Abstract

We report on the spectral intensity interferometer (SII) which is a frequency-domain variant of the fourth-order interferometry. In the SII, the power spectrum of the intensity is acquired for light fields of an interferometer. It produces a fringed spectral interferogram which can be acquired by means of an electric spectrum analyzer in keeping the relative time delay constant during the acquisition. Through both theoretical and experimental investigations, we have found that the SII interferogram provides the intensity correlation information without concern of field-sensitive disturbances which are vulnerable to minute variations of the optical paths. As an application example, a precision time-of-flight measurement was demonstrated by using a fiber-optic SII with an amplified spontaneous emission (ASE) light source. A large delay of 4.1-km long fiber was successfully analyzed from the fringe period. Its wavelength-dependent group delay or the group velocity dispersion (GVD) was also measured from the phase shift of the cosine fringe with a sub-picosecond delay precision.

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References

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  2. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. P. Hernday, “Dispersion measurements,” in Fiber Optic Test and Measurement, D. Derickson ed. (Prentice Hall PTR, 1998), pp.475–518.
  17. TIA Standard TIA-455–175-B, Meausrement Methods and Test Procedures – Chromatic Dispersion, 2003.
  18. S. Moon and D. Y. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett.21(17), 1262–1264 (2009).
    [CrossRef]

2012 (1)

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

2009 (2)

S. Moon and D. Y. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett.21(17), 1262–1264 (2009).
[CrossRef]

A. Beling and J. C. Campbell, “InP-based high-speed photodetectors,” J. Lightwave Technol.27(3), 343–355 (2009).
[CrossRef]

2006 (1)

2003 (4)

1996 (1)

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

1958 (1)

W. P. Alford and A. Gold, “Laboratory measurement of the velocity of light,” Am. J. Phys.26(7), 481–484 (1958).
[CrossRef]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Alford, W. P.

W. P. Alford and A. Gold, “Laboratory measurement of the velocity of light,” Am. J. Phys.26(7), 481–484 (1958).
[CrossRef]

Beling, A.

Bouma, B.

Bouma, B. E.

Campbell, J. C.

Cense, B.

Choma, M.

de Boer, J.

de Boer, J. F.

Diddams, S.

Diels, J.-C.

Fercher, A.

Fice, M. J.

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

Gold, A.

W. P. Alford and A. Gold, “Laboratory measurement of the velocity of light,” Am. J. Phys.26(7), 481–484 (1958).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Hitzenberger, C.

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Iftimia, N.

Izatt, J.

Kim, D. Y.

S. Moon and D. Y. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett.21(17), 1262–1264 (2009).
[CrossRef]

J. Y. Lee and D. Y. Kim, “Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry,” Opt. Express14(24), 11608–11615 (2006).
[CrossRef] [PubMed]

Lee, J. Y.

Leitgeb, R.

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Moon, S.

S. Moon and D. Y. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett.21(17), 1262–1264 (2009).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Park, B. H.

Pierce, M. C.

Renaud, C. C.

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

Rouvalis, E.

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

Sarunic, M.

Seeds, A. J.

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

Tearney, G.

Tearney, G. J.

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Yang, C.

Yun, S.

Am. J. Phys. (1)

W. P. Alford and A. Gold, “Laboratory measurement of the velocity of light,” Am. J. Phys.26(7), 481–484 (1958).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Moon and D. Y. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett.21(17), 1262–1264 (2009).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

E. Rouvalis, M. J. Fice, C. C. Renaud, and A. J. Seeds, “Millimeter-wave optoelectronic mixers based on uni-traveling carrier photodiodes,” IEEE Trans. Microw. Theory Tech.60(3), 686–691 (2012).
[CrossRef]

J. Lightwave Technol. (1)

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

Nature (1)

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Other (6)

L. Sarger and J. Oberlé, “How to measure the characteristics of laser pulses,” in Femtosecond Laser Pulses, Claude Rullière ed. (Springer, 1998), pp. 177–202.

P. Griffiths and J. A. de Haseth, “Chapter 2. Theoretical Background,” in Fourier Transform Infrared Spectrometry, 2nd Ed. (John Wiley & Sons, 2007), pp. 19–56.

Agilent Technologies Inc, “Spectrum Analysis Basics,” http://www.home.agilent.com/upload/cmc_upload/All/5952-0292EN.pdf .

P. Hernday, “Dispersion measurements,” in Fiber Optic Test and Measurement, D. Derickson ed. (Prentice Hall PTR, 1998), pp.475–518.

TIA Standard TIA-455–175-B, Meausrement Methods and Test Procedures – Chromatic Dispersion, 2003.

P. Hariharan, Optical Interferometry, 2nd Ed. (Academic Press, 2003).

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Figures (6)

Fig. 1
Fig. 1

Schematic plots on the spectral distribution of the signal components in ω and ω′.

Fig. 2
Fig. 2

Schematic of the experimental setup for Mach-Zehnder SII, constructed by fiber-optic components.

Fig. 3
Fig. 3

Fourth-order spectrum measured at fc = 2 GHz and a time delay of τ≈20 μs, made by 4.1-km long fiber.

Fig. 4
Fig. 4

Inverse Fourier transform of the measured data shown in Fig. 3.

Fig. 5
Fig. 5

FFT-filtered spectral interferogram (black solid line) and its sine function fit (orange dotted line)

Fig. 6
Fig. 6

Measured relative group delays (square dots) and the 2nd-order polynomial fit (red line) for the 4.1-km long fiber.

Tables (1)

Tables Icon

Table 1 Summary of the GVD measurement result

Equations (24)

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G(τ)= C τ { a(t) , b(t) } + a * (t)b (tτ) dt
E ˜ (ω) F ω { E (t) }= + E(t) e iωt dt
S (2) (ω) | E ˜ (ω) | 2 = | F ω { E (t) } | 2 .
S (4) (ω) | I ˜ (ω) | 2 = | F ω { | E(t) | 2 } | 2
H(τ) + | f 1 (t)+ f 2 (tτ) + λg(t) | 2 dt ,
H(τ)= + ( f 1 * (t) f 1 (t)+ f 1 * (t) f 2 (tτ)+λ f 1 * (t)g(t)+ f 1 (t) f 2 * (tτ) + f 2 * (tτ) f 2 (tτ)+λ f 2 * (tτ)g(t)+λ f 1 (t) g * (t) +λ f 2 (tτ) g * (t)+ λ 2 g * (t)g(t) )dt
S(ω) | F ω { f 1 (t)+ f 2 (tτ) + λg(t) } | 2 = | f ˜ 1 (ω)+ f ˜ 2 (ω) e iωτ + λ g ˜ (ω) | 2
S(ω)= f ˜ 1 * f ˜ 1 + f ˜ 1 * f ˜ 2 e iωτ + λ f ˜ 1 * g ˜ + f ˜ 1 f ˜ 2 * e +iωτ + f ˜ 2 * f ˜ 2 + λ f ˜ 2 * g ˜ e +iωτ + λ f ˜ 1 g ˜ * + λ f ˜ 2 g ˜ * e iωτ + λ 2 g ˜ * g ˜
H (t)= X 11 (t)+ X 12 (t)δ(tτ)+λ Y 1 (t)+ X 12 * (t)δ(t+τ) + X 22 (t)+λ Y 2 * (t)δ(t+τ)+λ Y 1 * (t)+λ Y 2 * (t)δ(tτ) + λ 2 g * (t)g(t)
X nm (t) f n * (t) f n (t)= C t { f n (t) , f m (t) },
Y n (t) f n * (t)g(t)= C t { f n (t) , g(t) }
a(ζ)b(ζ) + a(ν)b(ζν)dν .
H (2) (τ)= | E 1 (t)+ E 2 (tτ) | 2 dt = I 1 dt + I 2 dt +γ X 12 (τ)+γ X 12 * (τ)
S (2) (ω)= | E ˜ 1 | 2 + | E ˜ 2 | 2 +γ( E ˜ 1 * E ˜ 2 e iωτ + E ˜ 1 E ˜ 2 * e +iωτ )
H (4) (τ)= | E 1 (t) + E 2 (tτ) | 4 dt = | I 1 (t) + I 2 (tτ)+γ( E 1 * (t) E 2 (tτ)+ E 1 (t) E 2 * (tτ) ) | 2 dt
g(t)= E 1 * (t) E 2 (tτ)+ E 1 (t) E 2 * (tτ)
S (4) (ω)= I ˜ 1 * I ˜ 1 + I ˜ 1 * I ˜ 2 e iωτ + γ I ˜ 1 * g ˜ + I ˜ 1 I ˜ 2 * e +iωτ + I ˜ 2 * I ˜ 2 + γ I ˜ 2 * g ˜ e +iωτ + γ I ˜ 1 g ˜ * + γ I ˜ 2 g ˜ * e iωτ + γ 2 g ˜ * g ˜
E(t)= E 0 (t) e i( ω 0 t+ϕ(t) ) =A(t) e i ω 0 t
g ˜ (ω)=[ A ˜ 1 * (ω)( A ˜ 2 (ω) e iωτ ) ]δ(ω+ ω 0 ) +[ A ˜ 1 (ω)( A ˜ 2 * (ω) e +iωτ ) ]δ(ω ω 0 )
S (4) ( ω )= I ˜ 1 * I ˜ 1 + I ˜ 2 * I ˜ 2 + I ˜ 1 * I ˜ 2 e i ω τ + I ˜ 1 I ˜ 2 * e +i ω τ
g ˜ (ω)0   or    A ˜ 1 * (ω)( A ˜ 2 (ω) e iωτ )0   as    τΔω±
I ˜ 1 * ( ω ) I ˜ 2 ( ω )= I 0 2
S (4) ( ω )= S 0 +2 I 0 2 cos ω τ
Δτ(λ)= Δϕ(λ) 2π f c

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