Abstract

We demonstrate a simple and robust technique for removal of the carrier wave from a phase-modulated laser beam, using a noninterferometric method that is insensitive to the modulation frequency and instead exploits the polarization dependence of electro-optic modulation. An actively stabilized system using feedback via a liquid crystal cell yields long-term carrier suppression in excess of 28 dB at the expense of a 6.5 dB reduction in sideband power.

© 2012 Optical Society of America

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References

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  1. P. Palm, D. Hanke, W. Urban, and M. Mürtz, “Ultrahigh-resolution spectrometer for the 5 μm wavelength region,” Opt. Lett. 26, 641–643 (2001).
    [CrossRef]
  2. N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
    [CrossRef]
  3. J. I. Thorpe, K. Numata, and J. Livas, “Laser frequency stabilization and control through offset sideband locking to optical cavities,” Opt. Express 16, 15980–15990 (2008).
    [CrossRef]
  4. P. Bouyer, T. L. Gustavson, K. G. Haritos, and M. A. Kasevich, “Microwave signal generation with optical injection locking,” Opt. Lett. 21, 1502–1504 (1996).
    [CrossRef]
  5. K. Szymaniec, “Injection locking of diode lasers to frequency modulated source,” Opt. Commun. 144, 50–54 (1997).
    [CrossRef]
  6. J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
    [CrossRef]
  7. R. P. Abel, U. Krohn, P. Siddons, I. G. Hughes, and C. S. Adams, “Faraday dichroic beam splitter for Raman light using an isotopically pure alkali-metal-vapor cell,” Opt. Lett. 34, 3071–3073 (2009).
    [CrossRef]
  8. J. E. Bateman, R. L. D. Murray, M. Himsworth, H. Ohadi, A. Xuereb, and T. Freegarde, “Hänsch–Couillaud locking of Mach–Zehnder interferometer for carrier removal from a phase-modulated optical spectrum,” J. Opt. Soc. Am. B 27, 1530–1533 (2010).
    [CrossRef]
  9. M. Shahriar, “Demonstration of injection locking a diode laser using a filtered electro-optic modulator sideband,” Opt. Commun. 184, 457–462 (2000).
    [CrossRef]
  10. In our case, for example, New Focus Model 4431 employing MgO:LiNbO3.
  11. The maximum modulation depth achievable with most commercial EOMs is of the order of 1 radian.
  12. Although we currently assume a linear input polarization, no extra calculation is required to generalize our treatment to any input polarization.
  13. We now see that any phase relationship between the horizontally and vertically polarized components of the input light can be subsumed into this phase difference; hence our calculations are valid for any input polarization.
  14. The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
    [CrossRef]
  15. S. Wu, U. Efron, and L. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23, 3911–3915 (1984).
    [CrossRef]
  16. M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
    [CrossRef]
  17. See, for example, Thorlabs Product LCR-1-NIR.
  18. T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [CrossRef]
  19. This was implemented using an Atmel ATMEGA328P-PU microprocessor (mounted on an Arduino Uno board) and Analog Devices DAC8562 12 bit digital-to-analog converter.
  20. The long-term carrier suppression was slightly reduced by small variations in the modulation depth; with the enhancement of Section 4, we expect that performance would be limited by the polarizing beam splitters.

2010 (1)

2009 (1)

2008 (1)

2005 (1)

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

2004 (1)

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

2001 (1)

2000 (1)

M. Shahriar, “Demonstration of injection locking a diode laser using a filtered electro-optic modulator sideband,” Opt. Commun. 184, 457–462 (2000).
[CrossRef]

1999 (1)

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

1997 (1)

K. Szymaniec, “Injection locking of diode lasers to frequency modulated source,” Opt. Commun. 144, 50–54 (1997).
[CrossRef]

1996 (1)

1994 (1)

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

1984 (1)

1980 (1)

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

Abel, R. P.

Adams, C. S.

Aguiar-Ricardo, A.

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

Bateman, J. E.

Bouyer, P.

Brás, A. R. E.

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

Caldeira, J.

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

Casimiro, T.

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

Chu, S.

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

Couillaud, B.

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

Davidson, N.

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

Dyadyusha, A.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Efron, U.

Freegarde, T.

Garreau, J.

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

Gustavson, T. L.

Hanke, D.

Hänsch, T. W.

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

Haritos, K. G.

Hess, L.

Himsworth, M.

Hughes, I. G.

Kaczmarek, M.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Kasevich, M.

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

Kasevich, M. A.

Khoo, I. C.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Krohn, U.

Lecoq, Y.

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

Lee, H. J.

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

Livas, J.

Murray, R. L. D.

Mürtz, M.

Numata, K.

Ohadi, H.

Palm, P.

Ringot, J.

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

Shahriar, M.

M. Shahriar, “Demonstration of injection locking a diode laser using a filtered electro-optic modulator sideband,” Opt. Commun. 184, 457–462 (2000).
[CrossRef]

Siddons, P.

Slussarenko, S.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Szriftgiser, P.

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

Szymaniec, K.

K. Szymaniec, “Injection locking of diode lasers to frequency modulated source,” Opt. Commun. 144, 50–54 (1997).
[CrossRef]

Thorpe, J. I.

Urban, W.

Wu, S.

Xuereb, A.

Appl. Opt. (1)

Eur. Phys. J. D (1)

J. Ringot, Y. Lecoq, J. Garreau, and P. Szriftgiser, “Generation of phase-coherent laser beams for Raman spectroscopy and cooling by direct current modulation of a diode laser,” Eur. Phys. J. D 7, 285–288 (1999).
[CrossRef]

J. Appl. Phys. (1)

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

J. Chem. Eng. Data (1)

The full chemical composition of this widely used liquid crystal mixture is given by A. R. E. Brás, T. Casimiro, J. Caldeira, and A. Aguiar-Ricardo, “Solubility of the nematic liquid crystal E7 in supercritical carbon dioxide,” J. Chem. Eng. Data 50, 1857–1860 (2005).
[CrossRef]

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

Opt. Commun. (3)

M. Shahriar, “Demonstration of injection locking a diode laser using a filtered electro-optic modulator sideband,” Opt. Commun. 184, 457–462 (2000).
[CrossRef]

K. Szymaniec, “Injection locking of diode lasers to frequency modulated source,” Opt. Commun. 144, 50–54 (1997).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

N. Davidson, H. J. Lee, M. Kasevich, and S. Chu, “Raman cooling of atoms in two and three dimensions,” Phys. Rev. Lett. 72, 3158–3161 (1994).
[CrossRef]

Other (7)

In our case, for example, New Focus Model 4431 employing MgO:LiNbO3.

The maximum modulation depth achievable with most commercial EOMs is of the order of 1 radian.

Although we currently assume a linear input polarization, no extra calculation is required to generalize our treatment to any input polarization.

We now see that any phase relationship between the horizontally and vertically polarized components of the input light can be subsumed into this phase difference; hence our calculations are valid for any input polarization.

This was implemented using an Atmel ATMEGA328P-PU microprocessor (mounted on an Arduino Uno board) and Analog Devices DAC8562 12 bit digital-to-analog converter.

The long-term carrier suppression was slightly reduced by small variations in the modulation depth; with the enhancement of Section 4, we expect that performance would be limited by the polarizing beam splitters.

See, for example, Thorlabs Product LCR-1-NIR.

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Figures (5)

Fig. 1.
Fig. 1.

Optimized performance against modulation depth: the three lines plotted correspond to the maximum proportion of the input power that could be placed into the first-order sidebands without carrier removal, the proportion of this power that can be retained under polarization filtering arrangements, and hence the maximum proportion of the input power that can be placed into carrier-free first-order sidebands.

Fig. 2.
Fig. 2.

(a) Polarization optics for passive removal of the carrier; the wave plates after the EOM must be adjusted to compensate for any birefringence. (b) Equivalent arrangement using a liquid crystal cell for active compensation. The residual birefringence is monitored using a Hänsch–Couillaud scheme. BSa, nonpolarizing beam sampler; EOM, electro-optic modulator; LCC, liquid crystal cell; (N)PBS, (non)polarizing beam splitter; VCA, voltage-controlled amplifier. In practice, the electronic feedback was implemented digitally.

Fig. 3.
Fig. 3.

Spectra of light (a) leaving the EOM and (b) emerging from the carrier removal system. The modulation frequency is 2.7 GHz, and our optical spectrum analyzer has a free spectral range of 2 GHz, hence the apparent appearance of the first-order sidebands at a relative frequency of ±700MHz. The scales are consistent between the two panels.

Fig. 4.
Fig. 4.

Logarithmic plot of the optical spectra before (dotted lines) and after (solid lines) carrier removal, smoothed with a 20 MHz bandwidth moving average filter. The lower readings of the dotted trace are adversely affected by experimental noise and the finite resolution of the oscilloscope. The shoulders to the left of the carrier peak are higher order transverse modes, resulting from a small misalignment of the optical spectrum analyzer.

Fig. 5.
Fig. 5.

Error signal and carrier transmission (as a percentage of its maximum value) during a sweep of the peak-to-peak voltage applied to the LCC.

Equations (7)

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E=A(ei(ωt+mcosΩt)cosϑeiωtsinϑ).
E=A(J0(m)cosϑsinϑ)eiωt+A(cosϑ0)eiωtn0inJn(m)einΩt,
Esidebands=(sinϕcosϕ)Acosϑsinϕn0inJn(m)ei(ω+nΩ)t,
PS1=cos2ϑsin2ϕJ12(m)=cos2ϑtan2ϕ1+tan2ϕJ12(m)=cos2ϑJ12(m){1+[J0(m)cotϑ]2}.
S±=KA2[1/2±cosϑsinϑJ0(m)sinδ],
SE=S+S=2KA2cosϑsinϑJ0(m)sinδ,
S^m=Sm(S++S)=KA2[1/2+cosϑsinϑJ0(m)cosδ]KA2=12+cosϑsinϑJ0(m).

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