Abstract

In this work, we are reporting a new approach to compute the overlap efficiency of end pumped solid-state laser systems. Unlike existing methods in which the overlap integral is computed with a linearize approximation near the threshold, in this method the inverse of the overlap integral is computed numerically in the above threshold regime for several values of circulating fields. Now by fitting a linear curve to this data the overlap efficiency is obtained. The effect of the beam quality factor is also taken into account. It is demonstrated that the linearized approximation near the threshold can give rise to 50% error in overlap efficiency. The method was used to estimate the overlap efficiency in different types of axially pumped lasers.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. D. G. Hall, R. J. Smith, and R. R. Rice, " Pump size effects in Nd:YAG lasers," Appl. Opt. 19, 3041-3043 (1980).
    [CrossRef]
  2. D. G. Hall, "Optimum mode size criterion for low gain lasers," Appl. Opt. 20, 1579- 1583 (1981).
    [CrossRef]
  3. W. P.Risk, "Modelling of longitudinally pumped solid state lasers exhibiting reabsorption losses, "J. Opt. Soc. Amer. B 5, 1412-1423 (1988).
    [CrossRef]
  4. T. Y. Fan and Antonio Sanchez, "Pump source requirements for end pumped lasers," IEEE J. Quantum Electron. QE - 26, 311-316 (1990).
    [CrossRef]
  5. Paolo Laporta and Marcello Brussard, "Design criteria for mode size optimization in diode pumped solid state lasers," IEEE J. Quantum Electron. QE - 27, 2319-2326 (1991).
    [CrossRef]
  6. C. Pfistner, P. Albers, H. P. Weber, "Influence of spatial mode matching in end-pumped solid state lasers," Appl. Phys. B54, 83-88 (1992).
  7. Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, and S. C. Wang, " Optimization of fiber coupled laser diode end pumped lasers: Influence of pump beam quality," IEEE J. Quantum Electron. QE - 32, 2010-2016 (1996).
    [CrossRef]
  8. A. E. Siegman ,"Lasers", (University Science Book, Mill Valley, CA, 1986).
  9. A. E. Siegman and Steven W. Townsend, "Output beam propagation and beam quality from a multimode stable-cavity laser," IEEE J. Quantum Electron. 29, 1212-1217 (1996).
    [CrossRef]

Other (9)

D. G. Hall, R. J. Smith, and R. R. Rice, " Pump size effects in Nd:YAG lasers," Appl. Opt. 19, 3041-3043 (1980).
[CrossRef]

D. G. Hall, "Optimum mode size criterion for low gain lasers," Appl. Opt. 20, 1579- 1583 (1981).
[CrossRef]

W. P.Risk, "Modelling of longitudinally pumped solid state lasers exhibiting reabsorption losses, "J. Opt. Soc. Amer. B 5, 1412-1423 (1988).
[CrossRef]

T. Y. Fan and Antonio Sanchez, "Pump source requirements for end pumped lasers," IEEE J. Quantum Electron. QE - 26, 311-316 (1990).
[CrossRef]

Paolo Laporta and Marcello Brussard, "Design criteria for mode size optimization in diode pumped solid state lasers," IEEE J. Quantum Electron. QE - 27, 2319-2326 (1991).
[CrossRef]

C. Pfistner, P. Albers, H. P. Weber, "Influence of spatial mode matching in end-pumped solid state lasers," Appl. Phys. B54, 83-88 (1992).

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, and S. C. Wang, " Optimization of fiber coupled laser diode end pumped lasers: Influence of pump beam quality," IEEE J. Quantum Electron. QE - 32, 2010-2016 (1996).
[CrossRef]

A. E. Siegman ,"Lasers", (University Science Book, Mill Valley, CA, 1986).

A. E. Siegman and Steven W. Townsend, "Output beam propagation and beam quality from a multimode stable-cavity laser," IEEE J. Quantum Electron. 29, 1212-1217 (1996).
[CrossRef]

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 (4)

Figure 1.
Figure 1.

Variation of (a) match function and (b) overlap efficiency with pump-beam waist position with respect to entrance plane of gain medium. The pump beam profile is taken as an elliptic profile. The match function and overlap efficiency is computed with both, the linearize approximation near threshold and the proposed method.

Figure 2.
Figure 2.

Variation of inverse of overlap integral with normalised circulating field intensity in different pump beam conditions. A linear fit to these plots gives the value of constants C and D. Solid lines are the linear fit to the plotted data. z is the distance of pump beam waist from the entrance plane. The pump beam spot in the gain medium increases with z.

Figure 3.
Figure 3.

Variation of match function with mode waist radius ωm 0 for two different values of pump waist sizes. The pump beam profile is taken as an elliptic profile and ωp 0=[ωpx , ωpy ].

Figure 4.
Figure 4.

Variation of overlap efficiency η 0 with pump waist radius for four different values of beam quality factor M 2. (a) The mode waist radius ωm 0=100µm, (b) The mode waist radius ωm 0=300µm, (c) The mode waist radius ωm 0=500µm.

Equations (27)

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

g ( z ) = η q α a I p ( z ) I sat ( 1 + 2 I circ I sat ) ,
η q ω m ω p ,
I p ( x , y , z ) = P p A p ( z ) f p ( x , y , z ) Exp ( α a z ) ,
A p ( x ) = f p ( x , y , z ) d x d y ,
I circ ( x , y , z ) = P circ A m ( z ) f m ( x , y , z ) ,
Δ P circ = d I ( x , y , z ) d x d y = 2 0 l g ( x , y , z ) I circ ( x , y , z ) d z d x d y ,
G = 2 g ( x , y , z ) I circ ( x , y , z ) d V P circ
G = 2 η q α a P p Exp ( α a z ) f p ( x , y , z ) f m ( x , y , z ) A p ( z ) A m ( z ) ( 1 + 2 p circ f m ( x , y , z ) A m ( z ) ) d V ,
P p = P p / I sat
P circ = P circ / I sat = A m I circ ,
A m = 1 l 0 l f m ( x , y , z ) dx dy dz ,
G = 2 α 0 z + ln ( 1 R 1 R 2 ) L + T 1 + T 2 ,
P out = T 2 P circ ,
G = 2 η q α a P p [ C ( 1 + 2 D I circ ) ] ,
Exp ( α a z ) f p ( x , y , z ) f m ( x , y , z ) A p ( z ) A m ( z ) [ 1 + 2 A m I circ f m ( x , y , z ) A m ( z ) ] d V = C 1 + 2 D I circ ,
2 η q α a P p [ C ( 1 + 2 D P circ / A m ) ] = ( T + L ) ,
P circ = I sat A m 2 D [ 2 η q α a P P C T + L 1 ] ,
P out = T 2 η q α a P p C A m D ( T + L ) T 2 I sat A m 2 D ,
η o = α a C A m η a D ,
P out = T 2 ( T + L ) η q η a η o P p T 2 I sat A m 2 D ,
P th = I sat ( L + T ) 2 η q α a C ,
m = η o η a η q T 2 ( L + T ) ,
F = 2 α a C A m ,
f m ( x , y , z ) = Exp [ 2 x 2 ω mx 2 ( z ) 2 y 2 ω my 2 ( z ) ] ,
f p ( x , y , z ) = Exp [ 2 x 2 ω px 2 ( z ) 2 y 2 ω py 2 ( z ) ] ,
ω p ( z ) = ω p 0 [ 1 + ( M 2 z π ω p 0 2 ) 2 ] 1 2 ,
ω 0 θ = M 2 π ,

Metrics