Differential group refractive index dispersion of glasses of optical fibres measured by a white-

light spectral interferometric technique

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Meas. Sci. Technol. 18 (2007) 1547–1552 doi:10.1088/0957-0233/18/5/046

Differential group refractive indexdispersion of glasses of optical fibresmeasured by a white-light spectralinterferometric techniquePetr Hlubina, Radek Chlebus and Dalibor Ciprian

Department of Physics, Technical University Ostrava, 17. listopadu 15,708 33 Ostrava-Poruba, Czech Republic

E-mail: petr.hlubina@vsb.cz

Received 22 January 2007, in final form 9 February 2007Published 27 March 2007Online at stacks.iop.org/MST/18/1547

AbstractWe report on a white-light interferometric technique employing alow-resolution spectrometer to measure the differential group refractiveindex of glasses of optical fibres over a wide wavelength range. Thetechnique utilizes an unbalanced Mach–Zehnder interferometer with a fibreunder test of known length inserted in one of the interferometer arms and theother arm with adjustable path length. We record a series of spectralinterferograms to measure the equalization wavelength as a function of thepath length difference, or equivalently the group dispersion. Subtracting thegroup dispersion of the optical components present in the interferometeralong with the fibre, we measure the wavelength dependence of differentialgroup refractive index for pure silica and SK222 glasses. We confirm thatthe differential group dispersion measured for pure silica glass agrees wellwith that described by the dispersion equation.

Keywords: spectral interferometry, white-light source, low-resolutionspectrometer, Mach–Zehnder interferometer, group refractive index,dispersion, pure silica glass, SK222 glass

1. Introduction

A precise measurement of the group dispersion of opticalcomponents over a broad spectral range is important invarious research areas including applications of femtosecondlasers, material characterization and broadband opticalcommunications. White-light interferometry based on theuse of a broadband source in combination with a standardMichelson or a Mach–Zehnder interferometer is considered asone of the best tools for dispersion characterization of opticalguiding media such as optical fibres.

White-light interferometry usually utilizes a temporalmethod or a spectral method. The temporal method involvesmeasurement of the time of flight of optical pulses through asample. A method for measuring the group delay introducedby an optical material consists in placing the sample in one of

the interferometer arms and evaluating the temporal shift ofthe peak of the cross-correlation interferogram. As the centralwavelength is varied, the relative group delay of the differentfrequency components is observed directly [1]. Alternatively,the spectral phase over the full bandwidth of the white-lightsource can be obtained in a single measurement by a Fouriertransform of the cross-correlation interferogram [2–5]. Thegroup dispersion of the sample under study can be obtained bysimply differentiating the measured spectral phase.

The spectral method is based on the observation ofspectrally resolved interference fringes (channelled spectrum)in the vicinity [6, 7] of a stationary-phase point or far fromit [8–11] and involves measurement of the phase or periodof the spectral fringes. The group dispersion of the sampleunder study can be obtained by simply differentiating thespectral phase retrieved from a single interferogram. The

0957-0233/07/051547+06$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1547

P Hlubina et al

PC S2000

Spectrometer

Light source

Lens 1 Lens 2

Mirror 3

Mirror 4

Mirror 2

Beam splitter 1 Fibre under test Mirror 1

HL−2000

Micropositioner

Optical table

Optical fibre Collimator

Read optical fibre

Beam splitter 2

Micropositioners

Objective

Figure 1. Experimental set-up with an unbalanced Mach–Zehnder interferometer to measure the differential group refractive indexdispersion of glasses of optical fibres.

stationary-phase point [6] appears in the recorded spectralinterferogram when the group optical path difference (OPD)between two beams in the interferometer is close to zero.The main limitation of the method is reached for thick orstrongly dispersive materials because under such conditionsthe spectral interference fringes that are far from the stationary-phase point become difficult to resolve. Using a low-resolution spectrometer [12], the measurement of the grouprefractive index dispersion of a given material is still possiblein the vicinity of the stationary-phase point if one movesit in successive steps to different wavelengths and repeatsthe measurement. We measured in this way the dispersionof differential group refractive index of a pure silica beamsplitter present in a Michelson interferometer [12]. Themodification of the technique with a tandem configuration ofa Michelson interferometer and an optical fibre has been usedin measurement of the group dispersion in standard [13] andbirefringent [14, 15] fibres of a known length. Recently, theuse of the method with a Mach–Zehnder interferometer wasextended to two-dimensional spectral interferometry [16] orfor dispersion characterization of tapered fibres [17].

The aim of this paper is to present a white-light interferometric technique employing a low-resolutionspectrometer for measurement of the differential grouprefractive index of glasses of optical fibres over a widewavelength range. The technique utilizes an unbalancedMach–Zehnder interferometer with a fibre under test of knownlength inserted in one of the interferometer arms and the otherarm with adjustable path length. We record a series of spectralinterferograms to measure the equalization wavelength as afunction of the path length difference, or equivalently the groupdispersion over the wavelength range approximately from 500to 910 nm. Subtracting the group dispersion of a microscopeobjective in front and a lens behind the fibre present in theinterferometer, we measure the wavelength dependence of thedifferential group refractive index for pure silica and SK222glasses with a precision of 2 × 10−5. The group dispersion

measured for pure silica glass agrees well with that describedby the dispersion equation.

2. Experimental method

First, let us consider an unbalanced Mach–Zehnderinterferometer (see figure 1) with a fibre under test of length z

and refractive index n(λ) and optical components (lens 1 andlens 2) to which the effective thickness d and refractive indexnc(λ) correspond. The fibre is inserted into the first (test)arm of the interferometer and the other (reference) arm hasadjustable path length L in air so that the group OPD �

gMZ(λ)

between the beams in the interferometer is given by

�gMZ(λ) = L − l − N(λ)z − Nc(λ)d, (1)

where l is the path length in the air in the test arm and N(λ) andNc(λ) are the group refractive indices satisfying the relation

N(λ) = n(λ) − λdn(λ)

dλ. (2)

Let us consider now that the spectral interference fringesrecorded in the set-up have the largest period in the vicinity ofa stationary-phase point for which the group OPD is zero atone specific wavelength λ0, referred to as the equalizationwavelength [12]. The condition �

gMZ(λ0) = 0 gives for

the overall path length L = Lo = Lo(λ0) for whichthe equalization wavelength λ0 is resolved in the recordedspectrum the relation

Lo(λ0) = N(λ0)z + Nc(λ0)d + l. (3)

If we choose one of the equalization wavelengths, λ0r , asthe reference one, we can introduce the overall path lengthdifference �Lo(λ0) = Lo(λ0) − Lo(λ0r ) given by

�Lo(λ0) = �N(λ0)z + �Nc(λ0)d, (4)

where �N(λ0) = N(λ0) − N(λ0r ) and �Nc(λ0) = Nc(λ0) −Nc(λ0r ) are the corresponding differential group refractiveindices.

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Differential group refractive index dispersion

Second, let us consider the unbalanced Mach–Zehnderinterferometer in which the fibre is removed and which is usedfor measuring the group dispersion of the optical components.This group dispersion has to be subtracted from the overallgroup dispersion to determine the group dispersion of the fibrealone. The corresponding path length difference is denoted as�Lc(λ0) = Lc(λ0) − Lc(λ0r ) and is given by

�Lc(λ0) = �Nc(λ0)d. (5)

Using equations (4) and (5), we obtain the relation

�N(λ0) = [�Lo(λ0) − �Lc(λ0)]/z, (6)

which means that the differential group refractive index�N(λ0) of the fibre can be measured directly as a function ofthe equalization wavelength λ0 if the fibre length z is known.

3. Experimental set-up

The experimental set-up used in the application ofspectral-domain white-light interferometry for measuring thedifferential group refractive index dispersion of glasses ofoptical fibres is shown in figure 1. It consists of a white-light source: a quartz–tungsten–halogen lamp (HL-2000HP,Ocean Optics, Inc.) with launching optics, optical fibre ofcut-off wavelength as short as possible, a collimating lens,a bulk-optic Mach–Zehnder interferometer with plate beamsplitters (BSW07, Thorlabs), a micropositioner connected tomirrors 3 and 4 of the interferometer, a microscope objective,micropositioners, a fibre-optic spectrometer (S2000, OceanOptics, Inc.), an A/D converter and a personal computer. Thespectrometer resolution is given by a 50 µm core diameter ofthe read optical fibre to which a Gaussian response functionwith the width of about 3 nm corresponds [18].

In the test arm of the interferometer is inserted acombination of components (shown schematically in figure 1as lens 1, fibre under test and lens 2) represented by amicroscope objective (10×/0.30, Meopta), a fibre sampleand an achromatic lens (74-ACR, Ocean Optics, Inc.). Wemeasured two different fibre samples. The first sample ispure silica holey fibre (PM-1550-01, Thorlabs) of lengthz = 50 650 µm and the second sample is a holey fibre oflength z = 54 200 µm made of SK222 optical glass [19]. Thefibre lengths were measured by a micrometer with an accuracyof ±10 µm.

4. Experimental results and discussion

First, the overall group dispersion of a combination of the firstfibre sample and optical components was measured in the set-up shown in figure 1. Prior to the measurement we utilizedthe main advantage of the set-up, which is in fibre connectionof a light source (that can be varied) with the interferometer.We used a laser diode instead of the halogen lamp to check theprecise placement and alignment of the optical components inthe test arm by observing the interference fringes. The ring-shape optical field was revealed at the output of the test armindicating that the light was guided by the outer cladding ofthe fibre [15]. It should also be noted here that the alignmentof the components is much simpler in the interferometer witha single pass of light through the test arm than in a Michelsoninterferometer with two passes [20].

550 600 650 700 750 800 8500.7

0.8

0.9

1

1.1

1.2

F+OCs

OCs

Spe

ctra

l Sig

nal

Wavelength (nm)

Figure 2. Examples of the spectral signals recorded for two cases:pure silica fibre plus optical components (F+OCs) and opticalcomponents (OCs).

In the dispersion measurement, such a path length in thereference arm of the interferometer was adjusted to resolvespectral interference fringes. Figure 2 shows an example ofthe recorded normalized spectral signal (denoted as F+OCs)obtained by subtracting the reference signal (without theinterference) from the interferogram. It clearly shows theeffect of the limiting resolving power of the spectrometer onthe visibility of the spectral interference fringes identified onlyin the vicinity of the equalization wavelength λ0 = 748.23 nm,which was chosen as the reference one λ0r . Theequalization wavelength was determined with an error of0.32 nm corresponding to the wavelength difference foradjacent pixels of the spectrometer linear CCD-array detector[18].

Second, the group dispersion of the optical componentsfor which the equalization wavelength cannot be resolved withthe unbalanced Mach–Zehnder interferometer was measuredby a method of tandem interferometry [14]. The methodutilizes a Michelson interferometer placed in between thesource and the unbalanced Mach–Zehnder interferometer andthe adjustment of such an OPD in the Michelson interferometerto resolve the spectral interference fringes at the output ofthe Mach–Zehnder interferometer. We checked the preciseplacement and alignment of the microscope objective and theachromatic lens in the test arm by observing the interferencefringes when a laser diode was used instead of the halogenlamp. Figure 2 shows an example of the recorded spectralsignal (denoted as OCs) with the spectral interference fringesidentified only in the vicinity of the equalization wavelengthλ0 = 601.35 nm.

We measured the dependence of the adjusted path lengthdifference on the equalization wavelength for both cases. Wedisplaced the stage with mirrors 3 and 4 manually by using themicropositioner with a constant step of 10 µm and performedrecording of the corresponding spectral signals. The spectralsignals recorded for the first case revealed that the equalizationwavelength λ0 can be resolved in the spectral range from 508to 910 nm and that the path length difference �Lo varies from1480 to −340 µm. The measured values are shown in figure 3

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P Hlubina et al

500 550 600 650 700 750 800 850 900−400

0

400

800

1200

1600

F+OCs

OCsPat

h Le

ngth

Diff

eren

ce (

µm)

Wavelength (nm)

Figure 3. Path length difference measured as a function ofwavelength for two cases: pure silica fibre plus optical components(F+OCs) and optical components (OCs). The solid line is apolynomial fit.

500 550 600 650 700 750 800 850 900 950

−5

0

5

10

15

20

x 10−3

Diff

eren

tial G

roup

Ref

ract

ive

Inde

x

Wavelength (nm)

Figure 4. Differential group refractive index of pure silica measuredas a function of wavelength. The solid line corresponds to theory.

by the crosses. Similarly, the spectral signals recorded for thesecond case revealed that the equalization wavelength λ0 canbe resolved in the spectral range from 509 to 869 nm and thatthe path length difference �Lc varies from 470 to −90 µm.The measured values are shown in figure 3 by the crossestogether with the polynomial fit. Knowledge of the measureddependences and the fibre length z of the first sample enablesus to evaluate directly the differential group refractive index�N(λ0) as a function of the equalization wavelength λ0. Thefunction is represented in figure 4 by the crosses, and it isshown together with the theoretical function resulting from theSellmeier formula for pure silica [12]. This figure confirmsvery good agreement between theory and experiment.

We can estimate the precision of the differential grouprefractive index measurement. If the path length difference�L = �Lo − �Lc is adjusted with a precision of δ(�L) andthe length z of the fibre is known with a precision of δ(z),

550 600 650 700 750 800 8500.7

0.8

0.9

1

1.1

1.2

1.3

1.4 F+OCs

OCs

Spe

ctra

l Sig

nal

Wavelength (nm)

Figure 5. Examples of the spectral signals recorded for two cases:fibre made of SK222 glass plus optical components (F+OCs) andoptical components (OCs).

the differential group refractive index �N is obtained with aprecision given by the following formula:

δ(�N) =√[

δ(�L)

z

]2

+

[�L

δ(z)

z2

]2

. (7)

In our case, the precision δ(�L) is 1 µm and the precisionδ(z) is 10 µm so that the precision δ(�N) in determiningthe differential group refractive index is 2 × 10−5. Highermeasurement precision can be achieved, for example, using alonger fibre. However, there exists a maximum length of thefibre given by the limited resolving power of the spectrometer.

Finally we measured the group dispersion of the secondfibre sample made of SK222 glass, which is a multicomponentglass that exhibits a higher nonlinearity (up to a factor of2) than pure silica [19]. Figure 5 shows an example ofthe recorded spectral signal (denoted as F+OCs) with thespectral interference fringes identified only in the vicinityof the equalization wavelength λ0 = 747.91 nm, chosenas the reference one λ0r . Figure 5 also shows an exampleof the spectral signal (denoted as OCs) recorded for opticalcomponents. The dependence of the overall path lengthdifference on the equalization wavelength was once againmeasured when the stage with mirrors 3 and 4 was displacedmanually by using the micropositioner with a constant stepof 10 µm. The spectral signals recorded revealed that theequalization wavelength λ0 can be resolved in the spectralrange from 497 to 907 nm and that the path length difference�Lo varies from 2160 to −480 µm. The measured valuesare shown in figure 6 by the crosses and in comparison withthe values from figure 3 are greater. In the same figure areshown the measured values regarding the group dispersionof the microscope objective and the achromatic lens. Theyare represented by the crosses and are shown together withthe polynomial fit. Knowledge of the measured dependencesand the fibre length z of the second sample enables us toevaluate directly the wavelength dependence of the differentialgroup refractive index �N(λ0). The function is represented infigure 7 by the crosses, and it is shown together with a

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Differential group refractive index dispersion

500 550 600 650 700 750 800 850 900

−400

0

400

800

1200

1600

2000

F+OCs

OCsPat

h Le

ngth

Diff

eren

ce (

µm)

Wavelength (nm)

Figure 6. Path length difference measured as a function ofwavelength for two cases: fibre made of SK222 glass plus opticalcomponents (F+OCs) and optical components (OCs). The solid lineis a polynomial fit.

500 550 600 650 700 750 800 850 900

−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

Diff

eren

tial G

roup

Ref

ract

ive

Inde

x

Wavelength (nm)

Figure 7. Differential group refractive index of SK222 glassmeasured as a function of wavelength. The solid line is apolynomial fit.

polynomial fit. The differential group refractive index �N

of SK222 glass is obtained with a precision of 2 × 10−5.

5. Conclusions

We used a white-light interferometric technique employinga low-resolution spectrometer for measurement of thedifferential group refractive index of glasses of optical fibresover a wide spectral range (500 to 910 nm). The techniqueutilized an unbalanced Mach–Zehnder interferometer witha fibre under test of known length inserted in one of theinterferometer arms and the other arm with adjustable pathlength. From a series of recorded spectral signals we measuredthe equalization wavelength as a function of the path lengthdifference, or equivalently the group dispersion. Subtractingthe group dispersion of a microscope objective in front anda lens behind the fibre present in the interferometer arm,

we measured the wavelength dependence of the differentialgroup refractive index for pure silica and SK222 glasses witha precision of 2 × 10−5. We confirmed that the differentialgroup dispersion measured for pure silica glass agrees wellwith that described by the dispersion equation.

The use of the method, whose main advantage is ineasy inspection of the optical field at the output of the testarm, can be extended for measuring the group dispersionof core or cladding parts of fibres composed of differentglasses. Moreover, suitable excitation of an optical fibre,for example by means of a supercontinuum source [20],will enable measurement of the group dispersion for modesguided by the fibre. Experimental results regarding the groupdispersion of both the glass and guided modes of the opticalfibre are crucial for comparison with theoretical results in orderto verify the reliability of numerical modelling.

Acknowledgments

The research was partially supported by the GrantAgency of the Czech Republic (project no 102/06/0284),MSM6198910016, MSMT grant (OC142) within the COSTAction P11 and internal grant of TU Ostrava (IGS HGFVS B-TUO).

References

[1] Knox W H, Pearson N M, Li K D and Hirlimann C A 1988Interferometric measurements of femtosecond group delayin optical components Opt. Lett. 13 574–6

[2] Beck M and Walmsley I A 1990 Measurement of group delaywith high temporal and spectral resolution Opt. Lett. 15492–4

[3] Naganuma K, Mogi K and Yamada 1990 Group-delaymeasurements using the Fourier transform of aninterferometric cross correlation generated by white lightOpt. Lett. 15 393–5

[4] Diddams S and Diels J C 1996 Dispersion measurements withwhite-light interferometry J. Opt. Soc. Am. B 13 1120–8

[5] Galli M, Marabelli F and Gizzetti G 2003 Direct measurementof refractive-index dispersion of transparent media bywhite-light interferometry Appl. Opt. 42 3910–4

[6] Sainz C, Jourdain P, Escalona R and Calatroni J 1994 Realtime interferometric measurements of dispersion curvesOpt. Commun. 110 381–90

[7] Kumar V N and Rao D N 1995 Using interference in thefrequency domain for precise determination of the thicknessand refractive indices of normal dispersive materials J. Opt.Soc. Am. B 55 1559–63

[8] Liang Y and Grover C H 1998 Modified white-lightMach–Zehnder interferometer for direct group-delaymeasurements Appl. Opt. 37 4105–11

[9] El-Zaiat S Y 2004 Group refractive index measurements byfringes of equal chromatic order Opt. Laser Technol.37 181–6

[10] Lee J Y and Kim D Y 2006 Versatile chromatic dispersionmeasurement of a single mode fiber using spectral whitelight interferometry Opt. Express 14 11608–15

[11] Reolon D, Jacquot M, Verrier I, Brun G and Veillas C 2006High resolution group refractive index measurement bybroadband supercontinuum interferometry andwavelet-transform analysis Opt. Express 14 12744–50

[12] Hlubina P 2001 White-light spectral interferometry with theuncompensated Michelson interferometer and the grouprefractive index dispersion in fused silica Opt. Commun.193 1–7

1551

P Hlubina et al

[13] Hlubina P, Martynkien T and Urbanczyk W 2003Measurements of intermodal dispersion in few-modeoptical fibres using a spectral-domain white-lightinterferometric method Meas. Sci. Technol. 14 784–9

[14] Hlubina P, Martynkien T and Urbanczyk W 2003 Dispersionof group and phase modal birefringence in elliptical-corefiber measured by white-light spectral interferometry Opt.Express 11 2793–8

[15] Hlubina P, Szpulak M, Knyblova L, Statkiewicz G,Martynkien T, Ciprian D and Urbanczyk W 2006Measurement and modelling of dispersion characteristics oftwo-mode birefringent holey fibre Meas. Sci. Technol.17 626–30

[16] Kovacs A P, Osvay K, Kurdi G, Gobre M, Klebniczki J andBor Z 2005 Dispersion control of a pulsestretcher–compressor system with two-dimensional spectralinterferometry Appl. Phys. B 80 165–70

[17] Lu P, Ding H and Mihailov S J 2005 Direct measurement ofthe zero-dispersion wavelength of tapered fibres using

broadband-light interferometry Meas. Sci. Technol.16 1631–6

[18] Hlubina P, Gurov I and Chugunov V 2003 White-lightspectral interferometric technique to measure thewavelength dependence of the spectral bandpassof a fibre-optic spectrometer J. Mod. Opt.50 2067–74

[19] Mitrofanov A V, Linik Y M, Buczynski R, Pysz D, Lorenc D,Bugar I, Ivanov A A, Alfimov M V, Fedotov A B andZheltikov A M 2006 Highly birefringent silicate glassphotonic-crystal fiber with polarization-controlledfrequency shifted output: a promising fiber light source fornonlinear Raman microspectroscopy Opt. Express14 10645–51

[20] Labonte L, Roy P, Pagnoux F, Louradour F, Restoin C,Melin G and Burov E 2006 Experimental and numericalanalysis of the chromatic dispersion dependence upon theactual profile of small core microstructured fibres J. Opt. A:Pure Appl. Opt. 8 933–8

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