Abstract

Chromatic dispersion of a 37 cm long, solid-core photonic bandgap (PBG) fiber was studied in the wavelength range of 740–840 nm with spectral interferometry employing a Mach–Zehnder interferometer and a high resolution spectrometer. The interferometer was illuminated by a Ti:sapphire laser providing 20 fs pulses. A comparative study has been carried out to find the most accurate spectral phase retrieval method that is suitable for measuring higher order chromatic dispersion. The stationary phase point, the minima–maxima, the cosine function fit, the Fourier transform, and the windowed Fourier transform methods were tested. It was shown that out of these five techniques, the Fourier-transform method provided the dispersion coefficients with the highest accuracy, and it could also detect rapid phase changes in the vicinity of leaking mode frequencies within the transmission band of the PBG fiber.

© 2014 Optical Society of America

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2012 (1)

P. Hlubina, M. Kadulová, and D. Ciprian, “Spectral interferometry-based chromatic dispersion measurement of fibre including the zero-dispersion wavelength,” J. Eur. Opt. Soc. Rapid Pub. 7, 12017-1–12017-5 (2012).
[CrossRef]

2011 (2)

2010 (3)

K. Mecseki and A. P. Kovács, “Monitoring of residual higher-order dispersion of pulse compression by spectral interferometry,” AIP Conf. Proc. 1228, 251–256 (2010).
[CrossRef]

N. K. Berger, B. Levit, and B. Fischer, “Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses,” Opt. Commun. 283, 3953–3956 (2010).
[CrossRef]

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[CrossRef]

2009 (4)

T. M. Kardas and C. Radzewicz, “Broadband near-infrared fibers dispersion measurement using white light interferometry,” Opt. Commun. 282, 4361–4365 (2009).
[CrossRef]

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Laser Eng. 47, 1125–1130 (2009).
[CrossRef]

P. Hlubina, J. Luňáček, and D. Ciprian, “Spectral interferometry and reflectometry used for characterization of a multilayer mirror,” Opt. Lett. 34, 1564–1566 (2009).
[CrossRef]

Z. Várallyay, K. Saitoh, Á. Szabó, and R. Szipőcs, “Photonic bandgap fibers with resonant structures for tailoring the dispersion,” Opt. Express 17, 11869–11883 (2009).
[CrossRef]

2008 (4)

Z. Várallyay, K. Saitoh, J. Fekete, K. Kakihara, M. Koshiba, and R. Szipőcs, “Reversed dispersion slope photonic bandgap fibers for broadband dispersion control in femtosecond fiber lasers,” Opt. Express 16, 15603–15615 (2008).
[CrossRef]

J. Fekete, Z. Várallyay, and R. Szipőcs, “Design of high-bandwidth one- and two dimensional photonic bandgap dielectric structures at grazing incidence of light,” Appl. Opt. 47, 5330–5336 (2008).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

2007 (3)

2006 (3)

2004 (1)

2003 (1)

2002 (2)

2000 (3)

1999 (2)

Ch. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
[CrossRef]

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

1996 (2)

1995 (1)

1994 (1)

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

1985 (1)

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

1981 (1)

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981).
[CrossRef]

1978 (1)

Andrés, P.

Asundi, A. K.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[CrossRef]

Atkin, D. M.

Barkou, S. E.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Belabas, N.

Berger, N. K.

N. K. Berger, B. Levit, and B. Fischer, “Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses,” Opt. Commun. 283, 3953–3956 (2010).
[CrossRef]

Birks, T. A.

Bise, R.

Bjarklev, A.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Blondy, J.-M.

Börzsönyi, A.

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Broeng, J.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Bubnov, M. M.

Calatroni, J.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Cao, X.

Chériaux, G.

Chernikov, S. V.

F. Koch, S. V. Chernikov, and J. R. Taylor, “Dispersion measurement in optical fibres over the entire spectral range from 1.1 μm to 1.7 μm,” Opt. Commun. 175, 209–213 (2000).
[CrossRef]

Chlebus, R.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

Ciprian, D.

P. Hlubina, M. Kadulová, and D. Ciprian, “Spectral interferometry-based chromatic dispersion measurement of fibre including the zero-dispersion wavelength,” J. Eur. Opt. Soc. Rapid Pub. 7, 12017-1–12017-5 (2012).
[CrossRef]

P. Hlubina, J. Luňáček, and D. Ciprian, “Spectral interferometry and reflectometry used for characterization of a multilayer mirror,” Opt. Lett. 34, 1564–1566 (2009).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

P. Hlubina, M. Szpulak, D. Ciprian, T. Martynkien, and W. Urbanczyk, “Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry,” Opt. Express 15, 11073–11081 (2007).
[CrossRef]

Cohen, L. G.

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

Cui, S.

Debnath, S. K.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Laser Eng. 47, 1125–1130 (2009).
[CrossRef]

Dianov, E. M.

Diddams, S.

Diels, J.-C.

DiGiovanni, D. J.

Dong, X.

Dorrer, Ch.

Eggleton, B.

Eggleton, B. J.

Escalona, R.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Fang, Q.

Fekete, J.

Ferrando, A.

Février, S.

Fischer, B.

N. K. Berger, B. Levit, and B. Fischer, “Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses,” Opt. Commun. 283, 3953–3956 (2010).
[CrossRef]

Galle, M. A.

Genty, G.

Görbe, M.

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Guryanov, A. N.

Her, T. H.

Hlubina, P.

P. Hlubina, M. Kadulová, and D. Ciprian, “Spectral interferometry-based chromatic dispersion measurement of fibre including the zero-dispersion wavelength,” J. Eur. Opt. Soc. Rapid Pub. 7, 12017-1–12017-5 (2012).
[CrossRef]

P. Hlubina, J. Luňáček, and D. Ciprian, “Spectral interferometry and reflectometry used for characterization of a multilayer mirror,” Opt. Lett. 34, 1564–1566 (2009).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

P. Hlubina, M. Szpulak, D. Ciprian, T. Martynkien, and W. Urbanczyk, “Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry,” Opt. Express 15, 11073–11081 (2007).
[CrossRef]

Huang, L.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[CrossRef]

Jamier, R.

Jasapara, J.

Jin, L.

Joffre, M.

Jourdain, P.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Kadulová, M.

P. Hlubina, M. Kadulová, and D. Ciprian, “Spectral interferometry-based chromatic dispersion measurement of fibre including the zero-dispersion wavelength,” J. Eur. Opt. Soc. Rapid Pub. 7, 12017-1–12017-5 (2012).
[CrossRef]

Kai, G.

Kakihara, K.

Kardas, T. M.

T. M. Kardas and C. Radzewicz, “Broadband near-infrared fibers dispersion measurement using white light interferometry,” Opt. Commun. 282, 4361–4365 (2009).
[CrossRef]

Kemao, Q.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[CrossRef]

Khopin, V. F.

Kim, D. Y.

Kim, S.-W.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Laser Eng. 47, 1125–1130 (2009).
[CrossRef]

Knight, J. C.

Knox, W. H.

Koch, F.

F. Koch, S. V. Chernikov, and J. R. Taylor, “Dispersion measurement in optical fibres over the entire spectral range from 1.1 μm to 1.7 μm,” Opt. Commun. 175, 209–213 (2000).
[CrossRef]

Koshiba, M.

Kothiyal, M. P.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Laser Eng. 47, 1125–1130 (2009).
[CrossRef]

Kovács, A. P.

K. Mecseki and A. P. Kovács, “Monitoring of residual higher-order dispersion of pulse compression by spectral interferometry,” AIP Conf. Proc. 1228, 251–256 (2010).
[CrossRef]

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Lee, J. Y.

Lepetit, L.

Levit, B.

N. K. Berger, B. Levit, and B. Fischer, “Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses,” Opt. Commun. 283, 3953–3956 (2010).
[CrossRef]

Likforman, J. P.

Likhachev, M. E.

Litchinister, N. M.

Liu, J.

Liu, X.

Liu, Y.

Ludvigsen, H.

Lunácek, J.

P. Hlubina, J. Luňáček, and D. Ciprian, “Spectral interferometry and reflectometry used for characterization of a multilayer mirror,” Opt. Lett. 34, 1564–1566 (2009).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

Luo, F.

Luo, Z.

Ma, Q.

Marom, E.

Martijin de Sterke, C.

Martynkien, T.

McPhedran, R. C.

Mecseki, K.

K. Mecseki and A. P. Kovács, “Monitoring of residual higher-order dispersion of pulse compression by spectral interferometry,” AIP Conf. Proc. 1228, 251–256 (2010).
[CrossRef]

Miret, J. J.

Mogilevstev, D.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Mohammed, W.

Osvay, K.

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Pan, B.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[CrossRef]

Qian, L.

Radzewicz, C.

T. M. Kardas and C. Radzewicz, “Broadband near-infrared fibers dispersion measurement using white light interferometry,” Opt. Commun. 282, 4361–4365 (2009).
[CrossRef]

Sáinz, C.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Saitoh, K.

Salganskii, M. Y.

Semjonov, S. L.

Shang, H.-T.

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981).
[CrossRef]

Shen, W.

Silvestre, E.

Smith, P. W. E.

St. J. Russell, P.

Szabó, Á.

Szipocs, R.

Szpulak, M.

Taylor, J. R.

F. Koch, S. V. Chernikov, and J. R. Taylor, “Dispersion measurement in optical fibres over the entire spectral range from 1.1 μm to 1.7 μm,” Opt. Commun. 175, 209–213 (2000).
[CrossRef]

Urbanczyk, W.

Várallyay, Z.

Wang, Z.

White, T. P.

Windeler, R.

Windeler, R. S.

Xia, C.

Xu, Ch.

Yan, M. F.

Yariv, A.

Ye, Q.

Yeh, P.

Yuan, S.

Yue, Y.

Zhang, S.

Zhang, Y.

Zong, L.

AIP Conf. Proc. (1)

K. Mecseki and A. P. Kovács, “Monitoring of residual higher-order dispersion of pulse compression by spectral interferometry,” AIP Conf. Proc. 1228, 251–256 (2010).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (1)

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub. (1)

P. Hlubina, M. Kadulová, and D. Ciprian, “Spectral interferometry-based chromatic dispersion measurement of fibre including the zero-dispersion wavelength,” J. Eur. Opt. Soc. Rapid Pub. 7, 12017-1–12017-5 (2012).
[CrossRef]

J. Lightwave Technol. (2)

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

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (6)

Opt. Commun. (6)

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[CrossRef]

A. Börzsönyi, A. P. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Recorded normalized interferograms at (a) 400, at (b) 200, and at (c) 0 fs relative delays.

Fig. 3.
Fig. 3.

Difference between the fitted (a) third and (b) fourth-order polynomial and the measured group delay curve obtained by the SPP method. (c) Spectrum of the sample pulse (red) and of the Ti:S laser (dotted blue). The spectral positions of the leaking modes are denoted with dashed lines.

Fig. 4.
Fig. 4.

Measured (red) and fitted (dashed black) relative group delay as a function of the wavelength obtained by the SPP method.

Fig. 5.
Fig. 5.

Difference between the fitted (a) fourth and (b) fifth-order polynomial and the measured spectral phase curve obtained by the MM method. The spectral positions of the leaking modes are denoted with dashed lines.

Fig. 6.
Fig. 6.

Measured (red) and fitted (dashed black) spectral phase obtained by the MM method.

Fig. 7.
Fig. 7.

Normalized spectral interferograms with the results of the CFF with (a) fourth and (b) fifth-order polynomial in its argument (red, measured data; black solid line, fitted curve). The spectral positions of the leaking modes are denoted with dashed lines.

Fig. 8.
Fig. 8.

(a) Recorded spectral interferogram, (b) the FT of the interferogram, and (c) the retrieved (red) and the fitted (dashed black) spectral phase obtained by the FT method without the linear phase term.

Fig. 9.
Fig. 9.

Difference between the measured spectral phase obtained by the FT method and the fitted (a) fourth and (b) fifth-order polynomial. The spectral positions of the leaking modes are denoted with dashed lines.

Fig. 10.
Fig. 10.

Windowed FT of a spectral interferogram with the measured group delay curve obtained by the WFT method.

Fig. 11.
Fig. 11.

Difference between the measured and the fitted (a) third and (b) fourth-order group delay curves obtained by the WFT method. The spectral positions of the leaking modes are denoted with dashed lines.

Tables (1)

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Table 1. Dispersion Coefficients of a 37 cm Long PBG Fiber at 800 nm Obtained by the Five Evaluation Methods

Equations (13)

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I(ω)=Ir(ω)+Is(ω)+2Ir(ω)·Is(ω)·cos(Φ(ω)),
Φ(ω)=φ(ω)+ωτ,
φ(ω)=φ(ω0)+GD(ωω0)+GDD2(ωω0)2+TOD6(ωω0)3+FOD24(ωω0)4+QOD120(ωω0)5+,
GD=dφdω|ω=ω0,GDD=d2φdω2|ω=ω0,TOD=d3φdω3|ω=ω0,FOD=d4φdω4|ω=ω0,QOD=d5φdω5|ω=ω0
cos(Φ(ω))=I(ω)Ir(ω)Is(ω)2Ir(ω)·Is(ω),
d(cos(Φ(ω)))dω=sin(Φ(ω))·dΦdω=0,
dφdω=τ.
GDfit=a0+a1Δω+a2Δω2+a3Δω3+a4Δω4,
Φfit=b0+b1Δω+b2Δω2+b3Δω3+b4Δω4+b5Δω5,
Ifit=c1+c2cos(b0+b1Δω+b2Δω2+b3Δω3+b4Δω4+b5Δω5),
F{I(ω)}=F{Ir(ω)}+F{Is(ω)}+F{2Ir(ω)·Is(ω)·cos(Φ(ω))}.
I(t)=Ir(t)+Is(t)+Ii(tτ)+Ii(t+τ),
Iw(ω,Ω)=I(ω)exp[(ωΩΔΩ)2].

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