1. Introduction

Photonic crystal fibers (PCFs) [1-3] which, broadly speaking, include Bragg fibers [4-6] have attracted increasing interest over the past decade because of their unique property. Many researchers focus on the performance of PCFs as functional components or devices instead of a transimssion medium. PCFs’ applications in fiber filters, fiber sensors, fiber lasers, and dispersion compensation have been well investigated [7, 8]. Bragg fibers have recently received much attention for their interesting dispersion and modal properties and for advances in fabrication techniques [4-6, 9]. Tunable band-pass filter based on Bragg fiber has been demonstrated, although the bandwidth of the filter is quite large (several hundreds of nm) [10]. The well-known fiber Bragg grating (FBG) [11] and long period grating (LPG) [12] as two of the most important fiber filters and fiber sensor have been well developed due to their advantages including compactness and fiber compatibility and numbers of applications. In this paper, we propose a novel band-rejection fiber filter based on a Bragg fiber of transversal resonant structure. The proposed band-rejection fiber filter has similar transmision characteristics and principle as the LPG. The loss peak wavelength of the Bragg fiber can be adjusted by changing the index or thickness of the defect layer. The loss can be controlled by choosing suitable length of the Bragg fiber. Thus, more flexible control of characteristics of the fiber filter based on the Bragg fiber can be achieved comparing to the FBG or LPG. Moreover, the Bragg fiber can also be used as a fiber sensor with ability of refractive index and strain sensing.

2. Bragg fibers

Figure 1(a) shows the cross section and the refractive index profile of the Bragg fiber of transversal resonant structure. A hollow core (with refractive index unit) of radius r is surrounded by a multilayer cladding which consists of suitable designed alternating layers of high and low refractive indices. The high/low refractive index layers are shown in black/green. Among the N periodic two-layer structures in the radial direction of the Bragg fiber, a defect layer (shown as red part in Fig. 1(a)) with a refractive index n₀ and a thickness d₀ is introduced in the M_th two-layer structure, which results in resonant operation for some wavelengths. In this paper, we choose high/low refractive index of 3.5/1.45, with thicknesses of d ₁=0.2929Λ and d ₂=0.7071Λ (forming a quarter wavelength waveguide stack for the wavelength of 1.55µm (within the optical fiber comminication window)), where the thickness of the periodic two-layer structure is Λ=d ₁+d ₂=0.378µm. Different values of the refractive index n₀ and the thickness d₀ of the defect layer are chosen in the discussions we concern in this paper. It is well known that the light propagating in the Bragg fiber is confined by the one-dimensional photonic band gap of the multi-layer cladding. To understand the characteristics of the Bragg fiber, band structure of the planar dielectric mirror which consists of suitable designed alternating layers of high and low refractive indices with the same parameters of the periodic structures of the Bragg fiber mentioned above is shown in Fig. 2. The surface-parallel wave-vector component β and the frequency ω are with the unit of 2πc/Λ and 2π/Λ, respectively. The blue regions correspond to the situations where light can propagate in the planar dielectric mirror. The yellow region shows the band gap for the Bragg fiber with multi-layer cladding corresponding to planar dielectric mirror. The dotted line represents the light line (ω=cβ). Note that we only consider the TE mode band gap and the low loss TE₀₁ mode of the Bragg fiber for the ease of discussion in this paper. The red line in Fig. 1(b) show the dispersion characteristics of TE₀₁ mode for the Bragg fiber with 6 periodic two-layer structures (N=6) and a defect layer in the 3rd two-layer structure (M=3) in the cladding. The radius of the Bragg fiber is r=10Λ. The thickness of the defect layer is d ₀=1.4142Λ, which means we introduce a π phase shift in the periodic two-layer structures, but the refractive index of the defect layer remains the same as the low refractive index layer. We find the dispersion line almost remain unchanged when the thickness of the defect layer is set to d ₀=0.7071Λ, corresponding to a conventional Bragg fiber without a defect layer. However, as we show below, the Bragg fiber with a defect layer show resonant operation for some wavelengths and thus can be used as a fiber filter device.

 

Fig. 1. (a). Cross section and the refractive index profile of the Bragg fiber of transversal resonant structure. (b). Band structure of the planar dielectric mirror and dispersion property for TE₀₁ mode of the Bragg fiber of transversal resonant structure.

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Fig. 2. Confinement of the different Bragg fibers. In the left figure, the green, red and black lines correspondes to the Bragg fiber of 6 periodic two-layer structrues without defect layer, with a defect layer of d ₀=1.4142Λ, and with a defect layer of d ₀=2Λ, respectively. In the right figure, the green, red and black lines correspondes to the Bragg fiber of 8, 7, an 6 periodic two-layer structrues with a defect layer of d ₀=2Λ, respectively. Inset of the right figure shows the transmission spectrum of a 10-cm Bragg fiber with 8 periodic two-layer structures and one defect layer.

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3. Band-rejection fiber filter base on the Bragg fiber

For a Bragg fiber of 6 two-layer structures, a band gap region of TE₀₁ mode appears where (β,ω) locates in the red line in Fig. 1(b). The corresponding confinement loss of the Bragg grating as a function of wavelengths in the band gap region is shown as the green line in Fig. 2(a). Note that we apply a full-vector finite-element method and uniaxial perfectly matched layers to analyze the properties of the Bragg fiber. The confinement loss can be deduced from the imaginary part of the effective modal index [13]. Considering the symmetry of the cross section of the Bragg fiber, we choose one eighth-plane of the Bragg fiber’s cross section for calculation as shown in Fig. 3(a). When a defect layer with parameters (d ₀=1.4142Λ, n ₀=1.45) is introduced in the 3rd two-layer structures, a Bragg fiber of resonant structure is achieved and its confinement loss is shown as the red line in Fig. 2(a). A loss peak wavelength of about 1225nm appears inside the band gap region of the Bragg fiber. The peak wavelengths of the confinement loss are dominated by the parameters of the defect layer. The black lines in Fig. 2(a) and Fig. 2(b) show the confinement loss of the Bragg fibers with a defect layer with parameters of (d ₀=1.4142Λ, n ₀=1.8) and (d ₀=2Λ, n ₀=1.45), respectively, which indicates that the peak wavelength of the confinement loss can be shifted to optical fiber comunication window by adjusting parameters of the defect layer. The red/green lines in Fig. 2(b) show the confinement loss of the Bragg fibers when we add one/two periodic two-layer structures in the cladding, which indicates the confinement loss can be reduced effectively by adding more periodic two-layer structures in the cladding. These characteristics of the confinement loss indicate that a Bragg fiber of transversal resonant structure with a suitable length can be used as a band-rejection fiber filter. Inset of Fig. 2(b) shows the transmission spectrum of a 10-cm Bragg fiber with 8 periodic two-layer structures (N=8) and one defect layer with parameters (d ₀=2Λ, n ₀=1.45). The dip wavelength is around 1555nm with a peak loss of 16.4 dB. The 3 dB (10 dB) bandwidth of the band-rejection fiber filter is about 1.8 nm (5 nm).

 

Fig. 3. One eighth-plane of the Bragg fiber’s cross section for calculation (a) and power flow profiles of TE₀₁ modes and defect modes for wavelength of 1223nm (b), 1224nm (c), 1225nm (d), 1226nm (e) and 1227nm (f).

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Both the characteristics and the principle of such a band-rejection fiber filter based on the Bragg fiber are found to be similar as a LPG. For a LPG, mode coupling between the core mode and the cladding mode occurs because of the periodic index-modulation structures in the propagating direction of a single mode fiber. The coupling is wavelength-selective, which indicates that the LPG can be used as a band-rejection filter. For a Bragg fiber with defect layer, we can also find coupling between the TE₀₁ mode and the defect mode where most energy concentrates on the defect layer occurs for a certain wavelength. For a Bragg fiber of 6 two-layer structures with a defect layer in 3rd two-layer structure, we show the power flow profiles of TE₀₁ modes and defect modes for wavelength of 1223nm (b), 1224nm (c), 1225nm (d), 1226nm (e) and 1227nm (f) in Fig. 3. When the wavelength is near to 1225nm, part of energy with a relative large fraction of the TE₀₁ mode has released to the defect layer which results in relative large loss. Thus the defect layer results in transversal resonant operation for the resonant wavelength of 1225 nm. When the wavelength (e.g. 1550nm) is far from the resonant wavelength, we can find the TE₀₁ mode has a well confined power flow profile shown in bottom figure of Fig. 3(a). Confinement losses of the Bragg fibers of 7 periodic two-layer structures with a defect layer in 3rd periodic two-layer structure with parameters (d ₀=0.7071Λ, n ₀=6), a defect layer in 5th two-layer structure with parameters (d ₀=0.7071Λ, n ₀=5), and two defect layers in 3rd and 5th two-layer structures with parameters (d ₀=0.7071Λ, n ₀=5) and (d ₀=0.7071Λ, n ₀=6), are shown in Fig. 4 (a), (b) and (c), respectively, which indicates the similar filter characteristics of two LPGs in the single mode fiber where two different filters can be combined together with combined filter spectrum of each filter. Different from the LPG filter, the characteristics (such as the loss spectrum) of the band-rejection fiber filter based on the Bragg fiber is mainly depend on the defect layer (instead of the periodic structure for LPG) which show its advantage of easy design of a filter. Moreover, the loss level of the fiber filter can be well controlled by adjusting the length of the Bragg fiber.

 

Fig. 4. Confinement loss of the Bragg fibers of 7 periodic two-layer structures with a defect layer in 3^rd periodic two-layer structure (a), a defect layer in 5^th two-layer structure (b), and two defect layers in 3^rd and 5^th two-layer structures (c).

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4. Band-rejection fiber filter base on the Bragg fiber

Similar to the LPG, the Bragg fiber of transveral resonant structure can also be used as a fiber sensor. For a Bragg fiber of 6 two-layer structures with a defect layer of thickness of d ₀=2Λ, Figure 5(a) shows the loss peak wavelengths of the confinement loss as a function of the refractive index of the defect layer, which indicates the fiber sensor based on the Bragg fiber can achieve refractive index sensing for the medium in defect layer in a large sensing range. The sensitivity is about 7.6×10^-4/nm when the refractive index is around 1.45. Comparing with the LPG based refractive index sensor [14], the proposed fiber sensor based on the Bragg fiber have a larger sensing range with high sensitivity. Figure 5(b) shows the peak wavelengths of the confinement loss as a funchtion of the degree of deformation for thickness of the defect layer, which indicates the proposed fiber sensor based on the Bragg fiber can also be used for strain sensing. Different from LPG strain sensing, the proposed fiber sensor is sensitive to the strain in the radial direction of the fiber (instead of propagating direction for LPG strain sensor) which indicates its potential applications for gas/water pressure sensor as LPG does.

 

Fig. 5. (a). Peak wavelengths of the confinement loss as a function of the refractive index of the defect layer. (b) Peak wavelengths of the confinement loss as a funchtion of the degree of deformation for thickness of the defect layer.

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5. Conclusion

In conclusion, by employing a full-vector finite-element method, Bragg fibers of transversal resonant structure have been investigated. Mode coupling between the normal guiding mode and the defect mode occurs for some resonant wavelengths, which results in relatively large loss in the band gap of the Bragg fiber and thus a segment of the Bragg fiber can be used as a band-rejection fiber filter. Simulation results have shown that the characteristics of fiber filter based on the Bragg fiber are mainly dependent on the parameters of the defect layer. Complex loss spectrum of the fiber filter can been achieved by employing multiple defect layers in the cladding of the Bragg fiber. We have also shown that the Bragg fiber of transversal resonant structure can be used as a fiber sensor. The relationship between the loss peak wavelengths of the Bragg fiber and the refractive index (or the degree of deformation for thickness) of the defect layer has been investigated which indicates that the Bragg fiber has potential applications for refractive index and strain sensing.