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• Abstract

SECTION I

## INTRODUCTION

There is a growing interest in exploring optics fiber sensors based on their resistance to electromagnetic interference, electrical insulation, corrosion resistance, high sensitivity, light weight, small volume, measurement of various parameters (temperature, stress, vibration, rotation, electromagnetic field, chemical quantity and biomass, etc.) and other remarkable characteristics [1]. Being extremely sensitive to the changing of the refractive index of dielectric surrounding the metal nano-material, optical fiber surface plasmon resonance (SPR) sensors have attracted immense attentions with the peculiar properties of label-free sensing and real-time measurement capabilities [2], and have been implemented in plenty of sensing structures [3]. Especially, A myriad of SPR configurations for bio-molecular interactions, chemical detection, and immunoassays have also been recently investigated [4], [5]. Furthermore, photonic crystal fibers (PCFs) with an array of air holes along the propagation direction and the unique characteristics have presented an attractive platform for SPR sensing. Compared with the conventional fibers, PCFs can be used for sensing without additional processing of cladding physical or chemical to achieve close proximity of analyte to the fiber core. Therefore, many researchers have reported many PCF sensing devices fabricated by designing and manipulating some specific structures [6], [7], [8]. In addition, the sensing properties of PCF-based SPR sensor devices can be manipulated by infiltrating the air holes or hollow core with liquid, oil, liquid crystal, polymer or other materials [9]. Among the numerous studied PCF-based SPR refractive indices (RI) sensors, the researchers obtained that the plasmonic mode effective indices are affected by the variational analyte obviously. And, however, the effective indices of the core guiding mode are almost independent of the changing [7], [10], [11], [12], [13]. In spite of a variety of notable achievements, there still exist some challenging issues regarding on the confinement loss and sensitivity.

In general, PCF-based sensors taking LED (Light-Emitting Diode) or LD (Laser Diode) as light source, and the PCF is used as a sensor components or the optical element. However, the active sensing based on doped PCFs rarely has been reported. In this paper, first, we report an optical intra-cavity index sensor design utilizing the index-guiding $\hbox{Yb}^{3+}$-doped PCF filled with analyte and nanowires in the larger air holes, and present a comprehensive numerical analysis based on the finite element method (FEM). Second, we design a sensing system based on the proposed sensor. In such sensing system, pumped by 976 nm light, the output power of the $\hbox{Yb}^{3+}$-doped PCF laser at 1060 nm can be influenced obviously by a bit change of the refraction index of analyte in the air holes of PCF, which can achieve the intra-cavity fiber sensing. We have gotten the relationship between effective refractive index of analyte and the confinement loss, output power of intra-cavity index sensor and cavity loss coefficient, output power and the end reflectivity and some other some other influencing factors by finite element method, respectively. The numerical analysis shows the influence of different air-filling ratios and different analyte RI of ${\rm n}_{\rm a}\ >\ 1.45$ or ${\rm n}_{\rm a}\ <\ 1.45$ on the output power and confinement loss of the proposed sensor.

SECTION II

## SENSOR CONFIGURATION AND THEORETICAL MODELING

As shown in Fig. 1(a), a PCF-based SPR sensor is proposed. The PCF is formed of a standard index guiding fiber with hexagonal lattice air holes and the $\hbox{Yb}^{3+}$-doped fiber core. The diameters of air holes and fiber core are ${\rm d}_{1} = 1\ \mu\hbox{m}$ and ${\rm d}_{\rm c} = 1.3\ \mu\hbox{m}$, respectively. The pitch of the underlying hexagonal lattice is $\Lambda = 2 \ \mu\hbox{m}$. The analyte channels are formed of removing seven silica tubes in the first and second layers, of which cross section is shown in Fig. 1(b), which filled with analyte and silver nanowires with capillary effect and pressure with some setups, and the diameters of the nanowires are 100 nm. The refractive index of background material fused silica is 1.45 and the silver nanowire is referred to the Handbook of Optics [14]. The refractive index (RI) of the $\hbox{Yb}^{3+}$-doped fiber core is ${\rm n}_{\rm c} = 1.5823$, which can broaden the measurable range of analyte. Analyte with lower RI than 1.5823 is filled to guarantee the total index-guiding mechanism and the corresponding reflection condition for each analyte channel. The analyte channels feature symmetry to guarantee a polarization independent propagation characteristic.

Fig. 1. (a) Cross section of the SPR sensor based on fiber core $\hbox{Yb}^{3+}$-doped PCF. (b) The cross section of analyte channel filled with silver nanowires.

We use FEM to solve the light field mode and calculate the attenuation constant of the fundamental mode of PCF with different analytes, and the optical field distribution of the fundamental mode is shown in Fig. 2, from which we can see that the function of cladding air holes of the formed fundamental modes are confined well within the core.

Fig. 2. The optical field distribution of the fundamental mode (the wavelength of the incident light is 1060 nm, $\hbox{na} = 1.33$, ${\rm d}1/\Lambda = 0.4$, and the arrow indicates the polarization direction of magnetic field).

The SPR optical technique refers to the excitation of surface plasmon polaritons. Surface plasmons can be excited by light when the phase matching condition is met between the exciting light and the surface plasmons [15], which will generate a loss peak. Therefore, in order to make a comprehensive investigation about the SPR sensor based on $\hbox{Yb}^{3+}$-doped PCF, the attenuation constant of the fundamental mode is calculated for the incident light. We utilize the structure of PCF sensor with $\hbox{Yb}^{3+}$-doped fiber core in the simulation to calculate the effective indices of electromagnetic modes supported by the designed sensor and analyze the sensing characteristics. The confinement loss $\alpha_{loss}$ can be evaluated by TeX Source $$\alpha_{loss} = 10 \lg\ e \cdot \alpha = 10\lg e \cdot 2k_{0} \ \hbox{Im}[n_{eff}] = 8. 686 \cdot {2\pi \over \lambda} \cdot \hbox{Im} [n_{eff}] (\hbox{dB/cm})\eqno{\hbox{(1)}}$$ where $k_{0}$ is the wave number $(k_{0} = 2\pi/\lambda)$, $n_{eff}$ is the mode effective refractive index, the real part $\hbox{Re}[n_{eff}]$ expresses the dispersion and the imaginary part $\hbox{Im}[n_{eff}]$ expresses the loss. This article uses the mode power attenuation coefficient $\alpha$ to quantify the loss of the transmission mode, and uses dB/cm as the unit.

The relationship between effective refractive index of analyte (na) and the confinement loss is shown in Fig. 3, which represents that the confinement loss increases obviously when the ${\rm n}_{\rm a}\ >\ 1.45$ (the refractive index of the background material silica is 1.45), and is no longer flat. This indicates that the sensitivity will be very high when the ${\rm n}_{\rm a}$ is higher. So we can make the higher ${\rm n}_{\rm a}$ as the optimal choice.

Fig. 3. The relationship between effective refractive index of analyte (na) and the confinement loss $({\rm d}1/\Lambda = 0.4)$.
SECTION III

## DESIGN AND DISCUSSION OF THE ACTIVE SENSING SYSTEM

The study of introducing the external sensing source to sensor's interior with a doped PCF is to achieve the active sensing of the generation of laser detection, information sensing and signal transmission. To improve the detection sensitivity, an alternative technique for high sensitivity absorption measurement is intra-cavity laser spectroscopy [16]. The sensing system based on $\hbox{Yb}^{3+}$-doped PCF is shown in Fig. 4. We have gotten the relationship between effective refractive index of analyte and the confinement loss, output power of intra-cavity index sensor and cavity loss coefficient, output power and the end reflectivity by finite element method, respectively. The numerical analysis shows that the power change is larger in a small range of loss when the end reflectivity is higher, and the sensor's sensitivity will be higher for the change of refractive index of analyte.

Fig. 4. The structure of sensing system based on active photonic crystal fiber 1: laser diode (976nm); 2: isolator; 3: 976/1060 WDM device; 4: $\hbox{Yb}^{3+}$-doped PCF; 5: fiber mirror; 6: tunable optical fiber grating; 7: power meter.

The system of active PCF sensing, which have great practical value and innovative significance for their advantages of compact structure, high reliability, stability and sensitivity, is mainly consist of a standard low-power Laser diode (LD) for pumping low-doped $\hbox{Yb}^{3+}$ PCF through a wavelength division multiplexer (WDM), a fiber Bragg grating (FBG), and optical fiber mirror. In this system, we can make light source, SPR sensor and the transmission medium together to realize active PCF sensing. In this work, we make the $\hbox{Yb}^{3+}$ as the active medium, LD as pump sources. In such sensor, when pumped by 976 nm light, it will generate 1060 nm laser that is loaded to sensing light path by WDM [17], and the optical fiber mirror and tunable FBG constitute the laser cavity. When the phase matching condition is satisfied between the exciting light and the surface plasmons, the energy of a core-guided mode is transferred to plasmonic mode and it will generate a loss peak. The output power of the $\hbox{Yb}^{3+}$-doped PCF laser at 1060nm can be influenced obviously by a bit change of the refraction index of liquid in the analyte channels of the PCF to achieve the intra-cavity fiber sensing. With the sensing system we can achieve the purpose of measuring refractive index of analyte.

According to the C. barnard theory and $\hbox{Yb}^{3+}$-doped laser four-level transitions [18], and with the specific parameters of $\hbox{Yb}^{3+}$, we can get the simplified C. barnard formula in the steady state condition, and the threshold power $P_{p}^{th}$: TeX Source $$P_{p}^{th} = hN_{up}A_{eff}\left[ \alpha_{s}L - \log (\varepsilon R) \right] / \tau_{2}\sigma_{SE}\gamma_{S} \left(1 - e^{(\delta \alpha_{s} - \alpha_{p} L)}\right) (\varepsilon R)^{- \delta}\eqno{\hbox{(2)}}$$ where $\alpha_{p}$, $\alpha_{s}$ denotes the pump light absorption coefficient and signal light absorption coefficient, which can be influenced by the plasmon resonance. L is the length of the $\hbox{Yb}^{3+}$-doped PCF, $A_{eff}$ is the effective area, the net decay times from the metastable levels are denoted by $\tau_{2}$, $\sigma_{SE}$ is the cross section of signal light, $\delta$ is saturation power ratio, $\gamma_{S} = 1$. The effective mirror reflectivity can be denoted as $R = \sqrt{R_{1}R_{2}}$. Where $R_{1}$ is the reflectivity of optical fiber mirror and $R_{2}$ is the reflectivity of tunable optical fiber grating. The effective cavity transmission is defined as $\varepsilon= \varepsilon_{1}\varepsilon_{2}$. Where $\varepsilon_{1}$, $\varepsilon_{2}$ are the insertion loss of optical fiber mirror and tunable optical fiber grating, respectively. With the C.barnard theory and above parameters, the output power of the intra-cavity index sensor based on $\hbox{Yb}^{3+}$-doped PCF can be achieved: TeX Source $$P_{out} = \eta \left(P_{p}^{in} - P_{p}^{th}\right)\eqno{\hbox{(3)}}$$ where the slope efficiency and effective output transmission can be denoted respectively as: TeX Source \eqalignno{\eta =&\, \eta_{Q}\varepsilon_{2} (1 - R_{2}) \left[1 - e^{(\delta \alpha_{s} - \alpha_{p}) L} (\varepsilon R) ^{- \delta }\right]/ T_{eff}& \hbox{(4)}\cr T_{eff} =&\, \left(1 - \varepsilon_{2}^{2}R_{2}\right) + \left(1 - \varepsilon_{1}^{2}R_{1}\right) \varepsilon_{2}^{2}R_{2} / \varepsilon R.&\hbox{(5)}}

To investigate the influence of the reflectivity of tunable optical fiber grating, with the theory model we do some numerical simulations about the properties of the intra-cavity index sensor based on $\hbox{Yb}^{3+}$-doped PCF filled with analyte and nanowires. The relationship of output power and cavity loss coefficient with different ${\rm R}_{2}$ is shown in Fig. 5. It can be seen that the output power decreases as the increase of cavity loss and ${\rm R}_{2}$. Further more, with the increase of ${\rm R}_{2}$ the rate of change tends to be sharper. So we should select an appropriate value of ${\rm R}_{2}$ to make the change of output power sharp when we design the intra-cavity index sensor.

Fig. 5. The relationship of output power and cavity loss coefficient with different tunable grating reflectivity of $\hbox{Yb}^{3+}$-doped index sensor.

When the pump power are 4W, 8W, 10W, 12W, 15W, respectively, the relation of intra-cavity index sensor output power $P_{out}$ and ${\rm R}_{2}$ can be obtained, as shown in Fig. 6. It can be seen that with the fixed fiber length ${\rm L} = 10 \ \hbox{cm}$, the output power increases as the increase of ${\rm R}_{2}$ in a certain range.

Fig. 6. The relation of intra-cavity index sensor output power $P_{out}$ and ${\rm R}_{2}$.

The output coupler reflectivity can be defined as $R_{3}= [(n - n_{a})/ (n + n_{a})]^{2}$ [19]. Where ${\rm n}_{\rm a} = 1.33 - 1.55$ which is the refractive index of the analyte, and ${\rm n} = 1.45$(the RI of the fused silica). The relationship between output coupler reflectivity and the RI of analyte of the numerical modeling of the described $\hbox{Yb}^{3+}$-doped PCF-based sensor is shown in Fig. 7. It is seen a downtrend in the figure, which indicates that the lower of the output coupler reflectivity, the higher intra-cavity loss, and the higher resonance wavelength. The output coupler reflectivity decreases and the resonance peak shows a red-shift with the increase of the analyte RI.

Fig. 7. The relationship between the output coupler reflectivity (the dotted curve) and the resonance peak position (the solid curve) with the RI of analyte.

A key feature is to be noted in Fig. 7. In this particular design, the central core has been employed to tune the phase matching condition. In what follows, we investigate the effect of size variation of the air holes. To investigate the dependence of the propagation characteristics of this proposed SPR refractive index sensor based on active PCF on the structure parameters, a series of PCFs with different air-filling ratios ${\rm d}_{1}/\Lambda = 0.3, 0.4, 0.5$ have been simulated. The influence on the coefficient loss is shown in Fig. 8, which shows that when the RI of analyte is lower than 1.45, higher confinement loss can be obtained with lower air-filling ratio. However, on the country, a higher confinement loss can be obtained with the higher air-filling ratio when the RI of analyte is higher than 1.45. When the RI of analyte is around about 1.45, the mode index is stable basically because of the minute difference of the refractive index between the background material and analyte.

Fig. 8. The confinement loss as functions of analyte RI with different air-filling ratios ${\rm d}1/\Lambda = 0.3, 0.4, 0.5$.

For the proposed sensor, the resonant coupling between core-guided mode and plasmonic mode has an effect on the confinement loss in the PCF, which will influence the absorption of signal light and lead to the change of the output power. The relationships between output power and analyte RI (na) with different air-filling ratios ${\rm d}_{1}/\Lambda = 0.3, 0.4, 0.5$ are shown in Fig. 9. We can see an obvious downtrend when the analyte RI is higher than 1.45. Furthermore, the larger air-filling ratios present more obviously sharp downtrend, which indicates that we can make use of t the flat or sharp change to apply for different sensors.

Fig. 9. The output power as functions of analyte RI (na) with different air-filling ratios ${\rm d}_{1}/\Lambda =0.3, 0.4, 0.5$.
SECTION IV

## CONCLUSION

In this paper, we propose an intra-cavity index sensor based on ytterbium-doped PCF filled with nanowires and analyte in the lager air holes of optical fiber cladding. In such sensor, when pumped by 976 nm light, the output power of the ytterbium-doped PCF laser at 1060 nm can be influenced obviously by a bit change of the refraction index of analyte in the air holes to achieve the intra-cavity fiber sensing. We have gotten the relationship between effective refractive index of analyte and the confinement loss, output power of intra-cavity index sensor and cavity loss coefficient, output power and the analyte refractive index and some other influencing factors by finite element method, respectively. The numerical analyses show that the power change is larger in a little range of loss when the end reflectivity is higher, and the sensor's sensitivity will be higher for the change of refractive index of analyte. And the different air-filling ratios have different effects on the output power and confinement loss. Furthermore, it will present different trends with different analyte RI of $\hbox{na}\ >\ 1.45$ or $\hbox{na}\ <\ 1.45$. The intra-cavity PCF sensing system has great practical value and significance for their advantages of compact structure and high sensitivity.

## Footnotes

This work was supported by the National Basic Research Program of China (973 Program) under Grant 2010CB327801. Corresponding author: Y. Lu (e-mail: luying@tju.edu.cn).

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