Abstract

When an optical ring cavity is designed, the beam radii at some special positions, especially at the beam waists are very interested in, since the gain mediums, nonlinear crystals and others important optical elements are generally located at the beam waist. In this paper, we firstly presented a simple method for designing optical ring cavities based on the self-consistency theory and the fact that q parameter is uniquely determined by the waist beam radius and its position. This approach is different from ABCD method and it no longer requires cumbersome calculation. The calculations of designing optical ring cavities are simplified because q parameter only has imaginary part at beam waist plane. Moreover, designing the resonant cavity through the calculation of beam waist radii and their position has great practical significance, because it is very easy to adjust the waist radii and the positions at the important optical elements. We employed this method to design an end-pumped six-mirror ring cavity continuous-wave passively mode locked laser. The experiment of a highly stabilized continuous-wave mode locked (CWML) laser was investigated and the results coincided with the theoretical studies very well. The investigation results show that the simple method can be used to design optical ring cavities conveniently, intuitively and efficiently.

© 2014 Optical Society of America

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  1. M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
    [CrossRef]
  2. R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
    [CrossRef]
  3. H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
    [CrossRef]
  4. S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
    [CrossRef]
  5. S. Schwartz, G. Feugnet, and J. P. Pocholle, “Biasing the beat regime of a solid-state ring laser: from a magnetometer to a multioscillator rotation sensor,” J. Opt. Soc. Am. B 30(8), 2157–2160 (2013).
    [CrossRef]
  6. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
    [CrossRef]
  7. W. W. Rigrod, “The optical ring resonator,” Bell Syst. Tech. J. 44(5), 907–916 (1965).
    [CrossRef]
  8. K. K. Li, “Stability and astigmatic analysis of a six-mirror ring cavity for mode-locked dye lasers,” Appl. Opt. 21(5), 967–970 (1982).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. T. Skettrup, T. Meelby, K. Faerch, S. L. Frederiksen, and C. Pedersen, “Triangular laser resonators with astigmatic compensation,” Appl. Opt. 39(24), 4306–4312 (2000).
    [CrossRef] [PubMed]
  11. J. Kojima and Q. V. Nguyen, “Laser pulse-stretching with multiple optical ring cavities,” Appl. Opt. 41(30), 6360–6370 (2002).
    [CrossRef] [PubMed]
  12. J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
    [CrossRef]
  13. T. Skettrup, “Rectangular laser resonators with astigmatic compensation,” J. Opt. A, Pure Appl. Opt. 7(11), 645–654 (2005).
    [CrossRef]
  14. J. Yuan, M. X. Chen, X. W. Long, Y. Y. Tan, Z. L. Kang, and Y. Y. Li, “Beam position controlling method for 3D optical system and its application in non-planar ring resonators,” Opt. Express 20(17), 19563–19579 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. G. Zhang and S. Guo, Graphic analysis and design method of optical resonator, National Defense Industry Press, Beijing, (2003). (in Chinese)
  17. Q. Wen, L. Q. Sun, Y. Y. Wang, E. Y. Zhang, and Q. Tian, “An effective method for designing insensitive resonator of continuous-wave passively mode-locked laser,” Opt. Express 17(11), 8956–8961 (2009).
    [CrossRef] [PubMed]

2013 (1)

2012 (1)

2009 (1)

2007 (1)

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

2005 (1)

T. Skettrup, “Rectangular laser resonators with astigmatic compensation,” J. Opt. A, Pure Appl. Opt. 7(11), 645–654 (2005).
[CrossRef]

2002 (3)

J. Kojima and Q. V. Nguyen, “Laser pulse-stretching with multiple optical ring cavities,” Appl. Opt. 41(30), 6360–6370 (2002).
[CrossRef] [PubMed]

J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
[CrossRef]

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

2000 (1)

1996 (1)

S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
[CrossRef]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

1984 (1)

D. M. Kane and M. H. Dunn, “Stability calculations for a commercial ring dye-laser resonator with 2 foci,” Opt. Commun. 48(5), 295–300 (1984).
[CrossRef]

1982 (1)

1981 (1)

R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[CrossRef]

1967 (1)

1965 (1)

W. W. Rigrod, “The optical ring resonator,” Bell Syst. Tech. J. 44(5), 907–916 (1965).
[CrossRef]

Atherton, B.

S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
[CrossRef]

Bagayev, S. N.

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

Belkin, A. M.

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

Chen, M. X.

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Diddams, S.

S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
[CrossRef]

Diels, J. C.

S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
[CrossRef]

Dunn, M. H.

D. M. Kane and M. H. Dunn, “Stability calculations for a commercial ring dye-laser resonator with 2 foci,” Opt. Commun. 48(5), 295–300 (1984).
[CrossRef]

Faerch, K.

Feugnet, G.

Fork, R. L.

R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[CrossRef]

Frederiksen, S. L.

Garduño-Mejía, J.

J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
[CrossRef]

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Greene, B. I.

R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[CrossRef]

Jamasbi, N.

J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
[CrossRef]

Kane, D. M.

D. M. Kane and M. H. Dunn, “Stability calculations for a commercial ring dye-laser resonator with 2 foci,” Opt. Commun. 48(5), 295–300 (1984).
[CrossRef]

Kang, Z. L.

Kojima, J.

Kvashnin, N. L.

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

Laures, P.

Li, D. H.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Li, K. K.

Li, Y. Y.

Long, X. W.

Meelby, T.

Mohebi, M.

J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
[CrossRef]

Nguyen, Q. V.

Okhapkin, M. V.

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

Pedersen, C.

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Pocholle, J. P.

Rigrod, W. W.

W. W. Rigrod, “The optical ring resonator,” Bell Syst. Tech. J. 44(5), 907–916 (1965).
[CrossRef]

Sanders, V.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Schwartz, S.

Scully, M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Shank, C. V.

R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[CrossRef]

Skettrup, T.

Skvortsov, M. N.

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

Sun, L. Q.

Tan, Y. Y.

Tian, J. R.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Tian, Q.

Wang, P.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Wang, Y. Y.

Wang, Z. H.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Wei, Z. Y.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Wen, Q.

Yuan, J.

Zhang, E. Y.

Zhang, J.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Zhao, H.

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (1)

S. Diddams, B. Atherton, and J. C. Diels, “Frequency locking and unlocking in a femtosecond ring laser with application to intracavity phase measurements,” Appl. Phys. B 63(5), 473–480 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

R. L. Fork, B. I. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[CrossRef]

Bell Syst. Tech. J. (1)

W. W. Rigrod, “The optical ring resonator,” Bell Syst. Tech. J. 44(5), 907–916 (1965).
[CrossRef]

Chin. Phys. Lett. (1)

H. Zhao, P. Wang, Z. Y. Wei, J. R. Tian, D. H. Li, Z. H. Wang, and J. Zhang, “Highly efficient and stable ring regenerative amplifier for chirped-pulse amplification at repetition rate 1 kHz,” Chin. Phys. Lett. 24(1), 115–118 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

T. Skettrup, “Rectangular laser resonators with astigmatic compensation,” J. Opt. A, Pure Appl. Opt. 7(11), 645–654 (2005).
[CrossRef]

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

Opt. Commun. (3)

M. V. Okhapkin, M. N. Skvortsov, A. M. Belkin, N. L. Kvashnin, and S. N. Bagayev, “Tunable single-frequency diode-pumped Nd:YAG ring laser at 1064/532 nm for optical frequency standard applications,” Opt. Commun. 203(3-6), 359–362 (2002).
[CrossRef]

D. M. Kane and M. H. Dunn, “Stability calculations for a commercial ring dye-laser resonator with 2 foci,” Opt. Commun. 48(5), 295–300 (1984).
[CrossRef]

J. Garduño-Mejía, M. Mohebi, and N. Jamasbi, “The role of cavity design in a bi-directional Kerr lens mode locked ring Ti:Sapphire laser,” Opt. Commun. 207(1–6), 307–314 (2002).
[CrossRef]

Opt. Express (2)

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[CrossRef]

Other (1)

G. Zhang and S. Guo, Graphic analysis and design method of optical resonator, National Defense Industry Press, Beijing, (2003). (in Chinese)

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Figures (6)

Fig. 1
Fig. 1

Configuration of an optical ring cavity.

Fig. 2
Fig. 2

Beam waist radius w02 and the distance l22 between the beam waist position and the curved mirrors in image space vary with the distance l12 in the object space. The calculation parameters of the radii of curvature of concave mirrors M1 is 200 mm.

Fig. 3
Fig. 3

Beam waist radius w03 and the distance l32 as a function of the distance l2 between the curved mirrors M1 and M2, respectively. The calculation parameters of the radii of curvature of concave mirrors M1 and M2 are 200 mm and 500 mm respectively, l11 = 13 cm.

Fig. 4
Fig. 4

A six-mirror mode-locked ring laser.

Fig. 5
Fig. 5

Output power and total optical-optical efficiency versus input power at 808 nm, respectively. CW: clockwise; CCW: counter-clockwise; QSML:Q-switch mode locking; CWML: continuous wave mode locking.

Fig. 6
Fig. 6

Oscilloscope traces of both clockwise and counter-clockwise outputs of the ring laser.

Equations (14)

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U = A 0 q exp ( j π r 2 λ q ) .
1 q = 1 R j λ π w 2 .
q 2 = A q 1 + B C q 1 + D ,
1 q = j λ π w 0 2
w 0 ' 2 = f 2 w 0 2 ( l f ) 2 + ( π w 0 2 λ ) 2 ,
l ' = f + ( l f ) f 2 ( l f ) 2 + ( π w 0 2 λ ) 2 .
w 01 2 = f 3 2 w 03 2 ( l 33 f 3 ) 2 + ( π w 03 2 λ ) 2
l 33 = f 3 ± f 3 2 w 03 2 w 01 2 ( π w 03 2 λ ) 2
f 3 π w 03 w 01 λ
l 13 = f 3 + ( l 33 f 3 ) f 3 2 ( l 33 f 3 ) 2 + ( π w 03 2 λ ) 2
w 02 = λ f 1 π w 01 , l 21 = f 1 .
w 03 = λ f 2 π w 02 , l 32 = f 2 .
w 01 = λ f 3 π w 03 , l 13 = f 3 .
w 01 2 = λ π f 1 f 3 f 2 , w 02 2 = λ π f 1 f 2 f 3 , w 03 2 = λ π f 2 f 3 f 1 .

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