Abstract

We present a new method of optical frequency comb spectroscopy that combines cavity enhancement with frequency modulation to obtain immunity to laser frequency-to-amplitude noise conversion by the cavity modes and, thus, high absorption sensitivity over a broad spectral range. A frequency comb is locked to a cavity with a free spectral range (FSR) equal to 4/3 times the repetition rate of the laser, and phase-modulated at a frequency equal to the cavity FSR. The transmitted light is analyzed by a Fourier transform spectrometer with a high bandwidth detector. Phase-sensitive detection of the interferogram yields a noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS) signal. In the first demonstration, we record NICE-OFCS signals from the overtone CO2 band at 1575 nm with absorption sensitivity of 4.3×1010cm1Hz1/2 per spectral element, close to the shot noise limit.

© 2014 Optical Society of America

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  1. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
    [Crossref]
  2. F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
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  3. A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
    [Crossref]
  4. R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
    [Crossref]
  5. J. Ye, L. S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
    [Crossref]
  6. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
    [Crossref]
  7. C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
    [Crossref]
  8. S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
    [Crossref]
  9. J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
    [Crossref]
  10. J. Mandon, G. Guelachvili, and N. Picque, Opt. Lett. 32, 2206 (2007).
    [Crossref]
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    [Crossref]
  12. F. M. Schmidt, A. Foltynowicz, W. G. Ma, and O. Axner, J. Opt. Soc. Am. B 24, 1392 (2007).
    [Crossref]

2013 (1)

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

2012 (1)

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

2011 (1)

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

2010 (1)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

2009 (1)

J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
[Crossref]

2007 (4)

J. Mandon, G. Guelachvili, and N. Picque, Opt. Lett. 32, 2206 (2007).
[Crossref]

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

F. M. Schmidt, A. Foltynowicz, W. G. Ma, and O. Axner, J. Opt. Soc. Am. B 24, 1392 (2007).
[Crossref]

2006 (1)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

1998 (1)

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

Abd Alrahman, C.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Adler, F.

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

Axner, O.

Ban, T.

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

Bjork, B. J.

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

Cossel, K. C.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

Diddams, S. A.

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

Fleisher, A. J.

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

Foltynowicz, A.

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

F. M. Schmidt, A. Foltynowicz, W. G. Ma, and O. Axner, J. Opt. Soc. Am. B 24, 1392 (2007).
[Crossref]

Gohle, C.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Grilli, R.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Guelachvili, G.

J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
[Crossref]

J. Mandon, G. Guelachvili, and N. Picque, Opt. Lett. 32, 2206 (2007).
[Crossref]

Hall, J. L.

Hansch, T. W.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Hollberg, L.

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

Jones, R. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

Kassi, S.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

Ma, L. S.

Ma, W. G.

Mandon, J.

J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
[Crossref]

J. Mandon, G. Guelachvili, and N. Picque, Opt. Lett. 32, 2206 (2007).
[Crossref]

Maslowski, P.

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

Mbele, V.

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

Mejean, G.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Moll, K. D.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

Picque, N.

J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
[Crossref]

J. Mandon, G. Guelachvili, and N. Picque, Opt. Lett. 32, 2206 (2007).
[Crossref]

Romanini, D.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Safdi, B.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

Schliesser, A.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Schmidt, F. M.

Stein, B.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Thorpe, M. J.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

Udem, T.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Ventrillard, I.

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Ye, J.

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

J. Ye, L. S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
[Crossref]

Annu. Rev. Anal. Chem. (1)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, Annu. Rev. Anal. Chem. 3, 175 (2010).
[Crossref]

Appl. Phys. B (2)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[Crossref]

A. Foltynowicz, P. Maslowski, A. J. Fleisher, B. J. Bjork, and J. Ye, Appl. Phys. B 110, 163 (2013).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

J. Mandon, G. Guelachvili, and N. Picque, Nat. Photonics 3, 99 (2009).
[Crossref]

Nature (1)

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

R. Grilli, G. Mejean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, Phys. Rev. A 85, 051804 (2012).
[Crossref]

Phys. Rev. Lett. (2)

A. Foltynowicz, T. Ban, P. Maslowski, F. Adler, and J. Ye, Phys. Rev. Lett. 107, 233002 (2011).
[Crossref]

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Science (1)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, Science 311, 1595 (2006).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

Matching of the comb lines and their FM sidebands to the cavity modes. The transmitted modes and sidebands are shown by black solid lines, and the rejected modes and sidebands are shown by dashed colored lines, respectively.

Fig. 2.
Fig. 2.

Experimental setup: OFC, optical frequency comb; EOM, electro-optic modulator; FC, fiber collimator; λ / 2 , half-wave plate; PBS, polarizing beam splitter; λ / 4 , quarter-wave plate; FTS, Fourier transform spectrometer; PDH, Pound–Drever–Hall error signal generation; BPF, bandpass filter; G, amplifier; LPF, low-pass filter; Ph, phase shifter; FFT, fast Fourier transform.

Fig. 3.
Fig. 3.

Out-of-phase NICE-OFCS interferogram as a function of optical path difference (blue) together with the sine (dashed black) and cosine (dashed–dotted red) envelope factors, drawn as a guidance to the eye. The inset shows a zoom of the interferogram around OPD = 30 cm .

Fig. 4.
Fig. 4.

Zoom of the NICE-OFCS interferogram when the modulation frequency is (a) detuned by 20 kHz from the cavity FSR and (b) precisely tuned to the cavity FSR. NICE-OFCS signal from 1% of CO 2 in 500 Torr of N 2 when the modulation frequency is (c) detuned by 20 kHz from the cavity FSR and (d) precisely tuned to the cavity FSR. The normalized NICE-OFCS signal is shown in (e).

Equations (4)

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E ± = n k = 1,0 , 1 E n 4 J k ( β ) T n , k e i [ ( ω n + k ω m ) ( t ± Δ 2 c ) ] + c.c. ,
I ω m = 1 2 J 0 ( β ) J 1 ( β ) { sin ( ω m t ) n I n { cos ( ω n Δ c ) cos ( ω m Δ 2 c ) [ e δ n , 0 F δ n , 1 F sin ( ϕ n , 0 F + ϕ n , 1 F ) e δ n , 0 F δ n , + 1 F sin ( ϕ n , 0 F ϕ n , + 1 F ) ] + sin ( ω n Δ c ) sin ( ω m Δ 2 c ) [ e δ n , 0 F δ n , 1 F sin ( ϕ n , 0 F + ϕ n , 1 F ) + e δ n , 0 F δ n , + 1 F sin ( ϕ n , 0 F ϕ n , + 1 F ) ] } + cos ( ω m t ) n I n { cos ( ω n Δ c ) cos ( ω m Δ 2 c ) [ e δ n , 0 F δ n , 1 F cos ( ϕ n , 0 F + ϕ n , 1 F ) + e δ n , 0 F δ n , + 1 F cos ( ϕ n , 0 F ϕ n , + 1 F ) ] sin ( ω n Δ c ) sin ( ω m Δ 2 c ) [ e δ n , 0 F δ n , 1 F cos ( ϕ n , 0 F + ϕ n , 1 F ) + e δ n , 0 F δ n , + 1 F cos ( ϕ n , 0 F ϕ n , + 1 F ) ] } } ,
I ω m = 1 2 J 0 ( β ) J 1 ( β ) { sin ( ω m t ) n I n { cos ( ω n Δ c ) cos ( ω m Δ 2 c ) [ ϕ n , 1 F 2 ϕ n , 0 F + ϕ n , + 1 F ] + sin ( ω n Δ c ) sin ( ω m Δ 2 c ) [ ϕ n , 1 F ϕ n , + 1 F ] } + cos ( ω m t ) n I n { cos ( ω n Δ c ) cos ( ω m Δ 2 c ) [ δ n , 1 F δ n , + 1 F ] sin ( ω n Δ c ) sin ( ω m Δ 2 c ) [ 2 δ n , 1 F 2 δ n , 0 F δ n , + 1 F ] } } .
α min shot-noise = 2 e B η P 2 J 0 ( β ) J 1 ( β ) M N 1 L eff ,

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