Abstract

Recently, we have demonstrated large mode-hop free tuning of an external-cavity diode laser with an off-the-shelf laser diode. This novel approach employs a closed-loop control based on polarization spectroscopy. In this paper, we derive a model capable of describing multicavity laser systems with polarization-dependent elements. We successfully apply it to explain the peculiar form of our error signal.

© 2011 Optical Society of America

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References

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  1. C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
    [CrossRef]
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    [CrossRef]
  3. T. N. Anderson, R. P. Lucht, R. Barron-Jimenez, S. F. Hanna, J. A. Caton, T. Walther, S. Roy, M. S. Brown, J. R. Gord, I. Critchley, and L. Flamand, “Combustion exhaust measurements of nitric oxide with an ultraviolet diode-laser-based absorption sensor,” Appl. Opt. 44, 1491–1502 (2005).
    [CrossRef] [PubMed]
  4. E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
    [CrossRef]
  5. D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
    [CrossRef]
  6. T. Führer and T. Walther, “Extension of the mode-hop-free tuning range of an external cavity diode laser based on a model of the mode-hop dynamics,” Opt. Lett. 33, 372–374 (2008).
    [CrossRef] [PubMed]
  7. R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
    [CrossRef]
  8. T. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [CrossRef]
  9. K. S. Repasky, A. R. Nehrir, J. T. Hawthorne, G. W. Switzer, and J. L. Carlsten, “Extending the continuous tuning range of an external-cavity diode laser,” Appl. Opt. 45, 9013–9020(2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. J. Hult, I. S. Burns, and C. F. Kaminski, “Wide-bandwidth mode-hop-free tuning of extended-cavity GaN diode lasers,” Appl. Opt. 44, 3675–3685 (2005).
    [CrossRef] [PubMed]
  12. L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
    [CrossRef]
  13. H. van de Stadt and J. M. Muller, “Multimirror Fabry–Perot interferometers,” J. Opt. Soc. Am. A 2, 1363–1370 (1985).
    [CrossRef]
  14. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  15. F. Streichert and H. Ulmer, “JavaEvA—A Java Framework for Evolutionary Algorithms,” Technical Report WSI-2005-06. http://w210.ub.uni-tuebingen.de/dbt/volltexte/2005/1702/.

2009

D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
[CrossRef]

T. Führer, D. Stang, and T. Walther, “Actively controlled tuning of an external cavity diode laser by polarization spectroscopy,” Opt. Express 17, 4991–4996 (2009).
[CrossRef] [PubMed]

2008

2006

2005

2002

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

2000

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

1995

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

1991

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

1985

1980

T. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

1941

Anderson, T. N.

Bakowski, B.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Barron-Jimenez, R.

Barry, H. R.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Brown, M. S.

Burns, I. S.

Carlsten, J. L.

Caton, J. A.

Cornell, E. A.

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

Corner, L.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Couillaud, B.

T. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Critchley, I.

Depenheuer, D.

D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
[CrossRef]

Drever, R .W .P.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Esslinger, T.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Flamand, L.

Ford, G. M.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Freegarde, T.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Führer, T.

Gläßer, H.

D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
[CrossRef]

Gord, J. R.

Hall, J. L.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Hancock, G.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Hanna, S. F.

Hänsch, T.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

T. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Hawkins, O. T. W.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Hawthorne, J. T.

Hemmerich, A.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Hollberg, L.

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

Hough, J.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Hult, J.

Jacobs, R. M. J.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Jones, R. C.

Kaminski, C. F.

Kohl-Landgraf, J.

D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
[CrossRef]

König, W.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Kowalski, F. V.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Lucht, R. P.

Muller, J. M.

Munley, A. J.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Nehrir, A. R.

Peverall, R.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Repasky, K. S.

Ricci, L.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Ritchie, G. A. D.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

Roy, S.

Stang, D.

Streichert, F.

F. Streichert and H. Ulmer, “JavaEvA—A Java Framework for Evolutionary Algorithms,” Technical Report WSI-2005-06. http://w210.ub.uni-tuebingen.de/dbt/volltexte/2005/1702/.

Switzer, G. W.

Ulmer, H.

F. Streichert and H. Ulmer, “JavaEvA—A Java Framework for Evolutionary Algorithms,” Technical Report WSI-2005-06. http://w210.ub.uni-tuebingen.de/dbt/volltexte/2005/1702/.

van de Stadt, H.

Vuletic, V.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Walther, T.

Ward, H.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Weidemüller, M.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Wieman, C. E.

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

Zimmermann, C.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. B

D. Depenheuer, J. Kohl-Landgraf, H. Gläßer, and T. Walther “A pulsed laser system with large spectral coverage extended by non-linear frequency conversion,” Appl. Phys. B 97, 583–589(2009).
[CrossRef]

Appl. Phys. B.

R .W .P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B. 31, 97–105(1995).
[CrossRef]

Chem. Phys. Lett.

H. R. Barry, B. Bakowski, L. Corner, T. Freegarde, O. T. W. Hawkins, G. Hancock, R. M. J. Jacobs, R. Peverall, and G. A. D. Ritchie, “OH detection by absorption of frequency-doubled diode laser radiation at 308nm,” Chem. Phys. Lett. 319, 125–130 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

T. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Mod. Phys.

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

Rev. Sci. Instrum.

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

Other

F. Streichert and H. Ulmer, “JavaEvA—A Java Framework for Evolutionary Algorithms,” Technical Report WSI-2005-06. http://w210.ub.uni-tuebingen.de/dbt/volltexte/2005/1702/.

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Figures (4)

Fig. 1
Fig. 1

Setup of the ECDL and polarization diagnostics, as well as electronics. CL, collimation lens; G, grating; BS, beam sampler; PD, photodiode; PBS, polarizing beam splitter; QWP, λ/4-wave-plate; HWP, λ/2-wave-plate; PZT, piezoelectric transducer.

Fig. 2
Fig. 2

Normalized Stokes parameter S 1 for different settings of the λ / 4 -wave-plate (QWP) within the ECDL cavity. It is shown with respect to the elongation of the piezo actuators over time as measured with the photodiodes. The plots are ordered according to the rotation angle α of the intracavity QWP and scaled to fill their respective bounding box. The discontinuities in the signal mark mode-hops. Curves with settings of the QWP suited for locking are indicated by full lines.

Fig. 3
Fig. 3

Schematic view of two consecutive boundary surfaces out of a bunch of N. The field vector E out + is only valid for the last mirror pair.

Fig. 4
Fig. 4

Comparison of three error signals at three different λ / 4 -wave-plate (QWP) angular settings as a function of piezo voltage and the respective result of the fit. The gray areas depict the settings for which the model predicts resonance of the internal and external cavities.

Tables (2)

Tables Icon

Table 1 Parameters of the Model and Their Appropriate Lower and Upper Bounds for Fitting as Used by the Global Optimizers a

Tables Icon

Table 2 Values for the Parameters Used in the Model after a Two-Step Fitting Procedure Involving Global Optimizers and a Standard Levenberg–Marquardt Algorithm Including Error Estimates a

Equations (20)

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

E out + = E x E y ,
S 1 = I x I y = | E x | 2 | E y | 2 .
p ^ i = exp ( i φ i ) 0 0 exp ( i φ i )
Φ ^ 2 = p ^ 2 p ^ λ / 4 ( α ) .
p ^ λ / 4 ( α ) = R ^ ( α ) exp ( i π / 4 ) 1 0 0 i R ^ ( α ) .
r ^ i = r x , i 0 0 r y , i = ( 1 ^ t ^ i 2 ) 1 / 2 ,
t ^ i = t x , i 0 0 t y , i = ( 1 ^ r ^ i 2 ) 1 / 2 .
E i - = r ^ i E i + + t ^ i Φ ^ i E i + 1
Φ ^ i t ^ i E i + = Φ ^ i r ^ i Φ ^ i E i + 1 E i + 1 + .
t ^ = t ^ N ( A ^ B ^ r ^ N ) 1 ,
A ^ B ^ C ^ D ^ = i = 1 N 1 [ t ^ i 1 Φ i 1 r ^ i Φ ^ i r ^ i Φ ^ i 1 Φ ^ i ] .
I = I x I y = | t ^ E in | 2 .
SOP = ( I x I y ) / ( I x + I y ) ,
[ 1 ^ r ^ 1 1 ^ 0 t ^ 1 Φ ^ 1 Φ ^ 1 t ^ 1 0 1 ^ Φ ^ 1 r ^ 1 Φ ^ 1 r ^ i 1 ^ 0 t ^ i Φ ^ i Φ ^ i t ^ i 0 1 ^ Φ ^ i r ^ i Φ ^ i r ^ N 1 ^ 0 t ^ N 0 1 ^ ] · E 1 + E 1 E i + E i E N + E N E out + = E in 0 0 0 0 0 0 .
Φ ^ 1 = p ^ 1 1 0 0 y , y > 0
d 2 ( U ) = d 20 + d 21 U + d 22 U 2 ,
λ ( U ) = [ ( λ 0 d 2 ( U ) / d 20 + h 0 λ 0 ) mod ( h f ) ] + λ 0 .
p ^ 1 ( U ) = exp [ i 2 π d 1 / λ ( U ) ] 1 ^ ,
p ^ 2 ( U ) = exp [ i 2 π d 2 ( U ) / λ ( U ) ] 1 ^ ,
E in = 0.98 0.17 i 0.10 + 0.02 i .

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