)dx]dϕ.
Iz=1ξϕ(D/2)ϕ(D/2)exp[sec(ϕ)xmin(r,R,b)xmax(r,R,b)α(x)dx]dϕ.
Iz=1ξϕ(D/2)ϕ(D/2)epsec(ϕ)dϕ.
cos(φ)=b/R,sin(φ)=R2b2/R.
x=rcos(θ),y=r2x2=rsin(θ).
bR=brcos(θ)+R2b2rsin(θ).
θ±=arccos(b2±R2b2r2b2rR).
dIdλ=00min(r,R)J(r;λ)1s2eαdsdzMdbrdr
dIdλ=00min(r,R)J(r;λ)NzminNzmaxNρ[N]1s2exp[sec(ϕ)nNxmin[n]xmax[n]α(x)dx]dzMdbrdr.
M=|1R2b2±1r2b2|{1+1r2b2M+1r2b21R2b2MrR1R2b21r2b2MR<r.
dIdλ|jk=δAjkzminzmaxJ(r)eα(r)dss2dzrMdbdr.
f(r,b,z)f(rj,bk,z)+rbf|jk(z)·(rrj,bbk).
dIdλ|jk=δAjkzminzmaxfjk(z)dzrMdrdb+Ejk,
EjkδAjk(rrj)[r2b2rzminzmaxfrdz]jkrMdrdb+δAjk(bbk)[1r|1R2b2±1r2b2|1zminzmaxfbdz]jkrMdrdb.
Ajk=rjminrjmaxbkminbkmaxrMdbdr.
dIdλ(R,Z)rjbkbkrjAjkJjIjkz.
Γ(R,Z)rjbkbkrjAjk(δλLα(R,Z)LJjLIjkLz),
G1r=δArr2b2dbdr,G1R=δArR2b2dbdr,
G1r=b2r2b2+r22arctan(br2b2),G1R=r22arctan(bR2b2).
rminrmaxbminbmaxg(b,r)dbdr=G(bmax,rmax)G(bmin,rmax)G(bmax,rmin)+G(bmin,rmin).
G1r=r+22Δr2r+2r2,Δ=π2arctan(rr+2r2),G1R=12(r+22(R2)2)Δ+14(r+R2r+2rR2r2),Δ=(arctan(r+R2r+2)arctan(rR2r2)).
G1R=(R2)2Δr4R2r2,Δ=π2arctan(rR2r2).
f(z)={J0ξ(r,b)2+(zZ)2rrpump,0otherwise.
s±2=ξ2+(zZ)2=(r2b2R2b2)2+(zZ)2=(uv)2+(zZ)2.
s2r={0b=rR,2rb=R,2rb=r,R<r,0b<r,r=R,2r(uv)2uvotherwise,s2b={0b=rR,0b=R,0b=r,R<r,4b(1+v2|v2|)b<r,r=R,2b(u+v)2uvotherwise,
s2r={0b=r=R,(s=0),0r=R,2rb=r,r<R,2ruvuotherwise,s2b={0b=r=R,(s=0),0r=R,0b=r,r<R,2b(uv)2uotherwise.
Ijks=zminzmax1s4dz=1ξ3[12(ϕ+cosϕsinϕ)]ϕminϕmax.
Eλ(R,Z)rjbkbkrjJjL0[Fr|jkjk(r2rjr)Mdrdb+Fb|jkjk(brbkr)Mdrdb],
EΓ(R,Z)rjbkbkrj(δλLαL(R,Z)JjL0)[Fr|jkjk(r2rjr)Mdrdb+Fb|jkjk(brbkr)Mdrdb],
Fr|jk=[r2b2rs2rIs]jk,Fb|jk=[1r|1R2b2±1r2b2|1s2bIs]jk.
G1r=δArr2b2dbdr,G1R=δArR2b2dbdr,G2r=δAr2r2b2dbdr,G2R=δAr2R2b2dbdr,Gbr=δAbrr2b2dbdr,GbR=δAbrR2b2dbdr.
αds=αr2R22rRcos(θ)+(zZ)2.
dIdλ(R,Z)=J002π0rpumparctan(D/2Zξ)arctan(D/2Zξ)ξrdrdθ,
dIdλ(R)={2πJ00rpump2arctan(D2r)drR=0,Z=0,2J00π0rpump2rξ(r,R)arctan(D2ξ)drdθR>0,Z=0.
σa(λ)=1024e1016(λ930·109)2[m2],σe(λ)=341024e2·1016(λ955·109)2[m2],
J(r,ν,λ)={J0=νN0τσe(λ)σe(λ)dλrrpump,0otherwise.
α(r,ν,λ)={σa(λ)N0(1νσa(λ)+σe(λ)σa(λ))rrpumpσa(λ)N0otherwise=α1+{α0α1rrpump,|z|D/20otherwise,

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