Abstract

We present a simple fiber-based single-arm spectral interferometer to measure directly the second-order dispersion parameter of short lengths of fiber (<50 cm). The standard deviation of the measured dispersion on a 39.5-cm-long SMF28 fiber is 1×10-4 ps/nm, corresponding to 1% relative error, without employing any curve fitting. Our technique measures the second-order dispersion by examining the envelope of the interference pattern produced by three reflections: two from the facets of the test fiber and one from a mirror placed away from the fiber facet at a distance that introduces the same group delay as the test fiber at the measured wavelength. The operational constraints on system parameters, such as required bandwidth, wavelength resolution, and fiber length, are discussed in detail. Experimental verification of this technique is carried out via comparison of measurements of single mode fiber (SMF28) with published data and via comparison of measurements of a dispersion compensating fiber with those taken using conventional techniques. Moreover, we used this new technique to measure the dispersion coefficient of a 45-cm-long twin-hole fiber over a 70 nm bandwidth. It is the first time dispersion measurement on this specialty fiber is reported.

© 2007 Optical Society of America

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2006 (3)

2005 (2)

2004 (1)

2003 (5)

2002 (3)

2001 (1)

P. Blazkiewicz, W. Xu, D. Wong, S. Fleming, and T. Ryan, "Modification of thermal poling evolution using novel twin-hole fibers," IEEE J. Lightwave Technol. 19, 1149-1154 (2001).
[CrossRef]

2000 (2)

J. Gehler and W. Spahn, "Dispersion measurement of arrayed-waveguide grating by Fourier transform spectroscopy," Electron. Lett. 36, 338-340 (2000).
[CrossRef]

C. D. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, "Spectral resolution and sampling in Fourier transform spectral interferometry," J. Opt. Soc. Am. B 17, 1795-1802 (2000).
[CrossRef]

1999 (1)

J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35, 510-522 (1999).
[CrossRef]

1998 (1)

G. Hausler and M. W. Lindner, "Coherence radar and spectral radar - new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1989 (1)

P. Merrit, R. P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," IEEE J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

1985 (1)

L. G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," IEEE J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

1984 (1)

J. H. Wiesenfeld and J. Stone, "Measurement of dispersion using short lengths of an optical fiber and picosecond pulses from semiconductor film lasers," IEEE J. Lightwave Technol. 2, 464-468 (1984).
[CrossRef]

1982 (1)

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the measurement of chromatic dispersion in optical fibers using LEDs," IEEE Trans. Microwave Theory Tech. 82, 1497-1503 (1982).
[CrossRef]

Aksas, R.

L. Cherbi, M. Mehenni, and R. Aksas, "Experimental investigation of the modulation phase-shift method for the measure of the chromatic dispersion in a single-mode fiber coiled on a cover spool," Microw. Opt. Technol. Lett. 48, 174-178 (2006).
[CrossRef]

Bajraszewski, T.

R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, "Ultra high resolution Fourier domain optical coherence tomography," Opt. Express 12, 2156-2165 (2004).
[CrossRef] [PubMed]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002).
[CrossRef] [PubMed]

Belabas, N.

Berlemont, D.

Blazkiewicz, P.

P. Blazkiewicz, W. Xu, D. Wong, S. Fleming, and T. Ryan, "Modification of thermal poling evolution using novel twin-hole fibers," IEEE J. Lightwave Technol. 19, 1149-1154 (2001).
[CrossRef]

Chang, W.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Chemals, D. S.

J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35, 510-522 (1999).
[CrossRef]

Cherbi, L.

L. Cherbi, M. Mehenni, and R. Aksas, "Experimental investigation of the modulation phase-shift method for the measure of the chromatic dispersion in a single-mode fiber coiled on a cover spool," Microw. Opt. Technol. Lett. 48, 174-178 (2006).
[CrossRef]

Ciprian, D.

Claesson, Ã.

Cohen, L. G.

L. G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," IEEE J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

Costa, B.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the measurement of chromatic dispersion in optical fibers using LEDs," IEEE Trans. Microwave Theory Tech. 82, 1497-1503 (1982).
[CrossRef]

Debarge, G.

Dong, L.

Dorrer, C. D.

Douay, M.

Drexler, W.

Elzaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fercher, A.

Fercher, A. F.

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fleming, S.

P. Blazkiewicz, W. Xu, D. Wong, S. Fleming, and T. Ryan, "Modification of thermal poling evolution using novel twin-hole fibers," IEEE J. Lightwave Technol. 19, 1149-1154 (2001).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Fokine, M.

Fried, N. M.

U. Sharma, N. M. Fried, J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Fugimoto, J. G.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Gehler, J.

J. Gehler and W. Spahn, "Dispersion measurement of arrayed-waveguide grating by Fourier transform spectroscopy," Electron. Lett. 36, 338-340 (2000).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hasch, T.

J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35, 510-522 (1999).
[CrossRef]

Hausler, G.

G. Hausler and M. W. Lindner, "Coherence radar and spectral radar - new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

Hee, M. R.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hickernell, R. K.

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Hlubina, P.

Horiguchi, M.

Huang, D.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

Jackson, D.A.

P. Merrit, R. P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," IEEE J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

Jaouën, Y.

Joffre, M.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Kane, D. J.

Kane, Daniel J.

Kang, J. U.

U. Sharma, N. M. Fried, J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Kazansky, P. G.

Kazumasa, T.

Kerrinckx, E.

Kim, D. Y.

Kjellberg, L.

Kowalczyk, A.

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002).
[CrossRef] [PubMed]

Krummenacher, L.

Le, T.

Lee, J. Y.

Leitgeb, R.

Lepers, C.

Likforman, J. P.

Lin, C. P.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Lindner, M. W.

G. Hausler and M. W. Lindner, "Coherence radar and spectral radar - new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

Margulis, W.

Marquezini, M. V

J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35, 510-522 (1999).
[CrossRef]

Martynkien, T.

Mazzoni, D.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the measurement of chromatic dispersion in optical fibers using LEDs," IEEE Trans. Microwave Theory Tech. 82, 1497-1503 (1982).
[CrossRef]

Mehenni, M.

L. Cherbi, M. Mehenni, and R. Aksas, "Experimental investigation of the modulation phase-shift method for the measure of the chromatic dispersion in a single-mode fiber coiled on a cover spool," Microw. Opt. Technol. Lett. 48, 174-178 (2006).
[CrossRef]

Melin, G.

Merrit, P.

P. Merrit, R. P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," IEEE J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

Nilsson, L. E.

Obaton, A.-F.

Palavicini, C.

Peterson, K. A.

Peterson, Kirsten A.

Puleo, M.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the measurement of chromatic dispersion in optical fibers using LEDs," IEEE Trans. Microwave Theory Tech. 82, 1497-1503 (1982).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Quiquempois, Y.

Russell, P. S. J.

Ryan, T.

P. Blazkiewicz, W. Xu, D. Wong, S. Fleming, and T. Ryan, "Modification of thermal poling evolution using novel twin-hole fibers," IEEE J. Lightwave Technol. 19, 1149-1154 (2001).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Sharma, U.

U. Sharma, N. M. Fried, J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Shimizu, M.

Spahn, W.

J. Gehler and W. Spahn, "Dispersion measurement of arrayed-waveguide grating by Fourier transform spectroscopy," Electron. Lett. 36, 338-340 (2000).
[CrossRef]

Stingl, A.

Stinson, W. G.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Stone, J.

J. H. Wiesenfeld and J. Stone, "Measurement of dispersion using short lengths of an optical fiber and picosecond pulses from semiconductor film lasers," IEEE J. Lightwave Technol. 2, 464-468 (1984).
[CrossRef]

Swang, E. A.

D. Huang, E. A. Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fugimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Szpulak, M.

Tatam, R. P.

P. Merrit, R. P. Tatam, and D.A. Jackson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," IEEE J. Lightwave Technol. 7, 703-716 (1989).
[CrossRef]

Tignon, J.

J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35, 510-522 (1999).
[CrossRef]

Unterhuber, A.

Urbanczyk, W.

Vakhtin, A. B.

Vakhtin, Andrei B.

Vezzoni, E.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the measurement of chromatic dispersion in optical fibers using LEDs," IEEE Trans. Microwave Theory Tech. 82, 1497-1503 (1982).
[CrossRef]

Wax, A.

Wiesenfeld, J. H.

J. H. Wiesenfeld and J. Stone, "Measurement of dispersion using short lengths of an optical fiber and picosecond pulses from semiconductor film lasers," IEEE J. Lightwave Technol. 2, 464-468 (1984).
[CrossRef]

Wojtkowski, M.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002).
[CrossRef] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002).
[CrossRef]

Wong, D.

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Figures (6)

Fig. 1.
Fig. 1.

(a). General dual-arm balanced Michelson interferometer. The spectral interferogram is produced by two reflected waves U1 and U2 . (b) Single-arm interferometer where the spectral interferogram is produced by three reflected waves; Uo , U1 and U2 .

Fig. 2.
Fig. 2.

Simulated spectral interferogram produced by the setup in Fig. 1(b) for a 30-cm-long SMF28 as the test fiber, with α=γ=1. The parameters used for the SMF28 fiber are given in [27]. The thick green line represents the function calculated by Eq. (3), which is a close approximation of the upper envelope. Bmin denotes the minimum required bandwidth, and Bsource is the source bandwidth, which determines the extent of the interferogram. λ0 is the balanced wavelength. λ1 and λ2 are wavelengths corresponding to two adjacent troughs on one side of λ0.

Fig. 3.
Fig. 3.

(a). The dependence of wavelength resolution on the dispersion-length product (DLf). (b) The dependence of the minimum required bandwidth (Bmin) and the measurable bandwidth (Bmea), on the DLf product. Note we assume the values λo=1550nm and δLair=5µm and Bsource=130nm for these figures.

Fig. 4.
Fig. 4.

(a). Experimentally obtained spectral envelope for a 39.5cm SMF-28 fiber. (b) Measured dispersion compared to published dispersion [27] for the same fiber.

Fig. 5.
Fig. 5.

Comparison of dispersion values measured by two methods. The red points are obtained on a 100-m-long DCF using the Agilent 83427A Chromatic Dispersion Measurement System. The black points are obtained on a 15.5cm DCF using the SAI.

Fig. 6.
Fig. 6.

Dispersion measured using a 45-cm long Twin Hole Fiber

Equations (24)

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U 1 = α U 0 e j 2 β L f
U 2 = γ U 0 e j 2 β L f j 2 k 0 L air
I o = U 0 + U 1 + U 2 2 = U 0 2 1 + α e i 2 β L f + γ e i 2 β L f i 2 k o L a 2
= U 0 2 { 1 + α 2 + γ 2 2 γ + 4 γ cos 2 ( β L f + k o L a ) + 2 α ( 1 γ ) cos ( 2 β L f )
+ 4 α γ cos ( β L f + k o L a ) cos ( β L f k o L a ) }
I upper _ env U o 2 ( 1 + α 2 + γ 2 + 2 α ( γ 1 ) + 2 γ + 4 α cos ( ϕ envelope ) )
ϕ envelope ( λ ) = 2 π { 1 λ [ ( n eff ( λ o ) λ o d n eff d λ λ o ) L f L air ] + L f d n eff d λ λ o
+ L f ( λ λ o ) 2 2 ! λ d 2 n eff d λ 2 λ o + L f ( λ λ o ) 3 3 ! λ d 3 n eff d λ 3 λ o + }
Δ ϕ envelope = ϕ envelope ( λ 2 ) ϕ envelope ( λ 1 )
= 2 π ( [ ( λ 2 λ 0 ) 2 2 ! λ 2 ( λ 1 λ 0 ) 2 2 ! λ 1 ] d 2 n eff d λ 2 λ 0 + [ ( λ 2 λ 0 ) 3 3 ! λ 2 ( λ 1 λ 0 ) 3 3 ! λ 1 ] d 3 n eff d λ 3 λ 0 ) L f
D ( λ o ) = λ o c d 2 n eff d λ 2 λ o
L air = ( n eff ( λ o ) λ o d n eff d λ λ o ) L f
d L air d λ λ o = ( λ o d 2 n eff d λ 2 λ o ) L f = cD ( λ o ) L f
δ λ o = δ L air c L f D
ϕ envelope ( λ 1 ) ϕ envelope ( λ 0 ) = 2 π ( λ 1 λ 0 ) 2 2 ! λ 1 d 2 n eff d λ 2 λ 0 L f π
λ 1 λ 0 λ 0 cD L f
( λ 2 λ 0 ) 2 ( λ 1 λ 0 ) 2 λ o 2 cD L f
( λ 2 λ 0 ) 2 = [ ( λ 2 λ 1 ) + ( λ 1 λ 0 ) ] 2 2 λ o 2 cD L f
B min = 2 2 λ 0 cD L f
B mea = B source B min B source 2 2 λ 0 cD L f
B mea = B source 2 ( λ 1 λ 0 ) B source 2 λ 0 cD L f
B min B source
L f 8 λ o 2 cD B source 2
L f λ o 2 4 n eff Δ λ

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