Abstract

Based on the principle of phase locking of an axisymmetric–fold combination CO2 laser under the normal state condition, the mechanisms of phase locking are analyzed when the control mirror is misaligned. Then the overlapping rate (OR) of the mode volume is introduced: the main influences on phase locking are the OR, the average life of the light wave, the root mean square phase error, and the mode coupling coefficient; these influences on phase locking are studied. The distribution of the light intensity reflects the effect of phase locking. It is shown that the misaligned angle has little influence on the phase locking if it is within tolerance.

© 2008 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. Y. Xu, Y. Li, T. Feng, Y. Qiu, F. Fu and W. Guo, “Phase-locking principle of axisymmetric structural CO2 laser and theoretical study of the influences of parameters-changes on phase-locking,” J. Opt. Soc. Am. B 25, 1303-1311 (2008).
    [CrossRef]
  4. J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
    [CrossRef]
  5. Y. Li, J. Liu, M. Chen, and J. Guo, “Axisymmetric-fold combination laser resonator,” Opt. Eng. 44, 064204 (2005).
    [CrossRef]
  6. J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).
  7. J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).
  8. S. Li and W. Huang, Laser Apparatus--Theory and Design (National Defence Industry Press, 2005), Chap. 1 (Chinese).
  9. 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]
  10. R. Oron, L. Shimshi, S. Blit, N. Davidson, A. A. Friesem, and E. Hasman, “Laser operation with two orthogonally polarized transverse modes,” Appl. Opt. 41, 3634-3637 (2002).
    [CrossRef] [PubMed]
  11. B. Lv, Laser Optics (Sichuan U. Press, 1992), Chaps. 2 and 3 (Chinese).

2008

2006

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

2005

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

J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).

2004

J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).

2002

1993

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]

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]

Blit, S.

Capjack, C. E.

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.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

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

Davidson, N.

Feng, T.

Friesem, A. A.

Fu, F.

Guo, J.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

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

J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).

J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).

Guo, W.

Hasman, E.

Huang, W.

S. Li and W. Huang, Laser Apparatus--Theory and Design (National Defence Industry Press, 2005), Chap. 1 (Chinese).

Li, S.

S. Li and W. Huang, Laser Apparatus--Theory and Design (National Defence Industry Press, 2005), Chap. 1 (Chinese).

Li, Y.

Y. Xu, Y. Li, T. Feng, Y. Qiu, F. Fu and W. Guo, “Phase-locking principle of axisymmetric structural CO2 laser and theoretical study of the influences of parameters-changes on phase-locking,” J. Opt. Soc. Am. B 25, 1303-1311 (2008).
[CrossRef]

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

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

J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).

J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).

Liu, J.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).

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

J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).

Liu, Z.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

Lv, B.

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

Oron, R.

Qiu, Y.

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]

Seguin, H. J. J.

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]

Shimshi, L.

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]

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]

Xu, D.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

Xu, Y.

Yang, Y.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

Yelden, E. F.

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]

Zhang, L.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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]

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

Laser Infrared

J. Liu, Y. Li, and J. Guo, “Analysis of beam produced from two dimensional axisymmetric folded-combined cavity,” Laser Infrared 34, 178-181 (2004).

Opt. Eng.

J. Liu, Y. Li, J. Guo, M. Chen, Y. Yang, D. Xu, Z. Liu, and L. Zhang, “Research on near-field distributions of axisymmetric folded-combined CO2 laser,” Opt. Eng. 45, 074201(2006).
[CrossRef]

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

Opt. Tech.

J. Liu, Y. Li, and J. Guo, “Combination of the output multi-beam Gaussian beams from axisymmetric folded-combined cavity,” Opt. Tech. 31, 65-68 (2005).

Other

S. Li and W. Huang, Laser Apparatus--Theory and Design (National Defence Industry Press, 2005), Chap. 1 (Chinese).

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

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Figures (14)

Fig. 1
Fig. 1

Geometrical optical pathway diagrams of ASFC when the control mirror is misaligned.

Fig. 2
Fig. 2

Line-cavity diagram for calculating the stability output of the beam.

Fig. 3
Fig. 3

Diagram of coordinate system of the injected beam in cavity M 2 M 0 M 3 .

Fig. 4
Fig. 4

Section diagram of the common area of the injected beam and the eigenbeam at M 2 .

Fig. 5
Fig. 5

Relation diagram of the OR of the mode volume η ' and the injection angle θ 0 .

Fig. 6
Fig. 6

Relation diagram of the mode coupling coefficient c 00 ' and the injection angle θ 0 .

Fig. 7
Fig. 7

Distributions of equiphase surfaces when θ x = 30  arc  sec .

Fig. 8
Fig. 8

Distributions of equiphase surfaces when θ x = 60  arc  sec .

Fig. 9
Fig. 9

Distributions of equiphase surfaces when θ x = 90  arc  sec .

Fig. 10
Fig. 10

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

Fig. 11
Fig. 11

Diagrams of the light intensity distributions and light spot profile when θ x = 0 .

Fig. 12
Fig. 12

Diagrams of the light intensity distributions and profile of light spot when θ x = 30  arc  sec .

Fig. 13
Fig. 13

Diagrams of the light intensity distributions and profile of light spot when θ x = 60  arc  sec .

Fig. 14
Fig. 14

Diagrams of the light intensity distributions and profile of light spot when θ x = 90  arc  sec .

Tables (1)

Tables Icon

Table 1 Relations of Average Life of the Light Wave τ, Misaligned Angle θ x , and Number of Round Trips m

Equations (26)

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

c 00 = 2 / ω 0 " ω ' p ,
p = 1 ω 0 " 2 + 1 ω ' 2 + i k 2 ( 1 R 0 " 1 R ' ) ,
g ( l ) = g 0 1 + I ( l ) / I s ,
I m = I 0 exp [ 0 m × 4 L i g ( l ) d l ] .
g ( l ) = 4.5 α ( 1 l 4 L i m ) e l + α .
I ( ω ) ¯ = ( p 0 T R ) / ( π ω 2 ) .
I 0 = I ( ω ) ¯ exp ( 2 r 2 ω 2 ) ,
( d N 2 d t ) st ,
( d N 2 d t ) sp .
n ¯ = ( d N 2 d t ) st / ( d N 2 d t ) sp = ρ v c 3 8 π h v 3 .
( x m θ m ) = ( A B C D ) m ( x 0 θ 0 ) ,
( A B C D ) = ( 1 L i 0 1 ) ( 1 0 0 1 ) ( 1 L i 0 1 ) ( 1 0 2 ρ i 1 ) ( 1 L i 0 1 ) ( 1 0 0 1 ) ( 1 L i 0 1 ) ( 1 0 2 ρ i 1 ) .
ω i ' = ( d O m O 2 ) mm ,
s i = arccos ω i 2 ( ω i 2 + O m O 2 2 ω i ' 2 2 ω i O m O 2 ) + ω i ' 2 arccos ( ω i ' 2 + O m O 2 2 ω i 2 2 ω i ' O m O 2 ) O m O 2 ω i sin arccos ( ω i 2 + O m O 2 2 ω i ' 2 2 ω i O m O 2 ) .
V 00 = 1 2 π ( 2 L i ) ( ω i + ω 0 ' 2 ) 2 .
V 00 ' = 1 2 π ( 2 L i ) ( ω i " + ω 0 ' 2 ) 2 .
η ' = V 00 ' V 00 η .
τ = 2 ( 2 L i ) m ' / c .
c 00 ' = η ' c 00 .
Δ R rms = ( R ( t ) - R ¯ ) 2 ¯ ,
R ¯
ε 1 j ( x 1 , y 1 , z = 0 ) = A 0 exp [ ( x 1 x 0 j ) 2 + ( y 1 y 0 j ) 2 ω 0 j 2 ] ,
ε 2 j ( x , y ) = i e i k L λ B ' x o y A 0 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 ) .
I = j = 1 5 ε 2 j j = 1 5 ( ε 2 j ) * .
0 50  arc sec

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