Abstract

This paper presents a significant advancement in the referencing technique applied to frequency comb spectrometry (cFTS) that we proposed and demonstrated recently. Based on intermediate laser oscillators, it becomes possible to access the full delay range set by the repetition rate of the frequency combs, overcoming the principal limitation observed in the method based on passive optical filters. With this new referencing technique, the maximum spectral resolution given by each comb tooth is achievable and continuous scanning will improve complex reflectometry measurements. We present a demonstration of such a high resolution cFTS system, providing a spectrometry measurement at 100 MHz of resolution (0.003 cm–1) with a spectral signal to noise ratio of 440 for a 2 seconds measurement time. The resulting spectrum is composed of 105 · 103 resolved spectral elements, each corresponding to a single pair of optical modes (one for each combs). To our knowledge, this represents the first cFTS measurement over the full spectral range of the sources in a single shot with resolved individual modes at full resolution.

© 2010 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. P. Giaccari, J.-D. Deschênes, P. Saucier, J. Genest, and P. Tremblay, “Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method,” Opt. Express 16, 4347–4365 (2008).
    [Crossref] [PubMed]
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    [Crossref]
  5. A. Bartels, A. Thoma, C. Janke, T. Dekorsky, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
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    [Crossref] [PubMed]
  8. G. Taurand, P. Giaccari, J.-D. Deschênes, and J. Genest, “Time Domain Optical Reflectometry Measurements Using a Frequency Comb Interferometer,” Appl. Opt. 49, 4413–4419 (2010).
    [Crossref] [PubMed]
  9. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
    [Crossref]
  10. N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs (Invited),” J. Opt. Soc. Am. B 24, 1756–1770 (2007).
    [Crossref]
  11. C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
    [Crossref]
  12. J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
    [Crossref]
  13. C. Turcotte, “Laser a semi-conducteurs utilise comme reference metrologique dans un spectrometre par transformee de Fourier: effet du bruit,” Master’s thesis, Universite Laval, (1999).
  14. N. R. Newbury, I. Coddington, and W. C. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18, 7929–7945 (2010).
    [Crossref] [PubMed]
  15. W. C. Swann, J. J. McFerran, I. Coddington, N. R. Newbury, I. Hartl, M. E. Fermann, P. S. Westbrook, J. W. Nicholson, K. S. Feder, C. Langrock, and M. M. Fejer, “Fiber-laser frequency combs with subhertz relative linewidths,” Opt. Lett. 31, 3046–3048 (2006).
    [Crossref] [PubMed]

2010 (2)

2009 (2)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent linear optical sampling at 15 bits of resolution,” Opt. Lett. 34, 2153–2155 (2009).
[Crossref] [PubMed]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

2008 (3)

2007 (1)

2006 (3)

2004 (1)

1999 (1)

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Araki, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

Bartels, A.

Bernhardt, B.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Coddington, I.

Dekorsky, T.

Deschênes, J.-D.

Dorrer, C.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

Dreyhaupt, A.

Feder, K. S.

Fejer, M. M.

Fermann, M. E.

Först, M.

Genest, J.

Giaccari, P.

Gohle, C.

Guelachvili, G.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Hansch, T. W.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Hartl, I.

Helm, M.

Holzwarth, R

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Holzwarth, R.

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
[Crossref] [PubMed]

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Jacquet, P.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Jacquey, M.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Janke, C.

Kabetani, Y.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

Keilmann, F.

Kilper, D. C.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

Kobayashi, Y.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Kray, S.

Kurz, H.

Langrock, C.

McFerran, J. J.

Newbury, N. R.

Nicholson, J. W.

Ozawa, A.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

PicquÉ, N.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Raybon, G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

Raymer, M. G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

Reichert, J.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Saneyoshi, E.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

Saucier, P.

Spöler, F.

Stuart, H. R.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

Swann, W. C.

Taurand, G.

Thoma, A.

Tremblay, P.

Turcotte, C.

C. Turcotte, “Laser a semi-conducteurs utilise comme reference metrologique dans un spectrometre par transformee de Fourier: effet du bruit,” Master’s thesis, Universite Laval, (1999).

Udem, T.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Udem, Th.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Westbrook, P. S.

Winnerl, S.

Yasui, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

Yokoyama, S.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
[Crossref]

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

Nat. Photonics (1)

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R Holzwarth, G. Guelachvili, T. W. Hansch, and N. PicquÉ, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Opt. Commun. (1)

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hansch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent Multiheterodyne Spectroscopy Using Stabilized Optical Frequency Combs,” Phys. Rev. Lett. 100, 013902 (2008).
[Crossref] [PubMed]

Other (2)

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear Optical Sampling,” IEEE Photon. Technol. Lett.15, 1746–1748 (2003).
[Crossref]

C. Turcotte, “Laser a semi-conducteurs utilise comme reference metrologique dans un spectrometre par transformee de Fourier: effet du bruit,” Master’s thesis, Universite Laval, (1999).

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Figures (4)

Fig. 1
Fig. 1 Experimental setup. Solid lines = optical fiber, dashed lines = electrical cable, WDM = Wavelength division multiplexer, PC = Polarization controller, FBG = Fiber Bragg Grating, D = Balanced detector, ADC = Analog to digital converter.

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Fig. 2
Fig. 2 Corrected IGMs after correction and deconvolution (dispersion compensation). A) Complete measurement set. Each vertical line corresponds to a single IGM. B) Zoom on a single IGM.

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Fig. 3
Fig. 3 Spectrum of the complete corrected measurement (black) and spectrum of the average of the segmented IGMs (red). The features seem on (A) and (B) are absorption lines of the sample. In (C), the slow variation is a single absorption line and each vertical line corresponds to a single of beating mode. Part (D) shows a single transform-limited mode.

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Fig. 4
Fig. 4 Chirped IGM. Note the much larger horizontal scale and the 20 times lower peak value compared to the deconvolved IGM of Fig. 2(B).

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Equations (30)

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r 1 d [ k ] = A 1 ( Δ T r ( k ) ) exp [ j 2 π f c 1 Δ T r ( k ) + j Δ φ ( k ) ] ,
r 2 d [ k ] = A 2 ( Δ T r ( k ) ) exp [ j 2 π f c 2 Δ T r ( k ) + j Δ φ ( k ) ] ,
s md [ k ] = A m ( Δ T r ( k ) ) exp [ j 2 π f m Δ T r ( k ) + j Δ φ ( k ) ] ,
s md [ k ] r 1 d * [ k ] ‖ r 1 d [ k ] ‖ = A m ( Δ T r ( k ) ) exp [ j 2 π ( f m − f c 1 ) Δ T r ( k ) ] .
r grid [ k ] r 1 d * [ k ] r 2 d [ k ] ‖ r 1 d [ k ] ‖ ‖ r 2 d [ k ] ‖ = exp [ j 2 π ( f c 2 − f c 1 ) Δ T r ( k ) ] .
s 1 d [ k ] = P CW 1 P FC 1 , λ 1 exp [ j 2 π f cw 1 T r 1 ( k ) + j φ 1 ( k ) + j φ C W 1 ( k T r 1 ) ] ,
s 2 d [ k ] = P CW 1 P FC 2 , λ 1 exp [ j 2 π f cw 1 T r 2 ( k ) + j φ 2 ( k ) + j φ CW 1 ( k T r 2 ) ] ,
s 3 d [ k ] = P CW 2 P FC 1 , λ 2 exp [ j 2 π f cw 2 T r 1 ( k ) + j φ 1 ( k ) + j φ CW 2 ( k T r 1 ) ] ,
s 4 d [ k ] = P CW 2 P FC 2 , λ 2 exp [ j 2 π f c w 2 T r 2 ( k ) + j φ 2 ( k ) + j φ C W 2 ( k T r 2 ) ] ,
r 1 d [ k ] = s 1 d [ k ] s 2 d * [ k ] ,
r 2 d [ k ] = s 3 d [ k ] s 4 d * [ k ] .
r 1 d [ k ] = P CW 1 P FC 1 , λ 1 P FC 2 , λ 1 × exp [ j 2 π f cw 1 Δ T r ( k ) + j Δ φ ( k ) + j φ CW 1 ( T r 1 ( k ) ) − j φ CW 1 ( T r 2 ( k ) ) ] ,
r 2 d [ k ] = P CW 2 P FC 2 , λ 1 P FC 2 , λ 1 × exp [ j 2 π f cw 2 Δ T r ( k ) + j Δ φ ( k ) + j φ CW 2 ( T r 1 ( k ) ) − j φ CW 2 ( T r 2 ( k ) ) ] .
s 1 ( t ) = δ ( t − T r 1 ) exp ( j φ 1 ) ,
h 1 ( t ) = a 1 ( t ) exp ( j 2 π f c 1 t ) ,
s 1 f ( t ) = s 1 ( t ) * h 1 ( t ) = a 1 ( t − T r 1 ) exp [ j 2 π f c 1 ( t − T r 1 ) + j φ 1 ] .
s 2 f ( t ) = s 2 ( t ) * h 1 ( t ) = a 1 ( t − T r 2 ) exp [ j 2 π f c 1 ( t − T r 2 ) + j φ 2 ] .
s d ( t ) = h d ( t ) * | | s 1 f ( t ) + s 2 f ( t ) | | 2
s d ( t ) = h d ( t ) * ( | | s 1 f | | 2 ( t ) + | | s 2 f ( t ) | | 2 + 2 ℜ { s 1 f ( t ) s 2 * ( t ) } ) ,
s ˜ d ( t ) ≡ h d ( t ) * ( s 1 ( t ) s 2 * ( t ) )
s ˜ d ( t ) = ∫ u = o T d a 1 ( t − T r 1 − u ) a 1 * ( t − T r 2 − u ) h d ( u ) exp [ j 2 π f c 1 Δ T r + j Δ φ ] d u
s ˜ d ( t ) = ∫ u = o T d a 1 ( t − T r 1 − u ) a 1 * ( t − T r 2 − u ) h d ( u ) du exp [ j 2 π f c 1 Δ T r + j Δ φ ] .
s ˜ d ( t ) ≈ h d ( t − T r 1 ) ∫ u = − ∞ ∞ a 1 ( t − T r 1 − u ) a 1 * ( t − T r 2 − u ) d u exp [ j 2 π f c 1 Δ T r + j Δ φ ]
A 1 ( τ ) ≡ ∫ u = − ∞ ∞ a 1 ( u ) a 1 * ( u + τ ) d u ,
s ˜ d ( t ) ≈ h d ( t − T r 1 ) A 1 ( Δ T r ) exp [ j 2 π f c 1 Δ T r + j Δ φ ]
r 1 ( t ) = ∑ k h d ( t − T r 1 ( k ) ) A 1 ( Δ T r ( k ) ) exp [ j 2 π f c 1 Δ T r ( k ) + j Δ φ ( k ) ]
r 1 d [ k ] = h d ( 0 ) A 1 ( Δ T r ( k ) ) exp [ j 2 π f c 1 Δ T r ( k ) + j Δ φ ( k ) ]
r 1 d [ k ] = A 1 ( Δ T r ( k ) ) exp   [ j 2 π f c 1 Δ T r ( k ) + j Δ φ ( k ) ]
r 2 d [ k ] = A 2 ( Δ T r ( k ) ) exp [ j 2 π f c 2 Δ T r ( k ) + j Δ φ ( k ) ]
s md [ k ] = A m ( Δ T r ( k ) ) exp [ j 2 π f m Δ T r ( k ) + j Δ φ ( k ) ]

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