Journal of Modern Optics, 2016 VOL. 63, NO. 12, 1189 1195 http://dx.doi.org/10.1080/09500340.2015.1135257 Analysis of a highly birefringent asymmetric photonic crystal fibre based on a surface plasmon resonance sensor Chao Liu a, Famei Wang a, Shijie Zheng b, Tao Sun c, Jingwei Lv a, Qiang Liu a, Lin Yang a, Haiwei Mu a and Paul K. Chu d a School of Electronics Science, Northeast Petroleum University, Daqing, P.R. China; b School of Civil Engineering, Harbin Institute of Technology, Harbin, P.R. China; c Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore, Singapore; d Department of Physics and Materials Science, City University of Hong Kong, Hong Kong, China ABSTRACT A highly birefringent photonic crystal fibre is proposed and characterized based on a surface plasmon resonance sensor. The birefringence of the sensor is numerically analyzed by the finite-element method. In the numerical simulation, the resonance wavelength can be directly positioned at this birefringence abrupt change point and the depth of the abrupt change of birefringence reflects the intensity of excited surface plasmon. Consequently, the novel approach can accurately locate the resonance peak of the system without analyzing the loss spectrum. Simulated average sensitivity is as high as 1131 nm/riu, corresponding to a resolution of 1 10 4 RIU in this sensor. Therefore, results obtained via the approach not only show polarization independence and less noble metal consumption, but also reveal better performance in terms of accuracy and computation efficiency. ARTICLE HISTORY Received 6 May 2015 Accepted 17 December 2015 KEYWORDS PCF; SPR sensor; birefringent analysis; FEM; sensitivity 1. Introduction Surface plasmon resonance (SPR) sensing is attracting growing interest due to the excellent sensitivity to variation in refractive indexes of the surrounding dielectrics, and has potential applications in the fields of environmental monitoring, biotechnology, medical diagnostics and food safety [1 3]. Many types of optical fibre SPR sensors with diverse structures, such as D-shape, cladding-off, FBG-based SPR and PCF-SPR, have been demonstrated by both theoretical simulation and experiments [4 6]. Among the sensors mentioned above, PCF-SPR sensors have received enormous attention due to conspicuous advantages, such as great flexibility in the structure design, high sensitivity, as well as no electromagnetic interference [7 9]. Numerically simulations were carried out for PCF- SPR sensors via the loss spectrum analysis method based on the coupled mode theory [10 13]. However, coupled mode theory has limitation when the coupled intensity of PCF-SPR is obviously low. In particular, when the PCF- SPR structure is strongly asymmetric, more complicated mode coupling conditions in two orthogonal directions may further lead to birefringence phenomenon [14]. In order to obtain an obvious birefringent PCF-SPR phenomenon, Y. Du et al. reported that the wavelength-selective characteristics of high birefringence photonic crystal fibre (PCF) can be improved remarkably using gold nanowires. The resonance wavelength in the high birefringence PCF occurred at different points for various polarized directions, and the resonance strength in the x-polarized case was much weaker than that in the y-polarized case [15]. R. Otupiri et al. also presented a novel birefringent PCF- SPR biosensor with circular air holes to introduce birefringence into the structure, which had differential sensitivity when the fundamental modes HE x 11 and HEy 11 were considered in the loss spectrum. It has been demonstrated that this sensor can be useful for multianalyte, multichannel sensing and simultaneous detection of bulk and surface sensitivities [16]. However, when the transmission loss spectrum is flattened, as in many real cases, it becomes increasingly difficult to obtain abrupt change of birefringence by means of measuring the loss spectrum. In 2010, Yu et al. [14] proposed a zero-birefringence approach to locate the resonance peak for the PCF-SPR sensor with an asymmetrical structure by determining the zero-birefringence point of two degenerate modes instead of analyzing the loss spectrum. Nonetheless, it is worth to point out that many asymmetric sensors are not applicable to this approach due to the non-existent zero-birefringence point for specific asymmetric sensors. CONTACT Chao Liu liuchao@nepu.edu.cn; Tao Sun taosun@hotmail.com.hk 2016 Taylor & Francis
1190 C. LIU et al. Figure 1. Cross section of the PCF-SPR sensor. (The colour version of this figure is included in the online version of the journal.) Herein, we describe a novel birefringence analysis method in which the resonance wavelength is directly positioned at the abrupt change point of the birefringence curve and the depth of the abrupt change point is capable of reflecting the intensity of the excited surface plasmon. The birefringent analysis of the sensor is carried out numerically using the finite-element method (FEM). The novel approach offers salient advantages over conventional methods in terms of accuracy in determining the resonance wavelength and the efficiency in computational time and memory utilization. The numerical results not only show an average sensitivity up to 1131 nm/riu corresponding to a resolution of 1 10 4 RIU, but also indicate that the optical birefringence of the PCF-SPR sensor can be conveniently tuned by changing the parameters of the structure. 2. PCF-SPR sensor and numerical modelling The highly birefringent PCF-SPR sensor with a gold film as the sensitive layer is investigated using the COMSOL Multiphysics software [17]. Figure 1 displays the schematic diagram of the PCF-SPR sensor. The sensor contains a fibre core and two layers of holes and the fibre core is surrounded by two layers of holes arranged hexagonally. The holes in the second layer are considerably larger than those of the first layer. To lower the refractive index of the core-guided mode (in order to facilitate phase matching with a plasmon), a small hole is introduced at the centre of the fibre core and it in principle can be substituted by a smaller hole [10]. As shown in Figure 1, Λ = 2 μm, d l = 0.6Λ, and d c = 0.45Λ represent the pitch of the air holes, diameter of the second layer of holes, diameter of the first layer of holes and diameter of the fibre core, respectively. The fibre core and first layer of holes filled with air serve to reduce the effective refractive index of the core-guided mode and cladding and so that the light wave can be limited to the fibre core. The second layer of holes is filled with the analyte and gold layers with various thicknesses are grown on the wall of the analyte channel to excite SPR. The dielectric constant of gold is determined by the Drude model [10]. And n a = 1.0 represents the refractive index of air. The refractive index of the silica glass is given by the Sellmeier dispersion relation [9], whereas the refractive index (n c ) of the analyte flowing through the channel is between 1.34 and 1.48. This study focuses on the 2D simulation of the mode analysis of the PCF-SPR sensor and the propagation modes of the electromagnetic wave in this sensor are analyzed by the FEM based on the COMSOL software. When the transmission loss of the core mode is utilized to evaluate the SPR properties, a perfectly matched layer (PML) boundary condition is considered at the numerical calculation zone edges. It is well known that the PCF-SPR sensor suffers electromagnetic wave transmission loss. The guided core mode propagates in the fibre and excites the surface plasmon waves (SPWs) at the outer interface of the gold layer if they are phase-matched [17]. According to reference [13], the attenuation constant α loss is proportional to the imaginary part of the effective index and defined by Equation (1): α loss = 40π ( ) (1) λ ln 10 Im n eff 10 6 (db m), where λ represents the wavelength of the incident light in vacuum and Im(n eff ) represents the imaginary part of the effective refractive index of the guide mode. The cross section of the sensor is designed to be an asymmetrical structure inducing an uneven distribution of the refractive index thus causing the birefringence phenomenon. Since the phase and propagation constant of the x-polarized mode are different from those of the y-polarized mode, the sensing properties of the asymmetric sensor can be investigated by the birefringence analysis method. The refractive index difference of the fundamental mode of the two orthogonal polarizations is defined as the size of birefringence B: B = ( ) ( ) Re n x eff Re n y eff (2) 3. Numerical results Figure 2 shows the optical field distribution of the (a) x-polarized mode and (b) y-polarized mode, where the arrows represent the direction of polarization. The structure parameters are as follows: Λ = 2 μm, d l = 1.0Λ, d a = 1.34 and λ = 800 nm. It is found that the real part (1.420102) of
Journal of Modern Optics 1191 Figure 2. Optical field distribution: (a) x-polarized mode and (b) y-polarized mode, where the arrows represent the direction of the polarization. (The colour version of this figure is included in the online version of the journal.) the effective refractive index of the y-polarized mode is larger than that (1.419816) of the x-polarized mode and it is attributed to the strongly asymmetrical structure of the proposed sensor. Therefore, there is a difference in the effective refractive indexes between x-polarized and y-polarized modes for an analyte with a refractive index of 1.34 at 800 nm. The dependences of the real parts of the effective refractive index for the x-polarized and y-polarized modes on wavelength are shown in Figure 3(a). The real parts
1192 C. LIU et al. (a) Re(neff) (b) Loss(dB/cm) 1.426 1.424 1.422 1.420 1.418 1.416 100 80 60 40 20 0 (x) x polarization mode y polarization mode 720 740 760 780 800 820 840 860 Loss 0.00015 700 720 740 760 780 800 820 840 860 decrease gradually with increasing wavelength for both the x- and y-polarized modes. However, an abrupt change (y) 0.00045 0.00040 0.00035 0.00030 0.00025 0.00020 Figure 3. (a) The real part of the effective refractive index of x- polarized mode and y- polarized mode (b) Simulation of the loss spectrum and the birefringence curve of the fundamental mode (Λ = 2 μm, d l = 1.0, n c = 1.34). (The colour version of this figure is included in the online version of the journal.) 0.00045 0.00040 0.00035 0.00030 0.00025 0.00020 0.00015 30nm 40nm 50nm 720 740 760 780 800 820 840 860 Figure 4. Simulation of the birefringence curve of the sensor, for different gold layer thicknesses (Λ = 2 μm, d l = 0.6Λ, d c = 0.45Λ, n a = 1.34). (The colour version of this figure is included in the online version of the journal.) point exists at the incident wavelength of 770 nm for the real part of the effective refractive index in the x-polarized mode. Inset (x) and inset (y) in Figure 3(a) display the electric field distributions of the x-polarized mode and y-polarized mode for an analyte with a refractive index of 1.34 at 770 nm, respectively. It is clearly seen from inset (x) that confined energy exists at the metal surface and in the fibre core for the x-polarized mode, indicating that the core-guided mode and plasmonic mode become strongly resonant in the x-polarized mode. However, for the y-polarized mode, all the energy is confined to the core and there is no energy coupled to the metal surface. The gold-coated layer contributes to the excitation of SPWs in the x-direction, but there is no such effect from the metal in the y-direction. Therefore, the phase-matching coupling phenomenon can be confirmed by the abrupt change point of the x-polarized mode. Based on Equations (1) and (2), it can be concluded that the propagation loss of the sensor is proportional to the imaginary part of the effective refractive index. According to Equations (1) and (2), the loss spectrum and birefringence curve of the fundamental mode are illustrated in Figure 3(b). An obvious resonance peak is centred at 770 nm in the propagation loss spectrum and an abrupt change point also exists at 770 nm in the birefringence curve. In fact, the existing abrupt variation should not occur in the loss spectrum and birefringence with wavelength [18,19]. Therefore, this abrupt change is only ascribed to the SPR phenomenon excited at 770 nm, indicating that the resonance wavelength can be directly positioned at this birefringence abrupt change point. Moreover, the depth of the abrupt change of birefringence reflects the intensity of the excited surface plasmon. It is well known that the thickness of the metal thin film is one of factors that influence the half-width and depth of the resonance peak [20]. Hence, the influence of gold layer thickness on the sensing performance is systemically investigated. Figure 4 shows the birefringence curve of the fundamental mode of PCF-SPR sensor with different gold layer thicknesses. The resonance wavelength moves towards shorter wavelengths and the resonance intensity of the birefringence increases gradually with the gold layer thickness from 30 nm to 50 nm. The birefringence at the off-resonance wavelength increases with the gold layer thickness throughout the calculated thickness range. Because the existence of the fibre core can remarkably lower the effective refractive index of the guided core mode, the phase-matching condition between the guided core mode and plasmon mode will be alternatively satisfactory by adjusting the size of the fibre core. Figure 5 presents the birefringence curve of the core mode for various fibre core sizes. The resonance wavelength moves towards the longer wavelength when d c ranges from 0.4Λ to 0.6Λ.
Journal of Modern Optics 1193 Figure 5. Dependences of the birefringence curve of the sensor on the size of the fibre core d c (Λ = 2 μm, d l = 0.6Λ, t Au = 1.34). (The colour version of this figure is included in the online version of the journal.) Figure 7. The birefringence curve of the fundamental mode for the sensor with different sizes of analyte holes d l (Λ = 2 μm, d a = 1.34). (The colour version of this figure is included in the online version of the journal.) Figure 6. The birefringence curve of the sensor for several values of different sizes of air holes d a (Λ = 2 μm, d l = 1.0Λ, d c = 0.45Λ, t Au = 1.34). (The colour version of this figure is included in the online version of the journal.) The resonance intensity of the birefringence increases distinctly as d c varies between 0.4Λ and 0.5Λ, while the resonance intensity of the birefringence decreases remarkably with d c increasing from 0.5Λ to 0.6Λ. This implies that the size of the fibre core (d c ) has a great influence on the resonance wavelength and resonance intensity, which can be tuned to a desired value by adjusting d c. In order to easily satisfy the phase-matching conditions of SPR, a smaller fibre core is selected to lower the refractive index of the core-guided mode. Here, 0.45Λ is chosen as the size of the fibre core in our analysis. Figure 6 shows the birefringence curve of the fundamental mode as a function of the size of the air holes. The resonance wavelength moves towards shorter wavelengths and the resonance intensity of the birefringence decreases rapidly with increasing air hole size (d a ) from 0.5Λ to 0.7Λ. This (a) (b) 0.0014 0.0013 1.34 0.0012 1.36 0.0011 1.38 1.40 0.0010 1.42 0.0009 1.44 0.0008 1.46 0.0007 1.48 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.0000-0.0001-0.0002 720 740 760 780 800 820 840 860 880 900 920 940 960 Resonant wavelength(nm) 900 880 860 840 820 800 780 760 940 Resonant wavelength(nm) Linear Fit of Resonant wavelength 920 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 Refractive index(riu) Figure 8. (a) The birefringence curve of the fundamental mode for the sensor for different analytes. (b) Linear fitting lines of the fundamental mode resonance wavelength versus analyte RI of 1.34 1.48 (Λ = 2 μm, d l = 50 nm, n a = 1.0). (The colour version of this figure is included in the online version of the journal.)
1194 C. LIU et al. phenomenon can be attributed to energy leakage caused by the air layer. That is, the larger the diameter of the first air layer, the less energy the outer layer leaks thus resulting in weaker coupling between the plasmon mode and core mode. In order to further characterize the performance of the sensor, the analyte holes with different sizes of 0.8Λ, 0.9Λ and 1.0Λ are introduced to the PCF-SPR sensor. Figure 7 presents the birefringence curve of the fundamental mode of the PCF-SPR sensor with different analyte hole sizes. The resonance peak shifts to longer wavelengths and the resonance intensity of the birefringence increases with the analyte holes. Since the larger analyte holes make the gold layer to be closer to the fibre core, more core energy is transferred to the SPW energy leading to stronger coupling efficiency and resonance intensity. The decrease in the overall effective refractive index of the waveguide shifts the resonance to a longer wavelength [14]. The birefringence curve of the fundamental mode for diverse analytes is shown in Figure 8(a). The resonance wavelength shifts to longer wavelengths when the analyte refractive index ranges from 1.34 to 1.48. The resonance intensity of the birefringence increases gradually with increasing refractive indexes of the analyte. Based on the discussion above, we investigate the sensitivity of the PCF-SPR sensor in the analyte RI range of 1.34 1.48. The corresponding linear fitting curve of the resonance wavelength in relation to the analyte RI is presented in Figure 8(b). The fitting formula is expressed by: λ(nm) =1130.95n 749.64, 1.34 n a 1.48, where λ is the resonance wavelength of the sensor and n is the refractive index of the analyte. The slope of the equation reveals an average sensitivity of 1131 nm/riu within the relevant sensing range. The adjusted R-Square value of the λ fitting curve is 0.99741, indicating high linearity of the PCF-SPR sensor. The wavelength resolution of the detector is assumed to be Δλ min = 0.1 nm. The refractive index resolution of the proposed sensor can be defined as [17]: R =Δn a Δλ min Δλ peak. Hence, the peak shift in this work is estimated to be about Δλ peak = 20 nm according to Figure 8. When the variation in the analyte refractive index is Δn a = 0.02, the sensitivity of the proposed PCF-SPR sensor is approximately 1131 nm/riu for the refractive index ranging between 1.34 and 1.48 leading to a sensor resolution of 1 10 4 RIU. 4. Conclusion (3) A highly birefringent PCF-SPR sensor with a gold sensing layer is numerically investigated using the FEM. On the basis of polarization independence, it is found that the resonance wavelength of the PCF-SPR sensor is directly positioned at the abrupt change point of the birefringence curve. This approach not only reduces the calculation complexity, but also more easily and accurately determines the resonance wavelength. The simulation results obtained by the birefringence analysis demonstrate that the structure parameters of the sensor have a great influence on the resonance wavelength and resonance peak intensity. An average sensitivity of up to 1131 nm/riu corresponding to a resolution of 1 10 4 RIU is achieved from the sensor. The proposed method is beneficial to sensor design and fabrication. Disclosure statement No potential conflict of interest was reported by the authors. Funding This work was supported by the Natural Science Foundation of China 1 [grant number 51474069], [grant number 51374072], [grant number 51101027]; and Program for New Century Excellent Talents in Heilongjiang Provincial University 2 [grant number 1253-NCET-002]. References [1] Jorgenson, R.C.; Yee, S.S. Sens. Actuators, B 1993, 12, 213 220. [2] Jorgenson, R.C. Surface Plasmon Resonance Based Bulk Optic and Fiber Optic Sensors; University of Washington: Washington, DC, 1993; pp 40 56. 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