Design of a polarization splitter for an ultra-broadband dual-core photonic crystal fiber

Yongtao Li(李永濤) Jiesong Deng(鄧潔松) Zhen Yang(陽圳) Hui Zou(鄒輝) and Yuzhou Ma(馬玉周)

1Academic Affairs Office,Nanjing University of Posts and Telecommunications,Nanjing 210023,China

2College of Electronic and Optical Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210023,China

3State Key Laboratory of Luminescence and Applications,Changchun 130033,China

4Beijing Times Photoelectric Technology Co.,Ltd,Beijing 100094,China

Keywords: photonic crystal fiber,polarization splitter,broadband bandwidth,extinction ratio

1. Introduction

A polarization splitter, as an important component in an all-optical network system, plays a significant role in optical fiber communication and optical fiber sensing.[1]Its main function is to decompose a beam of light into two mutually orthogonal polarized beams. However, a polarization splitter based on a traditional dual-core (DC) fiber is not conducive to device integration because the small birefringence of the traditional fiber leads to a long polarization splitter. In addition, a polarization splitter based on a traditional dual-core fiber has strong wavelength dependence and a narrow working band, which limits its application range.[4]Since photonic crystal fibers (PCFs) became available in 1996, they have attracted extensive attention from researchers due to their infinite single-mode transmission, high birefringence,flexible nonlinear and adjustable dispersion and other unique characteristics.[5]Through flexible adjustment of medium materials as well as the size and position of air holes in the inner and outer cladding,researchers can obtain a fiber suitable for different optical devices. This provides another direction for the design of new polarization splitters, which solves the problems of traditional polarization splitters, such as a poor splitting effect, a narrow working band and difficulties with integration.[10–18]

A polarization splitter based on a DC PCF has flexible and controllable structural parameters, and can easily realize various novel characteristics and overcome the disadvantages of traditional fiber splitters such as a narrow band and wavelength dependence. In 2003, Zhang and Yang[10]proposed a polarization splitter based on a DC PCF for the first time;they could obtain high birefringence by increasing or decreasing the diameter of different air holes in the cladding. Superior to the traditional polarization splitter, this splitter achieved a working bandwidth of 40 nm near 1550 nm on the premise that the extinction ratio is greater than 10 dB.At the same time,the advantages of a PCF for designing a polarization splitter were also highlighted. In 2005,Florouset al.[11]put forward a PCF with elliptical holes. The fiber was capable of splitting a beam at 1310 nm and 1550 nm. In 2006, Rosaet al.[12]designed a PCF polarization splitter arranged in a square lattice,with a length of 20 mm and a working bandwidth of 90 nm. In 2012,Liuet al.[13]put forward a novel kind of polarization splitter in a DC elliptical hole hybrid PCF.As shown by the numerical results,an extinction ratio of-64 dB was achieved at a wavelength of 1550 nm. A 1.92 mm long splitter was suggested to achieve a bandwidth of 150 nm with an extinction ratio better than-10 dB. Only by changing the structural parameters of the optical fiber can the maximum working bandwidth reach 150 nm. Nevertheless,most of the above beam splitters do not meet the technical requirements of simple construction: the size, shape and location of the air holes are difficult to accurately control during production.[14]

The refractive index of the core is reduced by doping fluorine in the core,and hence the refractive index difference between fiber cores increases,leading to an increase in coupling strength and a reduction in the size of the DC fiber. In 2004,this method was first introduced into the design of wideband polarization splitters.[15]Laegsgaardet al.[15]suggested expanding the bandwidth of DC fiber by adding fluorine to the fiber core. This DC PCF with a low refractive index core reduced the coupling length in the short-wave band. In 2013,Hanet al.[16]designed a DC PCF polarization splitter with a fiber core doped with fluorine. Its length and bandwidth were 7.362 mm and 600 nm, respectively, when the extinction ratio was lower than-20 dB. In 2016, Zhaoet al.[17]introduced a modulation core and two fluorine-doped cores to achieve an ultrawide bandwidth. According to their numerical results,an ultra-broadband splitter with a bandwidth of 320 nm could be achieved by using a 52.8 mm long PCF.Although the coupling length of a fiber core doped with fluorine tends to be flat with change in the wavelength, the mode fields of the two cores overlapped with the high doping concentration. In the design process, the refractive index of fluorine is difficult to control accurately.[13]Beyond that, this method cannot increase the coupling length ratio, and the polarization splitter must have a long length,which is not conducive to integrated applications.[18]

Recently,researchers have found that many properties of DC PCFs can be combined with the surface plasmon resonance (SPR) effect. When the incident light energy is propagated inside a DC PCF coated with a metal(or other dielectric material)on the central air hole, the free electrons on the metal(or other dielectric material)surface of the most central air hole will interact with the incident light energy to produce the SPR effect and excite the surface plasmon polariton(SPP)mode on the metal(or other dielectric material)surface. Thus,the resonant coupling strength of a DC PCF can be changed to achieve the phase matching condition at a certain wavelength,and the length of the splitter can be reduced. In 2014,Chenet al.[19]reported a novel polarization splitter based on a DC silica glass PCF with a liquid crystal modulation core. Apart from that, an anisotropic nematic liquid crystal (NLC) of E7(material type)infiltrated into the central air hole leads to large birefringence,which makes splitters suffer a sharp increase in coupling length. The separate length was 0.175 mm and the extinction ratio-80.7 dB at the communication wavelength of 1550 nm. In 2016,Maet al.[18]proposed a DC PCF splitter with graphene covering the central air hole; this had a bandwidth of up to 610 nm and an extinction ratio of 56.3 dB at 1550 nm. The SPP mode was generated between pure quartz and graphene upon the incidence of light. The light energy was coupled from the core to the graphene surface,leading to an increase in the effective refractive index difference. At the same time, the coupling length remained flat in a wide range and the bandwidth was broadened. In 2017,Bai and Wang[20]designed a DC PCF polarization splitter based on gold line filling.The length of the device was 0.263 mm,and the extinction ratio at 1550 nm and the bandwidth were-70 dB and 124 nm,respectively. In 2021,Quet al.[21]investigated a DC PCF polarization beam splitter with a simple structure covering the E+S+C+L+U band based on the SPR effect. The total splitting bandwidth was 315 nm.By introducing gold line/film and other dielectric materials the plasma mode resonates with the core mode,thus enhancing the polarization characteristics of the fiber. In addition,the size of the splitter is also reduced.

In this paper, an ultra-wideband DC PCF polarization splitter based on fluorine/germanium doping and a graphene coating is proposed. Moreover, germanium is introduced to break the symmetry of the DC fiber to obtain higher mode birefringence and achieve stronger polarization characteristics.The coupling effect between the SPP mode on the surface of metal and graphene and the core mode is adopted to increase the difference in coupling length between the two polarization directions, which can be more favorable to the separation of polarization states. Moreover,this structure has a large fabrication tolerance. When the wavelength is 1550 nm, the spectral ratio can reach-98.6 dB. In the range of 1027 nm–1723 nm, the spectral ratio is less than-20 dB, resulting in a ultrawide working bandwidth of 696 nm, and the length of the beam splitter is only 4.78 mm. Compared with the known splitters of the same type, this splitter has better spectral efficiency. In addition, compared with the literature,[22]the operating bandwidth of this splitter is 78 nm wider. In short, it has great application prospects in future ultra-wideband,integrated and high-speed all-optical network systems.[18]

2. Structure and principle of the polarization splitter

2.1. Structure of the polarization splitter

Figure 1 shows the cross section of the DC PCF proposed in this paper. The fiber’s substrate material is pure quartz and the air holes have a filled regular hexagon arrangement,with a diameter ofdand a hole spacing ofΛ. Fiber core regionAis doped with fluorine, and regionBis doped with germanium.The diameter of the central air hole isdc. The outer layer is wrapped with a graphene thin wall, forming a ring structure.The thickness of the graphene ring ist, anddc=d-2t, as shown in Fig.2.

The effective refractive index of the pure quartz substrate material is calculated by the Sellmeier formula[6]

Here,A1= 0.6961663,A2= 0.4079426,A3= 0.8974794,λ1= 0.0684043 μm,λ2= 0.1162414 μm, andλ3=9.896161 μm (λis the wavelength). The absolute value of the difference between the refractive index of the fluorinedoped core and that of pure quartz isΔ1. Beyond that, the absolute value of the difference between the refractive index of the germanium-doped core and that of pure quartz isΔ2.Meanwhile,Δ1andΔ2are related to the concentrations of fluoride and germanium.[16]The effective refractive index of graphene[23]is(C1=5.446 μm-1)

Fig.1. Cross section of the DC PCF.

Fig.2. Cross section of the central air hole.

2.2. Theoretical basis

According to mode-coupling theory,there are four super modes in a DC PCF:the odd mode and even mode in the direction ofx-polarization,and the odd mode and even mode in the direction ofy-polarization.[24]Since the odd and even modes of the same polarization state are coupled along the propagation direction of the fiber, the polarized light energy is transferred from one fiber core to another one. When the incident light energy of one polarization direction in the fiber core is 0,the corresponding propagation distance is called the coupling lengthLc,which can be expressed as follows:[25]

3. Results and analysis

The object of research in this paper is PCF, and the research tool is COMSOL Multiphysics 5.6 simulation software.Meanwhile, the research method is the full vector FEM. The FEM provides high accuracy and flexible triangular meshes and is implemented to characterize the designed polarization splitter. Beyond that,the PCF is divided into 28376 triangular meshes. The number of mesh vertices is 14279 and the mesh area is 2.811×10-10m2. The scattering boundary condition is employed in the simulation process.[18]

The operating bandwidth and device size are two key parameters for evaluating the characteristics of the polarization splitters. Theoretically, the coupling length of the DC PCF(Lc), the coupling length ratio (δ) and the relative coupling length ratio(Lr)are closely related to these two indicators.The final structural parameters of the optical fiber ared=1 μm,Λ=2.2 μm,t=45.5 nm,andΔ1=Δ2=0.0002. In addition,the whole vector FEM is used for the research and analysis.

3.1. Coupling length and coupling ratio

The coupling length is an important parameter for measuring the coupling effect between two cores. With other conditions are unchanged, the shorter the coupling length, the stronger the coupling characteristics. As shown in Fig. 3(a),with or without graphene rings, the coupling length ofxandypolarization directionsLcvaries with wavelength. As displayed in Fig.3(b),when the thickness of the graphene ringtchanges,curves of thexandypolarization coupling lengthLcvary with wavelength. Figures 4(a)and 4(b)reveal the curves of coupling length ratio varying with wavelength in the two cases.

Fig.3. Plots of coupling length versus wavelength: (a)PCF with or without graphene;(b)different thicknesses of graphene(x-polarization).

As shown in Figs. 3(a) and 4(a), although the coupling length of the graphene ring-free structure is short, the coupling length ratio remains around 1.1, leading to large values formandn. However, this makes the device length longer.Apart from that, the addition of a graphene ring to the central air hole increases the coupling length, but the coupling length ratio also increases with increase in wavelength. The reason for this phenomenon is that there is an energetic coupling between the SPP patterns[27,28]generated by the inner walls of the graphene rings and the core patterns. Figure 5 displays the two-dimensional and three-dimensional mode field distributions of even modes in they-polarization direction of fiber core at different wavelengths. In addition, the direction of the red arrows in the two-dimensional figure represents the direction of the electric field, and the density represents the magnitude of the electric field. It can be observed from the figure that the energy of the mode field is mainly concentrated in the two core regions at the beginning, but with increasing wavelength the energy is transferred from the core to the central air hole. At this time,the coupling effect between the core mode and the SPP mode becomes increasingly obvious.As revealed in Fig.6,the mode field distribution of even modes in thex-polarization direction of the fiber core at different wavelengths is similar to that in they-polarization direction. The difference is that the energy of the central air hole is concentrated on the graphene ring in thex-polarization direction.Figure 7 displays the distributions of odd-mode two-dimensional and three-dimensional mode fields of the fiber core in theypolarization direction at different wavelengths. Obviously, at three different wavelengths there is no obvious energy coupling between the odd mode of the fiber core and the secondorder graphene SPP mode. Besides, the energy of the mode field is concentrated in fiber coresAandB, and there is no strong interaction with the graphene layer.

Fig. 4. Plots of coupling length ratio versus wavelength: (a) PCF with or without graphene;(b)different thicknesses of graphene.

Fig. 5. Two- and three-dimensional electrical field distributions of the ypolarization even mode at different wavelengths.

Fig. 6. Two- and three-dimensional electrical field distributions of the xpolarization even mode at different wavelengths.

Fig. 7. Two- and three-dimensional electrical field distributions of the ypolarization odd mode at different wavelengths.

Under the same wavelength, the coupling difference between odd and even modes and SPP modes will affect the change in the effective refractive index of the modes,as shown in Fig.8.As displayed in Fig.8(b),the two effective refractive index curves are very close compared with the two cases of the fiber with and without a graphene ring structure. Namely,the odd-mode effective refractive index in they-polarization direction has little numerical variation. As shown in Fig. 8(a),with increase in wavelength, the gap between the two curves becomes bigger. Apart from that, the even mode of theypolarization direction is greatly influenced by the graphene SPP mode. As a result, the change in the even-mode effective refractive index of they-polarization direction is greater than that of the odd-mode effective refractive index. Meanwhile,the two blue difference curves of amplitude changes in the figure reflect the differences more intuitively.working wavelength,the best value of graphene ring thickness when the coupling length ratio is 2:1 is selected. Generally speaking, takingλ=1550 nm, we could obtain the optimal value of the graphene thickness,t=45.5 nm.

Fig. 8. Plots of effective index versus wavelength: (a) y-polarization even mode;(b)y-polarization odd mode.

Fig.9. Plots of effective refractive index difference versus wavelength.

3.2. Relative coupling length ratio

According to the results of the mathematical analysis,whenλ0has a fixed value, the ratio of the coupling length of any wavelengthλto that of the working wavelengthλ0should be close to 1. In this way,the polarization splitter can obtain a wider working bandwidth. In this paper,the relative coupling length ratio is introduced to describe the above ratio,and can be expressed as follows:

According to Ref. [16], a fiber core doped with fluorine can make the relative coupling length ratio approach 1. In this research,the fiber core is co-doped with fluorine and germanium, and the two core areas are only doped with fluorine on one side and germanium on the other side to destroy the symmetry of the DC fiber. This is conducive to obtaining higher-mode birefringence and thus enabling the fiber to obtain stronger polarization characteristics. As displayed in Figs. 10(a) and 10(b), the order of magnitude of mode birefringence for the undoped fiber is 10-6,and the order of magnitude of mode birefringence is increased to 10-4in the case of fluoride and germanium co-doping.

Figure 11 shows the curve of the relative coupling length ratio for thex-polarization direction with and without fluoride and germanium in the fiber core changing with the wavelength.It is obvious that the structure can make the relative coupling length ratio approach 1 and the curve tends to be more obvious below a wavelength of 1550 nm. In fact,when the concentration of fluorine and germanium in the fiber core is too high(i.e.,when the values ofΔ1andΔ2get larger),the mode fields of the two cores will be squeezed to the center and overlapped,making it difficult to separate polarized light in two directions at the end of the splitter. Therefore, the values ofΔ1andΔ2should not be too high.

Fig.10. Plots of birefringence versus wavelength: (a)without F and Ge;(b)with F and Ge.

Fig. 11. Plots of relative coupling length ratio (x-polarization) versus wavelength.

3.3. Normalized power and extinction ratio

Figure 12 reveals that for wavelengthλ=1550 nm, the normalized power curve of a fiber core in the direction ofxpolarization andy-polarization varies with the transmission distance. As shown in Fig.12,when the beam is emitted into fiber coreA, the energy in the direction ofx-polarization andy-polarization will undergo periodic transfer in fiber coresAandB. Under this wavelength,when the transmission distancez=2Lxc=2Lyc=4.78 mm, thex-polarized light is in coreAand they-polarized light is coupled to coreB, implementing the complete separation of the two polarization directions.extinction ratio versus wavelength when the transmission distance is 4.78 mm. It can be observed from Fig. 13 that at a wavelength of 1550 nm,the extinction ratio of coresAandBis-98.6 dB and-68.8 dB, respectively. At the same time,the wavelength range for an extinction ratio less than-20 dB is 696 nm and 432 nm, respectively. Table 1 compares the performance of the polarization splitter designed in this paper and those in other references.It is obvious that the polarization splitter designed in this paper has some advantages in terms of the extinction ratio and the working bandwidth.

Fig.12. Normalized power versus propagation distance.

Fig.13. Extinction ratio versus wavelength.

The extinction ratio determines the effect of the polarization splitter. The larger the ratio is, the more favorable it is for the separation of the two polarization states. It is generally considered that the extinction ratio must be less than-20 dB to achieve the separation effect. Figure 13 shows the curve of

Table 1. Comparison of different polarization splitters.

3.4. Confinement losses

Optical fiber communication is inseparable from loss,and the transmission over a certain distance is closely related to loss. Confinement loss, as an important index of fiber transmission,can be calculated using

The units of confinement loss and wavelength are dB/cm-1and μm, respectively. In addition, Im(neff) refers to the imaginary part of the effective refractive index of the fundamental mode.

Figure 14 shows the confinement losses spectra of the four super modes. It can be seen that with increasing wavelength,the confinement of the energy in the transfer cores becomes weaker and the confinement losses get larger. Beyond that,the confinement loss of even modes in thex-polarization direction is the biggest. Notably,the loss of thex-polarization mode is greater than that of they-polarization mode in the whole range, because two pores doped with fluorine and germanium are placed in thex-direction. Furthermore,thex-SPP mode is more easily coupled with the graphene ring than they-SPP mode.[31]

3.5. Tolerance analysis

Fig.14. The confinement losses spectra of the four super modes.

Fig. 15. Plots of extinction ratio versus wavelength: (a) coupling length±1%;(b)thickness of graphene±1%.

Given that the fiber is affected by external factors in the actual drawing process, the fiber structure parameters will show a certain deviation. Figure 15(a) displays the change of extinction ratio with wavelength when the fiber coupling length deviates from the initial coupling length by±1%. As shown in the figure,a change of fiber coupling length of±1%has little impact on the working bandwidth of the polarization splitter, which is 650 nm and 730 nm, respectively. Figure 15(b)shows the change of extinction ratio with wavelength when the graphene ring thicknesstdeviates by±1%. It can be observed from the figure that the bandwidth of the polarization splitter becomes 686 nm whentdeviates by +1%.When the deviation oftis-1%, the bandwidth changes to 860 nm,and the curve of the extinction ratio moves up considerably. However, the extinction ratio is still around-20 dB,which has little impact on the polarization performance.Based on the above tolerance analysis, the fiber structure parameters changed by the external factors have little impact on the performance of the designed polarization splitter in the actual production process.

4. Conclusion

In this paper,a polarization splitter for an ultra-wideband,dual-core photonic crystal fiber was proposed. The optimal coupling length ratio of 2:1 and the relative coupling length ratio of nearly 1 were obtained by introducing a graphene ring and a fiber core doped with fluorine and germanium,which made the operating bandwidth of the polarization splitter wider and the device size smaller. According to simulation results,when the wavelength was 1550 nm,the extinction ratio could reach-98.6 dB.When the wavelength was between 1027 nm and 1723 nm(i.e.,a bandwidth of 696 nm),the spectral ratio was less than-20 dB and the length of the beam splitter was 4.78 mm. Compared with the known splitters,the operating bandwidth of this splitter was nearly 100 nm wider,while the size of the device was reduced by a third. In addition, the structure had a certain production tolerance. When the coupling length or graphene thickness showed a numerical deviation of±1%, good performance of the polarization splitter could be still guaranteed. Owing to the above excellent splitting characteristics,the proposed polarization splitter will be very important for applications in the field of ultrawideband optical communications and integrated optics.

Acknowledgment

Project supported by the State Key Laboratory of Luminescence and Applications(Grant No.SKLA-2020-01).