Abstract

We have demonstrated stabilization of a fiber-optic Mach–Zehnder interferometer, with a centimeter-scale path difference, to the transmission minimum for the carrier wave of a frequency-modulated laser beam. A time-averaged extinction of 32 dB, limited by the bandwidth of the feedback, was maintained over several hours. The interferometer was used to remove the carrier wave from a 780 nm laser beam that had been phase modulated at 2.7 GHz.

© 2013 Optical Society of America

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  1. R. Abel, U. Krohn, P. Siddons, I. Hughes, and C. Adams, “Faraday dichroic beam splitter for Raman light using an isotopically pure alkali-metal-vapor cell,” Opt. Lett. 34, 3071–3073 (2009).
    [CrossRef]
  2. D. Haubrich, “Lossless beam combiners for nearly equal laser frequencies,” Rev. Sci. Instrum. 71, 338–340 (2000).
    [CrossRef]
  3. A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
    [CrossRef]
  4. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
    [CrossRef]
  5. A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
    [CrossRef]
  6. Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach–Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27, 370–374 (2010).
    [CrossRef]
  7. T. Okamoto and I. Yamaguchi, “Multimode fiber-optic Mach–Zehnder interferometer and its use in temperature measurement,” Appl. Opt. 27, 3085–3087 (1988).
    [CrossRef]
  8. P. Connes and F. Reynauld, “Fiber tests on a radiotelescope,” in ESO Conference Workshop Proceedings, Garching, Germany, no. 29 (1988), pp. 1117–1129.
  9. I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
    [CrossRef]
  10. G. B. Xavier and J. P. von der Weid, “Stable single-photon interference in a 1 km fiber-optic Mach–Zehnder interferometer with continuous phase adjustment,” Opt. Lett. 36, 1764–1766 (2011).
    [CrossRef]
  11. 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]
  12. R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilisation using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  13. www.ozoptics.com .
  14. In our experiment, the light used to generate the locking signal was taken from the laser beam before the electro-optic phase modulator and hence contained only a single frequency component. If instead the sidebands are generated, for example, by modulation of the laser supply current, they will remain present in the monitor beam and could lead to additional features and false lock points. However, provided that the sidebands are separated from the carrier by integer multiples of ωs, they will merely change the magnitude of the error signal and not alter its form, although in the case of strong modulation, the sign of the error signal may be reversed.
  15. 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]
  16. 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]
  17. N. Cooper, J. Bateman, A. Dunning, and T. Freegarde, “Actively stabilized wavelength-insensitive carrier elimination from an electro-optically modulated laser beam,” J. Opt. Soc. Am. B 29, 646–649 (2012).
    [CrossRef]
  18. We used an Arduino Uno board ( http://www.arduino.cc ), an electronics prototyping platform employing an Atmel ATMEGA328P-PU microprocessor. Buffered by an additional field effect transistor, this regulated the TEC duty cycle using 12 bit pulse-width modulation.

2012

2011

2010

2009

R. Abel, U. Krohn, P. Siddons, I. Hughes, and C. Adams, “Faraday dichroic beam splitter for Raman light using an isotopically pure alkali-metal-vapor cell,” Opt. Lett. 34, 3071–3073 (2009).
[CrossRef]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[CrossRef]

2008

2004

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

2000

D. Haubrich, “Lossless beam combiners for nearly equal laser frequencies,” Rev. Sci. Instrum. 71, 338–340 (2000).
[CrossRef]

1994

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

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]

1992

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

1988

1983

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

Abel, R.

Adams, C.

Alt, W.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Bateman, J.

Bateman, J. E.

Chen, Q.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[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]

Connes, P.

P. Connes and F. Reynauld, “Fiber tests on a radiotelescope,” in ESO Conference Workshop Proceedings, Garching, Germany, no. 29 (1988), pp. 1117–1129.

Cooper, N.

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]

de Vreede, A.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

Dotsenko, I.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Drever, R.

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

Dunning, A.

Ekert, A.

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

Ford, G.

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

Freegarde, T.

Gomer, V.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Green, F.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

Hall, J.

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

Haubrich, D.

D. Haubrich, “Lossless beam combiners for nearly equal laser frequencies,” Rev. Sci. Instrum. 71, 338–340 (2000).
[CrossRef]

Himsworth, M.

Hough, J.

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

Hughes, I.

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]

Kowalski, F.

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

Krohn, U.

Kuhr, S.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[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]

Liu, S.

Livas, J.

Lu, P.

Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach–Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27, 370–374 (2010).
[CrossRef]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[CrossRef]

Men, L.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[CrossRef]

Meschede, D.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Metaal, E.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

Miroshnychenko, Y.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Muller, M.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Munley, A.

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

Murray, R. L. D.

Numata, K.

Ohadi, H.

Okamoto, T.

Palma, G.

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

Rarity, J.

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

Rauschenbeutel, A.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Reynauld, F.

P. Connes and F. Reynauld, “Fiber tests on a radiotelescope,” in ESO Conference Workshop Proceedings, Garching, Germany, no. 29 (1988), pp. 1117–1129.

Schrader, D.

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

Siddons, P.

Smit, M.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

Sooley, K.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[CrossRef]

Tapster, P.

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

Thorpe, J. I.

Verbeek, B.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

von der Weid, J. P.

Wang, D. N.

Wang, Y.

Ward, H.

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

Xavier, G. B.

Xuereb, A.

Yamaguchi, I.

Yang, M.

Appl. Opt.

Appl. Phys. B

I. Dotsenko, W. Alt, S. Kuhr, D. Schrader, M. Muller, Y. Miroshnychenko, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Application of electro-optically generated light fields for Raman spectroscopy of trapped cesium atoms,” Appl. Phys. B 78, 711–717 (2004).
[CrossRef]

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

Appl. Phys. Lett.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94, 131110 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

A. de Vreede, M. Smit, B. Verbeek, E. Metaal, and F. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP/InP,” IEEE Photon. Technol. Lett. 6, 402–405 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Ekert, J. Rarity, P. Tapster, and G. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69, 1293–1295 (1992).
[CrossRef]

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]

Rev. Sci. Instrum.

D. Haubrich, “Lossless beam combiners for nearly equal laser frequencies,” Rev. Sci. Instrum. 71, 338–340 (2000).
[CrossRef]

Other

P. Connes and F. Reynauld, “Fiber tests on a radiotelescope,” in ESO Conference Workshop Proceedings, Garching, Germany, no. 29 (1988), pp. 1117–1129.

We used an Arduino Uno board ( http://www.arduino.cc ), an electronics prototyping platform employing an Atmel ATMEGA328P-PU microprocessor. Buffered by an additional field effect transistor, this regulated the TEC duty cycle using 12 bit pulse-width modulation.

www.ozoptics.com .

In our experiment, the light used to generate the locking signal was taken from the laser beam before the electro-optic phase modulator and hence contained only a single frequency component. If instead the sidebands are generated, for example, by modulation of the laser supply current, they will remain present in the monitor beam and could lead to additional features and false lock points. However, provided that the sidebands are separated from the carrier by integer multiples of ωs, they will merely change the magnitude of the error signal and not alter its form, although in the case of strong modulation, the sign of the error signal may be reversed.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup of the MZI and surrounding optics. BS (beam splitter), AOM (acousto-optical modulator), OI (optical isolator), and TEC (thermoelectric cooler). Any of the light entering port A that emerges from port C is discarded, with unwanted feedback to the source laser being prevented by the optical isolator.

Fig. 2.
Fig. 2.

Theoretical form of the error signal as a function of the difference in frequency between the (unshifted) input light and an optical frequency that would minimize T AD , with ω AOM / 2 π = 80 MHz and ω s / 2 π = 2.7 GHz . Note that as ω AOM ω s , the error signal closely approximates a sinusoid.

Fig. 3.
Fig. 3.

Spectra of phase-modulated light (a) before and (b) after being passed through the interferometer while it was at a position of minimum carrier transmission to the relevant output. The modulation frequency is 2.7 GHz, and our spectrum analyzer is based on a cavity with a free spectral range of 2 GHz, hence, the apparent appearance of the first-order sidebands at ± 700 MHz relative to the carrier. Interferometric suppression of the carrier is in excess of 30 dB.

Fig. 4.
Fig. 4.

Power transmission T AD from port A to port D and error signal E s shown as functions of time during a rapid scan of the interferometer over several fringes. The noise on the error signal is primarily electrical in origin.

Fig. 5.
Fig. 5.

Fast Fourier transforms of the measured values of T AD ( t ) over a period exceeding 2 h during which the interferometer was either actively stabilized at a minimum of T AD (“locked” or lower trace) or allowed to drift freely (“unlocked” or upper trace). Spectral power density values are given relative to the maximum value measured, which was found at 0.674 mHz with the interferometer unlocked.

Equations (6)

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

δ ( ω ) = ω η ( ω ) Δ l / c ,
Δ δ ( ω m ) = δ ( ω 0 + ω m ) δ ( ω 0 ) = ( Δ l / c ) [ ( ω 0 + ω m ) η ( ω 0 + ω m ) ω 0 η ( ω 0 ) ] ,
Δ δ ( ω m ) Δ l c [ ω m η ( ω 0 ) + ω 0 d η d ω ω m ] = Δ l ω m c [ η ( ω 0 ) + ω 0 d η d ω ] = π ω m ω s ,
ω s = π c Δ l [ η ( ω 0 ) + ω 0 d η d ω ] .
| 1 + e i δ ( ω 0 + ω AOM ) | 2 | 1 + e i δ ( ω 0 ω AOM ) | 2 ,
E s | 1 + e i ( δ ( ω 0 ) + π ω AOM / ω s ) | 2 | 1 + e i ( δ ( ω 0 ) π ω AOM / ω s ) | 2 .

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