Abstract

A simple geometric-optics model is developed that describes the power extraction in chemical oxygen–iodine lasers (COILs) with unstable resonators. The positive and negative branch unstable resonators with cylindrical mirrors that were recently used in COILs are studied theoretically. The optical extraction efficiency, spatial distributions of the intracavity radiation intensity in the flow direction, and the intensity in the far field are calculated for both kinds of resonator as a function of both the resonator and the COIL parameters. The optimal resonator magnifications that correspond to the maximum intensity in the far field are found.

© 2009 Optical Society of America

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References

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  1. J. Handke, W. O. Schall, T. Hall, F. Duschek, and K. M. Grünewald, “Chemical oxygen iodine laser power generation with an off-axis hybrid resonator,” Appl. Opt. 45, 3831-3838(2006).
    [CrossRef] [PubMed]
  2. C. Pargmann, T. Hall, F. Duschek, K. M. Grünewald, and J. Handke, “COIL emission of a modified negative branch confocal unstable resonator,” Appl. Opt. 46, 7751-7756 (2007).
    [CrossRef] [PubMed]
  3. E. A. Sziklas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. 14, 1874-1889 (1975).
    [CrossRef] [PubMed]
  4. D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
    [CrossRef]
  5. H. Mirels, “Interaction between unstable optical resonator and CW chemical laser,” AIAA J. 13, 785-791 (1975).
    [CrossRef]
  6. B. D. Barmashenko and S. Rosenwaks, “Analysis of the optical extraction efficiency in gas-flow lasers with different types of resonator,” Appl. Opt. 35, 7091-7101 (1996).
    [CrossRef] [PubMed]
  7. B. Barmashenko, D. Furman, and S. Rosenwaks, “Analysis of lasing in gas-flow lasers with stable resonators,” Appl. Opt. 37, 5697-5705 (1998).
    [CrossRef]
  8. Yu. A. Anan'ev, Laser Resonators and the Beam Divergence Problem (Hilger, 1992), pp. 51- 60.
  9. J. Handke, “COIL radiation of high brilliance,” presented at the XVII International Symposium on Gas Flow and Chemical Lasers and High Power Lasers 2008, Lisbon, Portugal, 15-19 September 2008.

2007

2006

2002

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

1998

1996

1975

Anan'ev, Yu. A.

Yu. A. Anan'ev, Laser Resonators and the Beam Divergence Problem (Hilger, 1992), pp. 51- 60.

Barmashenko, B.

Barmashenko, B. D.

Duschek, F.

Furman, D.

Grünewald, K. M.

Hall, T.

Handke, J.

Jin, Y.

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

Mirels, H.

H. Mirels, “Interaction between unstable optical resonator and CW chemical laser,” AIAA J. 13, 785-791 (1975).
[CrossRef]

Pargmann, C.

Rosenwaks, S.

San, Y.

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

Sang, F.

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

Schall, W. O.

Siegman, A. E.

Sziklas, E. A.

Yu, D.

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

AIAA J.

H. Mirels, “Interaction between unstable optical resonator and CW chemical laser,” AIAA J. 13, 785-791 (1975).
[CrossRef]

Appl. Opt.

Opt. Eng.

D. Yu, F. Sang, Y. Jin, and Y. San, “Output beam analysis of an unstable resonator with a large Fresnel number for a chemical oxygen iodine laser,” Opt. Eng. 41, 2668-2674 (2002).
[CrossRef]

Other

Yu. A. Anan'ev, Laser Resonators and the Beam Divergence Problem (Hilger, 1992), pp. 51- 60.

J. Handke, “COIL radiation of high brilliance,” presented at the XVII International Symposium on Gas Flow and Chemical Lasers and High Power Lasers 2008, Lisbon, Portugal, 15-19 September 2008.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the flow and radiation path in the COILs equipped with (a) positive and (b) negative branch unstable resonators.

Fig. 2
Fig. 2

Dependence of extraction efficiency η ext of a positive branch unstable resonator in a supersonic COIL on ratio r between sections of the mirror lying downstream and upstream of the optical axis for different γ 0 , g th / g i = 0.5 , Y i = 0.5 , and T = 200 K .

Fig. 3
Fig. 3

Dependence of extraction efficiency η ext of an asymmetric r positive branch unstable resonator in a supersonic COIL on g th / g i for different γ 0 , Y i = 0.5 , and T = 200 K .

Fig. 4
Fig. 4

Dependence of extraction efficiency η ext of a negative branch unstable resonator in a supersonic COIL on g th / g i for different γ 0 and α = 2 d m / d , Y i = 0.5 , and T = 200 K .

Fig. 5
Fig. 5

Dependence of extraction efficiency η ext of different resonators in a supersonic COIL on g th / g i for γ 0 = 4 , Y i = 0.5 , and T = 200 K .

Fig. 6
Fig. 6

Dependence of extraction efficiency η ext of different resonators in a supersonic COIL on g th / g i for γ 0 , Y i = 0.5 , and T = 200 K .

Fig. 7
Fig. 7

Spatial distribution of the dimensionless intraresonator intensity at a distance along the flow for different resonators in a supersonic COIL: g th / g i = 0.2 , γ 0 = 4 , Y i = 0.5 , and T = 200 K . The distance is divided by l res .

Fig. 8
Fig. 8

Dependence of dimensionless axial light intensity (power per unit solid angle) F ¯ = F λ 2 / ( P av β l y l d 2 g i L ) in the far field on g th / g i for asymmetric r positive branch and negative branch resonators, different γ 0 , Y i = 0.5 , and T = 200 K .

Tables (1)

Tables Icon

Table 1 Analytical Expressions for Extraction Efficiency η ext for Different Types of Resonator

Equations (40)

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O 2 ( Δ 1 ) + I ( P 3 / 2 2 ) O 2 ( Σ 3 ) + I ( P 1 / 2 2 ) .
u d Y d x = g [ O 2 ] 2 I h ν ,
g = σ [ I ] 0 2 ( 2 K e + 1 ) Y 1 ( K e 1 ) Y + 1 1 1 + 2 I / I s ,
I s = h ν 2 k f [ O ] 2 3 σ [ ( K e 1 ) Y + 1 ]
P = P av η ext ,
P av = ( h ν ) [ O 2 ] u S ( Y i 1 2 K e + 1 ) [ 1 exp ( γ 0 ) ] ,
γ 0 l res / ( u t e ) ,
t e = 3 K e k f [ I ] 0 ( 2 K e + 1 )
η ext = Y i Y f Y i 1 / ( 2 K e + 1 ) 1 1 exp ( γ 0 ) ,
d x I d x = g g th I ,
I = ( h ν ) u [ O 2 ] 2 g th l res Y 0 Y ξ = I s , g g i 2 g th Y 0 Y ξ ,
I s , g ( h ν ) σ ( l res / u ) ( [ I ] 0 / [ O 2 ] 2 [ ( K e 1 ) Y i + 1 ] 2 K e + 1
d Y d ξ = g i g th [ Y 1 / ( 2 K e + 1 ) ] [ Y i + 1 / ( K e - 1 ) ] [ Y i 1 / ( 2 K e + 1 ) ] [ Y + 1 / ( K e - 1 ) ] ( Y 0 - Y ) / ξ 1 + 1 γ 0 g i g th [ Y i + 1 / ( K e 1 ) ] [ Y + 1 / ( K e 1 ) ] ( Y 0 Y ) / ξ [ Y i 1 / ( 2 K e + 1 ) ] .
Y ( ξ , Y 0 ) ξ = 1 / ( 1 + r ) = Y i ,
g 1 = [ g ( x ) + g ( α x ) + g ( x ) + g ( α x ) ] / 4 ,
α = 2 d m / d ,
t = { ξ , ξ > 0 - ξ , ξ < 0 ,
d Y 1 , 2 d t = g [ Y 1 , 2 ( t ) , I ( t ) ] [ O 2 ] 2 I ( t ) h ν ,
t d I d t = { g [ Y 1 ( t ) , I ( t ) ] + g [ Y 1 ( α t ) , I ( α t ) ] + g [ Y 2 ( t ) , I ( t ) ] + g [ Y 2 ( α t ) , I ( α t ) ] 4 g th 1 } I ( t ) ,
t = 0 , Y 1 = Y 2 = Y 0 ,
t = 1 / 2 , Y 2 = Y i .
I = I s 2 [ g i g th Y 0 1 / ( 2 K e + 1 ) Y i 1 / ( 2 K e + 1 ) Y i + 1 / ( K e 1 ) Y 0 + 1 / ( K e 1 ) 1 ] .
η ext = 1 ( g th / g i ) 2 .
F = c 2 π | 1 λ u ( x 1 , y 1 ) d x 1 d y 1 | 2 ,
- l y / 2 l y / 2 | f y ( y ) | 2 d y = l y .
F = P β l x l y / λ 2 = ( P av β l y / λ 2 ) l d ( M - 1 ) η ext ,
f - l y / 2 l y / 2 f ( y ) d y l y
F = ( P av β l y l d 2 g i L / λ 2 ) g th g i η ext
I ( M x ) = I ( x ) M exp [ 2 g L ] .
I ( M 2 x ) = I ( x ) M 2 exp { [ g ( x ) + g ( α x ) + g ( x ) + g ( α x ) ] L } .
d ( t I ) d t = g ( t ) + g ( t ) 2 g th I .
I ( t ) = ( h ν ) u [ O 2 ] 4 g th l res Y 2 ( t ) Y 1 ( t ) t = I s , g g i 2 g th Y 2 ( t ) Y 1 ( t ) t .
d Y 1 , 2 ( t ) d t = g i 2 g th [ Y 1 , 2 ( t ) 1 / ( 2 K e + 1 ) ] [ Y i + 1 / ( K e 1 ) ] [ Y i 1 / ( 2 K e + 1 ) ] [ Y 1 , 2 ( t ) + 1 / ( K e 1 ) ] × [ Y 2 ( t ) Y 1 ( t ) ] / t 1 + 1 γ 0 g i 2 g th [ Y i + 1 / ( K e - 1 ) ] [ Y 1 , 2 ( t ) + 1 / ( K e - 1 ) ] [ Y 2 ( t ) - Y 1 ( t ) ] / t [ Y i - 1 / ( 2 K e + 1 ) ] ,
Y 1 + Y 2 + 3 K e ( 2 K e + 1 ) ( K e - 1 ) ln [ ( Y 1 - 1 2 K e + 1 ) ( Y 2 - 1 2 K e + 1 ) ] = C .
Y th = Y i η ext , F P * [ Y i 1 / ( 2 K e + 1 ) ]
η ext , F P * = ( 1 g th / g i ) / [ 1 g th g i Y i 1 / ( 2 K e + 1 ) Y i + 1 / ( K e 1 ) ] for         γ 0
η ext , F P * 1 exp [ γ 0 ( 1 g th / g i ) / η ext , F P * ] 1 exp ( γ 0 ) for     finite   γ 0
η ext + ( 1 η ext , F P * ) ln ( 1 η ext ) = η ext , F P * γ 0 ( 1 g th / g i ) η ext ln ( 1 η ext )
( 1 - η ext / η ext , F P * ) ( 1 - η ext ) ν = r , ν = ( 1 - g th / g i ) / η ext , F P * for     γ 0
3 K e 2 K e + 1 ln [ ( 1 - η ext , F P * ) 2 1 η ext ] ( K e 1 ) ( Y i - 1 2 K e + 1 ) ( 2 η ext , F P * η ext ) = 0 for     γ 0

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