Surface plasmon induced broadband single-polarization filter based on high birefringence photonic crystal fiber

Journal Pre-proof Surface Plasmon Induced Broadband Single-Polarization Filter Based on High Birefringence Photonic Crystal Fiber Yujun Wang, JianPing Shen, jianshe Li, Shuguang Li

PII:

S0030-4026(20)30089-9

DOI:

https://doi.org/10.1016/j.ijleo.2020.164255

Reference:

IJLEO 164255

To appear in:

Optik

Received Date:

22 October 2019

Revised Date:

14 January 2020

Accepted Date:

17 January 2020

Please cite this article as: Wang Y, Shen J, Li j, Li S, Surface Plasmon Induced Broadband Single-Polarization Filter Based on High Birefringence Photonic Crystal Fiber, Optik (2020), doi: https://doi.org/10.1016/j.ijleo.2020.164255

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Surface Plasmon Induced Broadband Single-Polarization Filter Based on High Birefringence Photonic Crystal Fiber

Yujun Wang1, JianPing Shen2, jianshe Li1, Shuguang Li1*

1

State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for

Microstructural Material Physics of Hebei Province, School of Science, Yanshan University,

2College

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Qinhuangdao, 066004, P.R.China

of Electronic and Optical Engineering, Nanjing University of post and Telecommunicatio

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*Corresponding author. E-mail: [email protected]

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ns, Nanjing 210023, China

Highlights

A single-polarization filter comprising a gold-infiltrated and liquid

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crystal-filled PCF-SPR is designed and investigated by the full-vector finite element method. Compared with the traditional structures, we find that our structure

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

has higher birefringence.



The confinement losses of x-polarized mode are 99.87, 726.50, 474.60 dB/cm at wavelengths of 0.88, 1.02, 1.30 um, respectively, while the confinement losses of y-polarized mode are only 0.001,

0.004 and 0.046 dB/cm. 

When the transmission length of PCF is 2 mm, the optical bandwidth of ER less than -20 dB is as high as 900 nm, from 0.85 to 1.75 um.

Abstract A broadband and single-polarization filter based on high birefringence photonic crystal fiber

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(HB-PCF) with selectively infiltrated gold wires and liquid crystal is proposed, and its filtering characteristics are studied by the full-vector finite element method (FV-FEM). Two gold wires are selectively filled on both sides of the liquid crystal core to act as two defect cores. The results

show that the confinement loss of x-polarized core mode is much larger than that of y-polarized

core mode in the wavelength range of 0.85-1.75 μm. The confinement losses of x- and y-polarized core modes are 99.87 dB/cm and 0.001 dB/cm at 0.88 um, 726.50 dB/cm and 0.004 dB/cm at 1.02

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um, and 474.60 dB/cm and 0.046 dB/cm at 1.30 um, respectively. The bandwidth with extinction ratio less than 20 dB is 900 nm. Moreover, compared with the traditional structures, we find that

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our structure has higher birefringence. High birefringence helps to separate the resonant wavelengths of x- and y-polarized core modes. Therefore, the excellent properties of the proposed

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filter can make it widely used in sensing systems and broadband optical communication systems. Keywords: Broadband; Single-Polarization filter; High birefringence; Photonic crystal fiber;

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1. Introduction

Photonic crystal fibers (PCFs) [1], also known as microstructured optical fibers (MOFs) or holey fibers (HFs), are composed of microscopic air holes arranged periodically. Compared with traditional optical fibers, PCF has many unique characteristics, such as flexible structural design,

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endless single-mode transmission, anomalous dispersion, large mode field area and nonlinear effects. Meanwhile, the optical transmission performance of the PCF can be further expanded by

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filling some materials (e.g: liquid, active metal, liquid crystal, etc.) into the PCF air holes. In particular, metal-filled and metal-coated PCFs based on surface plasmon resonance (SPR) effect exhibit significant superior performance. SPR is a physical optical phenomenon occurring at the interface between metal and dielectric. When the frequency of incident photons is equal to that of free electrons on the metal surface, the energy of PCF core mode will be strongly coupled to the surface plasma mode, and the energy of core mode will drop rapidly, causing a peak in the loss spectrum. Therefore, SPR-based PCFs are widely used in optical sensors [2, 3], optical beam splitters [4] and optical filtering [5, 6]. The study of SPR-based PCF polarization filter is of great significance for obtaining better

polarization characteristics, replacing the current polarization devices in the field of optical communication and realizing the integration of communication devices. Wang et al. [5] proposed a dual-channel filter based on the gold wire infiltrated PCF, where the confinement losses of y-polarized core modes at 1.31 and 1.55 um are 126.10 and 326.30 dB/cm, while that of x-polarized core modes are 0.08 and 1.20 dB/cm. And the fiber length is 1100 um, the bandwidths of the above two bands are 20 and 60 nm, respectively. Yang et al. [6] designed a tunable single-polarization PCF polarization filter with high refractive index liquid filled and silver-coated. The resonance intensity of unwanted polarized modes are 53.1 dB/cm and 305.1 dB/cm at 1.31 and 1.55 um bands. At the same time, the optical fiber bandwidths of 1000 um length are 62 and 122 nm. Li et al. [7] reported a polarization filter with a 10 mm fiber length and a 440 nm wide bandwidth by changing the size of four air holes around the PCF gold-coated film. Shi et al. [8] designed a rectangular-lattice PCF polarization filter with gold coated in two large cladding air

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holes. The confinement loss of y-polarized core mode is 433.65 dB/cm at the wavelength of 1.55

um, and that of x-polarized core mode is 2.64 dB/cm. The bandwidth can be obtained 150 nm with the fiber length of 4000 um. However, most of the reported polarization filters operate only in the narrower communication bands and have relatively low unwanted mode losses. Therefore, the study of broadband filter with excellent polarization performance is of great significance for

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current broadband communication systems.

In this paper, we propose a HB-PCF polarization filter based on E7 type NLC and gold wire

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filling, which can cover almost all communication windows (O, E, S, C and L bands). The influence of fiber structure parameters on filter performance are studied by finite element method. It is found that the optical fiber filled with liquid crystal core and gold wire generates multiple

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resonance peaks, and the confinement loss of core mode in x polarization direction is much larger than that in y polarization direction. In addition, when the fiber length is 2000 um, the extinction ratio at the resonant wavelength of 1.02 um can reach -1262.05 dB. The bandwidth at the

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extinction ratio below 20 dB is as high as 900 nm, from 0.85 to 1.75 um.

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(a)

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2. Geometry And Simulation Method (b)

Fig. 1. Designed structure. cross section of the designed PCF (a), FEM mesh (b).

Fig. 1(a) shows the cross-section of the designed HB-PCF. As can be seen from Fig. 1(a), the proposed optical fiber is a hexagonal lattice consisting of two layers of cladding air-holes. Its lattice constant Λ is 4.8 μm. The dark blue core hole with a diameter of d0 = 1.7 μm is filled with E7 type NLC. On the one hand, the liquid crystal core can better confine the light transmission in the core and reduce the transmission loss. On the other hand, the birefringence of the structure can increase by utilizing the birefringence characteristic of the liquid crystal itself. Two gold wires with a diameter d1 of 1.7 μm are selectively infiltrated in the yellow labeled air holes on both sides of the liquid crystal core. And the distance L between the gold wire and the liquid crystal core is 2.5 μm. At the same time, in order to obtain higher birefringence, four large air holes having a diameter d2 of 4.6 μm are introduced near the core region, and the four air holes are marked with

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orange. The remaining cladding air hole diameter d is 2 μm. Nowdays, there are many fabrication techniques for PCF preform, such as sol-casting [9], drilling [10, 11] and extrusion [12, 13] and

stack-and-straw [14]. Considering the small horizontal distance between the two orange air holes, here we use high-precision ultrasonic drilling to fabricate PCF preform. Petrovich et al. have

successfully fabricated microstructured fiber with air hole spacing of only 50 nm by using this

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technique [15]. Firstly, we use high precision ultrasonic drilling to fabricate PCF perform in the

order of millimeter. Then, the fabricated PCF preform is drawn into the designed fiber by a fiber drawing tower. During the drawing process, the drawing temperature, rod dropping speed and

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drawing speed should be reasonably controlled to obtain the desired air hole size and fiber structure. Finally, the gold wires and liquid crystal are filled into specific air holes by technology [17], respectively.

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pressure-assisted melt-filling technology [16] and femtosecond laser-assisted selective infiltration

In this structure, the background material is pure silica, and its chromatic dispersion can be obtained by the Sellmeier equation [18]. The gold has strong corrosion resistance, good ductility

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and oxidation resistance. Moreover, in terms of filter bandwidth, it is superior to Ag and Al, so gold nanowire is selected as the SPR active metal. The material dispersion of gold is calculated using Drude-Lorentz model [19]. The core-filled E7 type NLC is an anisotropic material, which is

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defined by ordinary index no and extraordinary index ne. The relative permittivity tensor εr of E7

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can be written as follows [20]: n2o sin2φ + n2e cos2 φ (n2e − n2o ) sinφ cosφ 0 εr = ((n2e − n2o ) sinφ cosφ n2o cos 2 φ + n2e sin2 φ 0 ) 0 0 n2o

Where φ is the rotation angle of the NLC, and the reported experiment proves that the

rotation angle φ can be precisely controlled by applying two sets of external experimental electrodes [21]. Here, we choose φ = 90°. The no and ne of the E7 material can be calculated by the Cauchy model [20]: Be Ce ne = Ae + ( 2 ) + ( 4 ) λ λ

Bo Co no = Ao + ( 2 ) + ( 4 ) λ λ Here, Ae, Be, Ce, Ao, Bo and Co are the coefficients of the Cauchy model. At temperature T = 25°C, Ae = 1.6933, Be = 0.0078 μm2, Ce = 0.0028 μm4, Ao = 1.4994, Bo = 0.007 μm2 and Co = 0.0004 μm4. The electric field distribution and transmission characteristics of the proposed PCF filter are studied by FEM method with a cylindrical perfect matching layer (PML). PML is used to absorb the scattered energy incident at various angles, and the scattering boundary condition (SBC) outside the PML is used to reduce the reflected energy. In order to balance the speed and accuracy of the calculation, we use the coarse mesh size to divide the solution domain into 5,172 grid elements for solution calculation. The cross section of the fiber after the FEM mesh is shown in

α = 8.686 ×

2π λ

Im(neff ) × 104

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Fig. 2(b). The confinement losses of the x- and y-polarized core modes can be expressed as [22]:

where λ represents the wavelength of the incident light, Im(neff ) denotes the imaginary part of

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the effective refractive index, and α is the confinement loss.

ER = 20 lg {exp(α2 − α1 ) Lfiber }

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The extinction ratio (ER) can be defined as :

Here, α1 and α2 are the confinement losses of the x- and y-polarized core modes, respectively.

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Lfiber indicates the length of the fiber.

3. Results And Discussion

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Dispersion and confinement loss properties of the polarization filter

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Fig. 2. Real part of the mode refractive index (a) and confinement loss (b) of the proposed filter as a function of

wavelength. The insets (I)~(VIII) show the electric field distributions of y- (a) and x-polarized (b) core modes at

SPP mode at three resonance wavelengths.

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the wavelengths of 0.88, 1.02, 1.30 and 1.55 μm. The insets (IX) to (XI) show the electric field distributions of

Fig. 2 shows the modal refractive index and confinement loss of the designed polarization

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filter as a function of wavelength at T = 25℃, φ = 90°. As can be seen from Fig. 2(a), the real part of the refractive index of y-polarized core mode is obviously larger than that of x-polarized core mode. That is, the proposed PCF structure has high birefringence, and the two polarization core

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modes of x and y can be well separated as shown in Fig. 2 (b). From Fig. 2(a), the real part of the refractive index of x-polarized core mode is equal to that of 4-rd, 3-rd, 2-rd SPP modes in the x polarization direction at the wavelengths of 0.88, 1.02 and 1.30 μm, respectively. When combined with the mode loss spectrum of Fig. 2(b), the confinement loss of x-polarized core mode at

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wavelengths of 0.88, 1.02, and 1.30 μm is not equal to that of the above three SPP modes. These indicate that the x-polarized core mode and SPP mode occur the incomplete coupling [23].

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Meanwhile, from the electric field distributions of y- (Illustration (I)~(Ⅳ)) and x-polarized (Illustration (V)~(VIII)) modes at the wavelengths of 0.88, 1.02, 1.30 and 1.55 μm, it can be obtained that as the wavelength increases, the energy of y-polarized core mode is very well confined in the core region due to the existence of the liquid crystal core, while the partial energy of x-polarized core mode is obviously coupled to the surface of two gold wires, and surface plasma resonance occurs. Therefore, the confinement loss of x-polarized core mode is much larger than that of y-polarized core mode, and the confinement loss of y-polarized core mode is almost zero. 3.2 Influence of structural parameters d0, d1 and L on the performance of the polarization

(a)

(b)

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filter

Fig. 3. Confinement loss (a) and ER (b) of the PCF polarization filter vary with wavelength as d 0 increases from 1.3 to 1.7 μm. And the other structural parameters are d 1=1.7 μm, d2=4.6 μm, L=2.5 μm, d=2 μm, Λ=4.8 μm,

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T=25℃, φ = 90° and Lfiber=2 mm.

Fig. 3 shows the confinement loss (a) and ER (b) of the designed polarization filter as a

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function of wavelength when d0 is 1.3, 1.5 and 1.7 μm. As shown in Fig. 3(a), as d0 increases, the resonant wavelength of x-polarized core mode undergoes a blue shift. This is because the effective refractive index of x-polarized core mode increases as the diameter d0 of liquid crystal infiltrate

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hole increases, while that of SPP mode in the x-polarized direction remains almost unchanged. Thereby, the resonance peaks of x-polarized core mode move to the short wavelength direction. Moreover, Fig. 3(a) also reveals that the confinement loss of x-polarized core mode increases along with the increase of diameter d0, while that of y-polarized core mode is substantially zero.

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Since the increase of d0 shortens the distance of silicon bridge between the core mode and SPP mode in the x polarization direction, the energy transmitted in the core region leaks more easily to the surface of gold wires, increasing the coupling resonance strength between the two modes. The

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electric field energy of y-polarized core mode is always well constrained to transmit in the core region. Fig. 3(b) shows that the ER of the polarization filter varies with d0 when the fiber length is 2 mm. When d0 is 1.3, 1.5 and 1.7 μm, the ERs at the communication windows of 1.31 and 1.55

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μm are 445.4, 643.12, 820.7 dB and 401.2, 386.6, 399.1 dB, respectively. The bandwidth of ER with absolute value greater than 20 dB increases with the increase of d0.

(a)

(b)

Fig. 4. Confinement loss (a) and ER (b) of the PCF polarization filter vary with wavelength as d 1 increases from 1.3 to 1.7 μm. And the other structural parameters are d 0=1.7 μm, d2=4.6 μm, L=2.5 μm, d=2 μm, Λ=4.8 μm,

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T=25℃, φ = 90° and Lfiber =2 mm.

(a)

(b)

Fig. 5. Confinement loss (a) and ER (b) of the PCF polarization filter vary with wavelength as d 0=d1 increases

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from 1.1 to 1.7 μm. And the other structural parameters are d 2=4.6 μm, L=2.5 μm, d=2 μm, Λ=4.8 μm, T=25℃, φ= 90° and Lfiber =2 mm.

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Fig. 4 shows the variations of confinement loss and ER of polarization filter with the

operating wavelength when d1 is 1.3, 1.5 and 1.7 μm. From Fig. 4(a), we can see that with the increase of d1, the resonant wavelengths of peak 1 and peak 2 are red-shift. This is due to the fact that as the diameter d1 of gold wire infiltrate hole increases, the effective refractive index of SPP mode also increases, while that of x-polarized core mode remains almost unchanged. This eventually leads to the red shift of the two peak resonance points. From Fig. 4(a), we can also obtain that the variation of modal confinement losses of peak 1 and peak 2 is significantly different with the increase of d1. The confinement loss of peak 1 increases as d1 increases, while that of peak 2 decreases. This is because as the number of x-polarized surface plasmon polaritons

at peak 1 increases, while the number of x-polarized surface plasmon polaritons at peak 2 decreases. Thus, the coupling resonance intensity between the x-polarized core mode and SPP mode enhances at peak 1 and weakens at peak 2. Fig. 4(b) shows that when the fiber length is 2 mm and d1 increases from 1.3 to 1.7 μm, the bandwidth increases significantly. Therefore, the bandwidth of the polarization filter can be effectively adjusted by changing the diameter of d1. In order to reduce the manufacturing difficulty, we also studied the effects of d0 and d1 on the performance of the polarization filter. Fig. 5 shows the variations of modal confinement loss (a) and ER (b) as a function of wavelength when d0 = d1 = 1.1, 1.4, 1.7 μm and the fiber length is 2 mm. As can be seen from Fig. 5, the effects of simultaneous changes in d0 and d1 on the peak resonance wavelength, modal confinement loss and bandwidth are similar to that of individual d1 on the peak resonance wavelength, modal confinement loss and bandwidth. That is, the resonance

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wavelength of x-polarized core mode is red-shifted, the modal confinement loss in the x polarization direction increases at the peak 1 and decreases at the peak 2, and the bandwidth

becomes wider. The difference is that the reason for causing the red shift of resonance wavelength of x-polarized core mode is different. Here, the effective refractive indices of both x-polarized core mode and SPP mode increases. Under the interaction of two modes, the resonance points

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move to longer wavelength. Compared with d0, the diameter d1 of gold wire infiltrated hole has a

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greater impact on the modal loss and bandwidth of the proposed SPR-based PCF filter.

(a)

(b)

Fig. 6. Confinement loss (a) and ER (b) of the PCF polarization filter vary with wavelength as L increases from 2.5 to 2.7 μm. And the other structural parameters are d0= d1=1.7 μm, d2=4.6 μm, d=2 μm, Λ=4.8 μm, T=25℃, φ = 90° and Lfiber =2 mm.

Fig. 6 shows the variations of confinement loss (a) and ER (b) of the polarization filter with the distance L between the fiber core and gold wire. As can be seen from Fig. 6(a), as L increases,

the resonance wavelengths of peak 1 and peak 2 appear blue-shifted, and the blue-shift of the resonance wavelength of peak 2 is more pronounced. With the increase of L, the effective refractive indices of 3-rd and 2-rd SPP modes, which are resonantly coupled with the x-polarized core mode at peak 1 and peak 2, decreases, and the effective refractive index of 2-rd SPP mode at peak 2 changes more greatly, while the effective refractive index of x-polarized core mode remains basically unchanged. Therefore, under the interaction of x-polarized core mode and 3-rd, 2-rd SPP modes, the blue-shift amplitude of resonance wavelength at peak 2 is obviously larger than that at peak 1. Fig. 6(a) also reveals that the confinement loss of peak 1 increases first and then decreases with the increase of L, while that of peak 2 increases all the time. This is mainly due to the fact that the interaction between the x-polarized core mode and SPP mode excited by the gold-filled hole is first strengthened and then weakened at the peak 1 with the increase of L, and the energy of the fiber core coupled to the surface of gold wire increases first and then

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decreases, causing the surface plasmon resonance effect to first increase and then decrease. The

increase of confinement loss at peak 2 is due to the increase of L, which enhances the interaction

between the x-polarized core mode and SPP mode. The energy on the fiber core is easily coupled with the surface of gold wire, resulting in the enhancement of surface plasmon resonance effect. Fig. 6(b) shows that the proposed single polarization filter can achieve bandwidth tunable by

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changing the structural parameter L. The bandwidth of ER absolute value greater than 20 dB decreases as L increases.

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3.3 High birefringence

Fig. 7. Effective refractive index (a) and birefringence (b) of the four optical fiber structures as a function of operating wavelength, and the corresponding cross sections of the optical fibers (n)~(q). (n) is a hexagonal structure microporous PCF, (o) is a PCF with a liquid crystal core, (p) is a PCF with liquid crystal core and four large air holes. (q) is a PCF with liquid crystal core, four large air holes, two small air holes on both sides of the core. It should be noted that the four fiber structures are not filled with gold wire.

Fig. 7 shows the variations of effective refractive index (a) and birefringence (b) with the operating wavelength, and the corresponding cross sections of the optical fibers (n)~(q). It should be noted that the four fiber structures are not filled with gold wire. From Fig. 7(a), we can clearly

see that the effective refractive index of hexagonal structure microporous PCF without liquid crystal core in x- and y- polarization directions is much lower than that of PCF with liquid crystal core. When the fiber structure with liquid crystal-filled is changed from (o) to (q), the effective refractive index of y-polarized core mode at the same wavelength is basically unchanged while that of x-polarized core mode decreases gradually. That is, as shown in Fig. 7(b), the birefringence of optical fibers at the same wavelength becomes higher and higher as the fiber structure changes from (n) to (q). The birefringence of structures (n), (o), (p) and (q) at the wavelength of 1.55 μm is 6.64988E-7, 0.149599, 0.150480 and 0.152958, respectively. 3.4 Extinction ratio Fig. 8 shows the variation of ER with wavelength at different fiber lengths (a), and when the wavelengths are 0.88 and 1.02 μm, the extinction ratio and bandwidth vary with the fiber length

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(b). From Fig. 8, we can get that the absolute value of ER and bandwidth increase as the fiber

length increases. When the length of the fiber is 2 mm, the ER at the communication windows of 1.31 and 1.55 μm can reach 820.7 and 399.1 dB. Its bandwidth is up to 900 nm and the effective filtering wavelength ranges from 0.85 to 1.75 μm.

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Compared with reported optical fiber filters [5-7], we have considerable advantages. From Fig. 8(b), we can also clearly see that when the fiber length is longer than 1 mm, the bandwidth

around the wavelength of 0.88 μm is sharply increased. And the fiber length is equal to 1.25 mm,

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the effective filtering range of the bandwidth around the wavelengths of 0.88 and 1.02 μm coincide. Finally, the performance of the designed polarization filter is compared with the reported polarization filter [5, 6, 8, 24]. The results are shown in Table 1. From Table 1, we can obtain that

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the proposed polarized filter has a better ER and wider bandwidth compared with the reported SPR-based PCF filters. Its operating wavelength range is 0.85 to 1.75 μm, covering all communication bands from O to U, which facilitates its widespread use in coherent fiber-optic

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communication systems. Moreover, the proposed polarization filter has a bandwidth of up to 900 nm, while the optical fiber length is only 2 mm, which is also very important for the integration of

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communication devices.

(a)

(b)

Fig. 8 Extinction ratio varies with wavelength at different fiber lengths (a) and when the resonance wavelength is 0.88 and 1.02 μm, the extinction ratio and bandwidth vary with the fiber length (b).The structural parameters are d0=1.7 μm, d1=1.7 μm, d2=4.6 μm, L=2.5 μm, d=2 μm, Λ=4.8 μm, T=25℃ and φ = 90°. Table 1 Comparison with the reported SPR-based PCF filter

Resonant

Fiber structure

wavelength/μm

Gold-filled PCF filter with

Lfiber/μm

1.31

Confinement loss /dB/cm

Bandwidth ER/dB /nm

126.10

120.34

20

1100

increased air holes layer by 1.55

326.30

310.41

60

Silver-coated and

1.31

53.10

45.4

62

liquid-filled PCF filter [6]

1.55

Gold wire filled hexagonal

1.31

PCF filter [7]

1.55

PCF beam splitter with two

1.55

1.31

4000

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1.02

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1.30

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/

440

230.50

0.88

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133

433.65

/

150

102.60

95

40

245.00

200

100

99.87

-173.50

726.50

-1262.05

474.60

-824.46

1000

1.55

Our work

305.1

265.04 10000

holes inner wall coated with gold [25]

305.10

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two large air holes [8]

1000

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PCF filter with gold film in

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layer [5]

2000

900

Fig. 9 Cross sections of PCF in the Refs [5]-[8], [25].

4. Conclusion In this paper, a broadband polarization filter based on HB-PCF with selective filling of gold wires and liquid crystal is proposed, and its basic properties are analyzed by FEM. The numerical results show that the x-polarized core mode is coupled to the 4-rd, 3-rd and 2-rd SPP modes at wavelengths of 0.88, 1.02 and 1.30 um, respectively. The confinement losses of x- and y-polarized core modes are 99.87 and 0.001 dB/cm at λ = 0.88 um, 726.50 and 0.004 dB/cm at λ = 1.02 um, and 474.60 and 0.046 dB/cm at λ = 1.30 um, respectively. The proposed wideband polarization filter has a very large confinement loss in the x polarization direction between the wavelengths of 0.85 and 1.75 um, while the confinement loss in the y polarization direction is almost zero.

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Moreover, when the fiber length is 2 mm, the ERs of the above three wavelengths are -173.50,

-1262.05 and -824.46 dB, respectively. The bandwidth below -20 dB is as high as 900 nm with the fiber length of 2 mm, from 0.85 to 1.75 um, covering all O, E, S, C, L and U communication

bands. Therefore, due to these excellent properties, the proposed broadband polarization filter is

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Declaration of Interest Statement

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expected to be a candidate for filtering devices.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be

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construed as influencing the position presented in, or the review of, the manuscript entitled.

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Acknowledgment

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This work was supported by the Program of the Natural Science Foundation of Hebei Province (Grant No. F2017203193, F2017203110) and the Postdoctoral preferred funding research project of Hebei Province (Grant No. B2018003008)

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