Few-mode optical fiber surface plasmon resonance sensor with controllable range of measured refractive index

A few-mode optical fiber surface plasmon resonance sensor with graphene layer is investigated, firstly, with the aim of studying the behavior of the guided modes and, secondly, with the aim of determining the range of the measured refractive index for some selected few-mode fibers. The results show that as the number of modes propagated in the fiber increases, the maximum sensitivity of a particular mode decreases while the range of the measured refractive index of that mode increases. Also, it is shown that the range can be easily tuned with sensitivity consideration by only adjusting the operating wavelength without any modification of the sensor, which is desirable from practical point of view. In addition, it is shown that the core diameter of the fiber should be chosen according to sensitivity and range needing, where a compromise between them must be found. The study presented in this paper can significantly help in developing new sensing techniques, such as multi-parameter sensing, by monitoring the various responses of the modes. Also, it can be used to customize the sensor for specific sensing applications in various fields, especially to measure refractive indices in subranges of 1.38 to 1.46.


INTRODUCTION
Optical fiber sensors have been intensively investigated and reviewed in many research due to their high performance and unique capabilities [1], [2]. One of their uses is refractive index detection [3]- [6], which is significantly important in various fields. In recent years, optical fiber surface plasmon resonance (SPR) sensors have achieved a high impact due to their high performance. They have been used in various sensing applications, such as biosensing [7], disease diagnosis [8], corrosion monitoring [9], water quality detection [10], and liquid detection [11], [12]. Researchers have developed distinct structures of these sensors in order to enhance their sensing performance. A dual-truncated-cone structure of a fiber is used for excitation and reception of SPR signals in [13], where a Bessel-like beam is used as input source. Kadhim et al. [5] proposed a single-mode fiber SPR sensor using a multiple D-shaped Ag nanowire. A photonic crystal fiber SPR sensor is reported in [14], where a D-shaped sensor with V-groove analyte channel has been created. Hu et al. [3] proposed a fiber optic SPR refractive index sensor based on multimode-no-core-multimode fiber structure. A core-shift welding technology has been investigated in [15], where a light is directly injected into the sensing fiber cladding to obtain the evanescent field at the interface between the cladding and the air. Several types of optical fiber grating-based SPR sensors have also been proposed such as in [16]- [18]. Recently, many two-dimensional materials have been discovered to enhance the optical fiber SPR sensors performance. Among these materials is graphene, which has attracted high attention due to its superior performance. Nurrohman and Chiu [19] discussed the properties of graphene in general, its use in sensors, and current status and future prospects of graphene-based SPR sensors. Different configurations of graphene based SPR sensors have been investigated and designed to enhance the sensor performance. Zhou et al. [12] have designed an end reflection optical fiber SPR sensor, where one end of the fiber has been coated by silver film and graphene. In [20], SPR sensor based on photonic crystal fiber coated with a graphene layer was designed and numerically analyzed. A D-shape plastic optical fiber SPR sensor based on graphene/gold film has been investigated in [21]. Another D-shaped single-mode fiber SPR sensor has been proposed in [22] using composite nanostructure of MoS2-graphene.
To the best of our knowledge, no studies have investigated the role of each guided mode and its contribution to the SPR sensor's performance. This is very important since monitoring the various responses of the modes may significantly develop new sensing techniques, such as enabling simultaneous measurements of multiple parameters [1]. In the previous work [23], the performance of the fundamental linear polarized (LP01) mode in optical fiber SPR sensor has been studied for different operating wavelengths, where the study was related only to single-mode fiber. In this paper, the performance of guided modes in SPR sensor is examined for some selected few-mode fibers, which are an ideal compromise between singlemode and multimode fibers [24]. The study is applied on a D-shaped sensor structure with graphene layer due to its superior performance as mentioned earlier. However, it can also be applied, in a similar way, to other structures with different numbers and types of layers. The effect of changing the operating wavelength on the range of the measured refractive index and the sensitivity is investigated for some selected few-mode fibers. In addition, different thicknesses of graphene, metal, and residual cladding have been examined. The paper is carried out in four sections starting with the introduction. Section 2 describes sensor structure and modeling, followed by results and discussion in section 3. Finally, the conclusion is presented in section 4.

STRUCTURE DESIGN AND MODELING
The proposed D-shaped sensor is shown in Figure 1, where the cross-sectional view of the sensor and its detailed structure are illustrated in Figures 1(a) and 1(b), respectively. The proposed sensor is designed by side polishing a step-index fiber. The diameter of the core and the thickness of the residual cladding are 1 and 2 , respectively. The length of the sensing region is . The side-polished cladding is covered with a metal layer of 3 thickness. Graphene layers are placed over the metal layer in order to examine the sensor's performance enhancement. The thickness of these layers is 4 . The single layer thickness of graphene is 0.34 nm [24]. Thus, 4 can be expressed as 4 = × 0.34 , where is the number of graphene layers. The core, cladding, metal, graphene, and analyte refractive indices are denoted as 1 , 2 , 3 , 4 , and 5 , respectively. The core and cladding refractive indices are determined using the well-known equation [25], [26], where is the wavelength of the incident light in micrometers, and 1 , 2 , 3 , 1 , 2 , and 3 are Sellmeier coefficients.  Due to chemical stability of gold, it is used to be the metal layer in the sensor structure. To determine the wavelength-dependent refractive index of the gold, different models can be found in research. In this paper, a Lorentz-Drude model with two additional Lorentzian terms [27] has been adopted, where the accuracy of this model is sufficient and suitable over the spectral range used in our work. According to this model, the refractive index of the metal 3 is expressed by (2) [27], where and are Drude term parameters, , , and are parameters of first ( = 1) and second ( = 2) Lorentz oscillators. The refractive index of graphene is obtained from (3) [24], where constant ≈ 5.446 −1 and the light wavelength is given in micrometers.
To examine the performance of the individual modes propagating in the fiber and their contribution to the sensitivity of the SPR sensor, intensity interrogation technique is used, where the wavelength is kept fixed and thus the number of the propagating modes in the fiber can be determined and controlled by the value of the normalized frequency . The analysis in this research is provided for linear polarized modes. Each of these modes has distinct value of propagation constant , denoted as , where subscripts and characterize azimuthal and radial mode distribution, respectively. The mode of a specific value of is denoted as . The propagation constants can be determined by solving the characteristic equation [28], where is the Bessel function of the first kind and order , is the modified Bessel function of the second kind and order , and and are the normalized transverse propagation constants for which it holds that 2 + 2 = 2 .
To examine the role of each of the propagating modes on the sensor performance, the reflectivity for each propagating mode should be determined. The reflectivity ′ for a single reflection of the five-layer structure shown in Figure 1 can be written as (5) for = 1, 2, 3, 4 and = + 1, and is the angle of the incident light with respect to the normal to the core-cladding interface and can be determined as provided in [23]. The total reflectivity for the sensor of sensing length and with number of reflections is determined using (10) [29], where = /(2 1 ). Since intensity interrogation technique is used in this study, the sensor sensitivity is determined by (11) [29].

RESULTS AND DISCUSSION
By reference to Figure 1, the core diameter 1 , residual cladding thickness 2 , metal thickness 3 , graphene layer thickness 4 , and sensing length are taken to be 10 , 10 nm, 30 nm, 34 nm, and 4mm respectively. The Sellmeier coefficients appearing in (1) have values for undoped silica core and Fluorinedoped silica cladding according to [25]. The Lorentz-Drude parameters in (2) have values according to [27]. Figure 2 shows the performance of 01 mode shown in Figure 2(a), 11 mode shown in Figure 2(b), 21 mode shown in Figure 2(c), and 31 mode shown in Figure 2(d) for different wavelengths. Each of these wavelengths supports propagation of a few modes in the fiber. It is seen that the maximum sensitivity of a particular mode decreases as the wavelength decreases. In other words, as the number of modes propagated in the fiber increases, the maximum sensitivity of a particular mode decreases. It can be noticed that the sensitivity reaches small values for the guided modes in five-mode and six-mode fibers compared with the sensitivity values for the guided modes in fibers that support propagation of fewer number of modes. Also, comparing values of the maximum sensitivity for different propagating modes at a certain wavelength, it can be seen that as the order of the mode increases, the value of the maximum sensitivity increases. For example, at wavelength 850 (which supports propagation of 01 and 11 modes), the maximum sensitivity for 01 mode is 645.3 RIU -1 , while it is 915.2 RIU -1 for 11 mode. The modes performance in a fiber that supports propagation of two modes at 850 nm, and four modes at 620 nm, is shown in Figures 3 and 4, respectively. The mentioned results can also be illustrated by showing the dependence of sensitivity on wavelength for a certain analyte refractive index.  The full width at half maximum of sensitivity (FWHM) in our case is an important parameter that indicates the range of the measured refractive index, which is desired to be as wide as possible. Although the maximum sensitivity of a particular mode decreases as the wavelength decreases, FWHM increases for that mode, which means that the range of the measured refractive index becomes wider. This is obvious from the previous figures for the modes propagated in the single-mode, two-mode, and four-mode fibers. Table 1 shows the values of maximum sensitivity, range of measured refractive index (which is taken at the half maximum of sensitivity), and FWHM for each propagating mode in single-mode, two-mode, and four-mode fibers for some selected wavelengths. For simplicity and comparison purposes, and to contribute the effect of all propagating modes, average of sensitivities maxima (sensitivity average) is determined in Table 1 for the mentioned fibers. In addition, the range of the measured refractive index and the FWHM for the mentioned fibers are determined in Table 1 according to that illustrated in Figure 6, which is related to four-mode fiber. It is noticed that the range of the measured refractive index can be determined and controlled according to the operating wavelength used. If the number of propagated modes is limited to four modes, refractive indices in subranges of 1.38 to 1.46 can be measured. A wider range can be obtained by increasing the number of propagated modes, but at the expense of sensitivity. Tables 2 and 3 show how the previous results are affected if the core diameter is taken to be 14 and 16 . Comparing Tables 1 to 3, it is obvious that the sensitivity average of a fiber, that support propagation of a certain number of modes, increases as the core diameter increases. However, the range of the measured refractive index (and thus the FWHM) decreases.  Figure 6. Determination of sensitivity average and FWHM for four-mode fiber Choosing the core diameter depends on the range of the refractive index intended to measure. For example, according to Table 1, if the range of the refractive index intended to measure is 1.422 to 1.453 and the core diameter of the fiber is chosen to be 10 , then it is better to use the operating wavelength 850 nm (which supports propagation of two modes) with which a sensitivity average of 780.25 RIU -1 is reached (FWHM=0.031 RIU) rather than using the operating wavelength 620 nm (which supports propagation of four modes) with which a smaller sensitivity average of 183.2 RIU -1 is reached (FWHM=0.072 RIU). On the other hand, if the range of the refractive index intended to measure is wider, for example, 1.389 to 1.461, then it is better to operate with the 620 nm wavelength rather than the 850 nm, since the refractive indices in subranges 1.389 to 1.421 and 1.454 to 1.461 will have very small sensitivities with the 850 nm wavelength. Similarly, if the core diameter is changed, an appropriate operating wavelength can be chosen according to the refractive index range intended to measure. For example, according to Table 3, if the core diameter is chosen to be 16 , and the operating wavelength is chosen to be 1300 nm (to support propagation of two modes), the range of the measured refractive index will be narrower (1.434 to 1.447, FWHM=0.013 RIU), but with higher sensitivity average (1900 RIU -1 ). The refractive indices in this range can also be measured using the 900 nm wavelength (which supports propagation of four modes), but in this case the sensitivity average will be smaller (751.68 RIU -1 ), but on the other hand, a wider range of refractive index can be measured (1.423 to 1.452, FWHM=0.029 RIU). Thus, one of the initial steps at designing the sensor is to carefully choose the core diameter of the fiber according to the needing, where a compromise between the range of the measured refractive index and the sensitivity must be found. Figure 7 shows the sensitivity average (780.25 RIU -1 ) and the range of the measured refractive index (1.422 to 1.453) for which the FWHM= 0.031 RIU for two-mode fiber of core diameter 1 = 10 (at = 850 ) and how the sensitivity average increases to 1900 RIU -1 , while the FWHM decreases to 0.013 RIU (range: 1.434 to 1.447) when the core diameter increases to 16 (at = 1300 ). The effect of changing thicknesses of residual cladding, metal layer, and graphene layer is shown in Figures 8 to 10, respectively, for the propagated modes in two-mode fiber. It can be seen in Figures 8(a) and 8(b) that changing the residual cladding thickness affects very slightly the sensitivity average and does not affect the full width at half maximum of sensitivity (FWHM), whereas changing the thickness of the metal layer affects both the average sensitivity and the FWHM as shown in Figures 9(a), 9(b) and Table 4. Finally, the advantage of the technique used in this paper can be shown by comparing it with one of previous works. A refractive index SPR sensor based on photonic crystal fiber with dual coating layers is reported in [30], where a maximum sensitivity of 1739.26 RIU -1 is obtained (when intensity interrogation technique is used) for the measured refractive index 1.43 at the wavelength 1.58 . Figure 11 shows the performance of the sensor designed according to our work, where sensitivity average of 2143.5 RIU -1 ( 01 sensitivity: 1810 RIU -1 , 11 sensitivity: 2477 RIU -1 ) is achieved for the same measured refractive index, mentioned in the previous work, at wavelength 1.2 , which supports propagation of two modes ( 1 , 2 , 3 , 4 , and are taken to be 12 , 10 , 50 , 34 , and 4 , respectively). In addition, at the refractive index 1.431, a higher value of sensitivity average (2325 RIU -1 ) is reached. The sensitivity average, the range of the measured refractive index and the FWHM for this sensor at the wavelength 1.2 are determined in Table 5. Moreover, the proposed sensor is suitable for refractive index measuring in the range 1.402-1.448 (in the case of two mode propagation) comparing to the range 1.40 to 1.44 of the mentioned previous work. Figure 12 shows the average sensitivities for the measured refractive index ranges at certain wavelengths that support propagation of two modes in the fiber.     Figure 11. Performance of 01 and 11 in two-mode fiber ( = 1.2 , 1 = 12 ) Figure 12. Average sensitivities for measured refractive index ranges at certain wavelengths

CONCLUSION
The performance of D-shaped SPR sensor with graphene layer has been investigated when the optical fiber supports propagation of only few modes. Sellmeier equation has been used to determine the core and cladding refractive indices, whereas the Lorentz-Drude model with two additional Lorentzian terms has been used to determine the metal refractive index. The obtained results clearly show that as the wavelength decreases, the maximum sensitivity of a particular mode decreases while the FWHM increases. Also, at certain wavelengths, comparison of sensitivities for different propagating modes has been made. It is shown that as the order of the mode increases at a certain wavelength, the value of the maximum sensitivity increases. The obtained results also show how the range of the measured refractive index can be determined and controlled according to the used operating wavelength. Refractive indices in subranges of 1.38 to 1.46 can be measured if the number of propagated modes is limited to four modes. A wider range can be obtained by increasing the number of propagated modes, but at the expense of sensitivity. Finally, it is shown that metal layer thickness has greater effect on the sensor sensitivity and FWHM than thicknesses of residual cladding and graphene layer.