Ultra-Broadband Minuscule Polarization Beam Splitter Based on Dual-Core Photonic Crystal Fiber with Two Silver Wires

Abstract

This paper presents a polarizing beam splitter (PBS) based on a hexagonal lattice silver-filled photonic crystal fiber (PCF) with two silver wires, which possesses advantages such as a short splitting length, high extinction ratio (ER), and an ultra-wide bandwidth in commonly used communication bands. Utilizing the full-vector finite element method (FV-FEM), thorough investigations were conducted on lasers within the wavelength range of 1.1 to 1.9 μm. The PBS demonstrates a working bandwidth of 725 nm (1.14 to 1.865 μm) under an ultra-short splitting length of 55.3 μm, with an ER exceeding 20 dB, covering all bands of O + E + S + C + L + U optical communication, and achieving a maximum ER of 74.65 dB, where the surface plasmon resonance (SPR) effect of silver metal plays a significant role. It not only features an ultra-short splitting length and an ultra-wide splitting bandwidth but also exhibits excellent manufacturing tolerances and anti-interference capabilities. This polarizing beam splitter represents a promising candidate in communication and may find various applications in optical communication.

1. Introduction

PCF is an optical fiber with periodic microstructures, typically composed of periodically arranged air holes or fillings. The design of these microstructures effectively controls the propagation characteristics of light, including dispersion [1], mode field distribution [2], and optical bandgaps [3]. Due to its unique optical properties, photonic crystal fiber finds extensive applications in optical communication [4], sensing [5], and laser technologies [6]. A PBS based on PCF is an important optical device derived from PCF design [7,8]. It utilizes the special structure and optical properties of photonic crystal fiber to achieve polarization separation of incident light signals, directing light of different polarization states into respective output channels. Compared to traditional PBS, PCF PBS offers advantages such as higher ER, broader operating bandwidth, and shorter splitting length. Therefore, it holds significant potential for applications in optical communication systems.

PCF PBS simultaneously achieving short splitting length and extended operating bandwidth holds significant theoretical and practical value. Firstly, a short splitting length helps minimize energy loss during the splitting process, ensuring high-intensity signals reach the output terminal. This is crucial for maintaining signal strength and stability, particularly in long-distance fiber optic transmission or high-precision optical measurements. Simultaneously, an extended operating bandwidth implies that PCF PBS can effectively operate across a broader range of optical frequencies or wavelengths. This characteristic enables the beam splitter to accommodate diverse requirements for handling multiple optical signals without frequent device replacement or adjustment. Such capabilities are critical for various applications in optical communications, sensing, and scientific research, where different wavelengths or frequencies of light signals are commonly encountered. Consequently, integrating a short splitting length with an extended operating bandwidth enables PCF PBS to maximize signal integrity during light signal processing while efficiently facilitating beam splitting and transmission over a wider frequency range. This design not only enhances the flexibility and application scope of the device but also strengthens its practicality and performance in complex optical systems.

Certainly, the highest ER of a device holds significant importance. An increase in ER implies that the device can more effectively separate optical signals of different polarization states, thereby enhancing the beam splitting efficiency. A larger ER value indicates a greater power ratio between the two polarized light outputs, further improving the beam splitting effectiveness. In optical signal transmission, a high extinction ratio ensures high-quality transmission of target polarization state signals, significantly reducing error rates, particularly noticeable in high-speed data transmission. Moreover, a high extinction ratio enhances system sensitivity and dynamic range, optimizes optical path design and integration, thus enhancing overall system stability and resistance to interference.

In improving the performance of PCF PBS, doping with metals is a common method that has made progress in this direction. In 2017, Wang et al. proposed a tunable surface plasmon resonance polarizing beam splitter based on a gold-coated central hole in a magnetic fluid-filled dual-core PCF (DC-PCF) [9]. With an applied magnetic field of 760 Oe, this polarizing beam splitter exhibited a minimum splitting length of 5112 μm, a bandwidth of 189 nm, and an ER of −158 dB at a wavelength of 1.55 μm. However, the designed PCF PBS had a narrow operational bandwidth and a long splitting length. In 2020, Zhang et al. made significant progress in the splitting length by designing a PBS based on gold-filled DC-PCF [7]. By utilizing the surface plasmon resonance (SPR) effect to enhance the resonance coupling strength of the dual-core PCF, the fiber length was successfully shortened to 324.03 μm. However, despite the improvement in the splitting length, the operational bandwidth slightly decreased. At the splitting length of 324.03 μm, the bandwidth with ER less than −20 dB was 110 nm, and the maximum value of ER was −160.56 dB at a wavelength of 1.55 μm. In 2022, Mei et al. proposed a PBS based on SPR [10]. They established two solid silica cores near the center of the PCF by removing the air holes in the cladding and depositing a gold film on the outer surface of the central air hole of the PCF to excite SPR. Although they made significant progress in the operational bandwidth, reaching 314 nm, the splitting length slightly increased to 123.6 μm. Subsequently, in 2023, Chen et al. designed a broadband all-fiber PBS based on silicon DC-PCF and a gold layer [11]. Although its operational bandwidth reached 450 nm, covering the entire E + S + C + L communication band, the splitting length significantly increased compared to previous research results, reaching 0.66 mm. However, these designs failed to simultaneously optimize both the splitting length and the operational bandwidth. In summary, current research indicates that the performance of PCF PBS still needs further improvement. Previous research results have not been able to achieve both a wide operational bandwidth and a short splitting length simultaneously. Therefore, this paper comprehensively optimizes these two aspects of PCF PBS performance.

In our work, we propose a hexagonal structure dual-core photonic crystal fiber polarization beam splitter (HS-DC-PCF PBS), which features ultra-wide bandwidth and ultra-short splitting length, representing a new breakthrough in this field. The structure of HS-DC-PCF PBS is designed based on a hexagonal lattice, incorporating three sizes of air holes and two silver wires. Silver is one of the most commonly used materials to excite the SPR effect due to its faster electron mobility. The coupling length and coupling length ratio of HS-DC-PCF PBS are calculated using mode coupling theory and FV-FEM. The influence of fabrication tolerances of four different aperture sizes on the performance of HS-DC-PCF PBS is analyzed. Ultimately, a high-performance ultra-short HS-DC-PCF PBS is obtained, with a splitting length of only 55.3 μm and a maximum ER of 74.56 dB, providing a bandwidth of 725 nm, covering all communication bands of O + E + S + C + L + U. Compared to previous studies, the HS-DC-PCF presented in this paper achieves a wider operating bandwidth with a shorter splitting length, making it a universal candidate for optical systems and networks.

2. Design of the HS-DC-PCF PBS and Theory

Figure 1 illustrates the cross-section of the proposed HS-DC-PCF PBS. This structure consists of two different arrays of circular air holes and two elliptical air holes located at the center. The diameters of the two air holes filled with metallic silver are denoted by d₁, while the larger and smaller air hole diameters are represented by d₂ and d₃, respectively. The two elliptical air holes are distributed on either side of the fiber’s center, with d_a and d_b representing the major and minor axes’ diameters of the elliptical air holes, respectively. Cores A and B are surrounded by elliptical and two types of circular air holes. In the x-axis direction, the spacing between adjacent air holes (including elliptical ones) is denoted as Λ₁. In the y-axis direction, the spacing between two adjacent air holes with a diameter of d₃ is $\sqrt{3}/2$Λ₁, while the spacing between two adjacent air holes with diameters d₂ and d₃ is Λ₂. Pure silica is used as the background material for HS-DC-PCF. We utilized COMSOL Multiphysics 6.1 to establish the corresponding model and conducted simulations using FV-FEM. During the simulation process, to mitigate the transmission losses of optical energy, we incorporated a perfectly matched layer (PML) and scattering boundary conditions at the outer layer of the structure. These measures are aimed at minimizing reflections of light and preventing optical waves from reflecting back into the simulation region boundaries, thereby ensuring the accuracy of the simulation results. For the PML, its thickness is set to Λ₁, and the refractive index is set to 0.03 higher than that of the silica material [12]. Moreover, a grid was implemented to partition the model into small elemental domains, facilitating a more detailed capture of the micro-scale interactions between the device and light. This optimized grid partitioning also enhances computational efficiency and reduces computational costs.

We employ the Sellmeier dispersion equation to describe the refractive index of silica [13,14],

$$n_{\mathrm{silica}}(\lambda )=\sqrt{1+\frac{A_1{\lambda }^2}{{\lambda }^2-B_1^2}+\frac{A_2{\lambda }^2}{{\lambda }^2-B_2^2}+\frac{A_3{\lambda }^2}{{\lambda }^2-B_3^2}},$$

(1)

where λ is the wavelength of the incident light in free space, A₁ = 0.6961663, A₂ = 0.407926, A₃ = 0.8974794, B₁ = 0.0684043 µm, B₂ = 0.1162414 µm, and B₃ = 9.896161 µm.

The dielectric constant of silver was calculated using the Drude–Lorentz model [15,16,17],

$${\epsilon }_r={\epsilon }_{\infty }-\frac{{{\omega }_p}^2}{{\omega }^2+i\omega \gamma }-\frac{\Delta {\mathsf{\Omega }}^2}{\left({\omega }^2-{\mathsf{\Omega }}^2\right)+i\mathsf{\Gamma }\omega },$$

(2)

where ω represents the angular frequency of light, ε_∞ denotes the relative high-frequency dielectric constant, and ω_p and γ are the plasma and damping frequencies, respectively. Δ denotes the weighting factor of the resonance peak of the dielectric function, and its physical meaning is to describe the strong modulation or weighting of the dielectric function in certain frequency ranges. This modulation can be caused by external factors (e.g., stress, electric field, light field, etc.) that result in a significant change in the dielectric constant of the material at a particular frequency. Thus, Δ plays a role in the Drude–Lorentz model in modulating the frequency dependence of the dielectric function, reflecting the nonlinear nature of the material and its modulation or weighting at specific frequencies. Ω and Γ represent the frequency and spectral width of the Lorentz oscillator, respectively. The final values for each parameter are given in

Table 1. Optimized parameter values fitted to Silver’s experimental data.

ε∞	ωp/2π (THz)	γ/2π (THz)	Ω/2π (THz)	Γ/2π (THz)	Δ
2.4064	2214.6	4.8	1330.1	620.7	1.6604

.

The complex refractive index of silver is

$$n_{silver}=\sqrt{{\epsilon }_r}=n_{\mathrm{M}}+ik.$$

(3)

The real part n_M of the complex refractive index n_silver describes silver’s optical refractive properties, while its imaginary part k, referred to as the extinction coefficient, characterizes silver’s optical absorption properties.

According to the coupled mode theory, the performance characteristics of the proposed polarizing beam splitter can be analyzed by superimposing four modes. Figure 2 illustrates the four modes composed of even and odd modes of x-polarized (x-pol) and y-polarized (y-pol) light, namely x-pol odd mode, x-pol even mode, y-pol odd mode, and y-pol even mode. The coupling lengths for the x-pol and y-pol directions of the polarizing beam splitter can be calculated using the following relations [18,19,20]:

$${\mathrm{CL}}_x=\frac{\lambda }{2\left|n_x^{\mathrm{even}}-n_x^{\mathrm{odd}}\right|},$$

(4)

$${\mathrm{CL}}_y=\frac{\lambda }{2\left|n_y^{\mathrm{even}}-n_y^{\mathrm{odd}}\right|}.$$

(5)

Here, CL_x and CL_y represent the coupling lengths of the PBS in the x and y directions, respectively. λ denotes the wavelength of the incident light in free space, while $n_x^{\mathrm{odd}}$, $n_x^{\mathrm{even}}$, $n_y^{\mathrm{odd}}$, and $n_y^{\mathrm{even}}$ represent the effective refractive indices of the PBS in the corresponding modes. To split the two polarized light rays into two cores, it is necessary to maintain the relationship L = mCL_x = nCL_y, where m and n are positive integers. The coupling length ratio is defined as:

$$\mathrm{CLR}=\frac{{\mathrm{CL}}_y}{{\mathrm{CL}}_x}.$$

(6)

The CLR needs to be 2 (when CL_x < CL_y) to achieve optimal performance with shorter lengths [21,22].

The output power (Pout) of specific polarized light, either x-polarized (x-pol) or y-polarized (y-pol), can be measured using the following formula, where the input power (Pin) is in either core A or core B [23]:

$$P_{\mathrm{out},\mathrm{A}}^{X,Y}=P_{\mathrm{in}}{\cos }^2\left(\frac{\pi }{2}\frac{L}{{\mathrm{CL}}_{x,y}}\right),$$

(7)

$$P_{\mathrm{out},\mathrm{B}}^{X,Y}=P_{\mathrm{in}}{\sin }^2\left(\frac{\pi }{2}\frac{L}{{\mathrm{CL}}_{x,y}}\right),$$

(8)

where $P_{\mathrm{out},\mathrm{A}}^{X,Y}$ and $P_{\mathrm{out},\mathrm{B}}^{X,Y}$ represents the normalized power of x-pol or y-pol in cores A and B respectively, CL_x, CL_y denote the coupling lengths of x-pol or y-pol, and L is the length of the splitter.

The performance of a polarization splitter is commonly assessed by its ER. ER is defined as the ratio of the power of undesired polarization modes in the core region to the power of the desired polarization mode. For the aforementioned microstructure HS-DC-PCF, at the output port of core A or B, assuming the undesired polarization state in core A is y-pol, the ER calculation formula is as follows [24,25]:

$$\mathrm{ER}=10\lg \frac{P_{\mathrm{out}}^{\mathrm{X}}}{P_{\mathrm{out}}^Y}.$$

(9)

The ER serves as an important indicator of the effectiveness of the HS-DC-PCF PBS. An ER value surpassing 20 dB (or falling below −20 dB) indicates a significant power difference of 100 times between the two polarized lights, effectively separating the orthogonally polarized light beams. Hence, wavelength ranges exhibiting an ER exceeding 20 dB (or less than −20 dB) can be regarded as the operational bandwidth of the HS-DC-PCF PBS [26].

3. Simulation Results and Discussion

The coupling and transmission characteristics of HS-DC-PCF were investigated using the FV-FEM. The initial parameters of the structure were set as follows: d₁ = 0.5 µm, d₂ = 0.2 µm, d₃ = 1.4 µm, d_a = 0.72 µm, d_b = 0.5 µm, Λ₁ = 1.5 µm, and Λ₂ = 1 µm. Under these initial structural parameter settings, the relationship between the effective refractive indices of four different modes and wavelengths is depicted in Figure 2.

Observations from Figure 2 reveal a gradual decrease in the effective refractive indices of the four distinct modes (x-pol even mode, y-pol even mode, y-pol odd mode, and x-pol odd mode) with increasing wavelength. Furthermore, it is noted that the effective refractive indices of the even modes for x-pol and y-pol are very close, whereas there exists a discernible gap between the odd modes of x-pol and y-pol. This suggests a significant influence of the two silver wires on the effective refractive indices of the odd modes for both x-pol and y-pol, rendering them more distinguishable. Upon further scrutiny of Figure 2, it is evident that the discrepancy in effective refractive indices between the odd and even modes for x-pol and y-pol increases with wavelength, with the disparity being greater for the odd-even modes of y-pol compared to x-pol. This indicates a more pronounced effect of the two silver wires on y-pol light.

Additionally, we computed the dispersion relations between the four aforementioned modes and the second-order Surface Plasmon Polariton (2nd-SPP) modes corresponding to the core mode. It is readily observable from Figure 2 that the effective refractive indices of all four 2nd-SPP modes are significantly higher than those of the aforementioned four modes. This phenomenon is attributed to the SPR effect of the silver wires, resulting in wave vectors higher and wavelengths shorter than those in the optical medium. For wavelengths below 1.56 μm, the discrepancy in effective refractive indices between the odd-even modes of 2nd-SPP for both x-pol and y-pol is minimal, with the two curves nearly overlapping. However, as the wavelength exceeds 1.56 μm, the gap between them gradually widens while still maintaining relative proximity. Such relative density and high effective refractive indices stem from the unique coupling mechanism of the 2nd-SPP modes, wherein the electric fields on the metal surface interact with those in the medium, facilitating the formation and dominance of these modes. First- and third-order SPP modes were disregarded due to their lack of phase matching with the core mode.

Figure 3 illustrates the relationship between the CL_x, CL_y, and CLR of x-pol and y-pol odd and even modes with wavelength, which can be calculated, respectively, by Equations (4)–(6). It is observed from Figure 3 that CL_x is always greater than CL_y. As the wavelength increases, CL_x gradually decreases from 49.73 μm to 36.67 μm, while CL_y decreases from 31.77 μm to 17.87 μm. Since the decrease in CLy is greater than that of CL_x, the CLR curve shows an upward trend, increasing from 1.57 to 2.05. However, within the considered wavelength range of 1.1–1.9 μm, most CLR values remain below 2. Under this condition, although x-pol light and y-pol light can be separated, the splitting length is too long.

Figure 4a–d illustrates the modal electric field distributions of four different modes in HS-DC-PCF PBS when the incident light wavelength is 1.55 μm. In Figure 4a,b, the modal field energy of x-pol and y-pol odd modes is mainly concentrated in the core region. Conversely, in Figure 4c,d, a small portion of the energy of x-pol and y-pol even modes couples to the two silver wires, highlighting the significant influence of silver metal’s SPR effect on the polarization even modes. This phenomenon can be understood as the interaction between the even mode’s optical field and the silver wire surface, which excites SPPs. As the electrons on the metal surface oscillate, SPPs primarily concentrate near the silver wire. Therefore, a portion of the energy of even modes couples to these SPPs, resulting in the distribution of electric fields around the silver wire surface. Correspondingly, Figure 4e–h presents the 2nd-SPP modes corresponding to the modes in Figure 4a–d, where the electric field mainly concentrates on the surfaces of the two silver wires. Physically, this phenomenon can be explained by the local electric field on the surface of the silver wires driving the 2nd-SPP modes. Through interaction with the incident light waves, the free electrons on the surface of the silver wires oscillate, forming SPPs primarily concentrated near the surface of the silver wires. Therefore, the electric field of the 2nd-SPP modes also mainly distributes on the surface of the silver wires, thus achieving efficient energy transfer between the surface plasmon polaritons on the silver wire surface and the optical field.

In order to optimize the structure to achieve a CLR of 2, we analyzed the effects of each parameter, namely d₁, d₂, d₃, d_a, d_b, Λ₁, and Λ₂, on the structure at the most commonly used communication wavelength of 1.55 μm. We calculated the corresponding horizontal CL_x, vertical CL_y, and CLR for each structural parameter change, exploring their interrelationships. The influence of d1 on the CL_x, CL_y, and CLR of the HS-DC-PCF PBS is illustrated in Figure 5. As depicted in Figure 5, when d1 increases from 0.3 μm to 0.6 μm, CL_x gradually decreases from 40.50 μm to 38.83 μm, while CL_y decreases from 22.38 μm to 21.05 μm. The increase in d₁ affects the mode coupling with silver metal, reducing the coupling strength in the x-pol and y-pol directions. Additionally, due to the relatively larger rate of change in CL_y compared to CL_x, CLR slowly increases from 1.81 to 1.84 with the increase in d₁.

Figure 6 illustrates the impact of d₂ on the CL_x, CL_y, and CLR of the HS-DC-PCF PBS. To enhance the structure’s birefringence, increasing the diameter of the smaller air holes, d₂, from 0.2 μm to 0.6 μm results in CL_x decreasing from 38.52 μm to 25.19 μm. In contrast, CL_y initially slightly decreases from 21.26 μm to 17.49 μm. As d₂ increases, due to the greater decrease in CL_x compared to CL_y, CLR decreases from 1.81 to 1.44. This suggests that increasing d₂ enlarges the difference between the x-pol odd and even modes and y-pol odd and even modes in the two cores, particularly affecting the x-polarization odd and even modes. Therefore, reducing d₂ facilitates the transmission of x-pol and y-pol light between the two cores.

Figure 7 illustrates the influence of d₃ on the CL_x, CL_y, and CLR of the HS-DC-PCF PBS. It can be observed from Figure 7 that as d₃ increases from 1.2 μm to 1.5 μm, CL_x decreases from 52.04 μm to 33.53 μm, while CL_y decreases from 27.79 μm to 18.74 μm. The primary reason for this is that with the increase in d₃, the coupling strength of both x-pol and y-pol light intensifies, consequently reducing the coupling length required for x-pol and y-pol light to propagate from one core to another. Additionally, CLR also gradually decreases with the increase in wavelength, decreasing from 1.87 to 1.79.

Figure 8 illustrates the impact of d_a on the CL_x, CL_y, and CLR of the HS-DC-PCF PBS. From Figure 8, it can be observed that as the major axis of the elliptical air hole, d_a, increases from 0.6 µm to 0.8 µm, CL_x exhibits an upward trend, rising from 34.52 µm to 41.37 µm, while CL_y remains relatively stable with d_a variations, hovering around 21.2 µm, showing only minimal differences. This indicates that the variation in d_a primarily diminishes the coupling strength in the x-pol direction. Consequently, with the increase in d_a, due to the continuous enlargement of CL_x, CLR also exhibits an ascending trend, increasing from 1.67 to 1.92.

Figure 9 illustrates the impact of d_b on the CL_x, CL_y, and CLR of the HS-DC-PCF PBS. As d_b increases from 0.3 µm to 0.6 µm, both CL_x and CL_y show an increase, with CL_x rising from 29.87 µm to 44.64 µm, and CL_y increasing from 18.18 µm to 23.30 µm. Since the increase in CL_x is greater than that in CL_y, CLR also exhibits an upward trend, rising from 1.64 to 1.92. This indicates that the increase in d_b enhances the coupling strength in both the x-pol and y-pol directions.

Figure 10 depicts the influence of Λ₁ on CL_x, CL_y, and CLR of the HS-DC-PCF PBS. From Figure 10, it can be observed that as Λ₁ increases from 1.4 μm to 1.6 μm, CL_x gradually decreases from 49.49 μm to 33.06 μm, while CL_y remains stable around 21.3 μm. The primary reason for this is that the increase in Λ₁ leads to a larger horizontal spacing between all air holes, enhancing the coupling strength of the x-pol polarized light, resulting in a decrease in CL_x. Additionally, CLR also decreases with the increase in Λ₁, decreasing from 2.26 to 1.57.

Figure 11 illustrates the influence of Λ₂ on CL_x, CL_y, and CLR of the HS-DC-PCF PBS. From Figure 11, it can be observed that as Λ₂ increases from 0.9 μm to 1.2 μm, CL_x rapidly increases from 22.79 μm to 175.10 μm, while the rising trend of CL_y, although much smaller relative to CL_x, also increases rapidly from 15.01 μm to 48.21 μm. The primary reason for this is that as Λ₂ increases, the distance between core A and core B increases, weakening the coupling strength between the x-pol and y-pol polarized light, resulting in an increase in the coupling length. Additionally, since the increase in CL_x is always greater than the increase in CL_y, CLR also increases with the increase in Λ₂, rising from 1.52 to 3.63.

Through the analysis of Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 and by comprehensively examining the influence of various structural parameters on CL_x, CL_y, and CLR of the HS-DC-PCF PBS, the final optimized structural parameters were determined as follows: d₁ = 0.4 μm, d₂ = 0.3 μm, d₃ = 1.3 μm, d_a = 0.7 μm, d_b = 0.48 μm, Λ₁ = 1.4 μm, and Λ₂ = 1.03 μm.

Figure 12 illustrates the influence of the presence of silver wires in the structure on the characteristics CL_x, CL_y, and CLR of HS-DC-PCF PBS after structural parameter optimization. From Figure 12a, it can be observed that when there are no silver wires in the PCF, i.e., when all the holes are air holes, CL_x and CL_y are relatively small and exhibit a decreasing trend within the wavelength range of 1.1–1.9 μm. CL_x rapidly decreases from 40.79 μm to 18.70 μm, and CL_y decreases from 31.67 μm to 14.69 μm, showing a rapid change. However, the variation in CLR is not significant at this point, showing a slight increase followed by a decrease as the wavelength increases, from 1.2880 slightly increasing to 1.2882, then decreasing to 1.2729. It can be observed that CLR remains almost constant between 1.27 and 1.29, far from the ideal value of 2, which is unfavorable for manufacturing shorter PBS. In contrast, from Figure 12b, it can be seen that when silver wires are added to the PCF, the magnitudes of CL_x and CL_y increase compared to those without silver wires, with a greater impact on CL_x. As the wavelength increases from 1.1 μm to 1.9 μm, CL_x shows a trend of first decreasing and then increasing, gradually decreasing from 59.57 μm to 52.04 μm, then increasing to 59.40 μm. Meanwhile, CL_y exhibits a decreasing trend with increasing wavelength, gradually decreasing from 38.50 μm to 22.78 μm. At this point, CLR approaches the ideal value of 2, increasing from 1.55 to 2.61 as the wavelength increases. When the wavelength is 1.6 μm, CLR is closest to 2. By comparing these two situations, it can be found that the addition of silver wires in the structure is mainly to utilize the SPR effect of silver to achieve polarization beam splitting. When incident light interacts with the electromagnetic field on the surface of the silver wire, surface plasmon oscillations are induced, resulting in the SPR effect. This effect can couple with the optical field, leading to a specific electric field distribution around the silver wire, thereby affecting the polarization state of light. When incident light contains components of different polarizations, these components interact with the silver wire in different ways within the PCF, resulting in light with different polarization states being split into different paths at the output end, achieving the function of polarization beam splitting. The addition of silver wires greatly increases the coupling strength of x-pol and y-pol polarized light and makes the propagation path of light in the PCF more controllable, facilitating polarization separation, thereby achieving a shorter PBS splitting length and improving the performance of PBS.

As shown in Figure 13, according to Equations (7) and (8), normalized output power (NOP) of x-pol and y-pol polarized light in cores A and B can be plotted to illustrate their periodic variations along the propagation distance. When the NOP of x-pol or y-pol polarized light is maximum in one core, it must be minimum in the other core, while the beam is split into two cores. Since NOP is a function of propagation distance, the length of the splitter can be measured from the NOP output curves of the cores. From Figure 13, it can be observed that as the propagation length increases from 0 to 55.3 μm, the NOP of x-pol light completely transfers from core A to core B, then returns to core A and reaches a maximum of 1. Conversely, in core B, the NOP of x-pol light reaches a maximum, while the NOP of y-pol light reaches a minimum. Therefore, the shortest splitting length is 55.3 μm. At this point, x-pol light and y-pol light at a wavelength of 1.6 µm are completely separated in the two cores.

Figure 14 illustrates the variation of ER with wavelength when the proposed HS-DC-PCF PBS is operating with a splitting length of 55.3 μm. From Figure 14, it can be observed that as the wavelength increases from 1.1 μm to 1.22 μm, ER increases from 15.01 dB to the first peak value of 67.73 dB. As the wavelength continues to increase, ER first decreases and then increases again. At a wavelength of 1.47 μm, ER reaches its minimum value of 20.15 dB. Then, at a wavelength of 1.75 μm, ER reaches the second peak, also the maximum ER value, at 74.56 dB. When the wavelength exceeds 1.75 μm, ER decreases with the increasing wavelength. From Figure 14 and simulation data, it can be observed that when the wavelength is between 1.14 μm and 1.865 μm, the ER value of the HS-DC-PCF PBS remains above 20 dB. Therefore, the wavelength range of 1.14 μm to 1.865 μm serves as the operating band of the HS-DC-PCF PBS, with a bandwidth of 725 nm, covering the entire O + E + S + C + L + U communication bands.

In practical production, it is necessary to consider the manufacturing tolerance of the structure due to possible slight variations in parameters. Currently, mature manufacturing processes can control errors within 1%. In this study, when different structural parameters vary by ±1%, Figure 15a–g illustrates the changes in ER. From Figure 15a, it can be observed that when d₁ increases or decreases by 1%, the wavelength range greater than 20 dB slightly decreases, with a working bandwidth of approximately 700~710 nm. Similarly, from Figure 15b–e, it is found that when structural parameters d₂, d₃, d_a, and d_b vary by ±1%, ER changes insignificantly, with the wavelength range greater than 20 dB slightly narrowing, but all within around 700 nm. Additionally, from Figure 15, it can be seen that the horizontal spacing Λ₁ between adjacent air holes and the spacing Λ₂ of adjacent air holes with diameters d₂ and d₃ in the y direction have a significant impact on ER. From Figure 15f, it is known that when Λ₁ decreases by 1%, the wavelength range greater than 20 dB is 1.11 μm–1.81 μm, with a bandwidth of 700 nm; when Λ₁ increases by 1%, the wavelength range of the working bandwidth is again 1.18 μm–1.89 μm, with a bandwidth of 710 nm. Furthermore, when Λ₁ decreases, the overall trend of ER with wavelength shifts towards shorter wavelengths, exhibiting a blue shift phenomenon; when Λ₁ increases, the image shifts overall towards longer wavelengths, exhibiting a red shift phenomenon. On the other hand, from Figure 15e, it can be seen that when Λ₂ changes, the overall distribution change of ER is opposite to that when Λ₁ changes. When Λ₂ decreases, ER exhibits a red shift phenomenon, with a working bandwidth of 1.17 μm–1.9 μm, and a bandwidth of 730 nm; when Λ₂ increases, ER exhibits a blue shift phenomenon, with a working bandwidth again of 1.13 μm–1.81 μm, and a bandwidth of 680 nm. Upon final observation of Figure 15h, it is found that if all the aforementioned structural parameters maintain a manufacturing tolerance of ±1%, even under the most adverse conditions, the device still exhibits a relatively wide operational bandwidth. Specifically, when all parameters increase by 1%, the wavelength range achieving ER greater than 20 dB spans from 1.19 μm to 1.83 μm, with a bandwidth of 640 nm. Conversely, when all parameters decrease by 1%, the operational bandwidth remains substantial at 690 nm, covering wavelengths from 1.14 μm to 1.83 μm. In conclusion, despite possible ±1% errors in the manufacturing process, the designed HS-DC-PCF PBS still maintains good splitting performance.

Table 2. Comparisons between the HS-DC-PCF PBS and other reported DC-PCF PBSs.

References	Structure	Splitting Length (µm)	Bandwidth (nm)	Maximum or Minimum ER (dB)
[9]	Magnetic-fluid-core PCF with a gold film	5112	189 (<−20 dB)	−158
[7]	Diamond-shaped PCF with a gold-filled hole	324.03	110 (<−20 dB)	−160.56
[10]	Hexagonal structure PCF with a gold film	123.6	314 (>20 dB)	78
[11]	Hexagonal structure PCF with two gold rings	660	450 (>20 dB)	78
[29]	Hexagonal structure PCF with two elliptical gold wires	62.5	110 (<−20 dB)	−71
[30]	Ge20Sb15Se65 glass-based X-shaped PCF with two gold rods	230	358 (>20 dB)	46.62
[27]	Hexagonal structure PCF with two different elliptical holes without metals	2000	100 (<−20 dB)	−52.5
[28]	Rectangular and hexagonal structure PCF without metals	1970	340 (<−20 dB)	−81.45
[31]	Square structure PCF with two gold wires	56.33	530 (>20 dB)	132.92
This work	Hexagonal structure PCF with two silver wires	55.3	725 (>20 dB)	74.56

compares the simulated results of the proposed HS-DC-PCF PBS with other reported DC-PCF PBS. According to Table 2, the PCF PBS structures in previous literature [27,28] were devoid of metals and comprised solely of air holes. These PBS exhibited longer beam splitting lengths, reaching the millimeter scale, with insignificant operational bandwidths. In contrast, in other studies [7,9,10,11,29,30,31], metal-doped PCF PBS were employed to induce the SPR effect on metal surfaces. The results indicated a significant enhancement in the performance of PBS in terms of beam splitting length and bandwidth after the addition of metals. Some previous studies have reported beam splitting lengths reduced to less than 300 μm [10,29,30,31], while some have achieved bandwidths exceeding 400 nm [11,31]. The beam splitting length of the HS-DC-PCF PBS designed in this paper is 55.3 μm, with an operational bandwidth of 725 nm, not only exhibiting a shorter beam splitting length but also a wider bandwidth. Gold and silver are both commonly used materials capable of inducing SPR effects to enhance the coupling strength of x-pol and y-pol polarized light. Generally, silver is more prone to inducing SPR effects due to its higher electrical conductivity and lower electron scattering losses. This implies that silver more effectively supports surface plasmon oscillations, making SPR effects more likely to occur on silver surfaces. Furthermore, silver is more cost-effective, highlighting the performance advantages of HS-DC-PCF PBS, which not only demonstrate excellent performance in terms of beam splitting length and bandwidth but also offer higher cost-effectiveness.

4. Conclusions

In summary, this paper presents a novel ultra-short and ultra-wideband HS-DC-PCF PBS. The polarization and coupling characteristics of the HS-DC-PCF PBS were analyzed using the finite volume finite element method. Leveraging the SPR effect of silver metal, two silver wires were introduced into the hexagonal lattice to enhance the performance of the beam splitter. With optimized structural parameters, the HS-DC-PCF PBS achieved a minimum splitting length of only 55.3 μm and a maximum ER of 74.56 dB. Its operational bandwidth spans 725 nm (1.14 μm–1.865 μm), covering the O + E + S + C + L + U communication bands entirely. Furthermore, the designed HS-DC-PCF PBS exhibits excellent manufacturing tolerance and anti-interference capabilities, along with a favorable cost-effectiveness ratio, marking it as a prominent achievement in the field of PCF PBS research.

Connecting such a short PCF PBS in a practical optical fiber communication link presents a challenging technical issue. Traditional connection methods typically involve the use of standard fiber optic connectors, which usually employ an insertion style where the fiber end is inserted into the connector ferrule and secured by mechanical clamping or adhesive bonding. Due to the longer lengths of these connectors and relatively fixed insertion depths, connecting very short optical components, such as the 55.3 μm HS-DC-PCF PBS designed in this study, may lead to higher insertion losses. Methods to address this issue include the use of specially designed miniature fiber optic connectors with shorter lengths and more precise alignment mechanisms to ensure stable connections and minimal optical losses. Additionally, employing high-precision fiber fusion techniques is also an effective option, allowing for micrometer-level control of fiber end-face alignment to guarantee connection stability and performance. During installation, precise positioning tools and techniques are crucial to ensure accurate alignment between the fiber end-faces and the input and output ports of the polarization beam splitter. Subsequently, rigorous insertion loss testing and performance evaluation are necessary post-connection to verify stability and compliance with the expected performance requirements. These measures collectively ensure the successful connection and efficient operation of HS-DC-PCF PBS within practical optical fiber communication systems [32,33,34,35,36].

Moreover, in optical communication systems, the HS-DC-PCF PBS holds significant practical applications and future impacts. Firstly, it can be utilized for the polarization state separation and control of optical signals, thereby furnishing optical communication systems with efficient signal processing capabilities. Secondly, owing to its ultra-short and ultra-wideband characteristics, the designed HS-DC-PCF PBS is suitable for handling high-speed data transmission applications, such as data center interconnects and high-speed network communications. Additionally, its superior manufacturing tolerance and anti-interference capabilities position it as a stable and reliable optical device, promising widespread applications in industrial control, medical imaging, laser radar, and other domains. With the continual advancement and expanding application scope of all-optical communication technologies, the HS-DC-PCF PBS is poised to emerge as a key constituent in future optical communication systems, propelling the advancement of optical communication technology and fostering the development of the information society.