Abstract

An analytical model is formulated to support understanding and underpin experimental development of laser action in the promising diode end-pumped Alexandrite system. Closed form solutions are found for output power, threshold, and slope efficiency that for the first time incorporate the combined effects of laser ground state absorption and excited state absorption (laser ESA), along with pump excited state absorption (pump ESA), in the case of an end-pumping geometry. Comparison is made between model predictions and experimental results from a fiber-delivered diode end-pumped Alexandrite laser system, showing the impact of wavelength tuning, crystal temperature, laser output coupling, and intracavity loss. The model is broadly applicable to other quasi-three-level lasers with combined laser and pump ESA. A condition for bistable operation is also formulated.

© 2016 Optical Society of America

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References

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  1. J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
    [Crossref]
  2. J. W. Kuper, T. Chin, and H. E. Aschoff, “Extended tuning range of Alexandrite at elevated temperatures,” in Advanced Solid State Lasers (Optical Society of America, 1990), paper CL3.
  3. R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
    [Crossref]
  4. H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
    [Crossref]
  5. M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).
  6. A. Teppitaksak, A. Minassian, G. Thomas, and M. Damzen, “High efficiency >26  w diode end-pumped Alexandrite laser,” Opt. Express 22, 16386–16392 (2014).
    [Crossref]
  7. E. Arbabzadah and M. Damzen, “Fibre-coupled red diode-pumped Alexandrite TEM00 laser with single and double-pass end-pumping,” Laser Phys. Lett. 13, 065002 (2016).
    [Crossref]
  8. M. Shand and H. Jenssen, “Temperature dependence of the excited-state absorption of Alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
    [Crossref]
  9. Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
    [Crossref]
  10. S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
    [Crossref]
  11. M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
    [Crossref]
  12. D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134, A299–A306 (1964).
    [Crossref]
  13. M. Shand and J. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
    [Crossref]
  14. M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
    [Crossref]
  15. W. Kerridge-Johns and M. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
    [Crossref]
  16. E. Beyatli, I. Baali, B. Sumpf, G. Erbert, A. Leitenstorfer, A. Sennaroglu, and U. Demirbas, “Tapered diode-pumped continuous-wave Alexandrite laser,” J. Opt. Soc. Am. B 30, 3184–3192 (2013).
    [Crossref]
  17. M. Hercher, “An analysis of saturable absorbers,” Appl. Opt. 6, 947–954 (1967).
    [Crossref]
  18. R. Beach, “CW theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
    [Crossref]
  19. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
    [Crossref]
  20. B. Thedrez and C. Lee, “A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations,” IEEE J. Quantum Electron. 28, 2706–2713 (1992).
    [Crossref]
  21. W. Koechner, Solid-State Laser Engineering, 6th ed., Vol. 1 of Springer Series in Optical Sciences (Springer, 2006).
  22. E. Arimondo and B. Dinelli, “Optical bistability of a CO2 laser with intracavity saturable absorber: experiment and model,” Opt. Commun. 44, 277–282 (1983).
    [Crossref]
  23. X. Zhang and Y. Wang, “Optical bistability effects in a Tm, Ho:YLF laser at room temperature,” Opt. Lett. 32, 2333–2335 (2007).
    [Crossref]
  24. J. Liu, V. Petrov, U. Griebner, F. Noack, H. Zhang, J. Wang, and M. Jiang, “Optical bistability in the operation of a continuous-wave diode-pumped Yb:LuVO4 laser,” Opt. Express 14, 12183–12187 (2006).
    [Crossref]

2016 (1)

E. Arbabzadah and M. Damzen, “Fibre-coupled red diode-pumped Alexandrite TEM00 laser with single and double-pass end-pumping,” Laser Phys. Lett. 13, 065002 (2016).
[Crossref]

2015 (1)

W. Kerridge-Johns and M. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
[Crossref]

2014 (1)

2013 (1)

2007 (1)

2006 (1)

1996 (1)

R. Beach, “CW theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[Crossref]

1993 (1)

Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
[Crossref]

1992 (1)

B. Thedrez and C. Lee, “A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations,” IEEE J. Quantum Electron. 28, 2706–2713 (1992).
[Crossref]

1988 (2)

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

1986 (1)

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

1983 (2)

M. Shand and H. Jenssen, “Temperature dependence of the excited-state absorption of Alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
[Crossref]

E. Arimondo and B. Dinelli, “Optical bistability of a CO2 laser with intracavity saturable absorber: experiment and model,” Opt. Commun. 44, 277–282 (1983).
[Crossref]

1982 (2)

M. Shand and J. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
[Crossref]

M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
[Crossref]

1981 (1)

M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
[Crossref]

1980 (1)

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

1967 (1)

1965 (1)

W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[Crossref]

1964 (1)

D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134, A299–A306 (1964).
[Crossref]

Alfano, R.

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

Arbabzadah, E.

E. Arbabzadah and M. Damzen, “Fibre-coupled red diode-pumped Alexandrite TEM00 laser with single and double-pass end-pumping,” Laser Phys. Lett. 13, 065002 (2016).
[Crossref]

Arimondo, E.

E. Arimondo and B. Dinelli, “Optical bistability of a CO2 laser with intracavity saturable absorber: experiment and model,” Opt. Commun. 44, 277–282 (1983).
[Crossref]

Aschoff, H. E.

J. W. Kuper, T. Chin, and H. E. Aschoff, “Extended tuning range of Alexandrite at elevated temperatures,” in Advanced Solid State Lasers (Optical Society of America, 1990), paper CL3.

Baali, I.

Beach, R.

R. Beach, “CW theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[Crossref]

Beyatli, E.

Chin, T.

J. W. Kuper, T. Chin, and H. E. Aschoff, “Extended tuning range of Alexandrite at elevated temperatures,” in Advanced Solid State Lasers (Optical Society of America, 1990), paper CL3.

Damzen, M.

E. Arbabzadah and M. Damzen, “Fibre-coupled red diode-pumped Alexandrite TEM00 laser with single and double-pass end-pumping,” Laser Phys. Lett. 13, 065002 (2016).
[Crossref]

W. Kerridge-Johns and M. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
[Crossref]

A. Teppitaksak, A. Minassian, G. Thomas, and M. Damzen, “High efficiency >26  w diode end-pumped Alexandrite laser,” Opt. Express 22, 16386–16392 (2014).
[Crossref]

M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).

Demirbas, U.

Dinelli, B.

E. Arimondo and B. Dinelli, “Optical bistability of a CO2 laser with intracavity saturable absorber: experiment and model,” Opt. Commun. 44, 277–282 (1983).
[Crossref]

Erbert, G.

Gayen, S.

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

Grattan, K.

Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
[Crossref]

Griebner, U.

Harter, D.

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

Hercher, M.

Jenssen, H.

M. Shand and H. Jenssen, “Temperature dependence of the excited-state absorption of Alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
[Crossref]

M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
[Crossref]

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

Jiang, M.

Kerridge-Johns, W.

W. Kerridge-Johns and M. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
[Crossref]

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 6th ed., Vol. 1 of Springer Series in Optical Sciences (Springer, 2006).

Kuper, J. W.

J. W. Kuper, T. Chin, and H. E. Aschoff, “Extended tuning range of Alexandrite at elevated temperatures,” in Advanced Solid State Lasers (Optical Society of America, 1990), paper CL3.

Lee, C.

B. Thedrez and C. Lee, “A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations,” IEEE J. Quantum Electron. 28, 2706–2713 (1992).
[Crossref]

Leitenstorfer, A.

Leslie, K.

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

Liu, J.

McCumber, D.

D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134, A299–A306 (1964).
[Crossref]

Minassian, A.

A. Teppitaksak, A. Minassian, G. Thomas, and M. Damzen, “High efficiency >26  w diode end-pumped Alexandrite laser,” Opt. Express 22, 16386–16392 (2014).
[Crossref]

M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).

Morris, R.

M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
[Crossref]

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

Noack, F.

O’Dell, E.

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

Palmer, A.

Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
[Crossref]

Peterson, O.

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

Petricevic, V.

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

Petrov, V.

Rapoport, W.

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

Rigrod, W.

W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[Crossref]

Sam, R.

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

Samelson, H.

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

Sennaroglu, A.

Shand, M.

M. Shand and H. Jenssen, “Temperature dependence of the excited-state absorption of Alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
[Crossref]

M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
[Crossref]

M. Shand and J. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
[Crossref]

M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
[Crossref]

Sumpf, B.

Teppitaksak, A.

A. Teppitaksak, A. Minassian, G. Thomas, and M. Damzen, “High efficiency >26  w diode end-pumped Alexandrite laser,” Opt. Express 22, 16386–16392 (2014).
[Crossref]

M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).

Thedrez, B.

B. Thedrez and C. Lee, “A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations,” IEEE J. Quantum Electron. 28, 2706–2713 (1992).
[Crossref]

Thomas, G.

A. Teppitaksak, A. Minassian, G. Thomas, and M. Damzen, “High efficiency >26  w diode end-pumped Alexandrite laser,” Opt. Express 22, 16386–16392 (2014).
[Crossref]

M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).

Walling, J.

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

M. Shand and J. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
[Crossref]

M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
[Crossref]

M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
[Crossref]

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

Wang, J.

Wang, W.

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

Wang, Y.

Wernikowski, T.

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

Yeh, J.

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

Zhang, H.

Zhang, X.

Zhang, Z.

Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Gayen, W. Wang, V. Petričević, and R. Alfano, “Nonradiative transition dynamics in Alexandrite,” Appl. Phys. Lett. 49, 437–439 (1986).
[Crossref]

IEEE J. Quantum Electron. (7)

M. Shand, J. Walling, and H. Jenssen, “Ground state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
[Crossref]

M. Shand and H. Jenssen, “Temperature dependence of the excited-state absorption of Alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
[Crossref]

M. Shand and J. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
[Crossref]

J. Walling, O. Peterson, H. Jenssen, R. Morris, and E. O’Dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
[Crossref]

R. Sam, J. Yeh, K. Leslie, and W. Rapoport, “Design and performance of a 250  Hz Alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
[Crossref]

H. Samelson, J. Walling, T. Wernikowski, and D. Harter, “CW arc-lamp-pumped Alexandrite lasers,” IEEE J. Quantum Electron. 24, 1141–1150 (1988).
[Crossref]

B. Thedrez and C. Lee, “A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations,” IEEE J. Quantum Electron. 28, 2706–2713 (1992).
[Crossref]

J. Appl. Phys. (3)

W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[Crossref]

M. Shand, J. Walling, and R. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
[Crossref]

Z. Zhang, K. Grattan, and A. Palmer, “Thermal characteristics of Alexandrite fluorescence decay at high temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
[Crossref]

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

Laser Phys. Lett. (2)

W. Kerridge-Johns and M. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
[Crossref]

E. Arbabzadah and M. Damzen, “Fibre-coupled red diode-pumped Alexandrite TEM00 laser with single and double-pass end-pumping,” Laser Phys. Lett. 13, 065002 (2016).
[Crossref]

Opt. Commun. (2)

R. Beach, “CW theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[Crossref]

E. Arimondo and B. Dinelli, “Optical bistability of a CO2 laser with intracavity saturable absorber: experiment and model,” Opt. Commun. 44, 277–282 (1983).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134, A299–A306 (1964).
[Crossref]

Other (3)

J. W. Kuper, T. Chin, and H. E. Aschoff, “Extended tuning range of Alexandrite at elevated temperatures,” in Advanced Solid State Lasers (Optical Society of America, 1990), paper CL3.

W. Koechner, Solid-State Laser Engineering, 6th ed., Vol. 1 of Springer Series in Optical Sciences (Springer, 2006).

M. Damzen, G. Thomas, A. Teppitaksak, and A. Minassian, “Progress in diode-pumped Alexandrite lasers as a new resource for future space lidar missions,” in International Conference on Space Optics (2014).

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Figures (11)

Fig. 1.
Fig. 1. Energy structure of Alexandrite and the optical transitions for vibronic lasing. The bands represent the vibrational levels of both the T24 and A24 states. The dashed arrows are nonradiative decays and the double-ended arrows indicate thermal population equilibrium.
Fig. 2.
Fig. 2. Laser emission, ESA, and GSA cross sections against wavelength at 28°C. Emission and ESA data adapted from [13]. GSA cross sections are from Eq. (2) and magnified by a factor of 6.
Fig. 3.
Fig. 3. Pump and cavity configuration of the Alexandrite laser.
Fig. 4.
Fig. 4. Output laser power versus input pump power at three laser wavelengths, at a crystal temperature of 60°C. The inset shows the beam profile at the indicated point.
Fig. 5.
Fig. 5. Laser power against wavelength for two crystal temperatures, with an input pump power of 2.73 W. The dashed lines indicate the wavelengths shown in Fig. 4.
Fig. 6.
Fig. 6. Transmission T of an Alexandrite sample against the ratio of peak incident intensity I0p to saturation parameter Is, compared to the model for different γ.
Fig. 7.
Fig. 7. Diagram of the energy level structure of a quasi-three level laser, with a fourth level providing ESA at the pump wavelength.
Fig. 8.
Fig. 8. Pump quantum efficiency against laser output power for different ratios of σa/σe. R=99%, L=0.5%, l=10  mm, γ=0.8, A=π(100  μm)2, α0=521  m1, αe=78  m1, α1a=9  m1, and τf=262  μs.
Fig. 9.
Fig. 9. Normalized inversion (f) against distance into the gain medium for different laser output powers Pl, with σa/σe=1. Other parameters as in Fig. 8.
Fig. 10.
Fig. 10. Laser output power against pump input power for changing ratios of σa/σe. Other parameters as in Fig. 8.
Fig. 11.
Fig. 11. Experimental and theoretical data of the thresholds and slope efficiencies of laser operation against OC reflectance at different laser wavelengths, with crystal temperatures of 10°C and 60°C. In the theoretical plots, the solid lines correspond to γ=0.75 and the dashed lines to γ=0.

Tables (1)

Tables Icon

Table 1. Calculation Parameters Used in the Laser Modeling

Equations (36)

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

τf=τE[1+eΔE/kbT1+(τE/τT)eΔE/kbT],
σa(T,E)=σe(T,E)e[EE*(T)]kbT,
I0Is=1γ[(Tp/T0)γ1γ1][1Tp(Tp/T0)γ1γ],
I0(r)=I0pexp[2(r/w)2],
TG=02πrI(r)dr02πrI0(r)dr,
TG=40re2r2Tp(r)dr,
n1(z,t)t=1hνpσ0n0(z,t)I(z,t)cσen1(z,t)φ(z,t)+cσan0(z,t)φ(z,t)1τfn1(z,t),
dIl±dz=±[σen1(z,t)σan0(z,t)σ1an1(z,t)]Il±(z,t),
dIdz=[σ0n0(z,t)+σ1n1(z,t)]I(z,t),
R(1L)Gth2=1,
ln(Gth)=ln[(Il±(l)Il±(0))±1]=F(αe+αaα1a)αal,
F=ln[(1L)R]+2αal2(αe+αaα1a),
f1f=I/Is+φ/φa1+φ/φs,
I(0)Is(1+φ/φs)=(1+aγ)γ[eα1[Fa(lF)]11Teα1[Fa(lF)]],
I0thIs=1γ(eα1F11Teα1F),
Pa=A[I(0)I(l)]=P0(1T),
T=eα0leα0(1γ)F,
Pu=A0lσ0n0(z)I(z)dz=Aα0Is(1+φφs)[Fa(lF)],
ηa=1T,
ηp=α1(1+aγ)[1Teα1[Fa(lF)]eα1[Fa(lF)]1][Fa(lF)1T].
ηs=lnR2αe[F(σa/σe)(lF)]ηqηaηp,
ηs=ηocηqηaηp,
ηoc=(1γl)[lnRlnRln(1L)+2γlαal],
η0=λpλl[1γl1+(σa/σe)γ].
ηH1λpλlηp(1γl),
I0thhνpτfα0F[1+12α1F],
ηp11+aγ{112α1[Fa(lF)]}.
eα1F[1α1(lF)(σe/σa+γ)]<1,
dfdz=α0(1f)[1(1γ)f][(1+a)fa],
D(z)=D(0)eα0z,
D(z)={(1f)1γ[1(1γ)f]1γγ(1+aγ)[(1+a)fa]1+a1+aγfor  γ>0,(1f)(1+a)[f(1+a)a](1+a)exp[(1f)1]for  γ=0.
α0F=f0f(l)f(1f)[1(1γ)f][(1+a)fa]df,
α1(1+aγ)F=aγln[T]+ln[1+γf(l)1f(l)1+γf01f0].
ηl,ESA=2α1aFln[R(1L)]+2α1aF,
=γl[ln[R(1L)]+2αalln[R(1L)]+2γlαal],
ηH={1ηpηq(1ηl,ESA)for  P0P0th,1ηpηqfor  P0=P0th,

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