Abstract

The correction of setup and laser instabilities in a single-comb interferometric measurement using optical sampling by laser-cavity tuning is investigated. A two-reference solution that allows full correction of the interferogram is presented. The technique is compared to a slightly simpler one-reference correction. For the one-reference case, all the subtleties involved in this partial correction and the dependence between the achievable measurement accuracy and the setup parameters are highlighted. The parameters considered are the comb bandwidth, the laser-frequency noise, the required spectral resolution, the cavity scan speed, and the length of the delay line. For both referencing approaches, experimental results using a fiber delay line of 10 km and a 100 MHz mode-locked laser with its repetition rate swept at 500 Hz are shown.

© 2013 Optical Society of America

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References

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    [CrossRef]
  3. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
    [CrossRef]
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  7. C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.
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2011 (1)

2010 (3)

2008 (2)

2006 (1)

2005 (1)

N. Newbury and B. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[CrossRef]

2004 (1)

Baney, D. M.

D. M. Baney and W. V. Sorin, “High resolution optical frequency analysis,” in Fiber Optic Test and Measurement, D. Derickson, ed. (Prentice-Hall, 1998), pp. 169–219.

Bartels, A.

Coddington, I.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
[CrossRef]

Dekorsky, T.

Deschênes, J.-D.

Deschênes, J-D.

Dreyhaupt, A.

Fermann, M. E.

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

Genest, J.

Giaccari, P.

Giaccarri, P.

Gohle, C.

Hartl, I.

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

Helm, M.

Hochrein, T.

Holzwarth, R.

Janke, C.

Keilmann, F.

Koch, M.

Krumbholz, N.

Mei, M.

Mohr, C.

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

Newbury, N.

N. Newbury and B. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[CrossRef]

Newbury, N. R.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
[CrossRef]

Romann, A.

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

Ruehl, A.

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

Saucier, P.

Sorin, W. V.

D. M. Baney and W. V. Sorin, “High resolution optical frequency analysis,” in Fiber Optic Test and Measurement, D. Derickson, ed. (Prentice-Hall, 1998), pp. 169–219.

Swann, W. C.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
[CrossRef]

Taurand, G.

Thoma, A.

Tremblay, P.

Washburn, B.

N. Newbury and B. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[CrossRef]

Wilk, R.

Winnerl, S.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

N. Newbury and B. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[CrossRef]

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

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. (1)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
[CrossRef]

Other (2)

C. Mohr, A. Romann, A. Ruehl, I. Hartl, and M. E. Fermann, “Fourier transform spectrometry using a single cavity length modulated mode-locked fiber laser,” in Fiber Laser Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FWA2.

D. M. Baney and W. V. Sorin, “High resolution optical frequency analysis,” in Fiber Optic Test and Measurement, D. Derickson, ed. (Prentice-Hall, 1998), pp. 169–219.

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup. AOM, acousto-optic modulator; PBS, polarization beam splitter; PC, polarization controller; C, circulator; FBG, fiber Bragg grating; Det, detector.

Fig. 2.
Fig. 2.

(a) Corrected interferogram. The IGM is single sided since the HCN is placed in one arm of the interferometer. The IGM nonsymmetrical shape comes from the impulse response of the HCN cell and the cross correlation of the impulse response of both arms of the MZ (mostly from the delay line impulse response, which includes a group delay span of 40 ps). (b) Single IGM spectrum and the spectrum of 50 corrected IGMs averaged. Spectra of the two corrected references are also plotted. The zoomed parts on both references allow one to better analyze the ILS, which is the result of the 200 ps measurement window since it is fully corrected by the two-reference technique. (c) A zoom is made on the HCN lines; the dotted vertical lines represent the HCN line centers taken from the NIST SRM 2519a certificate of analysis.

Fig. 3.
Fig. 3.

(a) Sampling jitter (ΔT) extrapolated for different pulse buffer lengths. (b) Residual sampling jitter [Eq. (15)] extrapolated for different pulse buffer lengths. One line represents the residual sampling jitter at 6.25 THz (50 nm) from the reference and the other one for 1.25 THz (10 nm). The horizontal line represents the residual jitter of a hundredth of the optical period.

Fig. 4.
Fig. 4.

(a) Corrected spectra of both referencing signals are shown for different IGM speeds (100, 20, and 10 Hz). The arrows point to the frequency-noise PSD shape. (b) The one-reference correction was done with the reference at 1547.976 nm. (c) Zoom on the ILS at 1567.329 nm; it gives a closer look of the ILS resulting from the residual sampling jitter [where (f1f2) is approximately 10 nm].

Fig. 5.
Fig. 5.

(a) Trace in the middle shows the ILS at 1567.329 nm of a 20 Hz scan when the right phase ramp is removed (φCEO) to cancel φAOM and φCEOpzt. The two other ILS traces show the consequences of overevaluating and underevaluating the right phase ramp of 100 kHz. (b) Zoom on the ILSs.

Fig. 6.
Fig. 6.

First spectrum is from the fully (two-reference) corrected IGM. The second spectrum is obtained using the one-reference correction technique with the reference at 1547.976 nm. The third spectrum is obtained using the one-reference correction with the reference at 1567.329 nm. Spectra are zoomed on the HCN lines. Note that, with the one-reference approach, the spectrum shape is worse when it gets further from the reference.

Equations (15)

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MPD=N(fmin1fmax1),
N=L·fr·nc.
E1(t)=a1(tT1)exp[j2πfc(tT1)+jφ1]E2(t)=a2(tT2)exp[j2πfc(tT2)+jφ2],
sm[k]=Am(ΔT(k))exp[j2πfcΔT(k)+jΔφ(k)].
r1[k]=A1(ΔT(k))exp[j2πf1ΔT(k)+jΔφ(k)]r2[k]=A2(ΔT(k))exp[j2πf2ΔT(k)+jΔφ(k)],
ϕ1(k)=2πf1ΔT(k)+Δφ(k)ϕ2(k)=2πf2ΔT(k)+Δφ(k).
smϕ[k]=sm[k]exp[iϕ1(k)]=Am(ΔT(k))exp[j2π(fmf1)ΔT(k)].
ϕ2(k)ϕ1(k)=2π(f2f1)ΔT(k),
sm[k]=Am(ΔT(k))exp[j2πfcΔT(k)+jΔφ(k)].
Δφ(k)=φAOM(k)+φCEOpzt(k)+φn(k),
sm[k]=Am(ΔT(k))exp[j2πfmΔT(k)+jφn(k)]
ϕ1(k)=2πf1ΔT(k)+φn(k)ϕ2(k)=2πf2ΔT(k)+φn(k).
ϕ1(k)=2πf1(ΔT(k)+φn(k)2πf1)=2πf1τ(k),
ϕ2(k)=2πf2τ(k)+φn(k)(f1f2f1).
φn(k)2π(f1f2f2f1).

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