Abstract

A referenced passive spectroscopy scheme using infrared frequency combs is presented. We perform a noise analysis and compare the results with a classical Fourier transform spectrometer. Experimental results are shown and great agreement with theory is obtained.

© 2012 OSA

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References

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  1. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. 100, 13902 (2008).
  2. J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
    [CrossRef]
  3. J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358–23370 (2010).
    [CrossRef] [PubMed]
  4. F. R. Giorgetta, I. Coddington, E. Baumann, W. C. Swann, and N. R. Newbury, “Dual frequency comb sampling of a quasi-thermal incoherent light source,” in Conference on Lasers and Electro-Optics (2010).
  5. I. R. Coddington, W. C. Swann, and N. R. Newbury, “Frequency comb spectroscopy,” in Fourier Transform Spectroscopy (2009).
  6. 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(6), 4347–4365 (2008).
    [CrossRef] [PubMed]
  7. D. Derickson, “Noise sources in optical measurement” in Fiber Optic Test and Measurement (Prentice Hall PTR, 1998), pp. 597–613.
  8. J. W. Brault, “Fourier transform spectrometry,” in Saas-Fee Advanced Course 15: High Resolution in Astronomy (1985), Vol. 1, pp. 1–61.
  9. K. Petermann, Laser Diode Modulation and Noise (Springer, 1991).

2010 (1)

2009 (1)

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
[CrossRef]

2008 (2)

Coddington, I.

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

Deschênes, J.-D.

Genest, J.

Giaccari, P.

Giaccarri, P.

Guelachvili, G.

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
[CrossRef]

Mandon, J.

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
[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).

Picqué, N.

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
[CrossRef]

Saucier, P.

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).

Tremblay, P.

Nat. Photonics (1)

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3(2), 99–102 (2009).
[CrossRef]

Opt. Express (2)

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).

Other (5)

D. Derickson, “Noise sources in optical measurement” in Fiber Optic Test and Measurement (Prentice Hall PTR, 1998), pp. 597–613.

J. W. Brault, “Fourier transform spectrometry,” in Saas-Fee Advanced Course 15: High Resolution in Astronomy (1985), Vol. 1, pp. 1–61.

K. Petermann, Laser Diode Modulation and Noise (Springer, 1991).

F. R. Giorgetta, I. Coddington, E. Baumann, W. C. Swann, and N. R. Newbury, “Dual frequency comb sampling of a quasi-thermal incoherent light source,” in Conference on Lasers and Electro-Optics (2010).

I. R. Coddington, W. C. Swann, and N. R. Newbury, “Frequency comb spectroscopy,” in Fourier Transform Spectroscopy (2009).

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Figures (6)

Fig. 1
Fig. 1

Dual comb passive spectroscopy setup.

Fig. 2
Fig. 2

Autocorrelation of the laser source.

Fig. 3
Fig. 3

Zoom on the laser line.

Fig. 4
Fig. 4

Autocorrelation of the HCN filtered source. The clipped peak has a unitary amplitude

Fig. 5
Fig. 5

Squared SNR of the autocorrelation estimate as a function of the number of averaged traces.

Fig. 6
Fig. 6

Transmittance of the HCN filtered source. The red dotted lines represent the reference HCN line frequencies.

Tables (2)

Tables Icon

Table 1 SNR for FTS and Optical Sampling Spectroscopy

Tables Icon

Table 2 - Reference and Measured Frequencies of HCN Absorption Lines

Equations (21)

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M 1 = E 1 ( t 1 ) exp ( j θ 1 ) s * ( t 1 ) d t 1 M 2 = E 2 ( t 2 + τ ) exp ( j 2 π f c τ ) exp ( j θ 2 ) s * ( t 2 ) d t 2 ,
M 1 * M 2 = E 1 * ( t 1 ) exp ( j θ 1 ) s ( t 1 ) d t 1 E 2 ( t 2 + τ ) exp ( j 2 π f c τ ) exp ( j θ 2 ) s * ( t 2 ) d t 2 = exp ( j Δ θ ) exp ( j 2 π f c τ ) E 1 * ( t 1 ) E 2 ( t 2 + τ ) s * ( t 2 ) s ( t 1 ) d t 1 d t 2 ,
E { M 1 * M 2 } = E { exp ( j Δ θ ) } exp ( j 2 π f c τ ) × E 1 * ( t 1 ) E 2 ( t 1 + α + τ ) E { s * ( t 1 + α ) s ( t 1 ) } d t 1 d α = E { exp ( j Δ θ ) } exp ( j 2 π f c τ ) R s s ( α ) E 1 * ( t 1 ) E 2 ( t 1 + α + τ ) d t 1 d α = E { exp ( j Δ θ ) } exp ( j 2 π f c τ ) R s s ( α ) R 12 * ( α + τ ) d α ,
T = 2 K N / f r .
S N R t = S N R single T f r 2 N ,
S N R f = S N R single N T f r 2 .
S N R f ( max ) = T B W 2 N ,
B = P L p e a k P S B W L = P L P S B W L f r ,
N s h = E p h E s i g n a l = E p h P s i g n a l T ,
N s h S = E p h P S B W P D
N s h L = E p h P L f r .
N t h = N E P B W P D ,
P S > E p h B W L
P L > E p h B W L f r B W P D
P L P S > N E P 2 B W L f r B W P D .
s ( t ) = cos ( 2 π f t + ϕ ( t ) ) ,
S = cos ( θ ) cos ( θ + ϕ ( τ ) + 2 π f τ ) .
R s s ( τ ) = 1 2 e | τ | σ 0 2 2 cos ( 2 π f τ ) .
E { S 2 } = 0 2 π cos 2 ( θ ) cos 2 ( θ + ϕ + 2 π f τ ) 1 2 π 1 2 π | τ | σ 0 2 e ϕ 2 2 | τ | σ 0 2 d θ d ϕ = 1 4 [ 1 + 1 2 e 2 | τ | σ 0 2 cos ( 4 π f τ ) ] .
σ S 2 = E { S 2 } R S S 2 = 1 4 [ 1 + 1 2 e 2 | τ | σ 0 2 cos ( 4 π f τ ) e | τ | σ 0 2 cos 2 ( 2 π f τ ) ] = 1 4 [ 1 1 2 e | τ | σ 0 2 + 1 2 cos ( 4 π f τ ) ( e 2 | τ | σ 0 2 e | τ | σ 0 2 ) ] .
σ ¯ S 2 = 1 4 [ 1 1 2 e | τ | σ 0 2 ] .

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