Design and Numerical Analysis of a Single-Polarization Filter Based on PCF with Plasmonic Layers of Gold and Indium Tin Oxide

This paper presents a single-polarization ﬁlter based on PCF with plasmonic layers of gold and indium tin oxide (ITO). The plasmonic materials are metallic gold and ITO coated on the inner walls of two extra-large vertically arranged air holes. The resonance eﬀect is triggered by guided modes propagating through the silica core and coupling to the coating areas. The ﬁnite element method is used to analyze the properties of the ﬁlter for the two fundamental orthogonal polarizations. A ﬁltering eﬀect is achieved in the communication window by optimizing the structural factors as well as gold ﬁlm and ITO deposition thicknesses. When the ﬁlter is 1mm long, the obtained ﬁltering eﬀect is 1319.689dB/cm for the y-polarization and 31.881dB/cm for the x-polarization, thus eﬃciently attenuating the y-component at a communication window of 1.15 μ m. With a ﬁltering bandwidth of 602 nm, the proposed ﬁlter shows superior characteristics compared with previously reported results. Applications of the proposed plasmonic PCF-based ﬁlter can be found in polarization-maintaining and polarization-suppressing systems for optical sensing and broadband transmission.


Introduction
Photonic crystal fibers (PCFs) have gained extensive attention in a variety of sectors in recent decades. PCFs are new forms of optical fibers in which arbitrary air hole shapes such as longitudinal [1], spiral [2], and elliptical [3] exist throughout the fiber. Several functional devices based on PCFs have been developed, including sensors [4], rotators [5], lasers [1], amplifiers [6], and polarization filters [7]. Polarization filters, in particular, are essential components in high-speed optoelectronic and communication infrastructure. ese polarization filters are optical devices that discriminate by suppressing incident light based on polarization features and are commonly used to provide effective polarization state management [1,2]. Efficient polarization filters are easily achieved on PCF platforms due to the tunability of their structural parameters, in addition to their small and compact size, as well as their insusceptibility to electromagnetic influence [8].
Due to their high sensitivity [9], partially or fully metalized PCFs have advanced rapidly in recent decades [10]. ese can be made by infiltrating metal wires into the PCF air holes or by covering all or some selected inner walls of the air holes with single or multiple metal coatings [11]. With this arrangement, surface plasmon polaritons (SPPs) can occur on the metalized surfaces when light waves encroach the boundaries between the metalized sections and their dielectric surroundings. When the propagation constant of a particular SPP order and a core-guided wave become equal, the energy of the core-guided mode is transported to the SPP, establishing the surface plasmon resonance (SPR) condition. In this case, there are noticeable peaks in the output loss spectrum.
Furthermore, due to the tunability of the structural parameters of PCFs, it is possible to obtain a tunable cross talk ratio and a broad wavelength working range. Chen et al. developed a polarization filter based on liquid crystal penetrated PCFs with a gold wire. At 1550 nm, the mode loss was 446 dB/cm for the y-polarization and 0.8 dB/cm for the x-polarization [12]. Zhao et al. designed a type of goldcoated PCF filter. At 1550 nm, the loss in the y-polarization was 906.9 dB/cm, which was much larger than the x-polarization of [13]. A polarization filter based on high-birefringence PCF with gold nanowires was constructed and numerically investigated by Du  ere were six elliptical air holes and the cladding consisted of a solid core bounded by a three-layer regular hexagon cluster of circular air holes. Notably, the confinement loss of the y-polarized mode reached 442 dB/cm in the 1550 nm communication band, whereas the loss of the x-polarized mode was only 0.0316 dB/cm (Table 1).
Based on the preceding, it is clear that device performance enhancements such as competitive mode loss levels, crosstalk benchmarks, and filtering bandwidth are necessary. A single-polarization PCF filter is proposed and numerically evaluated in this paper. Within the walls of two extra-large, vertically arranged air holes of a PCF, dual layers of metallic gold and indium tin oxide (ITO) are deposited. e finite element method (FEM) is used to evaluate the filtering capabilities of the PCF filter. To achieve an optimal filtering performance, the influence of model parameters, GOLD, and ITO coating thickness are thoroughly investigated. e crosstalk performance and filtering bandwidth of the filter are also investigated.

Structural Design and Fundamental Theories
e sectional view of the PCF filter is presented in Figure 1(a). A three-dimensional view and the finite element mesh of the proposed filter are also shown in Figures 1(b) and 1(c), respectively. e structure of the filter consists of fractal layers of air holes organized into self-repeating patterns in vertical and horizontal transitions, respectively. e lattice pitch is designated as Λ and initially set at 1.60 μm. e diameters of the extra-large vertically disposed air holes are represented by d 1 with an initial value of 1.8 μm.
Other air holes, including the elliptical ones, denoted as d 2 , d 3 , d 4, and d 5 , d x , and d y are initially set to 0.6 μm, 1.6 μm, 1.0 μm, 0.5 μm, 0.3 μm, and 0.6 μm, respectively. e proposed structure is inherently birefringent due to the different air hole sizes surrounding the core area. e placement of the two extra-large horizontal air holes makes the coating process of ITO and gold films on the inner walls more convenient. e ITO layers are represented by blue rings, while the gold layers are represented by yellow rings with thicknesses denoted by t ITO and t GOLD , respectively. Initially, t ITO � 10 nm and t GOLD � 30 nm. e proposed can be actualized using current fabrication technologies such as stacking [23], extrusion [24], sol-gel casting [24], and drilling [25]. Small interhole distances can be maintained using high-precision ultrasonic drilling technology [25]. e preform can be drawn into fibers at the drawing tower [7]. e air hole sizes are controlled by manipulating the drawing speed and temperature [15]. Lastly, the plasmonic layers can be coated on the inner walls of the air holes by chemical vapor deposition [10] or sputtering technique [26]. e finite element method (FEM) in COMSOL ® Multiphysics was used to investigate the performance characteristics of the proposed filter. A perfectly matched layer (PML) [27] was applied to demarcate the computational area and to prevent back reflections of scattered waves. e working wavelength range in this investigation is 1.0 μm-1.6 μm.
e computational area was meshed into 10,770 elements. e mesh quality statistics include 33096 domain elements, 127 vertex elements, 2761 edge elements, and a minimum element quality of 0.3952. e refractive index of air was set at n air � 1. e host material is silica, and its dispersion relation follows the Sellmeier equation as follows [28]: where n and λ are the refractive index of silica and the wavelength of light, respectively. e material dispersion of gold was calculated by the Drude-Lorentz model [29].
where ε ∞ is the permittivity at infinite frequency, ε is a weighting factor, ω is the angular frequency of the interacting light, ω D and c D are the plasma frequency and damping frequency, respectively, and Ω L and Γ L are the frequency and the spectral width of the Lorentz oscillator, respectively. Here, ε ∞ � 5.9673 is the permittivity the high frequency, Δε � 1.09, ω D /2π � 2113.6 THZ, and cD/2π � 15.92 THZ. Ω L and Γ L are the frequency and the spectral width of the Lorentz oscillator, respectively, Ω L /2π � 650.07 THZ, and Γ L /2π � 104.86 THZ. e permittivity of ITO was computed as follows [30]: where ε ∞ is the intraband dielectric constant for the infinite value of frequency, λ c � 11.21076 × 10 6 � m is the collision wavelength for ITO, and λ c � 5.6497 × 10 7 m is the plasma wavelength for ITO. e mode confinement loss is a key benchmark for characterizing modal characteristics of filters. It can be expressed as follows [31,32]: where α loss (λ, n eff ) stands for confinement loss, λ specifies the operating wavelength, and Im(n eff ) represents the imaginary part of the complex refractive index of a guided mode. In the event of the phase of a core mode and that of an SPP mode matching, the core mode is usually strongly coupled to the SPP mode along the coated surface at a specific wavelength. Under this condition, the SPR effect is established. At the resonance wavelength, the mode confinement loss is the highest due energy transfer to the SPP modes. e structural parameters as well as the thicknesses of the gold and ITO films influence the resonance wavelength and loss.

Analysis of Numerical Results and Discussion
In Figure 2, the mode loss of the x-and y-polarizations as well as the dispersion relations between the y-polarization and the SPP modes is shown for d 1    polarized core modes is shown in Figure 2, with blue and red curves representing the loss spectrum of the x-and y-polarized core modes, respectively. e objective is to make the loss of desired polarized mode lower while increasing the loss of the undesired polarized mode. At the resonance wavelength of 1.15 μm, the confinement losses of the x-and y-polarizations are 31.83 and 1319.689 dB/cm, respectively. In effective polarization filtering, the mode loss of the wanted mode should be much smaller when compared with that of the unwanted polarized mode. e y-polarization loss is only examined because the x-polarization loss is negligible in comparison to that of the y-polarization mode. Consequently, the dispersion relations of the y-polarized and SPP modes are depicted in Figure 2(b) (blue and red solid lines are the real part of the effective refractive indices of the y-polarized core mode and that of the SPP mode, respectively). Due to the SPR effect, the effective refractive index of the y-polarized core mode mutates and intersects with that of the SPP mode at the resonance wavelength of 1.15 μm. It can be observed that the core mode for the y-polarization diminishes first before strengthening in the wavelength range of 1.10-1.20 μm. e energy of the y-polarized core mode is at its lowest at 1.15 μm. Because the energy of the y-polarized state was evacuated to the SPP mode, the SPP mode is modified leading to plasmonic resonance at 1.15 μm. All other y-polarization states are coupled to the SPP modes in the same way.

Impact of Different Diameters on the Filtering
Performance. Based on the cladding microstructure of the filter, the effective area of the core is controlled by the air hole sizes in the first ring. Consequently, the effects of d 2 and d 3 on the filtering characteristics are investigated to optimize the filtering performance. Figure 3 e intersection of the effective mode indices of each core-guided mode and its associated SPP mode is blue shifting with decreasing d 2 .
Here, the resonances are redshifting and occur at 1.11 μm, 1.12 μm, 1.15 μm, 1.18 μm, and 1.24 μm, respectively, with corresponding losses of 1306.622, 1362.054, 1319.214, 1233.735, and 993.499 dB/cm. It is clear from Figure 4(a) that larger mode losses correspond to higher values of d 3 and vice versa. is is because as d 3 becomes large, the effective core area reduces, leading to decrease in the effective mode index of the core mode. Also, when d 3 increases, the effective refractive index of silica decreases significantly due to broadening of air hole inclusions. When compared with d 2, d 3 has a substantial influence on the loss profiles and resonant peaks shifts. In Figure 4(b), the effective mode indices for various values of d 3 are presented when d 1 � 1.8 μm, t ITO � 15 nm, and t GOLD � 30 nm. e effective mode index of each guided mode traverses its associated SPP modes, causing the intersection to blueshift as d 3 decreases.

Impact of Various t GOLD on the Filter's Response.
e plasmonic layer thickness is an important factor in the polarization filter's performance. e impact of gold film thicknesses, t GOLD , is investigated herein. e loss spectrum for the filter is shown in Figure 5 with various t GOLD values in  International Journal of Optics e loss spectrum undergoes a blueshifts as t GOLD increases.
When the phase-matching wavelengths are 1.23 μm, 1.20 μm, 1.15 μm, 1.11 μm, and 1.09 μm, the corresponding losses are 1650.00 dB/cm, 1578.603 dB/cm, 1319.609 dB/cm, 1148.549 dB/ cm, and 1065.929 dB/cm, respectively. At lower t GOLD values, the corresponding losses are lower allowing effective interaction with the core-guided modes. However, higher t GOLD values produced higher losses due to plasmonic damping losses [33].

Impact of ITO ickness on the Filter's Response.
e influence of t ITO is investigated at this point. e corresponding loss spectra depicting the response of the     proposed filter are shown in Figure 6 in 5 nm steps. e peak shift is not affected by the loss t ITO thicknesses. e overall confinement loss increases for ITO thickness up to 30 nm and thereafter tends to decrease. e lowest losses of the ITO coating correspond the lowest thickness at t ITO � 10 nm. Conversely, higher t ITO thicknesses produces higher losses. Since higher t ITO values introduces higher damping losses [33], the filter performs better at higher t ITO.
As the confinement losses are significantly unchanged from t ITO � 10 nm to t ITO � 30 nm, we have confined our analysis to t ITO � 15 nm for further analysis. e reason was to avert the influence of t ITO on t GOLD.

Crosstalk Analysis of the Proposed Filter. Crosstalk (CT)
is another key characteristic that defines the effect of undesired polarized modes that can be used to assess the filter's transmission performance. As a function of fiber length, the CT can be stated as follows [13]: where α 1 , α 2 , and L denote the length of the filter and the loss of the x-and y-polarized core modes, respectively. Figure 7 describes the CT variants for the filter model with various values of L when t GOLD � 30 nm, t GOLD � 40 nm, and t GOLD � 50 nm, respectively. e length, L, of the filter was increased from 0.25 mm to 1 mm for the specified gold film

Conclusion
A single-polarization PCF filter based on PCF with layers of plasmonic gold and ITO has been proposed in this study.
e filter can easily be fabricated using current precision ultrasonic drilling technique. e FEM solver in COMSOL ® Multiphysics was used to analyze its characteristics. e proposed PCF filter is well suited for singlepolarization filtering since the loss of the x-polarized core mode is significantly lower than that of the y-polarized mode at a communication wavelength. At a communication window of 1.55 μm, an excellent filtering effect was obtained by selecting optimal structural parameters and plasmonic film thicknesses of gold and ITO. When the filter is 1 mm long, the obtained filtering effect is 1319.689 dB/cm for the y-polarization and 31.881 dB/cm for the x-polarization, thus efficiently attenuating the y-component at a communication window of 1.15 μm. With a filtering bandwidth of 602 nm, the proposed filter shows superior characteristics compared with previously reported results. e plasmonic PCF filter would be extensively useful in polarization state management and polarization suppression systems for optical sensing and broadband transmission.

Data Availability
e data set is available from the author upon request through email.

Conflicts of Interest
e authors declare that they have no conflicts of interest.  International Journal of Optics 7