Abstract

The transverse modes of a laser resonator containing a medium with a strong radial gain profile differ greatly from the modes of a similar resonator containing a low gain medium. Focusing and defocusing effects result from the gain profile and from the associated dispersion profile. The dispersion focusing causes an asymmetry in the power output as the laser is tuned across the gain line. The theory has been verified using a high gain 3.51-μ xenon laser.

© 1972 Optical Society of America

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References

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  1. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  2. L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
    [CrossRef]
  3. A. Szöke, A. Javan, Phys. Rev. 145, 137 (1966).
    [CrossRef]
  4. B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
    [CrossRef]
  5. A. Javan, P. L. Kelley, IEEE J. Quant. Electron. QE-2, 470 (1966).
    [CrossRef]
  6. L. W. Casperson, Ph.D. thesis, California Institute of Technology (1971), Chap. 5.
  7. D. H. Close, Phys. Rev. 153, 360 (1967), Eq. (44).
    [CrossRef]
  8. D. R. Armstrong, IEEE J. Quant. Electron. QE-4, 968 (1968).
    [CrossRef]
  9. L. W. Casperson, A. Yariv, Appl. Phys. Lett. 17, 259 (1970).
    [CrossRef]
  10. S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
    [CrossRef]
  11. A. D. White, Appl. Phys. Lett. 10, 24 (1967).
    [CrossRef]

1970 (2)

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 17, 259 (1970).
[CrossRef]

S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
[CrossRef]

1968 (3)

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
[CrossRef]

D. R. Armstrong, IEEE J. Quant. Electron. QE-4, 968 (1968).
[CrossRef]

1967 (2)

A. D. White, Appl. Phys. Lett. 10, 24 (1967).
[CrossRef]

D. H. Close, Phys. Rev. 153, 360 (1967), Eq. (44).
[CrossRef]

1966 (2)

A. Javan, P. L. Kelley, IEEE J. Quant. Electron. QE-2, 470 (1966).
[CrossRef]

A. Szöke, A. Javan, Phys. Rev. 145, 137 (1966).
[CrossRef]

1965 (1)

Armstrong, D. R.

D. R. Armstrong, IEEE J. Quant. Electron. QE-4, 968 (1968).
[CrossRef]

Borenstein, M.

B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
[CrossRef]

Byer, R. L.

S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
[CrossRef]

Casperson, L. W.

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 17, 259 (1970).
[CrossRef]

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

L. W. Casperson, Ph.D. thesis, California Institute of Technology (1971), Chap. 5.

Close, D. H.

D. H. Close, Phys. Rev. 153, 360 (1967), Eq. (44).
[CrossRef]

Gyorffy, B. L.

B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
[CrossRef]

Javan, A.

A. Szöke, A. Javan, Phys. Rev. 145, 137 (1966).
[CrossRef]

A. Javan, P. L. Kelley, IEEE J. Quant. Electron. QE-2, 470 (1966).
[CrossRef]

Kelley, P. L.

A. Javan, P. L. Kelley, IEEE J. Quant. Electron. QE-2, 470 (1966).
[CrossRef]

Kogelnik, H.

Lamb, W. E.

B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
[CrossRef]

Siegman, A. E.

S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
[CrossRef]

Szöke, A.

A. Szöke, A. Javan, Phys. Rev. 145, 137 (1966).
[CrossRef]

Wang, S. C.

S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
[CrossRef]

White, A. D.

A. D. White, Appl. Phys. Lett. 10, 24 (1967).
[CrossRef]

Yariv, A.

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 17, 259 (1970).
[CrossRef]

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 17, 259 (1970).
[CrossRef]

S. C. Wang, R. L. Byer, A. E. Siegman, Appl. Phys. Lett. 17, 120 (1970).
[CrossRef]

A. D. White, Appl. Phys. Lett. 10, 24 (1967).
[CrossRef]

IEEE J. Quant. Electron. (2)

A. Javan, P. L. Kelley, IEEE J. Quant. Electron. QE-2, 470 (1966).
[CrossRef]

D. R. Armstrong, IEEE J. Quant. Electron. QE-4, 968 (1968).
[CrossRef]

Phys. Rev. (3)

D. H. Close, Phys. Rev. 153, 360 (1967), Eq. (44).
[CrossRef]

A. Szöke, A. Javan, Phys. Rev. 145, 137 (1966).
[CrossRef]

B. L. Gyorffy, M. Borenstein, W. E. Lamb, Phys. Rev. 169, 340 (1968).
[CrossRef]

Other (1)

L. W. Casperson, Ph.D. thesis, California Institute of Technology (1971), Chap. 5.

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Figures (5)

Fig. 1
Fig. 1

Solid line is the normalized spot size as a function of frequency. Dashed line is the spot size neglecting dispersion focusing.

Fig. 2
Fig. 2

Normalized power output as a function of frequency for various values of the threshold parameter. Dashed line is the gain spectrum.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

Power output for decreasing cavity length with a discharge current of 18 mA.

Fig. 5
Fig. 5

Frequency of the power maximum vs the threshold parameter b. The solid line is a theoretical result obtained from Eq. (32) and the dashed line is a plot of Eq. (36). The circles are experimental values.

Equations (37)

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k = k 0 - 1 2 k 2 r 2 .
k = β + i α .
β = 2 π n / λ .
1 / q = ( 1 / R ) - i ( λ m / π w 2 ) ,
( 1 / q ) 2 + ( d / d z ) ( 1 / q ) + ( k 2 / k 0 ) = 0.
1 / q 2 = { [ ( 1 / q 1 ) cos ( k 2 / k 0 ) 1 2 z ] - [ ( k 2 / k 0 ) 1 2 sin ( k 2 / k 0 ) 1 2 z ] } ÷ { [ ( 1 / q 1 ) ( k 0 / k 2 ) 1 2 sin ( k 2 / k 0 ) 1 2 z ] + [ cos ( k 2 / k 0 ) 1 2 z ] } .
÷ { 1 / q = i ( k 2 / k 0 ) 1 2 } ,
q 2 = q 1 + z .
w = ( λ m / π ) 1 2 [ ± Re ( k 2 / k 0 ) 1 2 ] - 1 2
R = [ ± Im ( k 2 / k 0 ) 1 2 ] - 1 .
Im ( k 2 / k 0 ) > 0.
α 2 > 0 ,
w = ( λ m / π ) 1 2 { ± Re [ ( β 2 + i α 2 ) / β 0 ] 1 2 } - 1 2
R = { ± Im [ ( β 2 + i α 2 ) / β 0 ] 1 2 } - 1 .
w = ( ( π α 2 / 4 λ m ) { [ 1 + ( β 2 / α 2 ) 2 ] 1 2 + ( β 2 / α 2 ) } ) - 1 4 .
α 2 ( x ) = ( g 2 / 2 ) e - x 2 ,
n 2 ( x ) = ( λ g 2 / 2 π / 2 3 ) F ( x ) ,
F ( x ) = e - x 2 0 x e t 2 d t .
β 2 ( x ) = ( g 2 / π 1 2 ) F ( x ) .
w ( x ) = [ π g 2 8 λ m e - x 2 ( { 1 + [ 2 F ( x ) e x 2 π 1 2 ] 2 } 1 2 + 2 F ( x ) e x 2 1 2 ) ] - 1 2
w * ( x ) = e x / 4 2 ( { 1 + [ 2 F ( x ) e x 2 π 1 2 ] 2 } 1 2 + 2 F ( x ) e x 2 π 1 2 ) - 1 4 ,
α 2 ( y ) = ( g 2 / 2 ) [ 1 / ( 1 + y 2 ) ] ,
n 2 ( y ) = ( λ g 2 / 4 π ) [ y / ( 1 + y 2 ) ] .
w = { ( π g 2 / 8 λ m ) [ 1 / ( 1 + y 2 ) ] [ ( 1 + y 2 ) 1 2 + y ] } - 1 4 .
d I / d z = g I / ( 1 + s I ) 1 2 ,
d I / d z = g I / ( 1 + 1 2 s I ) .
d P / d z = g 0 P / [ 1 + 1 2 ( s P / π w 2 ) ] .
1 2 ( s / π w 2 ) ( P 2 - P 1 ) = 2 g 0 l - ln ( P 2 / P 1 ) ,
P 0 = ( 2 π w 2 / s ) [ T / ( 1 - R ) ] ( 2 g 0 l + ln R ) .
P 0 ( x ) = ( 4 r 0 / s ) ( π λ m / 1.44 g 0 ) 1 2 e x 2 / 2 [ T / ( 1 - R ) ] ( 2 g 0 l e - x 2 + ln R ) × ( { 1 + [ 2 F ( x ) e x 2 / π 1 2 ] 2 } 1 2 + [ 2 F ( x ) e x 2 / π 1 2 ] ) - 1 2 .
g 2 = g 0 ( 2.88 / r 0 2 ) .
P 0 * ( x ) = ( e - x 2 - b ) e x 2 / 2 ( { 1 + [ 2 F ( x ) e x 2 / π 1 2 ] 2 } 1 2 + [ 2 F ( x ) e x 2 / π 1 2 ] ) - 1 2 ,
b = - ( ln R / 2 g 0 l )
P 0 * ( x ) ( 1 - b ) - [ ( 1 - b ) / π 1 2 ] x + { [ ( 1 - b ) / 2 π ] - [ ( 1 + b ) / 2 ] } x 2 .
x max = { π - 1 2 - [ ( 1 + b ) / ( 1 - b ) ] π 1 2 } - 1 .
x max = - [ ( 1 - b ) / 2 π 1 2 ] .
w ( x ) = ( 8 λ m / π g 2 ) 1 4 .

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