Angular characteristics of a multimode fiber surface plasmon resonance sensor under wavelength interrogation
Zhixin Tan, Xin Hao, Xuejin Li, Yuzhi Chen, Xueming Hong, Ping Fan
AAngular characteristics of a multimode fiber surfaceplasmon resonance sensor under wavelengthinterrogation
Zhixin Tan , , , , ∗ , Xin Hao , Xuejin Li , , ‡ , Yuzhi Chen , ,Xueming Hong , , Ping Fan , Institute of High Energy Physics, Chinese Academy of Sciences (CAS)Beijing100049, China Dongguan Neutron Science Center, Dongguan 523808, China Shenzhen Key Laboratory of Sensor Technology, Shenzhen, Guangdong, China518060 College of Physics Science and Technology, Shenzhen University, Guangdong, China518060 College of Electronic Science and Technology, Shenzhen University, Guangdong,China 518060E-mail: [email protected] [email protected]
Abstract.
In this paper the angular characteristics of a multimode fiber SPR sensorare theoretically investigated. By separating the contributions of beams incident atdifferent angles, a compact model is presented to predict the shift of the resonancewavelength with respect to the angle and the environmental refractive index. The resultsuggests that the performance of conventional fiber SPR sensors can be substantiallyimproved by optimizing the incident angle. Furthermore, our investigation suggestssome problems in previous reports.
Keywords : Surface plasmons, Fiber-optic sensors, Plasmonics
Submitted to:
J. Phys. D: Appl. Phys. a r X i v : . [ phy s i c s . op ti c s ] N ov ngular characteristics of MM-fiber SPR sensor
1. Introduction
Recent applications of fiber SPR (Surface Plasmon Resonance) sensors to biochemicalanalysis have attracted much interest [1, 2, 3, 4, 5, 6, 7, 8, 9]. By integrating SPRregion on the cylindrical surface, a compact multimode fiber SPR sensor is produced.Fiber SPR sensor works based on attenuated total reflection (ATR) spectroscopy. Forwavelength interrogation, a modification of surface mass load on the fiber sensor willchange the resonance condition, which results in a spectral shift of the resonance dip.Compared with other variants, multimode fiber SPR sensors are simple, robust andeasy to produce [10, 11, 12]. To provide for a growing need in this developing field, webuilt a sensor system and created software for real-time measurement [12]. In such aconventional fiber SPR sensor, broadband light in various incident angles result in anasymmetric absorption curve, which requires high order polynomial fitting to resolvethe resonance wavelength.This implies that it is possible to improve sensor performanceby restricting the angular distribution of input light to a narrow range.Incident angle is an important parameter in surface plasmon resonance. Itdetermines the projection of the wave vector at the interface. A multimode fiber witha diameter of hundreds of microns is rigid enough to keep straight and to preserve thepropagation angle of a light beam. This is the experimental basis of our investigation.Although there are already many theoretical and experimental studies of multimodefibers [13, 14, 15], an analysis to distinguish the contributions of light beams withvarious incident angles is still missing. Meanwhile, the community lacks a clear picturefor sensor prediction and optimization. This motivates us to re-visit this subject froma theoretical perspective. In this paper we focus on the angular characteristics of themultimode fiber SPR sensor under wavelength interrogation. The main framework isbased on Kreschmann’s theory and Fresnel reflections in multilayer films.
2. The calculation model
The schematic of a multimode fiber SPR sensor is shown in Fig. 1. The light is launchedthrough a ring mask for angular control. Collimated beams are then focused at the centerof the input face of the fiber with a microscope objective. Assuming the fiber sensor isfabricated from a plastic cladding silica fiber with diameter d = 600 µm , the removedcladding length is L = 4 mm and the thickness of the gold film is t = 45 nm .Considering a circularly polarized light source, its transmission as a function ofincidence angle and wavelength is given by [13, 14]: T ( n e , θ, λ ) = 12 R Np ( n e , θ, λ ) + 12 R Ns ( n e , θ, λ ) (1)where N = L/d tan θ is the number of reflections. The transmitted light is divided intotwo components, with p- and s-polarization. The quantum factor of the CCD is notincluded since beams are considered in one angle with same efficiency. ngular characteristics of MM-fiber SPR sensor gold n e n c z θ Figure 1.
A multimode fiber SPR sensor with controlled light angle.
The cascaded reflectance in three-layer films is given as follows [13]: R = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) r cm + r me exp (2 ik mz t )1 + r cm r me exp (2 ik mz t ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (2)where the fiber-core, metal and environmental layers are denoted by c, m, and e,respectively. The fiber-core/metal and metal/environment interfaces are labeled as ‘cm’and ‘me’. The reflection coefficients with s- and p- polarized light on the interface aregiven for wave vectors along the z-axis and dielectric constants [13, 14]: r pcm = k cz /ε c − k mz /ε m k cz /ε c + k mz /ε m (3) r pme = k mz /ε m − k ez /ε e k mz /ε m + k ez /ε e (4) r scm = k cz − k mz k cz + k mz (5) r sme = k mz − k ez k mz + k ez (6)The refractive indices of the fiber core are interpolated from [16], while the dielectricconstants of gold are according to Johnson and Christy [17]. Wave vectors in differentmediums can be written as: k iz = ( ε i ω c − k x ) / (7) k x = n c πλ sinθ (8)where c is the speed of light and λ is the wavelength of the incident beam in free space.The letter i can be c, m, or e depending on the medium in question. k x is the componentof the wave vector parallel to the interface, which is conserved in all media. In principle,the incident angle of the light beam θ is bounded by the critical angle θ cr = sin − ( n cl /n c )and π/
2. The fiber numerical aperture NA = (cid:113) n c − n cl is also related to these indices.For a multimode fiber with a numerical aperture NA=0.50, the critical angle is 69 . ◦ if n c = 1 .
446 RIU is used. In our investigation, we discuss incident angles ranging from65 ◦ to 90 ◦ . ngular characteristics of MM-fiber SPR sensor
3. Results and discussions
Assuming the fiber SPR sensor is immersed in the water ( n e = 1 .
33 RIU), Fig. 2 (a)presents a three-dimensional plot of the transmission ratio T = T (1 . , θ, λ ) with respectto both the angle and the wavelength. For specific values of the incident angle ( θ rangingfrom 72 ◦ to 87 ◦ with an interval of 3 ◦ , as well as 89 ◦ ), black lines outline their absorptionspectra. The absorption peak positions (corresponding to minimum transmission) aretraced by a cyan line to show the overall tendency. Clearly, decreasing the incident angleincreases the resonance wavelength. The reason for this trend is not straightforward,since the surface plasmon vector k sp changes as the light wavelength increases. Toexplain this, we define an auxiliary parameter β ( λ ) = ε m ( λ ) ε e / ( ε m ( λ ) + ε e ), which isa function of the wavelength λ . To satisfy the resonance requirement, the componentof the wave vector along the interface should be equal to that of the surface plasmon: k x = k sp (9) n c πλ sin θ = 2 πλ (cid:113) β ( λ ) (10)Thus the resonance position is defined as a relationship between the angle and thewavelength. θ = sin − ( (cid:113) β ( λ ) /n c ) (11)In Fig. 2 (b), the blue line presents resonance points obtained from Eq. 11, while thecyan line is the locus of peak absorption from Fig. 2(a). The two curves do not perfectlyoverlap, since they arise from different models; the blue line is derived assuming anideal interface between two semi-infinite media, while the cyan line represents a workingsensor with a thin film. The discrepancy between the two models can be accountedfor by invoking an ‘effective’ dielectric constant. As the metal film thickness increases,the negative effective complex dielectric constant ε eff on the metal side of the interfacedecreases, which is equivalent to the increment of n e for they are equal in the expressionof β . Thus the resonance wavelength increases slightly and the cyan line moves towardthe blue line. In theory, the sensor interface approaches to the ideal model as the filmthickness increases.To investigate the performance of the fiber sensor in different environmentalconditions, resonance lines for n e from 1.33 RIU to 1.40 RIU are stacked in Fig. 2(c). The z-axis is the environmental refractive index. The lines are colored according tothe transmission ratios at the resonance positions, as indicated by the color-bar. Theheavy magenta lines are contours of constant incidence angle. These same magentalines are plotted in Fig. 2 (e) for clarity. In Fig. 2(f) we present the correspondingsensitivities, which is defined as the ratio of the shift of the resonance wavelength to thechange of environmental refractive index. For our case, we fit the discrete series first,and then calculate the corresponding value of the derivative of the fitted function. Themeaning of the heavy black line is discussed below. Furthermore, Fig. 2(d) presents thetransmission ratios for two specific values of the incident angle, θ = 81 and θ = 75, togive a direct impression of their shapes and FWHMs. ngular characteristics of MM-fiber SPR sensor ◦ to 90 ◦ in our setup. Therefore, there is no justificationfor using a base fiber with a numerical aperture larger than 0.5. Second, lower angles θ give higher sensitivity. The tradeoff is that its measurement range is narrower than thatwith large angles. To obtain high sensitivity, we should move the working position to amagenta line towards the right side of Fig 2 (c). For example, when n e = 1 .
35 RIU, thesensitivity is 2144 nm/RIU for a light beam with angle θ = 84 ◦ , while for a beamwith θ = 75 ◦ (near the edge of a multimode fiber with NA=0.39), the sensitivitycan be improved to 7101 nm/RIU, almost triple that for θ = 84 ◦ . These valuesare highlighted as red points in Fig. 2 (f). For an even higher environmental index n e = 1 .
37 RIU, the corresponding sensitivities are 17134 nm/RIU and 3719 nm/RIU,differing by a factor of five. Third, when the selection of the incident angle is adaptedto the environmental refractive index range to be measured, the maximum sensitivitiesunder different conditions are close to each other since their working positions are locatedon the right edge of the spherical face. For n e = 1 .
39 RIU, the corresponding sensitivityis 17832 nm/RIU if a light beam with θ = 78 ◦ is used. This result is close to the redpoint of 17134 nm/RIU under n e = 1 .
37 RIU in Fig. 2 (f).To compare our analysis with previous investigations, we model a multimodefiber SPR sensor with incoming light comprising a distribution of incident angles,corresponding to a numerical aperture NA=0.22. This model is henceforth referredto as a ‘conventional fiber sensor’. Other parameters are the same as for the previouslydiscussed single-angle model. Transmission ratios and resonance wavelengths fordifferent n e are calculated, taking into account the angular dependence of the powerdistribution and the CCD efficiency [13, 14, 15]. To allow direct comparison, weintroduce a concept of “effective angle”, whose value is interpolated from the resonancewavelength of the corresponding resonance line. Thus we project the result of theconventional fiber sensor onto the spherical face in Fig. 2 (c), as illustrated by the heavyblack line. As shown, the black line lies almost on top of the magenta line correspondingto θ = 84 ◦ , so the effective angle of the conventional fiber sensor is about θ = 84 ◦ . Theblack line lies entirely in the blue (high absorption) region, so the red (low absorption)zone near the edge of the plot, which corresponds to light beams in angles greaterthan 87 ◦ , is inactive in practice. It suggests that light beams being almost parallel tothe fiber axis, corresponding to the red edge of the surface in Fig. 2 (c), contributelittle to the sensor performance because of their weak absorption. As n e increases, theresonance wavelength increases and the wave vector k x = k sin θ decreases; this leads topreferential weighting of smaller angles, which should account for the deviation of theblack line towards a smaller effective angle at large refractive indices in Fig. 2(c).The transmission curves for a conventional fiber sensor for environmental indices n e = 1 .
33 RIU, n e = 1 .
365 RIU, and n e = 1 .
40 RIU are plotted in Fig. 2 (d) with legend‘NA’. The resonance absorptions are less than 0.4, which suggests a moderate resonance ngular characteristics of MM-fiber SPR sensor n e = 1 .
40 RIU, the FWHM of the spectrum is close to 200 nm and the bottom of thecurve is nearly flat, which makes it hard to identify the minimum position. Comparedto the red lines ( θ = 81 ◦ ), the FOM of the sensor is much poor. In Fig. 2 (e) and (f)we show resonance wavelengths and sensitivities of the conventional fiber sensor (blackline and star markers). These results are somewhat higher than for light with a singleincidence angle of θ = 84 ◦ . The sensitivity is 1523 nm/RIU at n e = 1 .
34 RIU, as labeledin (f). This value is close to what we found in our experimental study [12], if we neglectsome differences in sensor parameters.Except the low efficiency and moderated performance in the conventionalconfiguration, many earlier reports did not take a serious consideration for the angularcharacteristics of the fiber SPR sensor [12, 1, 2, 4]. For example, the Y-combiner,which is widely found in the literature and involves thermal tapering and then fusingtogether of fibers, will change the angular distribution of the propagating light and there-distribution in angle is out of control. Therefore it is impossible to trace the pathsof rays. But SPR effect strongly depends on the incident angle. Thus it leads to amess in theory. More attention should be paid to this issue. Based on our investigation,we recommend that researchers working on multimode fiber SPR sensors stick to theoriginal configuration without Y-combiner, although it is a bit inconvenience. Anotherimportant problem is the mismatch in aperture size between the fiber itself and thespectrometer, which had been neglected in both the experiment and its theoreticalsimulation. For compactness and convenience, most fiber SPR configurations use a fiberspectrometer to acquire spectra. However, the fiber spectrometer has its own numericalaperture, typically NA = 0.22. Obviously, under this configuration the large-anglecontributions are wasted, even though the base fiber has a large NA. A possible solutionis to use another microscopic objective to recover a quasi-collimated light beam before itenters the spectrometer; otherwise one could use a customized fiber spectrometer witha larger NA.About twenty years ago several fiber SPR sensors with oblique light input were builtfor angular interrogation [18, 19, 20]. Obviously, their configurations were much differentfrom our proposal as we use white light and wavelength interrogation while laser andangle shift are adopted in those reports. The kernel of our proposal is to purify the inputand evaluate the contribution separately. This can not be achieved in these mentionedpapers where non-meridian light beam dominate the effect. In addition, if the ring maskis thick enough, the skew rays should be reduced greatly in our configuration.The number of reflections N ( θ ) is determined by the fiber diameter and the sensinglength. Since power operation doesn’t change the position of the minima, these twoparameters have little effect on our model if the absorption threshold hasn’t beenreached. This is also demonstrated in Fig. 2 (b). The red line, which represents theresult of a single reflection of R p in Eq. (1), overlaps almost exactly with the cyan lineof minimum transmission; the small difference is a numerical artifact arising from the ngular characteristics of MM-fiber SPR sensor N ( θ ) increases, the resonance is intensified andthe red zone in Fig. 2(c) shrinks to the edge. Consequently, the importance of lightbeam with large angle increases; working positions of the conventional fiber SPR sensormove toward the edge and the sensitivity decreases. This should account partly fordifferences between our numerical results and previous reports [12, 15].As illustrated in Fig. 2(b), the film thickness make a slight difference between a fiberSPR sensor of finite thickness and the ideal model. If the film thickness changes, thecambered surface in Fig. 2 (c) shifts slightly. Furthermore, the sensitivity is determinedas a slope of the magenta curves. Thus the variation in performance is delicate andit is difficult to identify a general tendency. In contrary, the film thickness plays animportant role in the signal amplitude, which should be considered before other factors.Fiber SPR tips or tapered fiber SPR can also be described qualitatively in ourmodel. As proposed in works [21, 22], post-processing of the fiber will directlydecrease the incident angle of the main portion of the light with respect to the normalof the cone surface. Thus the effective working angle decreases and the sensitivityis improved. Meanwhile, our model helps to identify the maximum angle for post-processing: according to Fig. 2 (b), the tapering angle should be less than 20 ◦ underenvironmental index n e = 1 .
33 RIU.
4. Conclusions
In conclusion, we have numerically calculated and analyzed the angular characteristicsof a multimode fiber SPR sensor. A general model is presented for sensor prediction andoptimization. It suggests that small-angle components of the light beam have bettersensitivity. We have proposed an angular fiber SPR sensor based on a multimode fiber.For a specific measuring index, the performance of a multimode fiber SPR sensor canbe substantially improved by deliberate control of the beam angle.The author would like to thank Dr. Scott Edwards, Shenzhen University, forhis kind help in language editing. The work was supported by the National ScienceFoundation of China under Grant (No.61275125 and No.61308046), Basic ResearchProgram of Shenzhen and High-level Talents Project of Guangdong Province. [1] Jeroen Pollet, Filip Delport, Kris P.F. Janssen, Karolien Jans, Guido Maes, Helge Pfeiffer,Martine Wevers, and Jeroen Lammertyn. Fiber optic SPR biosensing of DNA hybridizationand dnaprotein interactions.
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Sensors and Actuators B: Chemical , 188(0):757 – 760, ngular characteristics of MM-fiber SPR sensor ngular characteristics of MM-fiber SPR sensor Figure 2. (a) Three-dimensional plot of the transmission ratio as a function of bothwavelength and incident angle, for n e = 1 .
33 RIU. (b) The ideal resonance requirement(blue), the general trend from the full model (cyan), and the result for a singlereflectance R p (red). (c) The stacked resonance positions for n e ranging from 1.33 RIUto 1.40 RIU. The black dots are the projected working position of a conventional fibersensor. (d) Sample spectra for beams with incident angles θ = 81 ◦ (red) and θ = 75 ◦◦