Abstract

We apply a genetic algorithm to optimize the pump cavity of a complex miniaturized diode-pumped laser to find a balance between the efficient energy transfer of the pump light and the homogeneous illumination of the laser crystal. These two points are in contradiction to each other, whereby a complex optimization situation is given. The genome determines the geometry of the internal optical elements of the pump cavity in which a laser rod is placed. After optimization of the internal optical elements, a homogeneous illumination over the crystal length and a coupling efficiency of 59% were achieved. The results showed that genetic algorithms can find solutions and blueprints for laser pump cavities of consistent quality.

© 2007 Optical Society of America

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  7. F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
    [CrossRef]
  8. S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
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  9. D. Graham-Rowe, "Electronic circuit 'evolves' from liquid crystals," New Sci. 181, 21 (2004).
  10. E. A. Williams, W. A. Crossley, and T. J. Lang, "Average and maximum revisit time trade studies for satellite constellations using a multiobjective genetic algorithm," J. Astronaut. Sci. 49, 385-400 (2001).
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  13. J. E. Beasley, J. Sonander, and P. Havelock, "Scheduling aircraft landings at London Heathrow using a population heuristic," J. Oper. Res. Soc. 52, 483-493 (2001).
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  14. E. K. Burke and J. P. Newall, "A multistage evolutionary algorithm for the timetable problem," IEEE Trans. Evol. Comput. 3, 63-74 (1999).
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  15. M. Jensen, "Generating robust and flexible job shop schedules using genetic algorithms," IEEE Trans. Evol. Comput. 7, 275-288 (2003).
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  16. D. L. Shealy, "Historical perspective of laser beam shaping," in Laser Beam Shaping III, F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Proc. SPIE 4770, 28-47 (2002).
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  17. H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.
  18. D. Wiesmann, U. Hammel, and T. Back, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
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  23. J. Meister, R. Franzen, C. Apel, and N. Gutknecht, "Multireflection pumping concept for miniaturized diode-pumped solid-state lasers," Appl. Opt. 43, 5864-5869 (2004).
    [CrossRef] [PubMed]
  24. J. Meister, R. Franzen, T. Mitra, and R. Bayer, "Vorrichtung und Verfahren zur Erzeugung von Laserlicht," German patent DE 100 13 371 B4 (2004).
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  26. C. Darwin, On the Origin of Species by Means of Natural Selection (John Murray, 1859).
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  30. T. Jensen, G. Huber, and K. Petermann, "Quasi-cw diode pumped 2.8 μm laser operation of Er3+-doped garnets," in Advanced Solid-State Lasers,S.A.Payne and C.Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 306-308.
  31. C. Ziolek, H. Ernst, G. F. Will, H. Lubatschowski, H. Welling, and W. Ertmer, "High-repetition-rate, high-average-power, diode-pumped 2.94 μm Er: YAG laser," Opt. Lett. 26, 599-601 (2001).
    [CrossRef]
  32. T. Jensen, "Upconversion-Prozesse and Wirkungsquerschnitte in Er3+-dotierten 3 μm Fluorid- und Granat-Lasern, gepumpt mit cw und quasi-cw Dioden-Arrays," Ph.D. dissertation (Institute of Laser Physics, University of Hamburg, 1996).
  33. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989), pp. 74-77.

2006 (1)

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

2005 (1)

R. E. Carley, E. Heesel, and H. H. Fielding, "Femtosecond lasers in gas phase chemistry," Chem. Soc. Rev. 34, 949-969 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (2)

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

M. Jensen, "Generating robust and flexible job shop schedules using genetic algorithms," IEEE Trans. Evol. Comput. 7, 275-288 (2003).
[CrossRef]

2002 (5)

D. L. Shealy, "Historical perspective of laser beam shaping," in Laser Beam Shaping III, F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Proc. SPIE 4770, 28-47 (2002).
[CrossRef]

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

E. Benini and A. Toffolo, "Optimal design of horizontal-axis wind turbines using blade-element theory and evolutionary computation," ASME J. Sol. Energy Eng. 124, 357-363 (2002).
[CrossRef]

Y. Lee and S. H. Zak, "Designing a genetic neural fuzzy antilock-brake-system controller," IEEE Trans. Evol. Comput. 6, 198-211 (2002).
[CrossRef]

P. Fleming and R. C. Purshouse, "Evolutionary algorithms in control systems engineering: a survey," Control Eng. Pract. 10, 1223-1241 (2002).
[CrossRef]

2001 (3)

C. Ziolek, H. Ernst, G. F. Will, H. Lubatschowski, H. Welling, and W. Ertmer, "High-repetition-rate, high-average-power, diode-pumped 2.94 μm Er: YAG laser," Opt. Lett. 26, 599-601 (2001).
[CrossRef]

E. A. Williams, W. A. Crossley, and T. J. Lang, "Average and maximum revisit time trade studies for satellite constellations using a multiobjective genetic algorithm," J. Astronaut. Sci. 49, 385-400 (2001).

J. E. Beasley, J. Sonander, and P. Havelock, "Scheduling aircraft landings at London Heathrow using a population heuristic," J. Oper. Res. Soc. 52, 483-493 (2001).
[CrossRef]

1999 (1)

E. K. Burke and J. P. Newall, "A multistage evolutionary algorithm for the timetable problem," IEEE Trans. Evol. Comput. 3, 63-74 (1999).
[CrossRef]

1998 (3)

D. Wiesmann, U. Hammel, and T. Bäck, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

D. Wiesmann, U. Hammel, and T. Back, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

A. Efimov, M. D. Moores, N. M. Beach, J. L. Krause, and D. H. Reitze, "Adaptive control of pulse phase in a chirped-pulse amplifier," Opt. Lett. 23, 1915-1917 (1998).
[CrossRef]

1997 (1)

E. E. Altshuler and D. S. Linden, "Design of a wire antenna using a genetic algorithm," J. Electron. Defense 20, 50-52 (1997).

1996 (1)

S. Mahfoud and G. Mani, "Financial forecasting using genetic algorithms," Appl. Artif. Intell. 10, 543-565 (1996).
[CrossRef]

1995 (1)

P. Charbonneau, "Genetic algorithms in astronomy and astrophysics," Astrophys. J. Suppl. S. 101, 309-334 (1995).
[CrossRef]

1992 (1)

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Altshuler, E. E.

E. E. Altshuler and D. S. Linden, "Design of a wire antenna using a genetic algorithm," J. Electron. Defense 20, 50-52 (1997).

Ando, Y.

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

Apel, C.

Asaka, T.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Bächtold, W.

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

Back, T.

D. Wiesmann, U. Hammel, and T. Back, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

Bäck, T.

D. Wiesmann, U. Hammel, and T. Bäck, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

Bayer, R.

J. Meister, R. Franzen, T. Mitra, and R. Bayer, "Vorrichtung und Verfahren zur Erzeugung von Laserlicht," German patent DE 100 13 371 B4 (2004).

Beach, N. M.

Beasley, J. E.

J. E. Beasley, J. Sonander, and P. Havelock, "Scheduling aircraft landings at London Heathrow using a population heuristic," J. Oper. Res. Soc. 52, 483-493 (2001).
[CrossRef]

Benini, E.

E. Benini and A. Toffolo, "Optimal design of horizontal-axis wind turbines using blade-element theory and evolutionary computation," ASME J. Sol. Energy Eng. 124, 357-363 (2002).
[CrossRef]

Burke, E. K.

E. K. Burke and J. P. Newall, "A multistage evolutionary algorithm for the timetable problem," IEEE Trans. Evol. Comput. 3, 63-74 (1999).
[CrossRef]

Carley, R. E.

R. E. Carley, E. Heesel, and H. H. Fielding, "Femtosecond lasers in gas phase chemistry," Chem. Soc. Rev. 34, 949-969 (2005).
[CrossRef] [PubMed]

Charbonneau, P.

P. Charbonneau, "Genetic algorithms in astronomy and astrophysics," Astrophys. J. Suppl. S. 101, 309-334 (1995).
[CrossRef]

Crossley, W. A.

E. A. Williams, W. A. Crossley, and T. J. Lang, "Average and maximum revisit time trade studies for satellite constellations using a multiobjective genetic algorithm," J. Astronaut. Sci. 49, 385-400 (2001).

Crowell, R. A.

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

Darwin, C.

C. Darwin, On the Origin of Species by Means of Natural Selection (John Murray, 1859).

Dewa, H.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Efimov, A.

Elles, C. G.

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

Ernst, H.

Ertmer, W.

Fielding, H. H.

R. E. Carley, E. Heesel, and H. H. Fielding, "Femtosecond lasers in gas phase chemistry," Chem. Soc. Rev. 34, 949-969 (2005).
[CrossRef] [PubMed]

Fleming, P.

P. Fleming and R. C. Purshouse, "Evolutionary algorithms in control systems engineering: a survey," Control Eng. Pract. 10, 1223-1241 (2002).
[CrossRef]

Franzen, R.

J. Meister, R. Franzen, C. Apel, and N. Gutknecht, "Multireflection pumping concept for miniaturized diode-pumped solid-state lasers," Appl. Opt. 43, 5864-5869 (2004).
[CrossRef] [PubMed]

J. Meister, R. Franzen, T. Mitra, and R. Bayer, "Vorrichtung und Verfahren zur Erzeugung von Laserlicht," German patent DE 100 13 371 B4 (2004).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989), pp. 3-5.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989), pp. 74-77.

Graham-Rowe, D.

D. Graham-Rowe, "Electronic circuit 'evolves' from liquid crystals," New Sci. 181, 21 (2004).

Gutknecht, N.

Hammel, U.

D. Wiesmann, U. Hammel, and T. Bäck, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

D. Wiesmann, U. Hammel, and T. Back, "Robust design of multilayer optical coatings by means of evolutionary algorithms," IEEE Trans. Evol. Comput. 2, 162-167 (1998).
[CrossRef]

Hanaki, H.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Havelock, P.

J. E. Beasley, J. Sonander, and P. Havelock, "Scheduling aircraft landings at London Heathrow using a population heuristic," J. Oper. Res. Soc. 52, 483-493 (2001).
[CrossRef]

Heesel, E.

R. E. Carley, E. Heesel, and H. H. Fielding, "Femtosecond lasers in gas phase chemistry," Chem. Soc. Rev. 34, 949-969 (2005).
[CrossRef] [PubMed]

Homan, O. J.

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

Huber, G.

T. Jensen, G. Huber, and K. Petermann, "Quasi-cw diode pumped 2.8 μm laser operation of Er3+-doped garnets," in Advanced Solid-State Lasers,S.A.Payne and C.Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 306-308.

Jensen, M.

M. Jensen, "Generating robust and flexible job shop schedules using genetic algorithms," IEEE Trans. Evol. Comput. 7, 275-288 (2003).
[CrossRef]

Jensen, T.

T. Jensen, "Upconversion-Prozesse and Wirkungsquerschnitte in Er3+-dotierten 3 μm Fluorid- und Granat-Lasern, gepumpt mit cw und quasi-cw Dioden-Arrays," Ph.D. dissertation (Institute of Laser Physics, University of Hamburg, 1996).

T. Jensen, G. Huber, and K. Petermann, "Quasi-cw diode pumped 2.8 μm laser operation of Er3+-doped garnets," in Advanced Solid-State Lasers,S.A.Payne and C.Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 306-308.

Judson, R. S.

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Kawamura, H.

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

Kobayashi, T.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Korovyanko, O. J.

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

Krause, J. L.

Lang, T. J.

E. A. Williams, W. A. Crossley, and T. J. Lang, "Average and maximum revisit time trade studies for satellite constellations using a multiobjective genetic algorithm," J. Astronaut. Sci. 49, 385-400 (2001).

Lee, Y.

Y. Lee and S. H. Zak, "Designing a genetic neural fuzzy antilock-brake-system controller," IEEE Trans. Evol. Comput. 6, 198-211 (2002).
[CrossRef]

Li, Y.

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

Linden, D. S.

E. E. Altshuler and D. S. Linden, "Design of a wire antenna using a genetic algorithm," J. Electron. Defense 20, 50-52 (1997).

Lubatschowski, H.

Mahfoud, S.

S. Mahfoud and G. Mani, "Financial forecasting using genetic algorithms," Appl. Artif. Intell. 10, 543-565 (1996).
[CrossRef]

Mani, G.

S. Mahfoud and G. Mani, "Financial forecasting using genetic algorithms," Appl. Artif. Intell. 10, 543-565 (1996).
[CrossRef]

Matsui, F.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Meister, J.

J. Meister, R. Franzen, C. Apel, and N. Gutknecht, "Multireflection pumping concept for miniaturized diode-pumped solid-state lasers," Appl. Opt. 43, 5864-5869 (2004).
[CrossRef] [PubMed]

J. Meister, R. Franzen, T. Mitra, and R. Bayer, "Vorrichtung und Verfahren zur Erzeugung von Laserlicht," German patent DE 100 13 371 B4 (2004).

Michod, R. E.

R. E. Michod, Darwinian Dynamics, Evolutionary Transitions in Fitness and Individuality (Princeton U. Press, 1999).

Mitra, T.

J. Meister, R. Franzen, T. Mitra, and R. Bayer, "Vorrichtung und Verfahren zur Erzeugung von Laserlicht," German patent DE 100 13 371 B4 (2004).

Mizuno, A.

H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi, H. Hanaki, and F. Matsui, "Development of adaptive feedback control system of both spatial and temporal beam shaping for UV-laser light source for RF gun," in Proceedings of LINAC 2004 (Lübeck, 2004), pp. 207-209.

Moores, M. D.

Moreno, E.

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

Newall, J. P.

E. K. Burke and J. P. Newall, "A multistage evolutionary algorithm for the timetable problem," IEEE Trans. Evol. Comput. 3, 63-74 (1999).
[CrossRef]

Orzati, A.

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

Otori, K.

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

Petermann, K.

T. Jensen, G. Huber, and K. Petermann, "Quasi-cw diode pumped 2.8 μm laser operation of Er3+-doped garnets," in Advanced Solid-State Lasers,S.A.Payne and C.Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 306-308.

Petzinger, T.

T. Petzinger, "At Deere they know a mad scientist may be a firm's biggest asset," the Wall Street Journal (July 14, 1995), p. B1.

Purshouse, R. C.

P. Fleming and R. C. Purshouse, "Evolutionary algorithms in control systems engineering: a survey," Control Eng. Pract. 10, 1223-1241 (2002).
[CrossRef]

Rabitz, H.

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Reitze, D. H.

Rey-de-Castro, R.

O. J. Korovyanko, R. Rey-de-Castro, C. G. Elles, R. A. Crowell, and Y. Li, "Optimization of a femtosecond Ti:sapphire amplifier using an acousto-optic programmable dispersive filter and a genetic algorithm," in Solid State Lasers XV: Technology and Devices, H. J. Hoffman and R. K. Shori, eds., Proc. SPIE 6100, 183-188 (2006).

Robin, F.

F. Robin, A. Orzati, E. Moreno, O. J. Homan, and W. Bächtold, "Simulation and evolutionary optimization of electron-beam lithography with genetic and simplex-downhill algorithms," IEEE Trans. Evol. Comput. 7, 69-82 (2003).
[CrossRef]

Sakai, H.

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

Sato, S.

S. Sato, K. Otori, A. Takizawa, H. Sakai, Y. Ando, and H. Kawamura, "Applying genetic algorithms to the optimum design of a concert hall," J. Sound Vib. 258, 517-526 (2002).
[CrossRef]

Shealy, D. L.

D. L. Shealy, "Historical perspective of laser beam shaping," in Laser Beam Shaping III, F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Proc. SPIE 4770, 28-47 (2002).
[CrossRef]

Sonander, J.

J. E. Beasley, J. Sonander, and P. Havelock, "Scheduling aircraft landings at London Heathrow using a population heuristic," J. Oper. Res. Soc. 52, 483-493 (2001).
[CrossRef]

Suzuki, S.

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Figures (10)

Fig. 1
Fig. 1

(Color online) Schematic of the pump cavity. Numbers 1–7 characterize the different parts of the pump cavity. Parts 1–4 assemble the complex front mirror system of parabolic mirrors (90° each). The laser rod (5) is positioned in the center of the cavity. Part 6 describes the light guides for pumping the laser crystal (2 of 4 are shown in the graph). Part 7 is the parabolic rear mirror (360° full angle). The value for the position of one mirror (x3) is shown exemplary, also the value for positioning the light guides ( xlight   guide and rlight   guide .

Fig. 2
Fig. 2

Flow chart of the genetic algorithm. For each member i=1n in a generation g, two randomly chosen parents from generation g1 provide one child G(g,i) . If the child is considered better [higher fitness function than old member G(g1,i) ], then it is used in the creation of the next generation g. If the child is not better, then the member of the old generation G(g1,i) is carried over into the new generation g as G(g,i) .

Fig. 3
Fig. 3

Graph of the fitness function IM/D2 versus the generation number. Each point represents a solution of the genetic algorithm.

Fig. 4
Fig. 4

Graph of the mesh integral versus the generation number.

Fig. 5
Fig. 5

Graph of the variable D, i.e., the number of poorly illuminated voxels, defined by having less than 5% intensity of the brightest voxel in the model.

Fig. 6
Fig. 6

(Color online) Side view of the pumping cavity, direct output from the ray tracer. The elements crystal rod and pumping chamber are drawn as a cross section in a lateral cut. All points of reflections of light rays are drawn in the image: The crystal rod is completely covered by points; also the four mirror segments and the back mirror can be seen because of the many light reflections on them. Additionally, many reflections take place on the cavity chamber wall itself, making it an essential part of the pumping optics. The solution shown illustrates a very good solution. However, this image does not give intensity information, which is shown in Fig. 7.

Fig. 7
Fig. 7

Side view of a laser rod in the xy plane. Brighter colors describe higher energy densities. Energy transfer is acceptable with IM=59% (8-bit gray scale with black denoting an energy density of 50  mJ/mm3 ). The average energy density over the irradiated volume with a length of 10 mm inside the pump cavity for the rod is 7 .4  mJ/mm3 .

Fig. 8
Fig. 8

Energy distribution of the pump energy in different yz slices of the rod at x positions of x=2 , 4, 6, 8, 10, 12, and 14  mm (from left to right). Brighter colors mean higher energy densities (8-bit gray scale with black denoting an energy density of 50 mJ∕mm3).

Fig. 9
Fig. 9

Side view of a laser rod in the xy plane. The initial population consists of solutions that have an energy transfer of IM=71% but also feature a hot spot. Brighter colors mean higher energy densities. (8-bit gray scale with black denoting an energy density of 240  mJ/mm3 ).

Fig. 10
Fig. 10

(Color online) Side view of the pumping cavity, direct output from the ray tracer. The elements crystal rod and pumping chamber are drawn as a cross section in a lateral cut. All points of reflections of light rays are drawn in the image: The crystal rod is only partially covered by points; also two of the mirror segments and the rear mirror can be seen because of the light reflections on them. Reflections on the cavity chamber wall itself are less obvious than in Fig. 6. The solution shown in this figure illustrates the starting genome of the GA. However, this image does not give intensity information, which is shown in Fig. 9.

Tables (1)

Tables Icon

Table 1 Values Used for the Variables n and s in the Evolutionary Process to Create a Modified Pump Cavity for Miniaturized Diode-Pumped Solid-State Lasers

Equations (4)

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

G := [f1,f2,f3,f4,x1,x2,x3,x4,frear,rlight   guide,xlight   guide].
IM := 1Elaser   rodV(r)d3r[0,1].
F := IMD2.
G=[40,11,30,30,5,2.3,5,4.6,15,3.6,4],

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