1. Introduction

Optical fiber biochemical sensors based on evanescent field sensing mechanism require a strong light-matter interaction. Fiber tapering [1,2] and side polishing [3] techniques have been proposed to enhance the power fraction in the cladding, ensuring to create an extremely strong evanescent field, by decreasing the distance between the waveguide and the detected environment. However, the fabrication repetition rate of sensors completed by tapering and polishing techniques is very low and meanwhile these special techniques are conducted only by skillful technicians. The microstructured fibers have attracted a tremendous amount of attention in recent years due to their exotic optical properties including low bending loss [4], endlessly single mode [5], high birefringence [6] and nonlinearity [7]. Furthermore, the microstructured fibers have been widely used in optical communications and sensors where these with few air holes are also extensively studied due to their simple fabrication technique [8]. The supercontinuum generations were studied in highly nonlinear suspended core silica fibers, in which an octave-spanning spectrum could be easily generated at a peak pump power level as low as ~1.5kW at 1μm [9]. Apart from the conventional hexagonal-pattern microstructured optical fibers [10], fibers with few air holes can also have a strong evanescent field and can be used as biochemical sensors. Many sensors based on microstructured fibers with few air holes have been reported [11–16]. The use of the suspended-core holey fiber for sensing applications was discussed and an evanescent field device was demonstrated for the sensing of acetylene gas at near-IR wavelength [11].The surface-plasmon-resonance sensor based on coating holes of a three-hole microstructured optical fiber had a refractive-index resolution of 1 × 10⁻⁴ for aqueous analytes [12]. The selective coating of microstructured fibers with metals was demonstrated experimentally and it can be used to fabricate an in-fiber absorptive polarizer [13]. Sudo et al developed spectral measurements of ethylene adsorbed in a single-mode fiber having a small vacant hole in the center of its fiber core [14]. The effect of filled metals on temperature sensitivity of birefringent side-hole fibers using a Sagnac loop interferometer was investigated [15]. The temperature sensitivity of modal birefringence of polarization-maintaining fibers with side holes was measured using a Sagnac loop interferometer and dB/dT could be made as high as an order of ~10⁻⁷/°C [16].

In the present paper, an embedded-core hollow optical fiber fabricated using a simple fabrication technique is proposed, in which an elliptical core is eccentrically positioned in the cladding with a large central air hole. The cladding between the core and the air-hole is extremely thin. The proposed fiber has a strong evanescent field due to small distance between the core and the inner air hole and can be suitable for analyzing characteristics of liquids or gases because of easily filling liquid and gas into the large central air hole. The asymmetric structured fiber has polarization-preserving property. We will study optical characteristics of the proposed embedded-core hollow optical fiber in details.

2. Embedded-core hollow optical fiber

The embedded-core hollow optical fiber we drew is sketched in Fig. 1(a) . Figure 1(b) is the zoom-in view of the core region marked by a red dashed circle in Fig. 1(a). The optical fiber consists of a central air hole, a semi-elliptical core, and an annular cladding. An elliptical core is eccentrically positioned in an annular cladding and a very thin cladding lies between the core and the air hole. The cross section of equivalent fiber's structure we adopted in the simulation is shown in Fig. 1(c). $n_1$, $n_2$ and $n_3$ are refractive indices of the core, the cladding and the air, respectively. $R_{\text{c}}$ and $R_{\text{a}}$ are radii of the cladding and the air hole, respectively. The thickness of the annular cladding is defined as $d^{\prime }=R_{\text{c}}-R_{\text{a}}$. $2a$ and $2b$are the lengths of long and short axes of the core and the ellipticity is defined as $e=b/a$. The cladding between the core and the air hole can be approximately regarded as a concentrically elliptical ring and the ellipticity is $e=b/a=b^{\prime }/a^{\prime }$, where $2a^{\prime }$and $2b^{\prime }$ are the lengths of long and short axes of the concentrically elliptical cladding, respectively. The shortest distance between the core and the air hole is $d=b^{\prime }-b$. The refractive index difference between the core and the cladding is 0.0052 and the refractive index of the core is 1.462 at $\lambda =0.65\text{μm}$ for the optical fiber sample, which was measured by the refracted near-field method. The diameter of the fiber is $125\text{μm}$, the long axis length of the core is $6.84\text{μm}$ and the ellipticity is 0.488, $d\approx 2.55\text{μm}$ and $d^{\prime }=22.5\text{μm}$. The cutoff wavelength of the lowest high-order mode is 0.934$\text{μm}$, which was determined experimentally by transmitted power method. The loss is around 0.7dB/m in the wavelength range $1.0-1.2\text{μm}$ and 1.4dB/m at $1.3\text{μm}$, which was measured by the cut-back method.

 

Fig. 1 Photograph of an embedded-core hollow optical fiber sample (a) and zoom-in view of the core (b), and the cross section of equivalent fiber (c).

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3. Mode characteristics

The mode characteristics for the embedded-core hollow optical fiber are analyzed numerically by the finite element method [17]. In the simulation, the cladding is pure silica and the core is silica doped with 3.4% mole fraction of GeO₂, which exactly matches the measured refractive index difference. The refractive indices of Ge-doped silica and silica are calculated based on the Sellmeier dispersion formula [18]. The normalized parameter is defined as $V=2\pi \sqrt{ab(n_1^2-n_2^2)}/\lambda$ [19]. The effective refractive indices of the fundamental modes (HE₁₁) polarized along the slow axis and the lowest high-order mode (TE₀₁) for the optical fiber with a circular core are shown in Fig. 2(a) , where $R_{\text{a}}=40\text{μm}$,$R_{\text{c}}=62.5\text{μm}$, $d^{\prime }=22.5\text{μm}$ , $n_3=1$ and $\lambda =1.3\text{μm}$. The fiber has a non-zero cut-off frequency for the fundamental mode and the cut-off parameters of the lowest high-order mode are slightly larger than 2.405. When $d$ increases, the cut-off parameter $V_{\text{FMC}}$ of the fundamental mode decreases and gradually tends to zero, while the cut-off parameter $V_{\text{HMC}}$ of the lowest high-order mode decreases to 2.405. For identical $V$, the effective indices gradually increase with increasing $d$ and finally tend to some certain value, because the effect of the inner air hole on the mode index becomes weaker and weaker. For the embedded-core hollow optical fiber with an elliptical core, the effective indices of the fundamental mode polarized along the slow-axis and the lowest high-order mode are shown in Fig. 2(b), where $d=2\text{μm}$and the core ellipticity ranges from 0.5 to 1.0. The cut-off parameter $V_{\text{HMC}}$of the high-order mode decreases with decreasing ellipticity. However, the effective indices of the fundamental mode are nearly independent of the core ellipticity for identical $V$.

 

Fig. 2 Mode characteristics of embedded-core hollow optical fibers with a circular core (a) and an elliptical core at $d=2\text{μm}$ (b).

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4. Birefringence of an embedded-core hollow optical fiber

The modal birefringence of the embedded-core hollow optical fiber is studied in detail. For the embedded-core hollow optical fiber with a circular core, the effects of $d$ and the normalized parameter $V$on the modal birefringence are illustrated in Fig. 3(a) , where the parameters of the fiber are the same as those in Fig. 2, and the dashed line and the dash-dotted line indicate cut-off lines of the fundamental modes and high-order modes, respectively. The birefringence increases with decreasing $d$ and reaches 4 × 10⁻⁵ approximately for$d=1\text{μm}$. For the case of $d=2\text{μm}$, the modal birefringences of the embedded-core hollow optical fiber with an elliptical core are shown in Fig. 3(b). The birefringence decreases with the increasing of $V$and it has the maximum near the normalized cut-off parameter of the fundamental mode. The birefringence firstly decreases and then increases with increasing the core ellipticity.

 

Fig. 3 Birefringence of embedded-core hollow optical fibers with a circular core (a) and with an elliptical core for $d=2\text{μm}$ (b).

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The effects of the core ellipticity on the birefringence are shown in Fig. 4 ($V=2$). Figure 4 shows that $d^{\prime }$ weakly affects the birefringence since two birefringence curves of $d^{\prime }=22.5\text{μm}$ and $d^{\prime }=40\text{μm}$well coincide with each other, and the birefringence reaches the order of 10⁻⁴ when the core ellipticity is larger than 1.5 for $d=1\text{μm}$. The birefringence falls to zero when the core ellipticity is about 0.9 because the slow and fast axes in the fiber are converted mutually. It is interestingly found that small ellipticity can cause the occurrence of zero-birefringence dips when$d$reduces. The ultra-low birefringence optical fiber can be achieved by design.

 

Fig. 4 Effects of the core ellipticity on the birefringence ($V=2$).

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Assuming that $d=2\text{μm}$, $V=2$ and $n_3=1$, the relation between the birefringence and the wavelength for different $e$ is shown in Fig. 5 . The birefringence increases with increasing the wavelength, consistent with conventional polarization maintaining fibers. The birefringence of optical fibers by filling different liquids into the air hole is shown in Fig. 6 , where $d=2\text{μm}$, $V=2$, $e=0.5$, and $\lambda =1.3\text{μm}$. The optical fiber maintains single mode operation in the full range of refractive indices of liquids we consider. The birefringence descends linearly as the refractive index of the liquid in the hole increases, resulting from the reduced asymmetry of the fiber.

 

Fig. 5 Effects of the wavelength on the birefringence($d=2\text{μm}$and $V=2$).

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Fig. 6 Effects of the liquid index on the birefringence ($e=0.5$, $V=2$).

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5. Loss and evanescent field

The embedded-core hollow optical fiber can generate a strong evanescent field that can bring a strong interaction between matter and light for the fiber core is adjacent to the air hole. The large size of the air hole makes gases or liquids easily filled into the air hole and therefore the embedded-core hollow optical fiber is suitable for chemical sensors and biosensors. The chemical ingredients of gases or liquids are determined by the absorption spectrum. The confinement loss is calculated by circular PML boundary conditions [20] and is defined as

 

Fig. 7 Confinement loss (a) and fractional power of the evanescent wave (b) ($n_3=1$).

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The evanescent field in the air hole of the optical fiber will be considered. The fractional power of the evanescent wave in the hole of the fiber is defined to be $\eta =P_h/P_t$, where $P_h$ denotes the energy leaking into the hole and $P_t$ is the total energy. Figure 7(b) shows the relation between the fractional power of the evanescent wave in the hole and the wavelength, where the parameters of the fiber are kept the same as those in Fig. 7(a). The evanescent field is obviously stronger for the mode polarized along the slow axis than along the fast axis. The evanescent field in the hole and the difference of the fractional power of the evanescent field between the modes along the fast and slow axes positively increase with the wavelength.

When the hole is filled by different liquids, the confinement loss and the fractional power of the evanescent field in the hole at $\lambda =1.3\text{μm}$for the mode polarized along slow axis are presented in Fig. 8 , respectively. The confinement loss reduces while the evanescent field increases with increasing the refractive index of the filled liquid. Both the confinement loss and the evanescent field increase obviously when$d$decreases. The fractional power of the evanescent field in the hole significantly increases after the liquid is filled. $\eta$ reaches up to 0.30% when $n_3=1.42$ and $d\approx 2\text{μm}$.

 

Fig. 8 Confinement loss (a) and fractional power of the evanescent wave in the hole (b) with the filled liquid's refractive index ($\lambda =1.3\text{μm}$).

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6. Bending loss of embedded-core hollow optical fiber

In this section, the bending characteristics of the optical fibers are investigated. We can predict that the embedded-core hollow optical fiber has anti-bending property for some bending directions due to its large air hole and large index contrast. However, the fiber core is close to the outer boundary of the cladding and the bending loss for +y bending direction, i.e. the eccentric direction of the fiber core, is greatly enhanced. The bending loss depends greatly on the bending orientation of the optical fiber. In the analysis of bending effects, a bent fiber is replaced by a straight one with an equivalent refractive index distribution [21]. Assuming that the fiber is bent towards x direction, the equivalent refractive index distribution can be described as

 

Fig. 9 Bending losses for +x (a) and +y (b) bending directions for different bending radii.

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The bending properties of the 2m-long fiber sample are measured without considering polarization effects during the experiment. It is difficult to control bending orientation of the optical fiber. We make a color mark at one side of the fiber along the fiber axis, then measure the bending properties of two opposite bending directions in the experiment. The measured spectra of two opposite bending directions are described in Fig. 10 , where the optical fiber is wound into three full loops with different bending radii. The fundamental mode of the optical fiber is cut off at 1375nm. From the experimental results compared with the simulated ones, the conclusion can be drawn that two opposite bending directions in Fig. 10(a) and Fig. 10(b) are believed to be close to -y and +y bending directions, respectively. The optical fiber is insensitive to the bending direction in Fig. 10(a) and has an observed loss only when the bend radius is less than 1.25cm, i.e. the fiber has a good resistance against bending towards this direction, whereas the fiber is sensitive to the bending direction in Fig. 10(b) and has a significant loss when the bend radius is about 2.0cm. Choosing an appropriate bending orientation, the optical fiber reveals a very small critical bending radius. The experimental results are basically consistent with the theoretical prediction.

 

Fig. 10 Measured loss spectra of two opposite directions for different bending radii.

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7. Matter-induced polarization rotation effects

For all cases mentioned above, the slow and fast axes of the embedded-core hollow optical fiber are always along x axis or y axis. However, if there is an angle $\varphi$ between the long axis of the elliptical core and x axis, defined as the orientation angle of the fiber core, the directions of the slow and fast axes will change when filled different liquids into the hole of the fiber. Therefore, this kind of fiber can be used for biological sensing and polarization interference devices. The orientation angle $\theta$ of the slow axis describes angles between the slow axis and x axis. For the fibers with different hole sizes ($R_a=40\text{μm}$ and $R_a=10\text{μm}$) and orientation angles of the fiber core ($\varphi$ = 30° and $\varphi$ = 45°), the orientation angles $\theta$ as a function of liquids' refractive indices are shown in Fig. 11 , where $e=0.5$, $d\approx 2\text{μm}$, $\lambda =1.3\text{μm}$. The slow axis rotates in counter-clockwise direction with increasing the refractive index of the filled liquid. The orientation angle $\theta$ increases with increasing the air hole size due to reducing the axial symmetry of the fiber, however, the impact of air hole size on the change of direction of the slow axis with the refractive index is nearly neglected. When the orientation angle $\varphi$ of the fiber core is 45°, the orientation angle $\theta$ of the slow axis achieves 8.5° rotation in the refractive index range from 1.33 to 1.4.

 

Fig. 11 Change of the slow axis direction.

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8. Conclusions

An embedded-core hollow optical fiber is investigated in detail in the present paper. The proposed hollow optical fiber has polarization-preserving property, but the birefringence is relatively low. The birefringence and the evanescent field of the hollow optical fiber are sensitive to both the ellipticity of the fiber core and the thickness of the cladding between the core and the air hole. The theoretical and experimental studies of the bending loss of the optical fiber are performed. The experimental results are basically consistent with the theoretical results, and the fiber reveals an outstanding anti-bending-loss performance in a certain direction due to its large index contrast and asymmetrical structure. If the orientation angle of the fiber core is not along x or y axes, the fiber can be used for biological sensing and polarization interference device since the directions of the slow and fast axes will change when different liquids are filled into the air hole. The embedded-core hollow optical fiber holds a strong evanescent field and therefore it is of importance for potential applications such as gas and biochemical sensors.