Optical Materials 25 (2004) 171–178

www.elsevier.com/locate/optmat

Optical analysis of infrared spectra recorded with taperedchalcogenide glass fibers

Steven MacDonald, Karine Michel, David LeCoq,Catherine Boussard-Pl�edel, Bruno Bureau *

Laboratoire des Verres et C�eramiques, UMR-CNRS 6512, Institut de Chimie de Rennes, Universit�e de Rennes 1,

Campus de Beaulieu, 35042 Rennes C�edex, France

Received 31 January 2003; accepted 10 April 2003

Abstract

Infrared fiber evanescent wave spectroscopy (FEWS) spectra of water–ethanol mixtures are recorded and recon-

structed thanks to a causal dispersion analysis technique. The complete expression of the complex reflection coefficients

was used to determine the transmitted signal. The problems of shifting peaks or overlapping absorption bands from

different chemical are well addressed. The effect of several parameters on the absorbance, such as the length of im-

mersion and the diameter of the fiber probe have been calculated and fit well with experimental data. More generally,

the agreement between experimental and calculated spectra suggest the presented analysis technique is more accurate

than other current analysis techniques.

� 2003 Elsevier B.V. All rights reserved.

PACS: 42.70.c; 42.70.k; 42.81; 82.80.c

1. Introduction

Fiber evanescent wave spectroscopy (FEWS) is

now widely used to record some infrared spectra in

many fields of applications [1–23]. This technique

enables remote sampling in the infrared by cou-

pling and optical fiber with a Fourier transforminfrared (FTIR) spectrometer. FEWS is an effi-

cient tool to collect spectra in hazardous or in-

convenient situations (environment, in vivo

studies, fermentation process, chemical reactions

* Corresponding author. Tel.: +33-2-2323-6573; fax: +33-2-

2323-5611.

E-mail address: bruno.bureau@univ-rennes1.fr (B. Bureau).

0925-3467/$ - see front matter � 2003 Elsevier B.V. All rights reserv

doi:10.1016/S0925-3467(03)00266-0

in microwave furnace, . . .), but also offers the ad-

vantage of great flexibility for experiments made in

the laboratory compared to the classical way to

record spectra: transmission or attenuated total

reflection (ATR). Two types of optical guides are

commonly used for FEWS in the mid-infrared,

silver halide fibers [6,15–18] and chalcogenide glassfibers [1–5,20,22]. The chalcogenide based-glasses

have favorable viscosity–temperature dependence

near the drawing temperature which allows a large

variation in the fiber diameter, from 500 to 50 lm[3], that permits changes in the sensitivity.

The typical analysis of those performing FEWS

is to assume that either the length of the immersed

fiber or an effective path length, based upon thedepth of penetration vs incident angle [7–23], is the

ed.

172 S. MacDonald et al. / Optical Materials 25 (2004) 171–178

transmission length through the sample. Each

method attempts to simplify the results for direct

comparison with transmission spectra. In both

cases the end result is a Beer�s law type analysis of

quasi-absorption from transmission through a

sample. The problems of shifting peaks are notaddressed. Currently, the analysis of the mea-

surements taken with these broadband optical

probes is problematic, as absorption bands from

different chemicals can overlap.

Very recently [24] a rigorous analysis of atten-

uated total reflection and transmission spectra was

performed by using the theoretical optical paths

for the both techniques together with Gaussiandispersion analysis (GDA) [25]. Simulations of the

whole mid-IR spectra in the range 500–4000 cm�1

match the experimental data very well. Among

other results, this preliminary work has permitted

to determine the dielectric functions of the com-

pound studied: water and ethanol.

The work presented here aims at using the di-

electric functions of water, ethanol and their mix-tures and a propagation model for a fiber probe to

give account of spectra recorded using a chalcog-

enide glass fiber sensor. For this, the complete

expression of the complex reflection coefficients

will be used to determine the transmitted signal.

The chemical system of de-ionized water and ethyl

alcohol was considered to validate the method.

This system was examined because the chemicalsare completely soluble in each other and have

overlapping absorption bands in the infrared.

Moreover, the dielectric function of these both

compounds are now well known.

2. Experimental

Samples of Te2As3Se5 (TAS) glass were pre-

pared using a fabrication method described in

detail in Refs. [1,4]. The rods of TAS glass are

drawn into a fiber with a diameter of approxi-mately 400 lm. The drawing process is described

in detail in Ref. [1]. During the drawing process a

length of the fiber was tapered to a diameter of 200

lm by momentarily accelerating the drawing and

thus reducing the fiber diameter for a short sec-

tion. The diameter of the fiber is monitored online.

The reduced diameter allows for a more flexible

sensing region, while the larger diameter of the rest

of the fiber allows easier coupling of the infrared

light to the fiber and is less fragile. The reduced

diameter also increases the optical sensitivity of the

fiber [3,5]. After cooling and remaining on a largespool for over two days, the fiber was cut to an

overall length of 2 m.

The experiments were carried out with a Vector

22 Bruker FTIR coupled to the TAS glass fiber

and an external mercury–cadmium telluride in-

frared detector [1–3,5]. The coupling of the fiber to

the spectrometer was done with two microposi-

tioning systems, one to couple the fiber to thesource and one to couple the fiber to the detector.

The fiber was adjusted to produce the maximum

signal on the detector. The sensing zone of the

fiber was placed in a glass sampling boat with a

contact length between the fiber and sample of

approximately 5 cm. All infrared spectra were re-

corded with a resolution of 2 cm�1 over the spec-

tral range from 800 to 4000 cm�1. All thecalculations were performed with custom written

software on a personal IBM type PC. The pro-

grams were written with Python for windows.

Python is a shareware computing language.

3. Theory

Maxwell�s equations are the starting point for

the study of electromagnetic phenomena and are

applicable to the study light propagation in an

optical fiber [26–31]. In order for total internal

reflections (TIR) to occur at the interface of the

cladding and the core, the following condition

must be met:

hP hc ¼ sin�1 n2n1

� �ð1Þ

where n1 is the index of refraction of the core

material, n2 the index of refraction for the cladding

material, hc, the critical angle, from normal, for

TIR, and h is the angle of incidence from normal.

Due to the high index of the TAS glass, close to 2.8

[1–5], this condition for TIR is fulfilled for any

optical ray entering in a mono index TAS fiber,

meaning that the numerical aperture of such a

S. MacDonald et al. / Optical Materials 25 (2004) 171–178 173

waveguide is equal to 1. Moreover, in order for

waves to propagate along the fiber, i.e. not de-

constructively interfere with each other, each re-

flection must be in phase with other reflected

waves. Only certain angles of incidence will meetthis condition, resulting in modes of propagation

for a particular wavelength. The number of bound

modes M for a circular fiber is estimated by the

following equation [30, p. 249]:

MðkÞ ¼ 2p2r2ðn21 � n22Þk2

ð2Þ

with r being the radius of the fiber, n1 the index of

the fiber core, and n2 the index of the cladding. Thenumber of modes is therefore dependent on both

the index of the core, index of cladding, diameter

of the fiber and the wavelength. With a fiber di-ameter of 200 lm, core index of 2.8 and cladding

index of 1, as for air, the number of bound modes

for each wavelength varies between roughly 37,500

at 12 lm (833 cm�1) and 1,350,000 at 2 lm (5000

cm�1). It is because of such large numbers of

bound modes that it is not practical to solve the

exact equations of propagation based on an elec-

tromagnetic analysis and obtained by consideringthe Maxwell�s equation [26–30]. In the present

situation, it is known that propagation within

waveguides can be efficiently described by classical

geometric optics. With these considerations a

model of the fiber optic probe�s response is pre-

sented to aid in predictions and to simulate data.

The complete solution of light propagation

along a fiber is complicated, but in the case of thefiber probe presented here as a sensor for IR

spectroscopy, many difficulties are removed due to

a background spectrum used as a reference. Thus,

the following effects can be neglected: the entrance

conditions of the infrared beam, the interaction

and attenuation along the optical signal trans-

portation section, the transition of the modes

during the taper to the sensing zone, the transitionback to the larger diameter clad section, the exit of

the beam from the fiber, the detection conditions,

and any effect of fiber bending or surface rough-

ness. Then, the only area to be considered is the

section of fiber in contact with the sample. Addi-

tionally only meridian rays are considered, those

are the rays that travel through the center of the

core. It is assumed that the effects due to non-

meridian rays cancel out. Moreover, since the

number of modes is large, a continuum of angles

per wavelength is present and integration, or

summation, over all angles will be a sufficient first

approximation. It is also assumed that each anglecarries equivalent power.

The number of reflections over length L of a

fiber with a diameter of d is dependent upon the

following:

Nðh; d; LÞ ¼ L � tanð90� hÞd

ð3Þ

with h, being the angle of incidence from normal.

Assuming equal components of polarization the

angle dependent reflectance is with RTM and RTE

being defined by equations

RTEðH;nt;niÞ¼n2t cosðHÞ�ni

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2t �n2i þn2t cosðHÞ2

q

n2t cosðHÞþniffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2t �n2i þn2t cosðHÞ2

q264

375

2

ð4Þ

RTMðH;nt;niÞ¼ni cosðHÞ�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2t �n2i þn2t cosðHÞ2

q

ni cosðHÞþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2t �n2i þn2t cosðHÞ2

q264

375

2

ð5Þ

and ni and nt again being defined by the complex

index of refraction, nt for the fiber and ni for the

sample,

Rðh; ni; ntÞ ¼ 0:5 � RTMðh; ni; ntÞ þ 0:5 � RTEðh; ni; ntÞð6Þ

The transmission of signal over length L, at angleh, will be

TLðL; h; ni; ntÞ ¼ Rðh; ni; ntÞNðh;d;LÞ ð7Þ

Assuming that the number of modes is large and

continuous, the total signal for a given wave-

length with a summation from 0� to 90� from

normal is

TLðni; ntÞ ¼X90h¼0

TLðL; h; ni; ntÞ: ð8Þ

174 S. MacDonald et al. / Optical Materials 25 (2004) 171–178

Note that only modes with angles greater than Hc

will propagate in the fiber and that only these

modes will persist in the sensing zone. The signal

to background is then calculated from

Signal

Background¼ TLðnsample; nfiberÞ

TLðnair; nfiberÞð9Þ

4. Results and discussion

The area of the peaks in the imaginary dielectric

function will be linearly proportional to the con-centration of molecules exhibiting absorption. As

such, for chemical systems, each chemical will

contribute to the total mixture dielectric function

linearly with concentration as

etotalðrÞ ¼Xj

CjejðrÞ ð10Þ

with ejðrÞ being the dielectric function of material

j with a concentration Cj. The approximation of

Eq. (10) does not consider intermolecule effectsthat should not be significant except possibly at

extreme concentrations. The determination of the

dielectric functions has been made by Gaussian

dispersion analysis using ATR and transmission

experimental data for water and ethanol [24]. The

values determined for water compare very well to

values in the literature. No known values of eth-

anol exist and it was necessary to calculate thedielectric values for ethanol. The authors refer to

[25] for a complete description of GDA. So, the

signal to background was calculated with the val-

ues of nsample being a mixture of the dielectric

functions calculated for water and ethyl alcohol,

nair being 1, and nfiber ¼ 2:8 being the index of the

fiber as estimated from the TAS glass bulk trans-

mission measurements. This last value is inagreement with the one previously published.

The measured fiber spectra for water, alcohol,

and a 1:1 volumetric mixture are shown in Fig. 1

as signal/background vs wavenumber together

with the calculated spectra. Other concentrations

of alcohol in water were measured, but are not

shown in these plots. The results of the fiber probe

for the different concentrations of ethyl alcohol

and water are similar to that of the liquid ATR cell

measurements [24] and measurements of other in-

vestigators [15,17,19–21]. Fig. 1 shows that be-

tween 2150 and 2250 cm�1 there is no transmission

through the fiber probe. This region is due to the

absorbance of the Se–H bonds from hydrogenimpurities in the Te2As3Se5 glass. Otherwise, the

agreement between experimental and calculated

spectra is very good, validating the assumption

done for the calculations.

Fig. 2a shows the absorbance vs wavelength for

various concentrations of alcohol and water in

smaller wavelength ranges. In the range from 2800

to 4000 wavenumbers the absorption peak of al-cohol (at 2950 cm�1) increases with increasing

concentration. The increase in peak height is ap-

proximately linear with concentration, as expected

by Beers law type analysis. The main difficulty

with Beers law analysis is that the peak positions

move with concentration, as shown in Fig. 2a

where the peak at 2950 drifts to lower wavenum-

bers. Our calculations give a good account of thesebehaviors as shown in Fig. 2b.

Additionally different values of diameter and

sensing length were substituted into the model to

see if the predictions follow the trends of experi-

mental measurements. In Fig. 3, the effect of the

diameter of the sensing zone is calculated. It ap-

pears that the absorbances increase exponentially

when the diameters decrease in total agreementwith the experimental results already published [3].

This result shows that, as far as possible, we have

to reduce the diameter of the sensing zone to im-

prove the sensitivity of the fiber sensor. Moreover

it has been already shown that the flexibility of the

system is higher for smaller diameters. Note that

for diameter close to 2 lm we would obtained

some almost monomode fibers (see Eq. (2)) andthe classical geometric optic assumptions used

above to make the calculation would no longer be

valid. In cases where the number of modes be-

comes small it would be necessary to solve the

Maxwell�s equations either by modal or by Green�sfunction methods [26–30]. This is not the case with

the fiber used here, as the smallest diameter ob-

tained is about 50 lm.The effect of the length of immersion is calcu-

lated and shown in Fig. 4 for three wavenumbers.

Fig. 1. FEWS experimental (B) and calculated (A) spectra of water (a), ethanol (b) and a 1:1 volumetric mixture (c) recorded thanks to

a chalcogenide glass fiber probe. The diameter of the fiber is 200 lm and the length of immersion is 5 cm.

S. MacDonald et al. / Optical Materials 25 (2004) 171–178 175

Fig. 2. (a) Zoom on the range from 2800 to 4000 wavenumbers evidencing the shift of the peak at 2950 cm�1 vs the alcohol con-

centration. (b) The calculated spectra give a good account of these behaviors.

Fig. 3. Theoretical evolution of the absorbance vs the diameter

of the sensing zone.

176 S. MacDonald et al. / Optical Materials 25 (2004) 171–178

Although the actual diameter of the fiber is not

perfectly constant, 200 lm was used as an average

diameter of the sensing zone. The calculated values

for 5 cm are in good agreement with the experi-

mental. More generally, the absorbance increasesquite linearly for the smaller length (until 5 cm).

This range corresponds to the one commonly used.

For longer sensing zones, the absorbances are not

proportional to the length of immersion anymore.

This result is in disagreement with some previous

works [23–32] where pseudo-Beer–Lambert�s lawsare used to explain the evolution of the experi-

mental data.

Fig. 4. Theoretical evolution of the absorbance vs the length of

immersion for three absorption peaks. The black point corre-

spond to the experimental values obtain with about 5 cm of

immersion.

S. MacDonald et al. / Optical Materials 25 (2004) 171–178 177

5. Conclusion

The calculations presented in this work have

permitted us to give an account of spectra re-

corded using a chalcogenide glass fiber sensor.

Among other results, the problems of shifting

peaks or overlapping absorption bands from dif-

ferent chemical are well addressed. For this, thedielectric values of the samples coupled with the

complete expression of the complex reflection co-

efficients have been used to determine the trans-

mitted signal. Note that evanescent waves are

electromagnetic waves that travel along an inter-

face when total internal reflection occurs. The ev-

anescent wave is an imaginary component of the

mathematical solution to total internal reflectionstraveling along the interface. The use of the term

evanescent wave spectroscopy in the context of

these large diameter fiber probes is incorrect be-

cause they carry no power and are not absorbed by

the cladding. Indeed, FATR, for fiber attenuated

total reflection, would be a better acronym.

Moreover, as expected by experiments, these

spectral simulations confirm that, as far as possi-ble, the spectroscopist has interest to reduce the

diameter of the sensor to improve the sensitivity.

For chalcogenide glasses, this can be achieved now

until about 50 lm thanks to a special chemical

solution that congruently dissolves the glass.

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