Abstract

Based on the injection-locking principle, the phase-locking mechanisms of axisymmetricfold combination CO2 lasers are analyzed. Then influences of parameters-changes on phase-locking are studied in detail, such as changes of cavity length and curvature radius, linewidth, phase error, and coherence time. It is shown that these factors almost do not influence the degree of mode coupling, but they could influence distribution of light intensity to some degree. Phase-locking can improve the value of maximum light intensity significantly; what is more, the numerical calculation indicates that the higher the fringe visibility the better the coherence.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. J. Seguin, “Power scaling of diffusion-cooled lasers,” Opt. Laser Technol. 30, 331-336 (1998).
    [CrossRef]
  2. W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
    [CrossRef]
  3. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
    [CrossRef]
  4. M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
    [CrossRef]
  5. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
    [CrossRef]
  6. Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
    [CrossRef]
  7. N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).
  8. H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8, 91-93 (1966).
    [CrossRef]
  9. C. J. Buczek and R. J. Freiberg, “Hybrid injection locking of higher power CO2 lasers,” IEEE J. Quantum Electron. QE-8, 641-650 (1972).
    [CrossRef]
  10. C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
    [CrossRef]
  11. J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
    [CrossRef]
  12. J. G. Coffer, J. M. Bernard, R. A. Chodzko, E. B. Turner, R. W. F. Gross, and W. R. Warren, “Experiments with active phase matching of parallel-amplified multiline HF laser beams by a phase-locked Mach-Zehnder interferometer,” Appl. Opt. 22, 142-148 (1983).
    [CrossRef] [PubMed]
  13. L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
    [CrossRef]
  14. K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
    [CrossRef]
  15. V. V. Apollonov, S. I. Derzhavin, V. I. Kislov, V. V. Kuzminov, D. A. Mashkovsky, and A. M. Prokhorov, “Phase-locking of the 2D structures,” Opt. Express 4, 19-26 (1999).
    [CrossRef] [PubMed]
  16. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015-12021 (2006).
    [CrossRef] [PubMed]
  17. F. R. Ruiz-Oliveras and A. N. Pisarchik, “Phase-locking phenomenon in a semiconductor laser with external cavties,” Opt. Express 14, 12859-12867 (2006).
    [CrossRef] [PubMed]
  18. G. Wei and B. Zhu, Laser Beam Optics (Beijing Industry College, 1987), Chap. 3 (in Chinese).
  19. R. L. Sinclair and J. Tulip, “Parameters affecting the performance of a rf excited CO2 waveguide laser,” J. Appl. Phys. 56, 2497-2501 (1984).
    [CrossRef]
  20. B. Lv, Laser Optics (Sichuan U. Press, 1992), Chaps. 2 and 3 (in Chinese).

2006

2005

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

1999

1998

H. J. J. Seguin, “Power scaling of diffusion-cooled lasers,” Opt. Laser Technol. 30, 331-336 (1998).
[CrossRef]

1996

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

1993

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

1992

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

1985

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

1984

R. L. Sinclair and J. Tulip, “Parameters affecting the performance of a rf excited CO2 waveguide laser,” J. Appl. Phys. 56, 2497-2501 (1984).
[CrossRef]

1983

1976

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

1973

C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
[CrossRef]

1972

C. J. Buczek and R. J. Freiberg, “Hybrid injection locking of higher power CO2 lasers,” IEEE J. Quantum Electron. QE-8, 641-650 (1972).
[CrossRef]

1966

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

1965

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).

Abramski, K. M.

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

Apollonov, V. V.

Baker, H. J.

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

Baker, J. T.

Basov, N. G.

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).

Belenov, E. M.

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).

Benham, V.

Bernard, J. M.

Bilida, W. D.

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

Buczek, C. J.

C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
[CrossRef]

C. J. Buczek and R. J. Freiberg, “Hybrid injection locking of higher power CO2 lasers,” IEEE J. Quantum Electron. QE-8, 641-650 (1972).
[CrossRef]

Capjack, C. E.

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

Chen, M.

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

Chodzko, R. A.

Coffer, J. G.

Colley, A. D.

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

Culpepper, M. A.

Derzhavin, S. I.

Florez, L. T.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

Freiberg, R. J.

C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
[CrossRef]

C. J. Buczek and R. J. Freiberg, “Hybrid injection locking of higher power CO2 lasers,” IEEE J. Quantum Electron. QE-8, 641-650 (1972).
[CrossRef]

Goldberg, L.

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

Gross, R. W. F.

Guo, J.

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

Hail, D. R.

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

Harbison, J. P.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

Kapon, E.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

Kislov, V. I.

Kuzminov, V. V.

Lachambre, J.-L.

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

Lavigne, P.

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

Letokhov, V. S.

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).

Li, Y.

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

Liu, J.

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

Lu, C. A.

Lv, B.

B. Lv, Laser Optics (Sichuan U. Press, 1992), Chaps. 2 and 3 (in Chinese).

Mashkovsky, D. A.

Nelson, D. J.

Noel, M.

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

Orenstein, M.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

Otis, G.

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

Pilkington, D.

Pisarchik, A. N.

Prokhorov, A. M.

Reshef, H.

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
[CrossRef]

Ruiz-Oliveras, F. R.

Sanchez, A. D.

Scifres, D. R.

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

Seguin, H. J. J.

H. J. J. Seguin, “Power scaling of diffusion-cooled lasers,” Opt. Laser Technol. 30, 331-336 (1998).
[CrossRef]

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

Shay, T. M.

Sinclair, R. L.

R. L. Sinclair and J. Tulip, “Parameters affecting the performance of a rf excited CO2 waveguide laser,” J. Appl. Phys. 56, 2497-2501 (1984).
[CrossRef]

Skolnick, M. L.

C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
[CrossRef]

Spring, J.

Steier, W. H.

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

Stoffel, N. G.

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

Stover, H. L.

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

Strohschein, J. D.

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

Taylor, H. F.

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

Tulip, J.

R. L. Sinclair and J. Tulip, “Parameters affecting the performance of a rf excited CO2 waveguide laser,” J. Appl. Phys. 56, 2497-2501 (1984).
[CrossRef]

Turner, E. B.

Ward, B.

Warren, W. R.

Wei, G.

G. Wei and B. Zhu, Laser Beam Optics (Beijing Industry College, 1987), Chap. 3 (in Chinese).

Weller, J. F.

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

Yelden, E. F.

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475-1482 (1993).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

Zhu, B.

G. Wei and B. Zhu, Laser Beam Optics (Beijing Industry College, 1987), Chap. 3 (in Chinese).

Appl. Opt.

Appl. Phys. Lett.

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupled-stripe diode laser arrays,” Appl. Phys. Lett. 46, 236-238 (1985).
[CrossRef]

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hail, “Phase-locked CO2 laser array using diagonal coupling of waveguide channels,” Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Large two-dimensional arrays of phase-locked vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 1535-1537 (1992).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and H. Reshef, “Phase locking in a multichannel radial array CO2 laser,” Appl. Phys. Lett. 62, 1311-1313 (1993).
[CrossRef]

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

IEEE J. Quantum Electron.

C. J. Buczek and R. J. Freiberg, “Hybrid injection locking of higher power CO2 lasers,” IEEE J. Quantum Electron. QE-8, 641-650 (1972).
[CrossRef]

J.-L. Lachambre, P. Lavigne, G. Otis, and M. Noel, “Injection locking and mode selection in TEA-CO2 laser oscillators,” IEEE J. Quantum Electron. 12, 756-764 (1976).
[CrossRef]

J. Appl. Phys.

R. L. Sinclair and J. Tulip, “Parameters affecting the performance of a rf excited CO2 waveguide laser,” J. Appl. Phys. 56, 2497-2501 (1984).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng. (Bellingham)

Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. (Bellingham) 44, 064204 (2005).
[CrossRef]

Opt. Express

Opt. Laser Technol.

H. J. J. Seguin, “Power scaling of diffusion-cooled lasers,” Opt. Laser Technol. 30, 331-336 (1998).
[CrossRef]

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, “Multi-channel slab CO2 laser excitation with resonant cavities,” Opt. Laser Technol. 28, 431-436 (1996).
[CrossRef]

Proc. IEEE

C. J. Buczek, R. J. Freiberg, and M. L. Skolnick, “Laser injection locking,” Proc. IEEE 61, 1411-1430 (1973).
[CrossRef]

Sov. Phys. Tech. Phys.

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845-850 (1965).

Other

G. Wei and B. Zhu, Laser Beam Optics (Beijing Industry College, 1987), Chap. 3 (in Chinese).

B. Lv, Laser Optics (Sichuan U. Press, 1992), Chaps. 2 and 3 (in Chinese).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Geometrical optical pathway and the model diagrams of ASFC.

Fig. 2
Fig. 2

Equivalent diagram of the ASFC and cavity M 0 M 1 of the calculating mode coupling coefficient.

Fig. 3
Fig. 3

Curvature radius of the equiphase surface diagram of the injected beam at M 0 for the concentric cavity.

Fig. 4
Fig. 4

Curvature radius of the equiphase surface diagram of the injected beam at M 0 for the stable cavity.

Fig. 5
Fig. 5

Curve diagram of the injected beam radius ω 0 at M 1 and the curvature radius ρ 0 x .

Fig. 6
Fig. 6

Curve diagram of the mode coupling coefficient c 00 and the curvature radius ρ 0 x .

Fig. 7
Fig. 7

Curvature radius of the equiphase surface diagram of the injected beam at M 0 when there is a linewidth.

Fig. 8
Fig. 8

Curve diagram of the injected beam radius ω * at M 1 and the curvature radius ρ 0 x when there is a linewidth.

Fig. 9
Fig. 9

Curve diagram of the mode coupling coefficient c 00 * and curvature radius ρ 0 x when there is a linewidth.

Fig. 10
Fig. 10

Curvature radius of the equiphase surface diagram of the injected beam at M 0 when the cavity length changes.

Fig. 11
Fig. 11

Curve diagram of the coupling coefficient c 00 * * and the curvature radius ρ 0 x when the cavity length changes.

Fig. 12
Fig. 12

Curvature radius of the equiphase surface diagram of the injected beam at M 0 when the curvature radius changes.

Fig. 13
Fig. 13

Curve diagram of the coupling coefficient c 00 + and the curvature radius ρ 0 x when the curvature radius changes.

Fig. 14
Fig. 14

Geometrical optical pathway diagram of the output beams of calculating the light intensity.

Fig. 15
Fig. 15

Places of the five beam waists in plane a when M 6 is under the normal state.

Fig. 16
Fig. 16

Plane and stereograph of distributions of light intensities and light-spot profile of coherent beams (a) z l b = 10 cm , (b) z l b = 10 cm , when there is phase error, (c) z l b = 10 cm , when there is a linewidth, (d) z l b = 10 cm when the cavity length changes, (e) z l b = 10 cm when the curvature radius changes, (f) z l d = 10.2 cm , (g) z l c = 9.8 cm , and (h) z l b = 10 cm , the plane and stereograph of distributions of light intensities and light-spot profile of partial-coherent beams, respectively.

Tables (2)

Tables Icon

Table 1 Characteristic Parameters of Using Phase-Locking

Tables Icon

Table 2 Fringe Visibility of Output Beam

Equations (13)

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

Δ R rms = ( R ( t ) R ¯ ) 2 ¯ ,
c 00 = 2 ω 0 ω p ,
p = 1 ω 0 2 + 1 ω 2 + i k 2 ( 1 R 0 1 R ) ,
ε 1 j ( x 1 , y 1 , z = 0 ) = A 0 j exp [ ( x 1 x 0 j ) 2 + ( y 1 y 0 j ) 2 ω 0 j 2 ] ,
q 2 = A 2 q 1 + B 2 C 2 q 1 + D 2 ,
( A 2 B 2 C 2 D 2 ) = ( 1 l x 0 1 ) ( 1 0 1 f 1 ) ( 1 l x cos θ 0 0 1 ) ( cos θ 0 cos θ g 0 0 n g cos θ g cos θ 0 ) ( 1 h g cos θ g 0 1 ) ( cos θ g cos θ 0 0 0 cos θ 0 n g cos θ g ) ,
1 f = ( n g 1 ) ( 1 ρ 0 x 1 ρ 1 x ) .
( ε 1 j ε 1 j * ) d x 1 d y 1 = c ,
ε 2 j ( x , y ) = i e i k L λ B x o y A 0 j exp [ ( x 1 x 0 j ) 2 + ( y 1 y 0 j ) 2 ω 0 j 2 ] exp { i k 2 B [ A ( x 1 2 + y 1 2 ) + D ( x 2 + y 2 ) 2 ( x 1 x + y 1 y ) ] } d x 1 d y 1 ,
( A B C D ) = ( 1 z l 0 1 ) ( 1 0 1 f 1 ) ( 1 l x 1 0 1 ) = ( 1 z l f l x 1 + z l z l l x 1 f 1 f 1 l x 1 f ) ,
ε 2 j ( x , y ) = i A 0 j π e i k L λ B α exp [ ( 1 ω 0 j 4 α 1 ω 0 j 2 ) ( x 0 j 2 + y 0 j 2 ) ] exp [ ( i k D 2 B + k 2 4 B 2 α ) ( x 2 + y 2 ) i k ( x 0 j x + y 0 j y ) ] ,
I = j = 1 5 ε 2 j j = 1 5 ( ε 2 j ) * .
V = I max I min I max + I min .

Metrics