Abstract

We report on the measurement of the group index of fused silica in the zero dispersion region by pulse delay measurements. Our results differ from the calculated values of the group index from the literature by less than 1·105. The dispersion within the 1200–1340 nm range is also studied by means of auto and cross-correlation measurements. The results are in good agreement with the known dispersion of fused silica.

© 2012 Optical Society of America

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References

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  1. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
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    [CrossRef]
  4. Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
    [CrossRef]
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    [CrossRef]
  7. P. Hlubina, “Group velocity dispersion in fused-silica sample measured using white-light interferometry with the equalization wavelength determination,” Optik 113, 149–152 (2002).
    [CrossRef]
  8. A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
    [CrossRef]
  9. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 2006).
  10. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
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  12. D. Herriot, H. Kogelnik, and R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3, 523–526 (1964).
    [CrossRef]
  13. E. R. Peck and K. Reeder, “Dispersion of air,” J. Opt. Soc. Am. 62, 958–962 (1972).
    [CrossRef]
  14. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).
  15. B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
    [CrossRef]

2007

A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
[CrossRef]

2002

P. Hlubina, “Group velocity dispersion in fused-silica sample measured using white-light interferometry with the equalization wavelength determination,” Optik 113, 149–152 (2002).
[CrossRef]

1996

1995

1990

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

1972

1966

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[CrossRef]

1965

1964

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Atkins, P.

P. Atkins and R. Friedman, Molecular Quantum Mechanics(Oxford University, 2005).

Bor, Z.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Brunner, F. D. J.

A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
[CrossRef]

Diddams, S.

Diels, J.-C.

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Friedman, R.

P. Atkins and R. Friedman, Molecular Quantum Mechanics(Oxford University, 2005).

Ghatak, A.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

Günter, P.

A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
[CrossRef]

Herriot, D.

Hlubina, P.

P. Hlubina, “Group velocity dispersion in fused-silica sample measured using white-light interferometry with the equalization wavelength determination,” Optik 113, 149–152 (2002).
[CrossRef]

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

Kogelnik, H.

Kompfner, R.

Kumar, V. N.

Malitson, I. H.

Osvay, K.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Peck, E. R.

Rácz, B.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Rao, D. N.

Reeder, K.

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 2006).

Schneider, A.

A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
[CrossRef]

Szabó, G.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Metrologia

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Opt. Commun.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

A. Schneider, F. D. J. Brunner, and P. Günter, “Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses,” Opt. Commun. 275, 354–358 (2007).
[CrossRef]

Optik

P. Hlubina, “Group velocity dispersion in fused-silica sample measured using white-light interferometry with the equalization wavelength determination,” Optik 113, 149–152 (2002).
[CrossRef]

Other

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 2006).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

P. Atkins and R. Friedman, Molecular Quantum Mechanics(Oxford University, 2005).

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for the measurement of the group index ng. BS, beamsplitter.

Fig. 2.
Fig. 2.

Experimental setup for the study of the dispersion of fused silica in the near-infrared. BS, beamsplitter.

Fig. 3.
Fig. 3.

Group index of fused silica. The blue squares correspond to the measured group index, whereas the solid line corresponds to the group index calculated from the Sellmeier equation given in [3].

Fig. 4.
Fig. 4.

Dispersion of fused silica at λ=1200nm: (a) spectral intensity, (b) autocorrelation signal for a FL pulse (AFL(τ)) and at the entrance of the Herriot cell (Ai(τ)), (c) cross-correlation signal, Co(τ), at the output of the Herriot cell.

Fig. 5.
Fig. 5.

Dispersion of fused silica. σFL is the pulsewidth of the FL pulses, and σi (resp. σo) the pulsewidth at the entrance (resp. exit) of the Herriot cell.

Equations (34)

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Ein(t)=E(t,z=0)=12Ai(t)ei[ωtφi(t)].
Ein(ω)=a(ω)eiϕi(ω),
=+Ein(t)eiωtdt.
Eout(ω)=a(ω)eiϕo(ω),
=Ein(ω)eiϕ(ω),
S(ω)=ε0cn(ω)π|Eout(ω)|2=ε0cn(ω)π|Ein(ω)|2.
ϕ(ω)=ϕ+m1m!ϕ(m)(ωω)m,
n2(λ)1=kBkλ2λ2λk2,
Eout(t)=E(t,z=L)=12Ao(t)ei[ωtφo(t)],
Io(t)=12ε0cn(ω)Ao2(t).
tm=+tmI(t)dt/+I(t)dt,
ωm=0+ωmS(ω)dω/0+S(ω)dω.
σt=(tt)2=t2t2,
σω=(ωω)2=ω2ω2,
σt×σω1/2,
σo2=σi2+T2(ω)T(ω)2,
σT=T2(ω)T(ω)2
σo2=σi2+σT2.
Ai(τ)=+Ii(t)Ii(tτ)dt,
Co(τ)=+Io(t)Ii(tτ)dt.
σc=τ2cτc2,withτmc=+τmCo(τ)dτ+Co(τ)dτ.
σc2=σo2+σi2σo=σc2σi2.
σi=12τ2iτi2,withτmi=+τmAi(τ)dτ+Ai(τ)dτ,
tsilica(L,λ)=+τCo(τ)dτ+Co(τ)dτ,
tair(L,λ)=+τCo(air)(τ)dτ+Co(air)(τ)dτ.
t=dϕodω=Lcng(λ),
ng(λ)=ng,air(λ)+cΔtL.
λ=λ=0+λS(λ)dλ/0+S(λ)dλ.
ng(λ)=ng,air(λ)+cΔtL,
ng(λ)=n(λ)λ(dndλ)λ.
δng=(δn)θ2+(δng)L2+(δng)Δt28·106,
IFL(t)|F1[S(ω)]|2,
Ti(ω)=dϕidω=ϕi(2)(ωω),
σo=σFL2+σTo2,

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