Abstract

We describe a class of techniques whereby a laser frequency can be stabilized to a fixed optical cavity resonance with an adjustable offset, providing a wide tuning range for the central frequency. These techniques require only minor modifications to the standard Pound-Drever-Hall locking techniques and have the advantage of not altering the intrinsic stability of the frequency reference. We discuss the expected performance and limitations of these techniques and present a laboratory investigation in which both the sideband techniques and the standard, non-tunable Pound-Drever-Hall technique reached the 100Hz/√Hz level.

© 2008 Optical Society of America

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  1. R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  2. J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
    [CrossRef]
  3. L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
    [CrossRef]
  4. H. Zhen, H. Ye, X. Liu, D. Zhu, H. Li, Y. Lu, and Q. Wang, "Widely tunable reflection-type Fabry-Perot interferometer based on relaxor ferroelectric poly(vinylidenefluoride-chlorotrifluoroethylene-trifluoroethylene)," Opt. Express,  16, 9595-9600 (2008).
    [CrossRef] [PubMed]
  5. F. Bondu, P. Fritschel, C. Man, and A. Brillet, "Ultrahigh-spectral-purity laser for the Virgo experiment," Opt. Lett. 21, 582-584 (1996).
    [CrossRef] [PubMed]
  6. J. Ye and J. Hall, "Optical phase locking in the mircoradian domain: potential applications to NASA spaceborne optical measurements," Opt. Lett. 24, 1838-1840 (1999).
    [CrossRef]
  7. R. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
    [CrossRef] [PubMed]
  8. E. Black, "An introduction to Pound-Drever-Hall laser frequency stabilization," Am. J. Phys. 69, 79-87 (2001).
    [CrossRef]
  9. K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
    [CrossRef]
  10. J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
    [CrossRef]
  11. S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
    [CrossRef]
  12. B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
    [CrossRef]
  13. P. Bender and K. Danzmann, and the LISA Study Team, "Laser interferometer space antenna for the detection of graviational waves, pre-Phase A report," Tech. Rep. MPQ233, Max-Planck-Institut f¨ur Quantenoptik, Gärching (1998). 2nd ed.
  14. P. Welch, "The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. AU-15, 70-73 (1967).
    [CrossRef]
  15. M. Tröbs and G. Heinzel, "Improved spectrum estimation from digitized time series on a logarithmic frequency axis," Measurement 39, 120-129 (2005).
    [CrossRef]

2008 (3)

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

H. Zhen, H. Ye, X. Liu, D. Zhu, H. Li, Y. Lu, and Q. Wang, "Widely tunable reflection-type Fabry-Perot interferometer based on relaxor ferroelectric poly(vinylidenefluoride-chlorotrifluoroethylene-trifluoroethylene)," Opt. Express,  16, 9595-9600 (2008).
[CrossRef] [PubMed]

2005 (1)

M. Tröbs and G. Heinzel, "Improved spectrum estimation from digitized time series on a logarithmic frequency axis," Measurement 39, 120-129 (2005).
[CrossRef]

2004 (1)

K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
[CrossRef]

2003 (2)

L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
[CrossRef]

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

2001 (1)

E. Black, "An introduction to Pound-Drever-Hall laser frequency stabilization," Am. J. Phys. 69, 79-87 (2001).
[CrossRef]

1999 (2)

J. Ye and J. Hall, "Optical phase locking in the mircoradian domain: potential applications to NASA spaceborne optical measurements," Opt. Lett. 24, 1838-1840 (1999).
[CrossRef]

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

1996 (1)

1983 (1)

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

1967 (1)

P. Welch, "The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. AU-15, 70-73 (1967).
[CrossRef]

1946 (1)

R. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
[CrossRef] [PubMed]

Alins, J.

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Black, E.

E. Black, "An introduction to Pound-Drever-Hall laser frequency stabilization," Am. J. Phys. 69, 79-87 (2001).
[CrossRef]

Bondu, F.

Brillet, A.

Camp, J.

K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
[CrossRef]

Conti, L.

L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
[CrossRef]

Drever, R.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ford, G.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Fritschel, P.

Gill, P.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Gray, M.

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

Hall, J.

J. Ye and J. Hall, "Optical phase locking in the mircoradian domain: potential applications to NASA spaceborne optical measurements," Opt. Lett. 24, 1838-1840 (1999).
[CrossRef]

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hänsch, T.W.

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Heinzel, G.

M. Tröbs and G. Heinzel, "Improved spectrum estimation from digitized time series on a logarithmic frequency axis," Measurement 39, 120-129 (2005).
[CrossRef]

Hong, F.

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Hough, J.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Kemery, A.

K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
[CrossRef]

Kolachevsky, N.

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Kowalski, F.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Li, H.

Liu, X.

Lu, Y.

Ma, L.

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Man, C.

Marin, F.

L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
[CrossRef]

Matveev, A.

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

McClelland, D.

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

Millo, J.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Munley, A.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Numata, K.

K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
[CrossRef]

Oxborrow, M.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Pfister, O.

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Pound, R.

R. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
[CrossRef] [PubMed]

Pugla, S.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Rosa, M. D.

L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
[CrossRef]

Shaddock, D.

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

Sheard, B.

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

Taubman, M.

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Tiemann, B.

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Tröbs, M.

M. Tröbs and G. Heinzel, "Improved spectrum estimation from digitized time series on a logarithmic frequency axis," Measurement 39, 120-129 (2005).
[CrossRef]

Udem, Th.

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Wang, Q.

Ward, H.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Webster, S. A.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Welch, P.

P. Welch, "The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. AU-15, 70-73 (1967).
[CrossRef]

Ye, H.

Ye, J.

J. Ye and J. Hall, "Optical phase locking in the mircoradian domain: potential applications to NASA spaceborne optical measurements," Opt. Lett. 24, 1838-1840 (1999).
[CrossRef]

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

Zhen, H.

Zhu, D.

Am. J. Phys. (1)

E. Black, "An introduction to Pound-Drever-Hall laser frequency stabilization," Am. J. Phys. 69, 79-87 (2001).
[CrossRef]

Appl. Phys. B (1)

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

IEEE Trans. Audio Electroacoust. (1)

P. Welch, "The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. AU-15, 70-73 (1967).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Hall, L. Ma, M. Taubman, B. Tiemann, F. Hong, O. Pfister, and J. Ye, "Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser," IEEE Trans. Instrum. Meas. 48, 583-586 (1999).
[CrossRef]

J. Opt. Soc. B (1)

L. Conti, M. D. Rosa, and F. Marin, "High-spectral-purity laser system for the Auriga detector optical readout," J. Opt. Soc. B 20, 462-468 (2003).
[CrossRef]

Measurement (1)

M. Tröbs and G. Heinzel, "Improved spectrum estimation from digitized time series on a logarithmic frequency axis," Measurement 39, 120-129 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

B. Sheard, M. Gray, D. McClelland, and D. Shaddock, "Laser frequency stabilization by locking to a LISA arm," Phys. Lett. A 320, 9-21 (2003).
[CrossRef]

Phys. Rev. A (2)

J. Alins, A. Matveev, N. Kolachevsky, Th. Udem, and T.W. Hänsch, "Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities," Phys. Rev. A 77, 053809 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, "Thermal-noise-limited optical cavity," Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

K. Numata, A. Kemery, and J. Camp, "Thermal-noise limit in the frequency stabilization of lasers with rigid cavities," Phys. Rev. Lett. 93 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
[CrossRef] [PubMed]

Other (1)

P. Bender and K. Danzmann, and the LISA Study Team, "Laser interferometer space antenna for the detection of graviational waves, pre-Phase A report," Tech. Rep. MPQ233, Max-Planck-Institut f¨ur Quantenoptik, Gärching (1998). 2nd ed.

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Figures (3)

Fig. 1.
Fig. 1.

Modulation structures for traditional and tunable modulation/demodulation locking. For DSB and ESB only the upper half (ωωc ) of the modulation structure is shown. The solid curve represents |F(ω)|2 and the dashed curve represents ∠F(ω), where F(ω) is the amplitude reflection coefficient of the cavity. For the frequency-tunable cases, the arrow labeled tune indicates the frequency spacing that is adjusted to tune the carrier, denoted by a thick line.

Fig. 2.
Fig. 2.

Arrangement of test cavity systems for experiments described in section 5. Table 2 lists the modulation/demodulation signals used for each locking technique. The reference beam was sourced from a laser locked to an independent cavity using the standard Pound-Drever-Hall technique.

Fig. 3.
Fig. 3.

Beat note frequency noise spectra for free-running lasers (FR), Pound-Drever-Hall locking (PDH), and single-sideband locking (SSB). For the “SSB w/mod” case, a frequency modulation with 1.00kHz amplitude at a frequency of ≈900µHz was added to the SSB tuning port. The measured amplitude of the reference tone is 0.983kHz after accounting for the spectrum’s equivalent noise bandwidth.

Tables (2)

Tables Icon

Table 1. Shot noise limited frequency noise for each locking technique at optimum modulation depth, assuming perfect contrast in the cavity resonance.

Tables Icon

Table 2. Modulation/Demodulation signals used for each locking technique. See Fig. 2 for corresponding block diagram. (PDH=Pound-Drever-Hall locking, SSB=single sideband locking, DSB=dual sideband locking, ESB=electronic sideband locking)

Equations (13)

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F S R c 2 L ,
= F S R ν F W H M ,
E ˜ = P 0 exp { i [ ω c t + β sin ( Ω t ) ] } ,
P ref , Ω = 2 P 0 J 0 ( β ) J 1 ( β ) Re [ F ( ω c ) F * ( ω c + Ω ) F * ( ω c ) F ( ω c Ω ) ] cos ( Ω t ) + 2 P 0 J 0 ( β ) J 1 ( β ) Im [ F ( ω c ) F * ( ω c + Ω ) F * ( ω c ) F ( ω c Ω ) ] sin ( Ω t ) ,
D P D H = 16 L P 0 c J 0 ( β ) J 1 ( β ) .
D S S B = 8 L P 0 c J 1 ( β ) [ J 0 ( β ) J 2 ( β ) ] .
E ˜ D S B = P 0 exp { i [ ω c t + β 1 sin ( Ω 1 t ) + β 2 sin ( Ω 2 t ) ] } .
D D S B = 16 L P 0 c J 1 2 ( β 1 ) J 0 ( β 2 ) J 1 ( β 2 ) .
E ˜ E S B = P 0 exp { i [ ω c t + β 1 sin ( Ω 1 t + β 2 sin Ω 2 t ) ] } .
s shpt , P = 2 h c λ P ref ,
( S shot , v ) P D H = 1 8 L h c 3 P 0 λ
= ( 277 μ Hz / Hz ) ( 20 cm L ) ( 10 4 ) ( 1 μ m λ ) 1 / 2 ( 1 m W P 0 ) 1 / 2 .
A M E S B 2 P 0 Ω 2 G ( Ω 1 ) J 1 ( β 2 ) J 0 2 ( β 1 ) ,

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