Effects of surface roughness on optical properties and sensitivity of fiber-optic evanescent wave sensors Nianbing Zhong,1,2 Xun Zhu,1,2 Qiang Liao,1,2,* Yongzhong Wang,1,2 Rong Chen,1,2 and Yahui Sun1,2 1
Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400030, China 2
Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China *Corresponding author:
[email protected] Received 1 March 2013; revised 6 May 2013; accepted 8 May 2013; posted 9 May 2013 (Doc. ID 186153); published 5 June 2013
The effects of surface roughness on the light transmission properties and sensitivity of fiber-optic evanescent wave sensors are investigated. A simple method of increasing the sensitivity based on the surface roughness (pit depth δ and diameter Δ) and incident angle U i of light rays on the fiber input end is proposed. We discovered that as 2δ∕Δ increases, the transmitted light intensity decreases, but the sensitivity initially increases and then decreases. In sensors containing fibers of various roughnesses, the sensitivity to glucose solutions reached −11.7 mW∕riu at 2δ∕Δ 0.32 and increased further to −15.3 mW∕riu with proper adjustment of U i. © 2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (080.0080) Geometric optics; (220.0220) Optical design and fabrication; (240.0240) Optics at surfaces. http://dx.doi.org/10.1364/AO.52.003937
1. Introduction
Fiber-optic evanescent wave (FOEW) sensors are widely accepted and applied in chemistry [1], biochemistry [2], life sciences [3], and environmental research [4] because they are responsive and provide fast, reliable results during real-time monitoring [5]. Further, the provided results are not affected by the bulk solution because the penetration depth of the evanescent field ranges from ten to several hundred nanometers, unlike that of fiber reflective sensors and transmissive sensors [6]. However, the sensitivity of FOEW sensors is directly affected by attenuation of the evanescent waves on the unclad fiber surface (sensing region) [7]. Different types of sensors based on variations in the shape of the unclad fiber region and fiber end region have been created to improve the sensitivity [8–11]. Pulido and Esteban [8] and Ahmad and Hench [12] discovered that the sensitivity of tapered fiber sensors depends 1559-128X/13/173937-09$15.00/0 © 2013 Optical Society of America
on the radius of the fiber, taper waist length, and launch angle. Gupta et al. [9,13] and Prabhakar and Mukherji [14] investigated the dependence of the sensitivity on the fiber bending diameter in U-shaped and C-shaped probes, respectively. In addition, the sensitivity of D-shaped sensors increases as the distance between the core layer and flat surface decreases [10,15]. The sensitivity of these sensors can be further optimized by creating double pass evanescent field absorption from a suitable fiber end shape (hemispherical, triangular, or wedgeshaped) [11,16,17]. However, although the sensitivity is improved by optimizing the shapes of the unclad fiber sensing region and unclad fiber end region, the unclad fiber surface exhibits a certain degree of roughness induced by the etching and grinding used during fabrication [18,19]. The surface roughness of the unclad fibers directly affects the optical reflectivity of the interface between the fiber and the surrounding environment; this is important for the construction of highsensitivity sensors [20]. Moreover, Kuang et al. [21] discovered that surface pits on the Y-branch coupler 10 June 2013 / Vol. 52, No. 17 / APPLIED OPTICS
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affect the rays reflected into the fiber’s receiving end, and a portion of their energy is lost to the pits when the incident angle of the rays before they enter the fiber is smaller than the critical angle. Interestingly, Zhuang et al. [22] pointed out that although surface defects in the fiber’s sensing region increase the light-scattering loss, thus reducing the effectiveness of optical signal transmission, sensors with rough surfaces exhibit higher sensitivity than those with smooth surfaces. On the other hand, for surface plasmon resonance sensors, Herrera et al. [23] discovered that the stability of the modified film on the unclad fibers and the sensor performance increase with the surface roughness. Also, some enhancements are studied by using the Rayleigh method for the transmitted scattered intensity for weakly random rough surfaces in the resonance condition in which surface plasmon waves are excited for p polarization [24], and many glucose sensors are developed [25]. However, a few papers reported that the characteristics of the surface roughness (pit depth and diameter) affect the optical transmission properties and sensitivity of the sensors, and discussed how to further improve the sensitivity of FOEW sensors with rough surfaces. To create high-sensitivity FOEW sensors, in this work, we perform theoretical and experimental investigations of the effects of surface roughness (surface pit depth δ and diameter Δ) on the light transmission and sensitivity of FOEW sensors. We also present a method of improving the sensitivity of FOEW sensors. 2. Theoretical Analysis A.
Optical Transmission of Fiber with Smooth Surface
When the unclad fiber presents a smooth surface, the transmission of light through an absorbing medium is described by the Lambert–Beer law, I out I in e−ξnL ;
(1)
where I in is the incident light intensity, L is the length of the unclad fiber (sensing) region, and ξn is the decay coefficient of evanescent waves in the medium. We can rewrite ξn as [26] ξn
αλn cos θi cot θi ; 2πrn2r cos θc cos2 θc − cos2 θi sin2 θφ 1∕2
(2)
where α is the bulk decay coefficient, λ is the freespace wavelength of the light launched into the fibers, n is the refractive index of the surrounding medium, θi (i 1; 2; 3; …; n) is the incidence angle of the light rays on the interface between the fiber core and the medium, and r is the fiber radius in the thinned region. Further, nr is the refractive index of the etched-fiber core at a radius r [nr nmax 1 − n2max − n2c ∕n2max r∕Rr 1∕2 and r < R, where nmax is the refractive index of the fiber core axis (i.e., at R 0), nc is the refractive index of the fiber cladding, and R is the radius of the fiber core]. 3938
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Fig. 1. Schematic diagram of light transmission in fiber with smooth surface.
Finally, θc is the critical angle for total reflection at the core–cladding interface of a typical fiber, and θφ is the skewness angle, as shown in Fig. 1. Equation (2) indicates that the decay coefficient decreases with decreasing θφ (for θφ from π∕2 to 0), reaching a minimum when θφ is zero. Thus, if we consider only the minimum decay coefficient, or the lowest FOEW sensor sensitivity, Eq. (2) can be simplified to ξn
nαλ cos θi cot θi : 2rπn2r − n2
(3)
Thus, by using Eqs. (1) and (3), the output optical intensity can be expressed as I out I in
exp −
nαλL cos θi cot θi : 2rπn2r − n2
(4)
Furthermore, Eq. (4) can be further simplified applying the Taylor expansion and using only the first two terms of the Taylor series when the refractive index of the surrounding medium is smaller than that of the fiber core, i.e., n∕nr < 1. Then, Eq. (4) can be expressed as αλL n3 n cos θ cot θ I out I in exp − i i : n2r rπn2r
(5)
Equation (5) shows that the output intensity decreases as n increases and θi decreases. B. Optical Transmission of Fiber with Rough Surface
If the unclad fiber has a rough surface, the propagation path of light will vary as θi, the angle of light incidence on an unclad fiber with a smooth surface (Fig. 1), changes to θ0i (Fig. 2). θ0i is expressed as θ0i θi − Ω θi − arctan2δ∕Δ;
(6)
where δ is the average pit depth, and Δ is the average pit diameter. The average pit parameters are a measure of the surface nonuniformity, which represents a field of varying depth and diameter (Fig. 2). The definitions are given by [27]
Fig. 2. Schematic diagram of light transmission in fiber with rough surface.
PN
hi
PN
Di
(7)
I 0in
where hi is the local depth, and Di is the local diameter, and N is the number of pit units in the observation region. By applying Snell’s law of refraction, the incidence angle θi at the interface between the core and the surrounding medium can be expressed as a function of the angle of light rays (U i ) on the input end of the fiber (Fig. 1). Thus, θi is expressed as
δ
i1
θi
N
and Δ
i1
N
;
π n − arcsin 0 sin U i ; nr 2
(8)
where n0 is the refractive index of air, U i ranges from 0 to U max (U max is the maximum incidence angle of light rays on the input end ofq the fiber, U max arcsinNA∕n0 arcsin 1∕n0 n2max − n2R , NA is the numerical aperture of a typical optical fiber, and nR is the refractive index of the fiber core at radius R). Then, using Eqs. (6) and (8), we can obtain the functional expression for θ0i in terms of U i and 2δ∕Δ when light is transmitted into the unclad fiber region with surface roughness: θ0i
π n − arcsin 00 sin U i − arctan2δ∕Δ; nr 2
(9)
where0 n0r nmax 1 − n2max − n2c ∕n2max r − h0i ∕ Rr−hi 1∕2 . We see that θ0i decreases with increasing 2δ∕Δ if U i is constant. Consequently, some of the light rays incident upon the core–medium interface will no longer be suitable for total reflection (i.e., θ0 i < θc ), so they will disappear from the interface via scattering and refraction. Therefore, the loss of transmitted light is not due to evanescent wave absorption in the surrounding media; rather, the surface roughness makes some of the light ineffective for optical signal transmission. In this case, compared to typical fibers with smooth surfaces, the intensity losses can be perceived as a change in the numerical aperture or U max [28]. In this work, the losses are expressed as a decrease in U max , so the effective incident light intensity (I 0in ) for fibers with rough surfaces can be expressed as
arcsin NA0 U0 I in max I in arcsinNA U max n h io δ U max − arcsin nmax sin arc tan2δ∕Δ n 2r U max
I in : (10)
Equation (10) shows that I 0in decreases as δ and 2δ∕Δ increase when n, nmax , U max , r, and I in are constant. Therefore, by using Eqs. (1), (9), and (10), the effective transmitted light intensity (I 0out ) through a rough fiber, in which the evanescent waves have decayed, can be written as I 0out
U max − arcsin
n
nmax n
h sin
io
δ 2r arctan2δ∕Δ
U max
0
I in e−ξ nL ; (11)
where ξ0 n is the evanescent wave decay coefficient for rough fibers, which will be discussed in detail in Subsection 2.C. As Eq. (11) shows, the output optical intensity is significantly affected by the surface pits, and the losses in the transmitted intensity consist of the losses in optical intensity via scattering, refraction, and absorption of evanescent waves at the rough unclad fiber’s surface. C.
Evanescent Wave Parameters
The sensitivity of FOEW sensors depends on the attenuation of the evanescent waves, which is affected by their effective intensity, decay coefficient, penetration depth, and optical path length on the unclad fiber surface. Before we investigate the sensitivity in Sections 3 and 4, we first examine these parameters. 1. Effective Evanescent Wave Intensity According to reports in the literature [29,30], the initial effective intensity of evanescent waves, I ew , decreases with decreasing I in for unclad fibers with smooth surfaces. Thus, this parameter for unclad fibers with rough surfaces, I 0ew , also decreases with decreasing I 0in because the scattering-refractionabsorption (I 0S−R ) increases. Furthermore, the effective incident light intensity I 0in is a function of 10 June 2013 / Vol. 52, No. 17 / APPLIED OPTICS
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I in and 2δ∕Δ, as shown in Eq. (10). Therefore, I 0ew is a function of I in and 2δ∕Δ, and can be expressed as I 0ew I in − I 0out − I 0S−R f I in ; 2δ∕Δ:
(12)
2. Effective Evanescent Wave Decay Coefficient The effective evanescent wave decay coefficient ξ0 n clearly affects the attenuation of evanescent waves, which is important for the construction of highsensitivity FOEW sensors. Although the effect of the shape of the unclad fiber region on ξ0 n has been studied extensively [7,8,10,11,14], the impact of roughness upon ξ0 n has rarely been reported. Thus, to further improve the sensitivity, it will be necessary to investigate the effect of surface pits on ξ0 n. When the light at the core–media interface satisfies the total reflection condition θi ≥ θc , the attenuation coefficient for unclad fibers with rough surfaces can be expressed using Eqs. (5) and (9) as αλ n3 ξ0 n n rπn0r 2 n0r 2 h i cos2 2π − arcsin nn00r sin U i − arctan2δ∕Δ i: h · sin π2 − arcsin nn00r sin U i − arctan2δ∕Δ (13)
4. Effective Evanescent Wave Optical Path Length At each point of reflection, the evanescent wave decays because it is absorbed by the surrounding medium. To investigate the number of total reflections and obtain the effective optical path length lew of evanescent waves at the fiber–media interface, we defined the path length of light through two consecutive total internal reflections as l. Then, the number of reflections of light rays in the unclad fiber region can be expressed as N
2L L ; l 2r tan θi
(16)
where L is the length of the unclad fiber. Furthermore, by using Eqs. (14) and (16), lew for a typical smooth fiber (Fig. 1) can be obtained as Lew N
2Dp tan θL Lλ
h i : 2πr tan θi n2r sin2 θi − n2 1∕2 tan arcsin nnr sin θi (17)
Next, by using Eqs. (9) and (17), the effective optical path length L0ew of evanescent waves for a fiber with a rough surface can be expressed as
io n h Lλ cot arcsin nn0r sin 2π − arcsin nn00r sin U i − arctan2δ∕Δ h i o1∕2 i: n h L0ew tan 2π − arcsin nn00r sin U i − arctan2δ∕Δ 2πr − h0i n0r 2 sin2 π2 − arcsin nn00r sin U i − arctan2δ∕Δ − n2 (18)
3. Effective Evanescent Wave Penetration Depth The effective penetration depth of evanescent waves is another important parameter that affects sensitivity. For a normal unclad fiber with a smooth surface, if the angle of incidence is larger than the critical angle (θi ≥ θc ), the penetration depth is given by (Dp ), Dp
λ : 2 2 2πnr sin θi − n2 1∕2
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3. Materials and System A. Unclad Fibers
(14)
Equation (14) shows that Dp is a fraction of the wavelength if θi is perpendicular to the fiber–media interface and can be as large as several wavelengths if θi θc. However, when the fiber’s cladding is removed and the unclad fiber has a rough surface, the penetration depth D0p depends on the angle U i , roughness 2δ∕Δ, and refractive index n of the surrounding medium. Thus, it can be expressed as D0p
L0ew increases with increasing 2δ∕Δ when U i (0 ≤ U i ≤ U max ) and n are constant; it also increases with increasing U i when 2δ∕Δ and n are constant.
We experimentally investigated the effects of surface roughness on the light transmission and sensitivity of FOEW sensors using graded-index multimode silica optical fibers [RRT (China) Co., Ltd., Shanghai, China] with a diameter of 125 1.0 μm, core diameter of 62.5 0.5 μm, cladding refractive index of 1.4500 0.0025, and core refractive index of 1.4765 0.0025. Following the literature [27,31], six fibers with different roughnesses, each 30 1.0 μm in diameter and 200 1.0 mm in length, were prepared.
λ h i o1∕2 : n n0 0 2 2 π 2π nr sin 2 − arcsin n0r sin U i − arctan2δ∕Δ − n2
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(15)
splitter (Beijing Glass Research Institute R&D Center, China) had a splitting ratio of 50∕50. The light source (DH-2000, Ocean Optics, USA) consisted of deuterium tungsten halogen sources (deuterium lamp, 25 W, and tungsten halogen lamp, 20 W) operating in the 190–2000 nm spectral region. The optical power meter (UV 0.2, Newport Corporation, USA; obtained from NBeT Group Corp., China) had a wavelength range of 200–1100 nm, power range of 100 pW to 0.2 W, and uncertainty of 1%–4%. We made the probe, which contained a UV/DB detector (Newport Corporation, USA) and an FC optical fiber connector. 4. Results and Discussion A. Optical Transmission Properties Fig. 3. SEM images (3.00k×) of unclad fibers [27,31].
The unclad fibers of Samples A, B, and C were fabricated in hydrofluoric acid (HFA) solutions with concentrations of 0.24 mol L−1, 0.15 mol L−1 , and 0.015 mol L−1 , respectively. In contrast, those of Samples D, E, and F were prepared in buffered HFA solutions with pH values of 2.73, 3.72, and 5.75, respectively. An ultrasonic power of 165 W and temperature of 40°C were used as the etching conditions on the basis of extensive information in the literature [27,31]. Figure 3 shows scanning electron microscopy (SEM) images of the surface profiles of the fibers, and Table 1 shows the average surface pit depth δ, pit diameter Δ, and ratio 2δ∕Δ: Δ, δ, and 2δ∕Δ were determined using a self-developed image analysis software as following three steps: First, surface profile was extracted from the SEM images of the etched fibers at the magnification 1.00k×; second, the pits depth (δ) and the pits diameters (Δ) were measured with a calibrated scale; third, ratio 2δ∕Δ was calculated by using the Eq. (7). B.
Measurement System
We designed a sensor measurement system (Fig. 4) consisting mainly of the fibers, a fiber collimator, a micrometer, an optical splitter, a light source, and an optical power meter. The fiber collimator [Chang Fu Technology (Beijing) Co., Ltd., China] had a numerical aperture of 0.55 and focused beam diameter of 2.8 mm. The micrometer (Mitutoyo, China) had a measuring range of 0–25 mm and resolution of 0.001 mm; it was used to adjust the incident angle U i of light rays on the fiber input end. The optical Table 1.
To investigate the effect of surface roughness on the light transmission properties of the unclad fibers, six fibers with different roughnesses (Fig. 3) were each measured at least three times. We used the following experimental procedure: (1) a measurement system with a light transmission path from ① to ⑤ and then to ⑥ was connected (Fig. 4); (2) the unclad fibers were kept straight (0° bends) and placed in a box filled with air at 25°C; (3) the transmitted light intensity of the fibers was detected directly by the power meter. Figure 5 shows the experimental data and simulated data for the transmitted light intensity for various values of 2δ∕Δ. The parameters used in the simulation are listed in Table 2. Both the experimental data and the predicted results shows that the transmitted light intensity significantly decreases with increasing 2δ∕Δ, especially at high values of 2δ∕Δ. The transmitted light intensity tends to reduce to almost zero when the local pit depth δ is close to the diameter of the fiber core. However, compared with the experimental data, the predicted results overestimate the transmitted light intensity with the maximum relative error of 12.8%. The reason should be attributed to the adoption of the mean value of δ, Δ, and 2δ∕Δ in the theoretical models, while the actual nonuniform variation of the pit depth and diameter results in further degradation of the light transmission. Furthermore, compared with the smooth-surfaced fibers (2δ∕Δ 0.00), the transmitted light intensity decreases to 78%, 70%, and 23% of normal when 2δ∕Δ is increased to 0.32, 0.42, and 0.62, respectively. These results reveal that the transmitted light intensity is significantly affected by the surface roughness. Moreover, as described by Eq. (12), one can see qualitatively that the initial effective evanescent
Fiber Surface Roughness Parameters
Samples Parameters Δ (μm) δ (μm) 2δ∕Δ
A
B
C
D
E
F
8.49 1.47 2.65 1.14 0.62 0.19
5.90 0.98 1.25 0.63 0.42 0.15
4.61 0.57 0.73 0.31 0.32 0.09
4.36 1.38 0.38 0.37 0.17 0.05
4.22 0.38 0.26 0.21 0.11 0.05
L 0 0
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Fig. 4. Schematic diagram of sensor measurement system.
Fig. 5. Effect of 2δ∕Δ on the transmitted light intensity.
wave intensity I 0ew at the fiber–media interface also decreases with increasing roughness. However, further experiments and analyses are needed to verify the effect of the surface roughness (2δ∕Δ) on the sensitivity. B.
Impact of Surface Roughness on Sensitivity
To investigate the sensitivity of the FOEW sensors containing fibers with rough surfaces, we first discuss the effect of surface roughness on the decay coefficient ξ0 n, penetration depth D0p , and optical path length L0ew using the theoretical analyses presented in Subsection 2.C. Figure 6 shows the results simulated using Eqs. (13), (15), and (18). (The parameters used in the simulation are also indicated in Table 2.) Figure 6 shows that ξ0 n, D0p , and L0ew increase with increasing roughness (2δ∕Δ). Thus, the sensitivity of FOEW sensors can be enhanced by increasing the value of 2δ∕Δ. However, as discussed in Subsection 4.A, we discovered that the initial effective evanescent wave intensity (transmitted light intensity) decreases with increasing 2δ∕Δ, which degrades the FOEW sensor sensitivity. To resolve the conflicting results and create high-sensitivity FOEW sensors, it is necessary to expand this experimental study of the effect of 2δ∕Δ on the sensitivity. Table 2.
α −5
1.5 × 10
3942
−1
m
To this end, we prepared glucose solutions (test solutions) as an absorbing medium by mixing glucose (C6 H12 O6 · H2 O, 99%) and distilled water. The concentrations of the solutions ranged from 10 g∕L to 160 g∕L, and the refractive index ranged from 1.3335 to 1.3513 (the refractive index was measured by a refractometer, NAR-1T solid, ATAGO, Japan). The experimental conditions were those described above (solution temperature of 25°C and light transmission path from ① to ⑤ and then to ⑥ in Fig. 4), and the unclad (sensing) region of the fibers was kept straight. The experiments were repeated three to five times for each condition. Figure 7(a) shows a graphical representation of the transmitted light intensity I 0out of sensors with different surface roughnesses for the refractive index range described above. Figure 7(a) shows that the I 0out value of the sensor with a smooth surface decreases linearly as n increases, but the linearity decreases with increasing surface roughness. Furthermore, we can see that the response of the FOEW sensors to the same concentration of glucose solution (i.e., the same n) varies for sensing regions with different surface roughness, the lines for 2δ∕Δ 0.32 and 0.42 cross at higher refraction indexes. The chief reason for the cross is due to the surface roughness in the fiber’s sensing region increases the light-scattering and refraction loss, thus reducing the effectiveness of optical signal transmission. According to Eq. (12), one can see that the initial effective intensity of evanescent waves (I 0ew ) also decreases with increasing 2δ∕Δ. Further, according to the Eq. (13), one can see that the attenuation coefficient for unclad fibers increases with increasing refraction index of glucose solution (n). This means that the light intensity of the unclad fiber sensor with large I 0ew will make greater the amount of attenuation. Thus, the lines for 2δ∕Δ 0.32 and 0.42 will cross with increasing refraction indexes. Further, to clearly show the effect of the surface roughness on the sensitivity, the FOEW sensors’ sensitivity was evaluated as the net change in the transmitted light intensity at unit refractive index. The sensitivity (ηsensitivity , mW∕riu) is rewritten as ηsensitivity
0n ΔI out I 01.3335 − I 01.3513 out out : Δn 1.3335 − 1.3513
(19)
The evaluated data are presented in Fig. 7(b). The sensitivity increases initially and then decreases. For the sensor with a roughness of 2δ∕Δ 0.32, the sensitivity reaches a peak of −11.7 mW∕riu. The effect of the roughness (2δ∕Δ) on the sensitivity can be explained as follows. First, the fiber surface will become coated with a high-concentration layer
Parameters Used in the Simulation
n
n0
nc
nmax
U max
Iin
L
d
λ
1.3325
1.0000
1.4500
1.4765
17°
0.5 mW
200 mm
15 μm
850 nm
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Fig. 7. (a) Functional relationship between transmitted light intensity and refractive index; (b) functional relationship between sensitivity and 2δ∕Δ.
Fig. 6. Simulated curves of effective decay coefficient ξ0 n, effective penetration depth D0p , and effective optical path length L0ew of evanescent waves versus 2δ∕Δ.
fiber and generates stronger evanescent wave decay for rough fibers than for smooth ones. Thus, the sensitivity increases but the linearity decreases with increasing surface roughness. However, the sensitivity decreases when 2δ∕Δ increases beyond 0.32, chiefly because the total amount of evanescent wave attenuation decreases as a result of the significant decrease in the original effective evanescent wave intensity, as discussed in Subsection 4.A. These facts also further verified that the sensitivity is affected by the surface roughness, and a higher sensitivity can be achieved by an appropriate increase in the roughness of the unclad (sensing) region. C.
of OH− ions when the unclad fiber is immersed in the solution. Thus, the fixed capacity of the fiber to hold glucose molecules can be enhanced by the ions, and glucose molecules attached to the surface of the sensing region can induce absorbance and increase the nonlinearity. Second, the fixed capacity of the fiber increases with increasing surface roughness because the effective surface area increases, so the absorbance and nonlinearity also increase with the roughness. Third, the Rayleigh scattering loss increases with increasing roughness, which also will increase the absorbance and nonlinearity [22,32]. In addition, as noted in the discussion of Eq. (9), increasing the roughness (2δ∕Δ) decreases the value of θ0i, which reduces the number of modes propagating within the
Enhancing Sensitivity
The theory described in Subsection 2.C and the simulated results in Fig. 6 have also shown that ξ0 n, D0p , and L0ew increase as the incident angle U i of light rays on the fiber input end increases for a given unclad fiber with a certain roughness (2δ∕Δ). To validate the theoretical results and further enhance the sensitivity of FOEW sensors, the effect of U i for values of 4° to 16° on the sensitivity was examined. In this experiment, glucose solutions with refractive indices of 1.3335 and 1.3513 were tested at 25°C. The light transmission path was set to ③-④-⑤-⑥ (Fig. 4). The experiments were repeated at least three times and yielded similar results, as shown in Fig. 8. The sensors’ sensitivity is significantly affected by U i , and the trend varies with the roughness (2δ∕Δ) 10 June 2013 / Vol. 52, No. 17 / APPLIED OPTICS
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Fig. 8. Functional relationship between sensor sensitivity and U i .
of the unclad fibers. For smooth fibers (2δ∕Δ 0.00), the sensitivity appears to be linearly proportional to U i . This fact can be explained by the increase in evanescent wave attenuation as ξ0 n, D0p , and L0ew increase owing to the increase in U i . However, for rough fibers, the sensitivity increases initially and then decreases with increasing U i. In particular, when 2δ∕Δ 0.32, the sensitivity is increased to −15.3 mW∕riu when U i increases to 12°; when 2δ∕Δ 0.42, the maximum sensitivity was obtained when U i increases only to 5°. After that, the sensitivity rapidly decreases to a level below that at U i 4°. The reason is that when U i is less than 12°, θ0i is larger than the critical angle θc in deionized water at 25°C. In this case (i.e., θ0i ≥ θc ), light energy is lost by evanescent wave absorption in the sensing region, and the evanescent wave decay increases as the decrease in θ0i becomes greater because of the increase in U i (see Fig. 9); thus, the sensitivity has been improved. However, when U i is greater than 12°, θ0i is smaller than the critical angle (see Fig. 9). In this case, considerable light energy is lost directly by refraction at the interface between the fiber core and the water. Consequently, evanescent waves in the sensing region will have low energy, causing ineffective optical signal transmission [21]. This will result in extremely low total attenuation of evanescent waves by absorption and scattering in the glucose solutions. Thus, with only a slight decrease in the output light intensity of the sensor through the glucose solutions compared with that through deionized water, the sensitivity decreases as U i increases. Furthermore, for lower 2δ∕Δ values, such as 2δ∕Δ 0.17, the peak will not appear; and also the peak will not appear for higher 2δ∕Δ values, such as 2δ∕Δ 0.62. The reasons can be explained as following: first, one can obtain the angle of light incidence on an unclad fiber with a rough surface as described Eq. (9), i.e., θ0i π∕2 − arcsinn0 ∕n0r sin U i − arctan2δ∕Δ; second, one can obtain total reflection critical angle θ0c when light is transmitted into the unclad fiber region with surface roughness, i.e., θ0c arcsinn∕n0r , where n0r 3944
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Fig. 9. Simulated curves: (a) shows angle θ0i versus angle U i , (b) shows total reflection critical angle θ0c versus refraction index of glucose solutions n. 0
nmax 1 − n2max − n2c ∕n2max r − h0i ∕Rr−hi 1∕2 (n0r notes the refraction index of fiber core at local pit depth h0i ). According to these equations as above mentioned, one can obtain the simulated results about the incidence angle θ0i versus angle U i and total reflection critical angle θ0c versus refraction index of glucose solutions n. Figure 9 shows the simulated results (the parameters used in the simulation are also listed in Table 2). For sample 2δ∕Δ 0.17, one can see that the angle θ0i is greater than the angle θ0c at U i 16° and n 1.3513, so the attenuation of the light intensity from the interface via evanescent-wave absorption. In this case, the fiber surface has no scattering and refraction. Then, the peak will not appear for lower 2δ∕Δ values, such as 2δ∕Δ 0.17. For sample 2δ∕Δ 0.62, one can see that the angle θ0i is less than the angle θc at U i 1° and n 1.3335, so they will disappear from the interface via scattering and refraction. In this case, the fiber surface has no evanescent wave presence. Then, the peak will also not appear for higher 2δ∕Δ values, such as 2δ∕Δ 0.17. In conclusion, the above discussion indicates that our new approach can further improve the sensitivity of FOEW sensors by appropriate adjustment of U i, especially for unclad fibers with appropriate rough surfaces.
5. Conclusions
Intensive theoretical and experimental research on the effect of fiber surface roughness on the optical properties of FOEW sensors was conducted. We discovered that as the roughness 2δ∕Δ increases, ξ0 n, D0p , and L0ew increase, whereas I 0out and I 0ew decrease. The sensitivity of FOEW sensors using the fibers increased initially and then decreased rapidly with increasing 2δ∕Δ. In addition, an approach to improving the sensitivity was proposed in which the incident angle U i of light rays on the fiber input end served as the control parameter. We also observed that the sensitivity is increased significantly by selecting the appropriate U i value for a given fiber with a certain roughness. In conclusion, we showed that a high-sensitivity FOEW sensor can be created by combining an appropriate surface roughness with a suitable value of U i. This approach can be used to further improve the performance of fiber-optic biochemical and biomedical sensors. This work was supported by the Key Projects of the National Natural Science Foundation of China (51136007), the National Natural Science Foundation of China (50976130), and the Key Program of Natural Science Foundation of Chongqing (cstc2013jjB9004). References 1. A. H. Jalal, J. S. Yu, and A. G. A. Nnanna, “Fabrication and calibration of Oxazine-based optic fiber sensor for detection of ammonia in water,” Appl. Opt. 51, 3768–3775 (2012). 2. C. L. Linslal, P. M. S. Mohan, A. Halder, and T. K. Gangopadhyay, “Eigenvalue equation and core-mode cutoff of weakly guiding tapered fiber as three layer optical waveguide and used as biochemical sensor,” Appl. Opt. 51, 3445–3452 (2012). 3. Z. J. Zhao and Y. X. Duan, “A low cost fiber-optic humidity sensor based on silica sol-gel film,” Sens. Actuators B 160, 1340–1345 (2011). 4. P. Lu, J. Harris, X. Z. Wang, G. B. Lin, L. Chen, and X. Y. Bao, “Tapered-fiber-based refractive index sensor at an air/solution interface,” Appl. Opt. 51, 7368–7373 (2012). 5. A. Messica, A. Greenstein, and A. Katzir, “Theory of fiberoptic, evanescent-wave spectroscopy and sensors,” Appl. Opt. 35, 2274–2284 (1996). 6. R. Philip-Chandy, P. J. Scully, P. Eldridge, H. J. Kadim, M. G. Grapin, M. G. Jonca, M. G. D’Ambrosio, and F. Colin, “An optical fiber sensor for biofilm measurement using intensity modulation and image analysis,” IEEE J. Sel. Top. Quantum Electron. 6, 764–772 (2000). 7. R. Aneesh and S. K. Khijwania, “Titanium dioxide nanoparticle based optical fiber humidity sensor with linear response and enhanced sensitivity,” Appl. Opt. 51, 2164–2171 (2012). 8. C. Pulido and Ó. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B 146, 190–194 (2010). 9. B. D. Gupta and N. K. Sharma, “Fabrication and characterization of U-shaped fiber-optic pH probes,” Sens. Actuators B 82, 89–93 (2002). 10. G. Quero, A. Crescitelli, M. Consales, A. Buosciolo, M. Giordano, A. Cutolo, and A. Cusano, “Evanescent wave long-period fiber grating within D-shaped optical fibers for high sensitivity refractive index detection,” Sens. Actuators B 152, 196–205 (2011).
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