научная статья по теме THEORETICAL INVESTIGATION OF ABSORPTION AND SENSITIVITY OF NANO-PLASMONIC TAPERED FIBER OPTIC SENSORS Физика

Текст научной статьи на тему «THEORETICAL INVESTIGATION OF ABSORPTION AND SENSITIVITY OF NANO-PLASMONIC TAPERED FIBER OPTIC SENSORS»

ОПТИКА И СПЕКТРОСКОПИЯ, 2015, том 118, № 6, с. 1022-1031

^^^^^^^^^^^^^^^^ ФИЗИЧЕСКАЯ

ОПТИКА

УДК 535.32

THEORETICAL INVESTIGATION OF ABSORPTION AND SENSITIVITY OF NANO-PLASMONIC TAPERED FIBER OPTIC SENSORS © 2015 г. H. R. Askari and F. Mokhtaree

Department of Physics, Faculty of Science, Vali-e-Asr University, Rafsanjan, IRAN E-mail: hraskari@mail.vru.ac.ir, hraskarivaliasr@yahoo.com, f_mokhtaree@yahoo.com Received March 20, 2014; in final form, September 15, 2014

In this paper, a theoretical investigation for the performance a tapered fiber optic sensor based on surface plasmon resonance (SPR) is proposed. The tapered fiber optic sensor is considered for three different taper profiles, namely, linear, parabolic, and exponential-linear. The tapered fiber optic sensor is coated with thin nanoparticle metallic films. The nanoparticle metallic film consists of spherical metallic nanoparticles embedded in a host material. The performance has been analyzed in terms of sensitivity and absorption of the sensor. It is shown that sensitivity and absorption of sensors depends on parameters such as taper ratio, taper profile, nanoparticle film thickness, nanoparticle radius, sensing region length, fiber core diameter and concentration of sensing layer.

DOI: 10.7868/S0030403415030046

1. INTRODUCTION

In the past few years, the cooperation of optical fiber technology and surface plasmon resonance (SPR) has been a subject of intensive research. The sensitivity enhancement has been a critical research issue in the area of fiber optic SPR-based sensors. Several theoretical as well as experimental studies have been carried out to improve the performance of fiber optic SPR sensors. Various techniques such as bimetallic layers, nanoparticle layers, long range SPR, doped fiber core sensors, SPR with long period grating and SPR with fiber Bragg grating have been proposed to improve the sensitivity and overall performance of the sensor. Apart from above techniques, SPR sensors with tapered optical fiber have drawn the attention of a few researchers. For instance, the use of single mode tapered fiber sensor with symmetric and asymmetric metallic coatings has been proposed. In the case of asymmetric metallic coating multiple SPR peaks are observed. In addition, the use of dual-tapered and tet-ra-tapered fiber SPR probes for gas and liquid sensing, asymmetric double-layer-covered (metal + dielectric) tapered fiber sensor and a truncated tapered fiber optic SPR sensor for detection of refractive index have been reported. Different taper profiles have been used for sensing using different technique such as evanescent field absorption and fluorescence imaging [1]. However, the cooperation of optical fiber technology and localized surface plasmon resonance (LSPR) of self-assembled nanoparticles for sensing purposes is relatively new. In the recent times, a very significant work has been carried out describing fiber optic chemical and biochemical probes based on LSPR [2]. Since nanoparticles have exceptional properties and poten-

tial characteristics for technological applications [3]. As the optical properties of these particles depend mainly on their size and shape, it was noticeable for researchers for quite a long time [4, 5]. The absorption phenomenon has been calculated by solving Maxwell's equations for an electromagnetic field interacting with a spherical metal particle under the appropriate boundary conditions [6]. Mie was the first to describe, theoretically, this phenomenon by solving Maxwell's equations for an electromagnetic field, interacting with a spherical metal particle under the appropriate boundary conditions [6]. But Mie's theory, in its original form, is not applicable to nanoparticle films with high volume fractions where a nanoparticle embedded in a host matrix is subjected to an average polarization field due to both matrix, and surrounding nanoparticles. Such additional effects significantly change the optical properties of the high volume-fraction nanoparticle materials. Among various theories, Maxwell-Garnett (MG) theory is the most efficient theory to account for the above effects [7, 8].

Salari et al. [9] have been considered absorption and sensitivity of nano-plasmonic fiber optic sensors. In the present work, we have theoretically investigated the performance of a tapered fiber optic SPR sensor based on silver nanoparticle films. The performance has been analyzed in terms of sensitivity and absorption of the sensor. For this analysis, spectral interrogation mode has been used. The spectral dependence of the dielectric functions of the fiber core and the silver nanoparticle films has been taken into account in the form of Sellmeier relation and a combination of Drude model of metals and Maxwell-Garnett's theory, respectively [10]. In the present study, the effects of var-

d\

Zd = n2d SPW

£„ = n

Dielectric Metal layer

Optical prism

V

Light

Fig. 1. Surface plasmon resonance based on the classical Kretschmann configuration.

ious parameters like taper profile, taper ratio, different film thickness, nanoparticle radius and concentration of the absorbing sample on the sensor's sensitivity and absorption have also been studied. The nanoparticle film has been found to improve the performance of the sensor.

2. THEORY 2.1. Surface Plasmon Resonance

In order to describe the SPR, the classical Kretschmann configuration is used (Fig. 1). One side of the glass prism is coated with a thin metallic film in contact with the sensed medium (sample). Surface plasmons, which are collective oscillations of free electron, propagate along the interface between the sensed material and metal film. Surface plasmon is sensitive to the optical properties of both media, the sensed medium and metallic film. Surface plasmon can only be excited by TM-polarized electromagnetic waves (¿-polarized).

In order to study SPR, attenuated total reflection (ATR) method is frequently used, i.e, measuring the variation in reflected light intensity according to a sharp dip at resonance frequency.

The Fresnel reflection coefficient in the interface of i and j media for TM-polarized light is obtained as

êp(®) =

k, jê j (CO) - k j 1ê, (rn) kt jéj(ro) + kjjê, (ra)'

(1)

symbol "a" over quantities denotes that they are complex and ê(œ) is the dielectric function of the medium.

Where k is the wave vector of electromagnetic wave in the medium, k = k0Vê.

The total reflectivity of TM-polarized wave from prism-metal interface is given by

rp (œ) = r32P (œ) +

+

ê32p (c)ê2ip (c)ê23p (ö>) exp [2,kê21(œ)d]

'32pV 1

(2)

■ ê3ip(c)ê32 p(c) exp [2ik2±(c)d]

where tiJp(œ) is the Fresnel transmission coefficient in the interface of i and j media, and d is the thickness of metal film. Using the Fresnel coefficient, the total reflectance is obtained as

R(C =

ê32 p (c) + ê2i,,(M)ê32 ,,(co)exp|2ik 21(m)d|

1 - ê3ip(®)ê32 p (C exp [2/k21(ro)d]

(3)

At the SPR condition, the Fresnel reflection coefficient diverge in the interface of metal-sample [11]. Therefore, using Eq. (2) the following surface plasmon dispersion relation is obtained as

kii(G>) = k„(o>) =

CjJÄi®L = ^,/é¡(C)sin (0

cy ê1(ro) + ê 2(ro) c

(4)

where k^ is component of wave vector parallel to the interface of two media i and j. If the system has more than 3 layers, N-layer model is considered. The layers are stacked along the z-axis as shown in Fig. 2 and the incident beam has been ^-polarized. The arbitrary medium layer is defined by thickness dk, dielectric constant e k, permeability ^ k, and refractive index nk. All the layers are assumed to be uniform, isotropic, and non-magnetic optically. By using the boundary conditions of components of fields and solutions of Maxwell equations, the relation between the tangential components of the electric and magnetic fields in

the interface of the k and (k + 1)th layers, Ekx, Bky, (the boundary plane zk+1) and the one of the (k — 1)th

and kth layers (the boundary plane zk), E(k _r is given by (Fig. 2)

'J(k-1)x, B(k-1)y,

Reflected light \1

Incident light

-N-2

N-1

N _ Transmitted light

Fig. 2. Y-layer model for the calculation of reflection coefficient.

2

3

4

2Pi

i * i

I Gold layer |

>1 I

I I

Fig. 3. Typical SPR based fiber optic sensor with tapered probe.

Pi

P0

- Parabolic

Linear

■ Exp. Linear

L

E kx = Tk E(k-1)x

Bky _ B(k=1)y _

(5)

where

Tk =

(6)

' cos((kdk) isin((kdk)/pk Jpk sin((kdk) cos((kdk) So that

pk =slek/^k cos 0k =Jek - n\ sin2 0,/Vm7, (7) and

(k = knk cos0k = k4v~kPk. (8)

The tangential components of fields at the boundary of the first layer, Elx and Bly have been related to tangential components of the field's Nth layer, ENx and BNy by the following matrix

ENx = j E1x (9)

_BNy J \_Bly _

where

N-1

T = nfk

(10)

k=2

T is known as the characteristic matrix of the combined structure. Using the definition of Fresnel reflective coefficient, rp forp-polarized incident wave is given by

= R = T2l - T11pN) + (T22 - ^Pn )p1 A (TuPn - T21) + (T22 - T12PN )p1 '

(11)

where Tij is the component ij of matrix T. Finally, the reflection intensity coefficient for the p-polarized light is

Rp = \rp\

Fig. 4. Three different taper profiles showing the linear, parabolic, and exponential-linear variation of core radius of taper with distance z from the input end of the taper.

2.2. Tapered Fiber Optic and its Guided Transverse Magnetic Modes

In this paper, we use a multimode fiber instead of prism. The theoretical model is based on the principle of ATR with Kretschmann configuration. The plastic cladding from the middle portion of a step index multimode fiber is removed and the unclad portion is tapered. The unclad tapered fiber region is then coated with a thin metallic layer such as gold, silver or spherical metallic nanoparticles, which is surrounded by sensing medium (Fig. 3). Different taper profiles can be generated during fabrication, using "Flame Brush" technique as suggested by Birks an

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