Theoretical Modelling of An End Face Reflection based Tapered Fiber Optic SPR Sensor with Different Probe Designs

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1 Theoretical Modellig of A Ed Face Reflectio based Tapered Fiber Optic SPR Sesor with Differet Probe Desigs Rajeesh. K. Verma Departmet of Physics Cetral Uiversity of Rajastha Bader Sidri, Ajmer, Idia Abstract - The theoretical modellig of a SPR based tapered fiber optic sesor is preseted with the ed face as a reflectig surface. The performace of the sesor is evaluated i terms of its sesitivity ad detectio accuracy with taper ratio. Apart from this, the effect of various taper profiles o to the sesitivity of the sesor is also studied. It has bee foud i the preset study that the ed face reflectio techique reduces the size of the sesor probe ad maes it miiaturized. The maximum sesitivity of the expoetial taper profile maes it a optimum taper profile amog the three profiles amed liear, parabolic ad expoetial. Keywords - Surface Plasmos, Fiber Optics, Tapered Fiber, Plasmos I. INTRODUCTION Surface plasmos resoace (SPR) is a very promisig tool for the sesig of various biochemical ad gaseus sesig [- ]. A vast umber of researchers are egaged i this upcomig area to explore various possibilities i terms of maig fiber optic probes for the cotiuous moitorig of chages occurrig i biochemical, chemical ad gasesus media [-7]. Recetly may theoretical models have bee proposed for the better sesig mechaisms such as localized surface plasmo based fiber optic sesors [3], use of coductig metal oxides is also a importat study []-[4]. I the last year people have fabricated ad characterized the fiber optic sesig probes for ph sesig [] ad HS gas sesig []. Sesig of Pheolic compouds ad Ammoia gas sesig has also bee proposed []-[3]. Fiber optic gratig is also beig used i cojuctio with spr to mae a miiaturized fiber optic probe for sesig the refractive idecies [4]-[5]. Most recetly people are also proposig certai models o optical waveguides which ivolves artificially structured materials such metamaterials as a SPR active material [6]. I this study a theoretical model has bee proposed which ivoles the multimoded tapered optical fibers. Cotrary to the covetioal fiber optic probes, i the preset probe the oe of the ed face is coated with a silver paste to mae it reflectig. This probe proposed i the model will be miiaturized as well as it will wor as a poit sesor as its oe ed ca be dipped directly i to the medium to which we are goig to sese. The performace parameters such as sesitivity have also bee evaluated i terms of the taper ratio. Effect of various taper profiles such as liear, parabolic ad expoetial liear has also bee studied ad a comparative aalysis has also bee provided i terms of the best taper profile for the sesitivity amog the rest of the two. II. THEORETICA MODE The theoretical model is based o the priciple of atteuated total reflectio (ATR) with Kretschma cofiguratio. The plastic claddig from the middle portio of a step idex multimode fiber is removed ad the uclad portio is tapered. The uclad tapered regio is the cut from the poit where the waist diameter is miimum. The uclad tapered fiber regio is the coated with a thi gold layer, which is further surrouded by sesig medium (Fig. ). Claddig Sesig Regio i Core Figure : A typical SPR based fiber optic sesor with tapered probe. Differet taper profiles ca be geerated durig fabricatio usig Flame Brush techique as suggested by Birs ad i [3]-[4]. The method uses a poit lie heat source (a gas burer) which heats oly a small sectio of the fiber at a time. This burer is made to travel at costat speed i a oscillatory maer alog the distace of the fiber (to be tapered) so that i each cycle of oscillatio every elemet of the fiber is heated idetically. If the speed of the burer is large compared to the tapered elogatio speed the a time averaged hot zoe is set up i the fiber which satisfies the coditio that the fiber sectio beig heated is always cylidrical ad is always heated uiformly. Allowig the hot zoe legth to chage as taper elogatio precedes ay shape of the fiber taper ca be geerated. Three taper profiles amely liear (P), parabolic (PP), ad expoetial liear Gold layer Reflectig Surface IJERTV3IS

2 (EP) have bee studied i literature for a fiber optic evaescet field absorptio sesor as show i Fig. []. We cosider these profiles for SPR based fiber optic tapered sesor. The differet parts of the sesor are discussed below. C. Reflectio Coefficiet (R p ): We cosider N-layer model to obtai the expressio for amplitude reflectio coefficiet for p-polarized icidet beam as show i Fig. 3 [5]. Figure : Three differet taper profiles showig the liear, parabolic, ad expoetial-liear variatio of core radius of taper with distace z from the iput ed of the taper. A. Core of the optical fiber For theoretical modelig, the optical fiber cosidered is a step-idex multimode plastic clad silica fiber. Siced the refractive idex of the silica varies with the wavelegth therefore the wavelegth depedece of the refractive idex () of the silica core is give by Sellmeier dispersio relatio: 3 a b a b a b a, a, a3, b, b, ad b3 are the Sellmeier coefficiets ad λ is the wavelegth of light used i μm. The values of these coefficiets are give i the table below [5]: a a a b b.644 b B. Dispersio relatio for plasmoic material For the wavelegth depedece of the dielectric costat of the plasmoic material we have used the Drude model, give as m c mr i mi i () where λp ad λc deote the plasma wavelegth ad collisio wavelegth, respectively. For gold, the followig values of the plasma wavelegth ad collisio wavelegth are used: P = M AND C = M [6] p c 3 () Figure 3: N-ayer model to determie the reflected light itesity. I the preset study, N is equal to 3. The layers are assumed to be staced alog the z-axis. The arbitrary medium layer is defied by thicess d, dielectric costat ε, permeability μ, ad refractive idex. The tagetial fields at the first boudary Z = Z = are related to those at the fial boudary Z = ZN- by U U M V V N N I Eq. (3) U ad V are the tagetial compoets of electric ad magetic fields at the boudary of first layer, respectively; UN- ad VN- are the correspodig fields at the boudary of Nth layer ad M, ow as characteristic matrix of the combied structure, is give by with where N M M M M M M q M cos cos iq si / cos d (3) (4) isi / q cos si (5) / (6) z z / si ad θ is the agle of the ray ormal to the th iterface. The amplitude reflectio coefficiet (r p ) for p-polarized icidet wave is give by (7) IJERTV3IS

3 r p M MqN q M M qn M M q q M M q N Fially, reflectace (Rp) for p-polarized light is. D. Reflected Power R p r p The light is lauched ito the oe ed of the fiber through a broadbad light source with proper optics. The other ed is polished with silver paste to mae it reflectig. The light rays that travels to the fiber gets reflected bac due to this mirror ed face. The ed through which light is lauched is coected with two way reflectio probe. Oe ed is used for light lauchig ad other is used for collectig light bac. This reflectig ed is coected to a detectio system to record the output sigal. Cosider the propagatio of all the guided rays lauched i the fiber usig a collimated source ad a microscope objective. The objective focuses the beam at the ed-face of the fiber at axial poit. The agular power distributio of rays guided i the fiber with as the agle of the ray with the ormal to the core-claddig iterface is give by [] si cos dp d cos () To determie the effective reflected power, the reflectace (Rp) for a sigle reflectio is raised to the power of the twice the umber of reflectios the specific propagatig agle udergoes with the sesor iterface (Due to reflectig ed each ray retraces its path). The guided rays i the uiform core fiber eter the sesig tapered regio as show i Fig.. Assumig adiabatic (slow) taperig, if (z) is the taper radius at a distace z from the iput ed of the taper the the agle of the ray will trasform ito agle (z) i the tapered regio ad is give by [] z cos cos z N i i ta () I above equatio, i ad are, respectively, the radii of the iput (i.e. z = ) ad output ed (i.e. z = ) of the taper. Further, the secod term o right had side is the taper agle () ad is the taper legth. The taper radius varies with z i differet fashio for differet profiles give as [7] iear: z i i (8) (9) () Expoetial liear: e Parabolic: z i e e P i z z i z / (3) (4) If (, ) is the rage of icidet agles of the rays lauched at the iput ed of the taper, the at a distace z, this rage alters to [(z), (z)] due to variatio i core diameter i tapered regio ad the trasmitted power at the output ed of the fiber is give by P Nref (, z) dz RP tras dz ( ( si cos si cos cos ) cos ) d d (5) The expressios for (z) ad (z) ca be foud by substitutig the value of i Eq. (). For (z), si cl. Further, Nref ad for (z), is the umber of reflectios the ray of agle udergoes i the fiber with radius (z) i the legth ad is give as E. Sesitivity N ref (, z) ( z) ta (6) I ay fiber optic SPR sesor based o wavelegth iterrogatio, the light from a polychromatic source is lauched ito oe of the eds of the fiber ad the spectrum of the trasmitted light received at the other ed is recorded to ow the resoace wavelegth (the wavelegth correspodig to miimum trasmissio) correspodig to the refractive idex of the sesig layer. If sesig regio has a refractive idex value of s ad m is the dielectric costat of the metal layer i cotact with sesig regio, the the surface plasmo resoace occurs whe the followig coditio is satisfied / ms si Re m s (7) I Eq. (7), the expressio o the left had side is the propagatio costat (Kic) of the light icidet at a agle while the right had side represets the real part of surface IJERTV3IS

4 plasmo propagatio costat (KSP). I the SPR sesor based o wavelegth iterrogatio, Fixed agles of icidece are used ad resoace wavelegth (λres) is determied correspodig to refractive idex of the sesig layer (s). If the refractive idex of the sesig layer is altered by δs, the resoace wavelegth shifts by δλres. The sesitivity (S) of a SPR sesor with spectral iterrogatio is thus defied as [5] S res s (8) b. III.RESUTS AND DISCUSSIONS Various importat parameters used i the preset study have bee tae as: umerical Aperture of the fiber =., diameter of the fiber core (i) = 6 m, sesig regio legth () =.5 cm, gold layer thicess = 5 m. I order to aalyze the effect of taper ratio ad taper profiles o the sesitivity, first of all we have to aalyze the plasmoic resoace coditio give by Eq. (7). As it is evidet from Eq. (7), propagatio costat (KSP) of surface plasmo wave (SPW) depeds o the wavelegth of the light as well as o the dielectric costat of metal layer (m) ad refractive idex (s) of sesig regio. Whereas, the propagatio costat (Kic) of the icidet wave depeds o the agle ad wavelegth of the light ray as well as o the refractive idex of the fiber core. Figure 4a depicts the variatio of KSP (i.e. for s =.333), KSP (for s =.343) ad Kic with wavelegth for the case whe o taperig of the fiber probe is doe. The agle of the ray is tae at the middle of the correspodig agle (, ). As ca be see, KSP ad Kic curves cross each other at m for s =.333 ad at m for s =.343. Thus, a shift (δλres) of 34.6 m i resoace wavelegth is observed for δs =.. Now, the ext tas is to estimate the effect of taper profile (Eqs. - 4) ad taper ratio (i/o ) o the shift (δλres) for the same value of δs. Figure 4b shows the variatio of KSP, KSP, Kic (P), Kic (PP) ad Kic (EP) with wavelegth for taper ratio of 3.. The curves correspodig to KSP ad KSP are similar to those i Fig. 4a. a. Figure 4: Variatio of propagatio costats for SPW ad icidet wave with wavelegth for (a) Taper ratio =. ad (b) Taper ratio = 3.. A oticeable chage i Fig. 4b ca be see i terms of threefold variatio of Kic correspodig to three differet taper profiles. This happes due to two reasos: oe, the agular rage (, ) is differet for differet taper profiles, ad secod, the depedece of both ad o the taper ratio (Eq. ). Cosequetly, the curves correspodig to KSP ad KSP will itersect these three Kic curves at six differet poits. I Fig. 4b, the above itersectios correspodig to P, PP, ad EP have bee show with the help of two each solid, dashed, ad dotted arrows, respectively. Table below shows the poits of itersectio ad correspodig shift (δλres) for three taper profiles ad three taper ratios. It is quite visible from Fig. 4b ad from Table above that for a give δs, maximum shift (i.e. δλres) is obtaied for EP whereas miimum shift is foud for PP. For P, the correspodig shift is foud to be i betwee the two. The similar tred was observed for all profiles at several agles i the correspodig rage (, ) ad at several taper ratios betwee. ad.. This observatio prepared the groud to chec the preset case whe all the guided rays are lauched together i the tapered fiber. The calculatios for trasmitted power for a give refractive idex of the sesig regio, usig Eq. (5), were IJERTV3IS

5 carried out with all the guided rays lauched separately for all the three taper profiles with differet taper ratios. From the plot of SPR spectrum resoace wavelegth (λres) was determied. To appreciate the shift i resoace wavelegth (i.e. δλres) due to the chage i the refractive idex (δs) much more precisely, the refractive idex chage (δs) was arrowed by taig the values of s ad s as.333 ad.335, respectively, (i.e., δs =.). As was expected from above discussio, the shift (δλres) was foud to be maximum for EP ad miimum for PP with P lyig i betwee the two. The sesitivity of the sesor was calculated as defied by Eq. (8). Figure 5 gives the correspodig variatio of the sesitivity (i m per RIU) with taper ratio for all the three taper profiles. The figure shows that the sesitivity icreases with a icrease i taper ratio for ay taper profile. Further, the sesitivity is maximum for expoetial-liear profile (EP). The miimum sesitivity is observed for parabolic profile (PP). For the preset set of desig parameters metioed above, a sigificat sesitivity ehacemet of more tha 8% i compariso to utapered fiber optic SPR sesor is observed at a taper ratio of 3. for expoetial-liear taper profile (EP). Figure 5: Variatio of sesitivity (i m per RIU) with taper ratio for three differet taper profiles. Apart from this explaatio of the sesitivity ehacemet with taper profile ad taper ratio i terms of the shiftig of resoace poit (i.e., K SP = K ic ), aother physically logical reaso ca be give i terms of evaescet wave absorptio. By taperig the fiber we ited to broade the agular rage from (, ) to (, ), because lower value of agle meas more spreadig of the evaescet field ito the regio adjacet to fiber core. Hece the couplig betwee evaescet wave ad SPW will become stroger ad sesitivity is boud to icrease due to taperig. Now, as far as the effect of taper profile is cocered, the agular rage (, ) i tapered regio will be maximum for EP ad miimum for PP accordig to Eqs. (3) ad (4). This is why sesitivity is foud to be maximum for EP. Furthermore, this improved couplig betwee evaescet wave ad SPW due to tapered fiber causes SPR curve to broade. However, the degree of SPR curve broadeig is much lesser tha the sesitivity ehacemet with taper ratio ad taper profile. IV.CONCUSIONS I summary, a comprehesive theoretical model of a ed face reflectig tapered fiber optic probe has bee preseted to evaluate the ifluece of taperig o the performace of a fiber optic SPR sesor. It is foud from the study that the sesitivity of the sesor icreases quite sigificatly with taper ratio. Also, the use of expoetial-liear taper profile istead of liear or parabolic taper profile further improves the sesitivity. Therefore, high taper ratio with expoetialtaper profile is recommeded to desig a highly sesitive fiber optic SPR probe. The light lauchig optics is also used for collectig the reflected light therefore it is more miiaturized as compared to other fiber optic probes. REFERENCES []. R. C. Jorgeso, S. S. Yee, A fiber-optic chemical sesor based o surface plasmo resoace, Ses. Actuators B vol. pp []. O. Esteba, R. Aloso, C. Navarrete, C. A. G. Cao, Surface plasmo excitatio i fiber-optic sesors: a ovel theoretical approach J. ightwave Techol. Vol. pp.448. [3].. K. Chau, Y. F. i, S. F. Cheg, T. J. i, Fiber-optic chemical ad biochemical probes based o localized surface plasmo resoace, Ses. Actuators B vol.3 pp. 6. [4]. S. A. Zyio, A. V. Samoylov, E. R. Surovtseva, V. M. Mirsy, Y. M. Shirsov, Bimetallic layers icrease sesitivity of affiity sesors based o surface plasmo resoace, Sesors vol. pp.6. [5]. A. K. Sharma, B. D. Gupta, O the performace of differet bimetallic combiatios i surface plasmo resoace based fiber optic sesors, J. App. Phys. vol [6]. A.K. Sharma, B.D. Gupta, Fiber optic sesor based o surface plasmo resoace with Ag-Au alloy aoparticle films, Naotechology vol. 7 pp.4 6. [7]. G. G. Neiger, P. Tobisa, J. Homola, S. S. Yee, og rage surface plasmos for high resolutio surface plasmo resoace sesors, Ses. Actuators B 74 pp. 45. [8]. Raja, A. K. Sharma, B. D. Gupta, Fiber optic sesor based o log rage surface plasmo resoace, J. Opt.: Pure ad App. Opt. vol.9 pp [9]. A. K. Sharma, Raja, B. D. Gupta, Ifluece of dopats o the performace of a fiber optic surface plasmo resoace sesor, Opt. Comm. vol.74 pp []. S. K. Misra ad B. D. Gupta, Surface plasmo resoace based fiber optic ph sesor utilizig Ag/ITO/Al/hydrogel layers, Aalyst vol.38 pp []. R. Tabassum, S. K. Misra ad B. D. Gupta, Surface plasmo resoace-based fiber optic hydroge sulphide gas sesor utilizig Cu ZO thi films Physical Chemistry Chem. Phys. vol []. S. Sigh, S. K. Misra ad B. D. Gupta, SPR based fibre optic biosesor for pheolic compouds usig immobilizatio of tyrosiase i polyacrylamide gel, Sesors ad Actuator B vol. 86 pp [3]. S. K. Misra, D. Kumari ad B. D. 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6 [8]. A. Diez, M. V. Adres, J.. Cruz, I lie fiber optic sesors based o excitatio of surface plasmo modes i metal-coated tapered fibers, Ses. Actuators B vol. 73 pp. 95. [9]. Y. C. Kim, W. Peg, S. Baerji, K. S. Boosh, Fiber-optic surface plasmo resoace for vapor phase aalyses, Opt. etters vol 3 pp.8 5. []. F.J. Bueo, O. Esteba, N.D. Herrera, M.C. Navarrete, A.G. Cao, Sesig properties of asymmetric double layer covered tapered fibers, App. Opt. vol. 43 pp []. B. Gruwald, G. Holst, Fiber optic refractive idex microsesor based o white light SPR excitatio, Ses. Actuators A vol. 3 pp []. B. D. Gupta, C. D. Sigh, Fiber optic evaescet field absorptio sesor: effect of lauchig coditio ad the geometry of the sesig regio, Fiber ad Itegrated Optics vol.3 pp [3]. G. Che, Profile optimizatio of tapered waveguide sesors by fluorescece imagig, Proc. SPIE 5589 (4) 7. [4]. T.A. Birs, Y.W. i, The shape of fiber tapers, J. ightwave Techol. Vol. pp [5]. A.K. Ghata, K. Thyagaraja, Itroductio to Fiber Optics, Cambridge Uiversity Press, 999, 85. [6]. M.A. Ordal,.. og, R.J. Bell, S. E. Bell, R.R. Bell, R.W. Alexader Jr., C.A. Ward, Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, ad W i the ifrared ad far ifrared, Appl. Opt. vol pp IJERTV3IS

TO DETERMINE THE NUMERICAL APERTURE OF A GIVEN OPTICAL FIBER. 2. Sunil Kumar 3. Varun Sharma 4. Jaswinder Singh

TO DETERMINE THE NUMERICAL APERTURE OF A GIVEN OPTICAL FIBER Submitted to: Mr. Rohit Verma Submitted By:. Rajesh Kumar. Suil Kumar 3. Varu Sharma 4. Jaswider Sigh INDRODUCTION TO AN OPTICAL FIBER Optical