Surface plasmon resonance sensor using anoptical fiber with an inverted graded-index profile

Fabrice Bardin, Ivan Kasık, Alain Trouillet, Vlastimil Matejec, Henri Gagnaire, andMirek Chomat

A new optical fiber sensor based on surface plasmon resonance is described. It uses an optical fiber withan inverted graded-index profile. A theoretical analysis of the optical propagation when a point lightsource was used and a computation of the optical power transmitted by the fiber were performed.Experiments were carried out to measure changes of the transmitted power caused by refractive-indexvariations of the surrounding dielectric medium. Both the simulation and experiments have shown thatthe sensor exhibits high sensitivity for changes of the surrounding medium in a refractive-index rangefrom 1.33 to 1.39. © 2002 Optical Society of America

OCIS codes: 060.2370, 240.6680.

1. Introduction

During the past 20 years, the surface plasmon reso-nance �SPR� technique has been intensively investi-gated for the detection of chemical and biochemicalspecies.1 Several companies such as Biacore ABproduce sensors that use this technique.2 Thesesensors are made up of a thin metallic layer appliedon the boundary between a glass substrate and thetested dielectric medium. The detection principle isbased on an optical process in which monochromaticTM-polarized light satisfying the resonance conditionexcites a charge-density wave, surface plasma �SP�wave, propagating along the interface between themetallic layer and the dielectric medium. The res-onance condition depends on the wavelength, the an-gle at which the light strikes the substrate–metalinterface, and the dielectric constants of all the ma-terials involved. It is related to a dip on the angularor spectral distribution of the output optical signal.Changes of the refractive index of the tested medium

F. Bardin, A. Trouillet �alain.trouillet@univ-st-etienne.fr�, andH. Gagnaire are with the Laboratoire Traitement du Signal etInstrumentation, Unite Mixte de Recherche, Centre National de laRecherche Scientifique 5516, 23, rue du Docteur Paul Michelon,42023 Saint-Etienne Cedex 2, France. I. Kasık, V. Matejec, andM. Chomat are with the Institute of Radio Engineering and Elec-tronics, Academy of Sciences of the Czech Republic, Chaberska 57,182 51 Prague 8, Czech Republic.

Received 25 July 2001; revised manuscript received 17 Decem-ber 2001.

0003-6935�02�132514-07$15.00�0© 2002 Optical Society of America

2514 APPLIED OPTICS � Vol. 41, No. 13 � 1 May 2002

changes the shape of this distribution, which can beused for the detection.

Several SPR sensing structures with the metalliclayer applied on a bulk dielectric prism,3 planar wave-guides,3 multimode3–6 fibers, and single-mode7,8 fibershave been studied. The well-known Kretschmannconfiguration with the metallic layer deposited directlyon a bulk prism is one of the most flexible means forthese measurements, because in this case the wave-length, angle, and polarization of the incident lightcan be easily controlled. However, requirements forthe miniaturization of sensing devices, multichannelanalysis, and capability of performing remote sensingare the reasons why SPR sensors based on opticalfibers are also investigated.

The first optical fiber SPR sensing structure basedon a multimode optical fiber with a uniform silica corewas developed by Jorgenson and Yee.4 The fiberwas axially excited by white light and the spectralinterrogation was used. In another arrangement,Trouillet et al. used specific launching of monochro-matic light through an inclined collimated beam.5,6

However, in both of these experimental arrange-ments one may observe broad resonance curves be-cause optical rays strike the substrate�core�–metalboundary at a relatively wide range of incident an-gles. As a way to make this range as narrow aspossible, a kind of multimode fiber with an invertedgraded-index �IGI� profile excited under proper con-ditions can potentially be used. Such fibers havealready been used for the evanescent-wave detectionof refractive-index changes of the cladding. It hasbeen theoretically shown that the ray paths in the

core of an IGI fiber excited with a point light sourcesuitably positioned on the fiber axis can be controlledin such a way that all the rays strike the core–cladding boundary at nearly the same angles.9 Thisadvantageous property was confirmed experimental-ly.10

This paper presents an SPR sensing structurebased on a multimode IGI fiber that is excited axiallyby a single-mode fiber. This structure is theoreti-cally investigated by using the ray-optics approach.The results of the calculations are compared with theexperimental ones.

2. Principle

The principle of the investigated SPR sensor is basedon the determination of refractive-index changes ofthe medium surrounding the IGI fiber coated with athin metallic layer by means of changes of the trans-mitted optical power P. This section deals with therefractive-index profile of the investigated IGI fiberand computation of the transmitted optical power.

A. Refractive-Index Profile

For the theoretical description of IGI-fiber waveguideoptics, the WKB approach combined with a pertur-bation method as well as ray optics have already beenused.9,11 In this paper the last approach is used andchanges of the optical power transmitted through theIGI fiber are expressed in terms of the reflection andrefraction of rays. The analysis is carried out for anarrangement in which the optical fiber is illuminatedby a point light source positioned on the fiber axis ata distance h from the input fiber face. Thus, thetheoretical analysis can be confined to meridionalrays.

On the basis of simple theoretical considerations, itcan be shown that there is an ideal IGI profile forwhich every meridional ray strikes the core–claddinginterface at the same angle of incidence �. Thisprofile can be described by the following equation:

n2�R� � na2 sin2��� �

R2

H2 � R2 , 0 � R � 1,

� n12, R � 1. (1)

In Eq. �1�, a is the core radius, R � r�a is the nor-malized radial distance of a point on the input fiberface in which the ray enters the fiber, H � h�a is thenormalized distance between the source and the end-face fiber, na is the refractive index of the core at thecore–cladding boundary, and n1 is the refractive in-dex of the cladding. This ideal IGI profile can beapproximated by a parabolic IGI profile.9

The actual refractive-index profile of the IGI fiberfabricated on the basis of the modified chemical vapordeposition �MCVD� process and used in the experi-ments is shown in Fig. 1 �solid curve�.9 This profile

can be approximated by the following equation:

n�R� � m1 � m2 R � m3 R2 � m4 R3 � m5 R4

�m6

1 � m7 R2 , 0 � R � 0.86,

� na , 0.86 � R � 1,

� n1 , R � 1. (2)

Here the coefficients m1 � 1.45, m2 � �5 � 10�6,m3 � 0.004, m5 � 0.006, m6 � 0.0025, and m7 � 669were determined by a least-squares regression. Theparameter na is equal to 1.457; that is, it is equal tothe refractive index of a layer of pure silica remainingafter the etching of the MCVD preform by hydroflu-oric acid. The fraction in Eq. �2� characterizes theprofile imperfection at the core axis �a central peak�that arises during the preform fabrication. This in-crease of the refractive index of the last depositedlayer is an inherent feature of the standard MCVDmethod, similar to the central dip in standardgraded-index preforms.

By fitting the ideal IGI profile to the IGI part of theactual profile in Fig. 1, values of 84.38° for the angle� and 6.0 for the parameter H were determined. Itis worth noting that the term na sin��� in Eq. �1� isthe effective index �neff� of all the optical rays thatpropagate in the fiber. The value of neff � 1.45 canbe calculated by using the parameters shown above.This value is the same as neff of a SP wave that can beexcited by using a silver-coated silica fiber sur-rounded by an external medium with a refractiveindex equal to 1.38 �Ref. 12�. Thus, the main advan-tage of the ideal IGI profile is that all the rays areable to excite exactly the same SP wave. For theactual profile this condition cannot be fully satisfied.Nevertheless, even in this case one can expect verysharp resonance curves. It may be noted that a SPwave with the same neff can also be excited by usinga gold-coated fiber and an external medium with therefractive index equal to 1.35 �Ref. 12�.

Fig. 1. Ideal refractive-index profiles compared with the actualrefractive-index profile of the IGI preform and its polynomial ap-proximation at a wavelength of 670 nm.

1 May 2002 � Vol. 41, No. 13 � APPLIED OPTICS 2515

B. Ray Trajectories

Trajectories of meridional rays in the IGI fiber withthe refractive-index profile described by Eq. �2� werecalculated by using the following differential equa-tion:

dZdR

�neff

2

n2�R� � neff2 , (3)

where Z is the normalized distance z�a along the fiberaxis. From results of these calculations one can findthat there are two main types of trajectories. Tra-jectories of the first type are formed of arched pathsvery similar to hyperbolic cosine functions. The tra-jectories of the second type cross the fiber axis. Theyare similar to hyperbolic sine functions. Becauseboth types of these trajectories cannot be expressedanalytically, they were instead determined numeri-cally from Eq. �3� by using the Runge Kutta methodof the fourth order. Examples of the calculated tra-jectories are shown in Fig. 2. Comparing these tra-jectories with those calculated for a parabolic IGIprofile, which were published elsewhere,9 one canfind that they are similar with the exception of anarrow part around the fiber axis where central per-turbation of the actual refractive-index profile exists.The angle � at which a ray strikes the core–claddingboundary and the normalized spatial period p, whichis defined as the axial distance between two succes-

sive reflections of the ray from the core boundary,were determined from the calculated trajectories.

The dependence of the angle � on the angle ofincidence � on the input fiber face for different valuesof the normalized distance H is shown in Fig. 3. Itcan be seen that for H � 6.5, the values of angle � fallinto a narrowest range between 84.2° and 84.5°.

A relationship between the normalized spatial pe-riod p and the angle � for several values of H is shownin Fig. 4. From this figure one can see that thecurves for values of H higher than 6.57 exhibit adiscontinuity. In this case and for the lowest valuesof angle � the trajectories are hyperbolic sinelikefunctions, whereas for the highest values of � thetrajectories are hyperbolic cosinelike functions. Incontrast, for values of H lower than 6.57 only hyper-bolic sinelike trajectories exist and the p��� curvesare continuous. A critical value of H � 6.57 wasdetermined by using a trial and error method. InFig. 4 one can see that the values of the normalizedspatial period p range from 25 to 150 �i.e., the spatialperiod ranges from 5 to 30 mm for the core radiusequal to 200 �m�.

Similar calculations were performed for a step-index profile corresponding to a pure silica core �astandard polymer clad silica, or PCS, fiber�. In thiscase one can see from Fig. 3 that the values of angle� fall to a broader range between 85° and 90°.

C. Model of Changes of the Transmitted Optical Power

The theoretical modeling was performed for an SPRoptical fiber sensing structure depicted in Fig. 5. Inthe calculations the optical fiber was assumed to becomposed of three parts, namely, a central sensingpart consisting of the IGI core coated with a metallic

Fig. 2. Illustration of the two kinds of trajectories in the case ofthe approximated refractive-index profile versus the angle of inci-dence � on the input fiber face.

Fig. 3. Dependence of the angle of incidence � on the angle ofincidence � for different normalized distances H between thesource and the input face of an IGI or a PCS fiber.

Fig. 4. Dependence of the normalized spatial period p on theangle of incidence � for different normalized distances H.

Fig. 5. Schematic illustration of the sensing device.

2516 APPLIED OPTICS � Vol. 41, No. 13 � 1 May 2002

layer and immersed into a tested medium, and inputand output parts belonging to the original IGI fiber.

The transmitted optical power P can be expressedby the following integral over the cross section S ofthe fiber:

P �1S

S

PinRcN1N3Rm

N2dS. (4)

In Eq. �4�, Rc and Rm are the reflection coefficients forthe optical power on the cladding and metallic layers,respectively. They were calculated by using theclassical matrix approach for multilayer structuresunder the assumption of a planar core–claddingboundary.13 They depend on the thickness and per-mittivity of all the layers, light polarization, wave-length, and angle �. This angle was determinedfrom the calculated trajectories �see Subsection 2.B�.It should be noted that the reflection coefficient on themetallized part of the fiber depends significantly onthe light polarization, as only TM-polarized light canexcite SP waves.

The symbols N1 and N3 denote the number of re-flections on the first and third parts of the fiberwhereas N2 is the number of reflections on the met-allized part. They were determined from the periodp and the length of each part.

As the beam from the excitation single-mode fiberexhibited a nearly Gaussian distribution of the out-put power, each incident ray carried different opticalpower. The width of this Gaussian distribution wasdetermined experimentally and used for the compu-tation of the factor Pin in Eq. �4�.

The symbol S denotes the illuminated area of theinput fiber face. Because there is a central peak onthe actual IGI profile, this central part of the fiber canbe considered as a secondary waveguide in which thelight is confined and thus does not experience reflec-tions at the core–cladding boundary. Therefore,this part of the input face was not included in theintegration in Eq. �4�. In order to obtain relativeoptical power, values of P calculated from Eq. �4� weredivided by the value of the power determined for airas the surrounding medium.

The results of the computation performed forsilver- and gold-coated fibers for different normalizeddistances H are shown in Fig. 6. One can observethat the SPR sensor can be used for detection in arefractive-index range from 1.36 to 1.39 when asilver-coated fiber is used and between 1.33 and 1.37when a gold-coated fiber is used.

3. Experiment

The experimental setup is shown in Fig. 7. The lightfrom a 1-mW laser diode operating at 670 nm waslaunched in a single-mode fiber with a core diameterof 4 �m and a numerical aperture of 0.12. A fiberwith such a small core can be considered a point lightsource. The output end of this fiber was positionedon the axis of the IGI fiber with a core diameter of 400�m at the distance h, which was adjusted by micropo-

sitioning stage. The transmitted optical power fromthe IGI fiber was measured with a power meter�Hewlett-Packard Lightwave multimeter 8153A�.

The IGI sensing fibers were fabricated as follows.The original polysiloxane cladding was mechanicallystripped from the IGI fiber over a length L rangingfrom 15 to 50 mm and the bare core was immersed inchromosulfuric acid to dissolve the residuals. Theinput and output faces of the fiber were polished toreduce light diffusion. A metallic coating was depos-ited on the bare core by using a thermal evaporationsystem that limited the total length of the fiber to 20cm. The fiber was rotated around its axis during theevaporation in order to achieve a homogeneous layer.On the basis of previous research the thickness of theapplied metallic layers was chosen in a range from 45to 55 nm.12

The sensitivity of the devices to refractive-indexchanges of the surrounding medium was tested byimmersing the metallized part of the fiber in immer-sions with varied refractive indices. The immer-sions were mixed of pure water �n � 1.33� andglycerol �n � 1.47�. The actual refractive index ofeach immersion was measured with an Abbe refrac-tometer.

4. Results

The influence of four factors and parameters onchanges of the transmitted optical power was stud-ied: the type of metallic coating, the distance h be-

Fig. 6. Calculated relationship between the relative transmittedoptical power and the refractive index of the surrounding mediumfor an IGI fiber with a core diameter of 400 �m metallized by silver�ε � �18.5 1.25i� or gold �ε � �14 1.25i� coatings for differentnormalized distances H of a 670-nm source. The thickness andlength of the metallic coatings are 50 nm and 15 mm, respectively.

Fig. 7. Experimental setup for the IGI fiber sensor.

1 May 2002 � Vol. 41, No. 13 � APPLIED OPTICS 2517

tween the source and sensing fibers, the lateral offsety of these fibers, and the length L of the sensing area.

The relationships between the relative transmittedoptical power and the refractive index of the sur-rounding medium measured for a silver layer and agold layer and several distances h are shown in Fig.8. From this figure one can conclude that these fi-bers can be used for the detection in an index rangefrom 1.33 to 1.39, depending on the metal used.There are two linear parts on both sides of the min-imum of each resonance curve. These parts definetwo refractive-index ranges in which the sensor canbe operated. The sensitivity to refractive-indexchanges can be expressed through slopes of theselinear parts. When the 0.2-�W detection limit of thepower meter is taken into account, a resolution of 5 �10�5 refractive-index units �RIU� in a range of refrac-tive index of the surrounding medium between 1.381and 1.388 can be achieved with a silver-coated fiber �a55-nm-thick silver coating, an L of 1.5 cm, and an h of0.5 mm�. With a gold-coated fiber and in similarexperimental conditions, a resolution of 8 � 10�5 RIUin a range of refractive index of the surrounding me-dium between 1.367 and 1.380 can be achieved. Onecan observe that the sensitivity to refractive-indexchanges becomes negligible near the minimum ofthe resonance. As expected, there is an optimumdistance h for which the resonance effect is mostpronounced. This distance is 0.8 mm �H � 4� forsilver-coated fibers and 0.5 mm �H � 2.5� for gold-coated fibers.

The influence of the lateral offset y of the axes ofthe excitation and sensing fibers is shown in Fig. 9.This offset widens the resonance. Moreover, thisphenomenon was found to be the same for the twosymmetrical positions in respect to the IGI fiber axis.

The influence of the length L of the sensing part isshown in Fig. 10. When this length was increasedfrom 1.5 to 5 cm, the minimum of the relative opticalpower for the 55-nm-thick silver layer decreased from30% to 7%. Similar results were obtained for thegold layer.

5. Discussion

The calculated curves and experimental results arein good agreement with respect to the range of therefractive index in which the transmitted opticalpower changes. However, the model cannot give fulldescription of the effect of the light source distance hon the resonance curves. There are differences be-tween the optimum values of h determined from theexperimental curves �see Fig. 8� and those obtainedon the basis of the trajectory calculations �see Sub-section 2.B� and on the basis of the computation of therelative transmitted optical power �see Subsection2.C�. Experimental optimum distances h were mea-sured in a range between 0.5 and 1.2 mm �H between2.5 and 6.0�, whereas Fig. 6 shows that the theoret-ical optimum distance H between 7.5 and 10 can beexpected for the same conditions. One reason forthese differences may be in the existence of the cen-tral peak, which acts as a secondary waveguide.Coupling between the light propagating in the cen-tral peak and that excited by rays incident upon theIGI part of the core were not taken into account in thecomputation. Another reason for these differencescould be the lateral offsets of the source with respectto the axis in the experimental setup. Because of

Fig. 8. Experimentally determined relationship between the rel-ative transmitted optical power and the refractive index of thesurrounding medium for different distances h of the source.

Fig. 9. Experimental dependence of the relative transmitted op-tical power on the refractive index of the surrounding medium fordifferent lateral offsets y.

Fig. 10. Experimental dependence of the relative transmittedoptical power on the refractive index of the surrounding mediumfor different lengths L of the sensing silver-coated part.

2518 APPLIED OPTICS � Vol. 41, No. 13 � 1 May 2002

this offset, skew rays are excited in the fiber whereasonly meridional rays were taken into account in thecomputation.

Comparing calculations and experimental resultsin Figs. 6 and 8, one can observe that there is a bigdifference between the curves in respect to the depthof the minimum of the relative optical power. Asthere is no control of the polarization state of opticalwaves propagating through the fiber, one can expectthis minimum to be higher than 0.5. However, theexperimental data in Fig. 8 show that the minimumvalues of this power are significantly lower than 0.5.Moreover, it was found that this value can be de-creased to at least 0.1 when the length L of the sens-ing part is increased �see Fig. 10�. Such aphenomenon can be explained by the TE–TM polar-ization conversion between two ray reflections. TheTE-polarized waves totally reflected at the first re-flection at the core–metal boundary partly changetheir polarization state to TM-polarized waves, whichare absorbed at the next reflection. This polariza-tion conversion may be related to the effect of bothlocal fiber imperfections and the central peak. Anempirical optical power conversion coefficient can beused to take into account the conversion in the com-putation. Results obtained with the value of theconversion coefficient equal to 0.3 are shown in Fig.11. They are in good agreement with the experi-mental results shown in Fig. 10.

The results obtained with a standard PCS fiberwith the same experimental conditions are shown inFig. 12. The comparison of curves in Figs. 10 and 12shows that using the IGI fiber instead of the PCSfiber enables us to improve the sensitivity by a factorof 2–3.

The main practical inconvenience to developing aprototype concerns the alignment between the single-mode fiber and the IGI fiber. In order to overcomethis drawback, the use of a multimode optical fiberwith a core diameter of 50 �m has been investigatedas a substitute for the single-mode fiber and to min-

imize alignment offsets. The performances of thesensor have not been modified by such a change in theexperimental setup. Furthermore, mechanical con-nections have been successfully realized and werepreviously reported.10 The principle is close to thosethat are used in commercial optical fiber connectors.They provide an unbending attachment of the opticalfibers.

6. Conclusions

A new fiber-optic chemical sensor for the detection ofsmall variations of refractive index that uses SPR hasbeen presented. This sensor is based on an originaloptical fiber with an inverted quasi-parabolicrefractive-index profile. It has been shown thatsuch a profile allows a very narrow range of angles atwhich the rays strike the core–cladding boundary,provided that the fiber is properly axially illuminatedby a single-mode fiber. This specific launching ofmonochromatic light at 670 nm into the fiber allowsus to use simple and compact optical elements.

The experimental results and performed calcula-tions have shown that a resolution of 5 � 10�5 RIUcould be achieved in a range of refractive index of atested medium between 1.33 and 1.39, depending onthe type of the metallic coating. In comparison withstandard PCS fibers used with the same experimen-tal conditions, an improvement of the resolution hasbeen demonstrated. Further applications to the de-tection of hydrocarbons or the determination of bind-ing kinetic data for biological analytes will beperformed with selective coatings applied on thesensing part of the IGI fibers.

The IGI optical fibers investigated in this paperwere fabricated under the financial support of theGrant Agency of the Czech Republic �Project 102�99�0548�.

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Fig. 11. Calculated dependence of the relative transmitted opti-cal power on the refractive index of the surrounding medium fordifferent lengths of the sensing part with an empirical power con-version coefficient from TE to TM polarization of 0.3.

Fig. 12. Comparison of the experimentally determined depen-dence of the relative transmitted optical power on the refractiveindex of the surrounding medium for PCS and IGI fibers.

1 May 2002 � Vol. 41, No. 13 � APPLIED OPTICS 2519

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