Pramana – J. Phys. (2021) 95:9 © Indian Academy of Scienceshttps://doi.org/10.1007/s12043-020-02056-y

Comparative performance study of liquid core cylindrical Braggfibre waveguide biosensors

NITESH K CHOURASIA1, ANKITA SRIVASTAVA2, VINAY KUMAR3

and RITESH KUMAR CHOURASIA3 ,∗

1School of Materials Science and Technology, Indian Institute of Technology (BHU), Varanasi 221 005, India2Department of Physics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India3University Department of Physics, Lalit Narayan Mithila University, Darbhanga 846 008, India∗Corresponding author. E-mail: riteshphyzics@gmail.com; dr.riteshchaurasia@gmail.com

MS received 18 June 2020; revised 14 September 2020; accepted 8 October 2020

Abstract. The performance study of various sensing parameters such as sensitivity, detection accuracy and qualityparameter of liquid core Bragg fibre waveguide biosensor based on defect mode has been theoretically studiedand compared with experimental findings of a similar structure without defect mode. The electromagnetic wavepropagation in the present structure has been modelled using the transfer matrix method and Henkel formalismin cylindrical coordinates. The present multilayer structure can provide a band gap between 617 and 929 nmwavelength range at angle of incidence θ = 70◦. Due to the presence of a defect layer, a defect mode at 690 nmwavelength is observed in this band-gap region. This defect mode can be treated as a sensing signal in the presentstudy. It is observed that the obtained sensitivity (S ≈ 334 nm/RIU) through the defect mode is almost the sameas the experimental findings (S ≈ 330 nm/RIU) of a similar structure without the defect layer. But the obtainedmaximum detection accuracy (68.6) and quality parameter (160.4/RIU) of the present structure with defect layeris much larger than the values in a similar structure without defect layer (6.9 and 15/RIU). The present structurehaving a liquid-filled core, is therefore, favoured and useful in promising biosensing applications.

Keywords. Multilayer cylindrical structure; defect mode; biosensors; Henkel formalism; detection accuracy;quality parameter.

PACS Nos 07.05.Tp; 42.25.Bs; 87.85.fk; 42.79.Dj; 02.30.Gp; 42.81.Pa

1. Introduction

During the last decade, various optofluidic microstruc-ture waveguides have drawn much attention fromresearchers and scientists because of their applicationsin biosensing. These waveguides have played vital rolesin the detection of DNA [1], antibody–antigen interac-tions [2], cells and bacteria [3], various proteins [4],etc. It is a well-known fact that these biological ele-ments typically exist in aqueous solution. Therefore,to enhance the interaction of light with these biolog-ical elements, it is more appropriate that the guidingregion of the fibre waveguide is a fluid column. However,for guiding through a waveguide, the refractive indexof the core must be larger than the refractive index ofthe cladding layer so that total internal reflection (TIR)takes place. The refractive index of pure water is 1.33,

while the refractive index of glass is approximately 1.45.Therefore liquid-filled silica fibre waveguide cannot beused as an optical fibre waveguide. To obtain the liquid-filled fibre waveguide, polymers are used by variousresearchers.

A teflon (RI = 1.29−1.31) based liquid-filled fibrewaveguide of 250 μm core radius was proposed byDallas and Dasgupta [5]. These fibre waveguides havebeen successfully fabricated with large core diame-ter but it is difficult to achieve a single-mode fibrewaveguide from such a structure because the core-cladding index difference is very low (0.03) whichrequires the core thickness of the order of 0.5−1 μmwhich is difficult to achieve with teflon material. Fur-ther, Wolfe et al [6,7] used two different liquids withdifferent refractive indices inside a larger fluidic chan-nel and called it liquid–liquid core fibre waveguide.

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The performance of these waveguides is limited bythe change in index contrast due to core-claddingintermixing and the diffusion of analyte moleculesof interest into the cladding regions. The antireso-nant reflecting optical waveguides having liquid-filledcore regions, which have advantages like low opti-cal loss, radically improve the beam quality of theradiation, ultra-high sensitivity, etc. are also demon-strated by Campopiano et al [8]. The periodic binarylayered microstructures are also identified as suit-able structures for bio and chemosensing applica-tions [9] in which the resonant response or efficienttransmission abilities of these structures have beenexplored.

With the above discussions, an idea came into mindthat hollow core Bragg fibre waveguides based on cylin-drical multiclad structure may be suitable candidatesfor both biological and chemical sensing applications.These waveguides can also provide greater design flex-ibility because of their large core dimensions. Theterahertz (THz) spectral characteristics of a hollow corecylindrical multilayer structure, fabricated with a sim-ple technique, are presented by Dupuis et al [10]. Thelow loss design of these structures can also be doneby the periodic arrangements of polymers [11]. Thedesign principles and experimental realisation of a novelBragg fibre waveguide-based biosensor through trans-mittance spectra without defect layer are demonstratedby Qu Skorobogatiy [12]. Bragg fibre waveguides arewell known for their ability to guide light with lowtransmission losses due to the Bloch wave band gapsproduced by their binary layered claddings [13–16].The spectral properties of band gaps are strictly depen-dent on the thickness of the layer, refractive indexof the layer, angle of incidence and the refractiveindex of the medium in which the light is incident[17,18].

Basically, researchers have taken low refractive indexcontrast Bragg fibre for biosensing applications becauseits wide band-gap region is less, which is used as a sens-ing signal. Furthermore, the high refractive index con-trast chalcogenide glass arsenic tri-selenide (As2Se3)and polymer film polyether imide (PEI)-based cylin-drical multiclad Bragg fibre waveguide structure withliquid core has also been used for biosensing applica-tions [19]. Rowland et al [19] experimentally demon-strated the variation in transmission peak of the fun-damental band gap towards shorter wavelengths byincreasing the liquid-filled core index without the defectlayer. Moreover, to enhance the overall performanceof the sensor, narrow transmission bandwidth is desir-able as the sensing parameters are inversely propor-tional to the full-width half-maxima (FWHM) of thetransmission peaks. To obtain a narrow transmission

bandwidth, a conical hollow-core cylindrical multi-layer structure was used by some investigators [20].In this regard, the cylindrical multiclad Bragg fibrewaveguide structure [21–23] must show a photonicband gap (where a range of wavelengths is stoppedto propagate through the fibre waveguide with vari-ous applications) [24–27]. This property of the periodicstructures can be used to obtain a narrow transmis-sion bandwidth in the band-gap region by introducing adefect layer in the cladding periodicity. This defect layeris just introduced by breaking the periodic symmetryor introducing a new layer in the periodic arrange-ment.

Therefore, in the present communication, a liquid-filled core Bragg fibre waveguide structure has beenconsidered. Due to the presence of this defect, a nar-row pass band in the band-gap region will appear, whichis sensitive to the biological elements filled in the coreregion. Transfer matrix method and Henkel formalismhave been employed to study the propagation character-istics. This paper is organised as follows: In §2, basicmathematical equations and theoretical formulation ofthe proposed structure are given. The obtained resultsare discussed and thoroughly illustrated in §3. A con-clusion is drawn in §4.

2. Theoretical background

2.1 Transfer matrix formalism for cylindricalmultilayered structure

The schematic head-on wrap-off view is shown infigure 1a, cross-sectional view, thickness and refrac-tive index profile of the proposed structure is shownin figure 1b and the schematic set-up of the Braggfibre waveguide biosensor with the liquid core is shownin figure 1c. The central region of the present struc-ture is a hollow core channel that can be used as aflow cell which will be filled with liquid containingbiological elements. Further, this central region is sur-rounded by high and low refractive index polymericdielectric media with respective refractive indices andthicknesses nH , dH , nL ,dL . The chosen polymer mate-rials are supposed to be non-magnetic. To obtain defectmode, a defect layer of refractive index nD and thick-ness dD is introduced. The optical path length of theelectromagnetic waves in different periodic layers issupposed to be a quarter of the wavelength and aregiven by nHdH = nLdL = nDdD = λc/4, whereλc is the design wavelength of the present structure.The chosen index profile of such a structure is as fol-lows:

Pramana – J. Phys. (2021) 95:9 Page 3 of 9 9

n(r) =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

nc, 0 ≤ r < rc;nH , rc ≤ r < r1;nL , r1 ≤ r < r2;::nH , rn−2 ≤ r < rn−1;nL , rn−1 ≤ r < rD;nD, rD ≤ r < rD′ ;nH , rD′ ≤ r < rn+1;nL , rn+1 ≤ r < rn+2;::etc.

(1)

Reflection and transmission response of this waveguidecan be obtained by the cylindrical wave transfer matrixmethod [28]. The Maxwell’s equations for a layer hav-ing permittivity ε and permeability μ are expressed as[29]

∇ × E = − jωμH (2)

∇ × H = jωεE . (3)

Considering the temporal part of all the fields asexp( jωt), the relation between the longitudinal andtransverse components of the electric and magneticfields is established in a cylindrical coordinate (r, θ, z)system [29]. The Helmholtz wave equations in the cylin-drical coordinate system are written as

r∂

∂r

(r∂Hz

∂r

)− r2 1

ε

∂ε

∂r

∂Hz

∂r+ ∂

∂θ

(∂Hz

∂θ

)

+ ω2μεr2Hz = 0 (for TE-polarisation) (4)

r∂

∂r

(r∂Ez

∂r

)− r2 1

μ

∂μ

∂r

∂Ez

∂r+ ∂

∂θ

(∂Ez

∂θ

)

+ ω2μεr2Ez = 0 (for TM-polarisation). (5)

The above equations can be solved using the methodof separation of variables. The field solution for thecylindrical wave is derived for radial and angular parts[28–30]. The solution for TE-polarised wave has threenon-zero components (HZ , Eθ , Er ), and they are writ-ten as

HZ (r, θ) = [AJm(kr) + BYm(kr)]e jmθ , (6a)

Eθ = 1

− jωε

∂Hz(r, θ)

∂r, (6b)

Er = m

ωε

Hz(r, θ)

r, (6c)

where Jm and Ym are Bessel and Neumann functions, Aand B are arbitrary constants, k = (ω/c) n is the wavevector in a medium, c is the speed of light in free spaceand n is the refractive index of that medium. For anoblique incidence case on the core–cladding interface,this wave vector will have a perpendicular component

Figure 1. (a) Schematic head-on and wrap-off view of liq-uid-filled core Bragg fibre waveguide with a defect layer, (b)cross-sectional view, thickness and refractive index profile ofthe proposed structure with liquid core and a defect layer and(c) schematic set-up of the Bragg fibre waveguide biosensorwith a defect layer.

k⊥ = k cos(θ) and parallel component k|| = k sin(θ)

of the incident wave vector k. The elements of transfermatrix T̂ , which correlate the field vector at an initialposition rc to some other point r is determined by usingAbeles theory dealing with multilayer structure [28–30]and is given by

T̂ =[T11 T12T21 T22

], (7)

9 Page 4 of 9 Pramana – J. Phys. (2021) 95:9

T11 = π

2krc

[Y ′m (krc) Jm (kr)− J ′

m (krc) Ym (kr)],

(8a)

T21 = jπ

2krc p

[Y ′m (krc) J

′m (kr)− J ′

m (krc) Y′m (kr)

],

(8b)

T22 = π

2krc

[Jm (krc) Y

′m (kr)−Ym (krc) J

′m (kr)

],

(8c)

T12 =− jπ

2

krcp

[Jm (krc) Ym (kr)−Ym (krc) Jm (kr)] ,

(8d)

where p=√

με

is the intrinsic impedance of the medium(p= 377� for free space). Also, the elements of thedefect transfer matrix T̂D can be written by usingthe above steps. Since the transfer matrix elementsare dependent on the radii of two interfaces, for thenth layer, the matrix T̂n can be obtained by replacingrc → rn−1, r → rn, k → kn and p → pn . In addi-tion to this, as the structure is periodic, one can taken(r) = nH if n = odd and n(r) = nL if n = even.For an N -period bilayer periodic cylindrical structurewe have a total of 2N layers. Thus, the total transfermatrix is given by[V (r f )U (r f )

]=T2N ...........T2T1

[V (rc)U (rc)

]= T̂

[V (rc)U (rc)

],

(9)

where U (r) and V (r) are the solutions of Helmholtzequation at position r .

Analogous to Fresnel’s equation in a planar geome-try, the wave reflection and transmission in a multilayercylindrical structure is obtained using the above transfermatrices [28]. The reflection coefficient for a multilayercylindrical structure can be given by

rM

= (T ′21− j p0c

(2)m0T

′11)+ j p f c

(2)m f (T

′22− j p0c

(2)m0T

′12)

(−T ′21+ j p0c

(1)m0T

′11)+j p f c

(2)m f (−T ′

22+ j p0c(1)m0T

′12).

(10)

In the above expression, T ′11, T ′

12, T ′21 and T ′

22 are thematrix elements of the inverse of the matrix T̂ of eq. (9)and

C (1,2)ml = H (1,2)′

m (klrl)

H (1,2)m (klrl)

with l = 0, f, (11)

where H (1)m and H (2)

m are Henkel functions of a firstand second kind respectively, m is the azimuthal vari-ation of the field. Now, the reflectance is calculated as

R = |rM |2, and for non-absorbing media, the percent-age transmittance is calculated as T = (1 − R) ×100the value of which lies between 0 and 100%. The expres-sion for TM-polarised wave can be obtained by simplyreplacing μ ↔ ε and j ↔ − j the formula of TE-polarised wave.

2.2 Resonant sensing through changes in the real partof bioanalyte refractive index

The change in spectral shift occurs due to changes in thereal part of the refractive index of the bioanalyte fillingthe core. According to classical perturbation theory, thechanges in the refractive index of a guided mode neffare related to the changes in the real part of the refrac-tive index of the analyte infiltrating the core [32]. Theapproximated expression for the hollow core waveguideis given by

neff = Re(na) · f + Re(na) · frad, (12)

where f is the overlap factor and frad is the radiationlosses of a photonic band gap guided mode due to spec-tral shift of a band gap caused by changes in the realpart of the refractive index of the analyte filling the core.From the basic theory of cylindrical multilayer structure,the wavelength λc of the fundamental reflector band gapcan be approximately calculated as follows [12–32]:

λc

2= [dH (n2

H − n2c)

1/2 + dL(n2L − n2

c)1/2]. (13)

Variations in the real part of the refractive index of theanalyte filling the core can modify the resonant condi-tion of the cylindrical multilayer structure, thus leadingto changes in the centre positions of the band gap, whichconstitute the sensing mechanism of the sensor. Theabove theory can be validated by performing simulationbased on the transfer matrix method discussed already.One can also investigate the spectral sensitivity of theBragg fibre waveguide biosensor to change in the realpart of the analyte refractive index filling the fibre core.The theoretical expression of spectral sensitivity of theBragg fibre waveguide sensor is found to be

S =∣∣∣∣λc

nc

∣∣∣∣

= 2

⎡⎣dh

(n2h

n2c

− 1

)−1/2

+ dl

(n2l

n2c

− 1

)−1/2⎤⎦ . (14)

From the above equation, it is clear that the sensitiv-ity of a sensor increases with the increasing refractiveindex of the analyte filling the core. Hence, the shift ofresonance wavelength should have a polynomial depen-dence on the increasing refractive index of the analyte.

Pramana – J. Phys. (2021) 95:9 Page 5 of 9 9

Figure 2. The photonic band gap (PBG) representation of Bragg fibre waveguide biosensor at different core refractive indicesand the respective spectral shifts in transmisson peak.

(a)

(b)

(c)

Figure 3. Comparison of the spectral shifts obtained from (a) experimental [19], (b) our proposed simulation and (c) approx-imation using eq. (13).

It can also be verified by the simulated result usingthe above transfer matrix method for a Bragg fibrewaveguide biosensor.

2.3 Performance parameter for the present Braggfibre waveguide biosensor

In the present study, the performance of the presentbiosensor is analysed on the basis of its sensitivity, detec-tion accuracy and overall quality parameter. In general,

the sensitivity of a sensor is defined as the ratio of thesensor-measured output to the change in physical quan-tity to be measured. Mathematically, in the wavelengthinterrogation method, the sensitivity of the sensor isdefined as the ratio of the spectral shift in resonancewavelength to the small change in aqueous medium oranalyte refractive index.

S = λres/na, (15)

9 Page 6 of 9 Pramana – J. Phys. (2021) 95:9

(a)

(b)

(c)

Figure 4. The variation of sensitivity with angle of incidence at fixed core refractive index and the respective linear fit.

(a)

(b)

(c)

Figure 5. The variation of detection accuracy with angle of incidence at fixed core refractive index and the respective linearfit.

where λres is the change in resonance wavelength andna is the change in refractive index in an aqueousmedium. Another important parameter is the detectionaccuracy that describes the true value of the measurand.The detection accuracy (DA) of a sensor is the ratio

of change in resonance wavelength with respect to thefull-width half-maximum (FWHM) of the defect modepeak.

DA = λres/λ0.5, (16)

Pramana – J. Phys. (2021) 95:9 Page 7 of 9 9

(a)

(b)

(c)

Figure 6. The variation of quality parameter with angle of incidence at fixed core refractive index and the respective linearfit.

where λ0.5 is the spectral width at 50% of trans-mittance. The FWHM corresponding to cylindricalmultilayer structured resonance curve should be as smallas possible so that the error in determining the reso-nance wavelength is minimum. The quality parameteris another parameter, which shows the overall perfor-mance of the sensor in terms of sensitivity and detectionaccuracy. The quality parameter (Q) is defined as

Q = S/λ0.5, (17)

where S is the sensitivity of the cylindrical multilayerstructured sensor and λ0.5 is the FWHM.

3. Results and discussion

In order to see the performance of the present Bragg fibrewaveguide biosensor, a cylindrical multilayer structureof 15 cm length having a hollow core radius rc =165 μm is chosen. The core is surrounded by periodicconcentric cladding layer of the high refractive indexmaterial arsenic triselenide (nH = 2.82) and the lowrefractive index material polyetherimide (nL = 1.66)

[16] with thicknesses dH = 76 μm and dL = 124 μmrespectively [19]. In this structure, a defect layer oflow index material (polyetherimide) having a refractiveindex of nD = 1.66 and quarter-wave stack thicknessdD = λc/4nd is introduced after the 5th unit cell of

H/L bilayers by breaking the symmetry. Also, the liq-uid with bioelement used to fill the core of waveguidehave refractive indices 1.4019, 1.4620 and 1.5780 (allstandardised at a center wavelength λc = 589.3 nm at atemperature of 25◦ C.

The transmission spectra of the present structureare plotted with the help of eq. (10). Figure 2 showsthe transmittance spectra of the proposed Bragg fibrewaveguide biosensor having different core refractiveindices with a fixed width of defect thickness. For aparticular angle of incidence θ = 70◦ with emptycore, a transmission pass band (defect mode) appearsat λpeak = 690 nm (blue line with a circle symbolcalled reference signal) in the band-gap region. TheFWHM of this peak is approximately 1.1 nm. Further,this defect mode is shifted towards the lower wavelengthregion, i.e. λpeak = 574 nm, 546 nm and 497 nm with anincrease of respective core refractive indexnc ≈ 1.4018,1.4720 and 1.5780. The obtained FWHM of these peaksare λFWHM = 1.8 nm, 2.1 nm and 3.2 nm respec-tively. As the introduction of the defect layer in thepresent structure is a novel concept, we compare ourpresent findings with the existing experimental resultsobtained in a similar waveguide structure without defectlayer, as presented by Rowland et al [19]. They havefound the peaks of the lobe at wavelength λpeak =700 nm, 555 nm, 533 nm and 500 nm with respectivecore refractive indices nc ≈ 1.0000, 1.4018, 1.4720 and1.5780. The obtained FWHM values of these lobs lie at

9 Page 8 of 9 Pramana – J. Phys. (2021) 95:9

Figure 7. The variation in band gap with angle of incidenceat fixed core refractive index.

λFWHM = 30 nm, 21 nm, 33 nm and 40 nm respec-tively. Thus, the above result and discussion validateour simulated model. Also, by comparing the FWHMof these two cases, it is clear that the FWHM value inour proposed structure is much smaller than the FWHMvalue obtained in [19]. Therfore, the present multilayerwaveguide structure can be used as an inline optical filterto block certain wavelengths, or as a wavelength-specificreflector.

The allowed wavelength, which passes through themultilayer waveguide structure in a specified photonicband gap (PBG) region, is generally known as the cen-tral wavelength. The centre wavelengths of the presentbiosensor with respect to the core refractive index areplotted in figure 3a (experimental [19]), figure 3b (ourproposed simulation) and figure 3c (theoretical eq. (13)[12]). Qu and Skorobogatiy [12] found that the theo-retically obtained variation in the centre wavelength vs.core refractive index is in good agreement with exper-imental findings for low index contrast [12–32]. It isclear from figure 3 that our proposed simulation result(figure 3b), experimental result [19] (figure 3a) and cal-culated results (figure 3c) from eq. (13) are in goodagreement for high index contrast and validated. Further,if all the points (for sensitivity, detection accuracy andquality parameter) are plotted on a single graph, thereis a possibility of overlap of the fitted lines. Therefore,these figures have subfigures identified with indicatorsa, b and c.

Figures 4a–4c show the variation of sensitivity withvarious angles of incidence ranging from θ = 40◦to 70◦for respective core refractive index nc ≈ 1.4018, 1.4720and 1.5780. It is clear from figures 4a–4c that the sensi-tivity varies (increasing) approximately linear (adjusted

R2 value is found to be approximately 0.999 whichgives more accountability and precise view of linearity)with the angle of incidence and maximum sensitivityis obtained when the core refractive index approachesthe low refractive index polymer cladding layer, i.e. fornc ≈ 1.5780. This linear variation can also be validatedusing eq. (14, which also indicates that the sensitivityshould vary with the core refractive index, and also, thesensitivity of the sensor increases as the core refrac-tive index approaches the lower refractive index layer.The maximum sensitivity from our proposed structureis S ≈ 334 nm/RIU (figure 4c), which is approxi-mately the same (S ≈ 330 nm/RIU) as reported byRowland et al [19] in the experiment without the defectlayer.

Figures 5a–5c and 6a–6c show the variation of detec-tion accuracy and quality parameter with the angle ofincidence for core refractive indices nc ≈ 1.4018,1.4720 and 1.5780 respectively. It is clear from thesefigures that the maximum detection accuracy and over-all performance (quality parameter) vary (increasing)approximately linear (adjusted R2 value is found to beapproximately 0.999 each which gives more account-ability, correlation and precise view of linearity) withthe angle of incidence. The maximum detection accu-racy and quality parameters are obtained when angleof incidence θ = 70◦. At this angle of incidence, themaximum obtained detection accuracy (68.6) and over-all performance (160.4/RIU) of the present structureare improved considerably from 6.9 and 15/RIU asobtained in similar biosensor [19] without defect layer.This improvement is obtained only due to the sharpFWHM of the defect mode.

Figure 7 shows the variation of band gap at a fixedcore refractive index with different angles of incidence.Band gap corresponding to different refractive indicesincreases with increasing angle of incidence due to thefact that the optical path length increases. Also, bandgap is maximum in the case of the empty core while itis smaller for the liquid-filled core.

4. Conclusions

The sensing performance of the Bragg fibre waveguidebiosensor with defect mode is compared with a sim-ilar structure without defect layer [19]. Although theobtained sensitivity in our present case is similar to thoseobtained in [19], the overall performance and detec-tion accuracy of our present biosensor are much betterthan those reported in [19]. In our present case, the passband (defect mode) in the band-gap region senses sig-nal, and therefore, the FWHM of the pass-band peakis very small compared to the band-gap region, which

Pramana – J. Phys. (2021) 95:9 Page 9 of 9 9

is treated as sensing signal in similar structure-basedbiosensor [19] without defect layer.

Acknowledgements

This research did not receive any specific grant fromfunding agencies in the public, commercial, or non-for-profit sectors. The authors acknowledge Dr VivekSingh, Institute of Science, Department of Physics,BHU, Varanasi for his continuous valuable support.

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