A Novel Ultra-Broadband Polarization Filter Based on a Microstructured Optical Fiber with a Gold-Coated Air Hole

In this paper, a pentagonal microstructured optical fiber polarization filter by utilizing a surface plasmon resonance effect is proposed. The characteristics of the mode-coupling and filtering of the filter are studied by making use of the full-vector finite element method. The performance of the filter is greatly affected by the structure parameters. The losses of Y and X polarization of the fiber core are 665.97 and 0.17 dB/cm at 1.55 μm, respectively, and the loss ratio is 3917.47. This shows that the filter has a greater loss ratio. Moreover, both the extinction ratio and tolerance are also researched, which shows that the proposed filter has a wider filtering bandwidth and better fabrication tolerance. The designed filter has an important role in wavelength-division multiplexing (WDM) and coherent optical fiber communication systems.


Introduction
The porous structure of the microstructured optical fiber (MOF) provides convenience for the filling of functional materials, such as liquid crystal [1,2], liquid [3], magnetic fluids [4,5], semiconductor [6], polymer [7,8], and metal [9,10]. In recent years, MOF devices based on material filling, especially metal-filled or coated, which are performed selectively in the hole of a MOF, have become a hot issue of study. When the light travels through the metal-filled or coated MOF and the frequency of the photon bound to the metal surface and the free electron on the metal surface matches, the energy of the electromagnetic field is converted to the vibrational energy of the free electron. The energy on the metal surface will be increased; that is, the surface plasmon resonance (SPR) effect takes place [11]. The MOFs based on SPR play an important role in sensors [12], splitters [13], and polarization filters [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], etc. Polarization effects play a key role in a wide range of polarization-sensitive optical fiber systems. Polarization filters can realize only one polarization light transmission, which can be used in resonant fiber-optic gyroscopes to reduce the effects of various optical noises. Moreover, due to the single polarization transmission, the single polarization filter has become a trend to use as a polarization multiplexer in wavelength-division multiplexing (WDM), a polarization switch in Figure 1 displays the structure of the microstructured optical fiber (MOF) polarization filter. The cladding is arranged in pentagonal structure with four layer air holes. Λ = 2 µm is the distance between two adjacent holes. The hole with d 1 is on the left and right side of the core. The two holes with d 2 are under the core. The hole with d 3 is coated with gold, and the thickness of the gold film is denoted by t. The other holes are the same with d = 1.2 µm.

Structure of MOF Filter
Micromachines 2020, 11, x FOR PEER REVIEW 3 of 11 Figure 1 displays the structure of the microstructured optical fiber (MOF) polarization filter. The cladding is arranged in pentagonal structure with four layer air holes. Ʌ = 2 μm is the distance between two adjacent holes. The hole with d1 is on the left and right side of the core. The two holes with d2 are under the core. The hole with d3 is coated with gold, and the thickness of the gold film is denoted by t. The other holes are the same with d = 1.2 μm. In the process of numerical simulation, the silica is used as a substrate material, and its dispersion is expressed by the Sellmeier equation [31]. According to the current reports relating to the MOF filters based on SPR, generally, gold, silver, copper, and aluminum are widely used as the plasmonic material. Gold is chemically stable, and it also shows a larger resonance peak. Therefore, gold is the most commonly used as an excitation plasmonic material. The dielectric constant of gold is described by the Drude-Lorentz model [32], and the refractive index of air is 1. Set the outer layer of the MOF to a perfectly matched layer and scattering boundary condition, which can absorb radiation energy and reduce the reflection energy.

Structure of MOF Filter
The confinement loss (CL) of the fiber is described as follows [33]: Here, Im(neff) and λ is the imaginary part of effective refractive index (neff) of the fiber core and the light wavelength, respectively. The unit of CL and λ is dB/cm and μm. The size and range of the loss can reflect the performance of the filter to some extent.
The normalized output power (Pout(x, y)) of X and Y polarization is calculated as follows [34]: Here, Pin(x, y) is the input power and is normalized to 1; L is fiber length.
The performance of the filter is measured by utilizing the ER, and it can be calculated by the ratio of X polarization output power to Y. The calculation expression of ER is as follows [35]:  In the process of numerical simulation, the silica is used as a substrate material, and its dispersion is expressed by the Sellmeier equation [31]. According to the current reports relating to the MOF filters based on SPR, generally, gold, silver, copper, and aluminum are widely used as the plasmonic material. Gold is chemically stable, and it also shows a larger resonance peak. Therefore, gold is the most commonly used as an excitation plasmonic material. The dielectric constant of gold is described by the Drude-Lorentz model [32], and the refractive index of air is 1. Set the outer layer of the MOF to a perfectly matched layer and scattering boundary condition, which can absorb radiation energy and reduce the reflection energy.
The confinement loss (CL) of the fiber is described as follows [33]: Here, Im(n eff ) and λ is the imaginary part of effective refractive index (n eff ) of the fiber core and the light wavelength, respectively. The unit of CL and λ is dB/cm and µm. The size and range of the loss can reflect the performance of the filter to some extent.
The normalized output power (P out (x, y)) of X and Y polarization is calculated as follows [34]: Here, P in (x, y) is the input power and is normalized to 1; L is fiber length. The performance of the filter is measured by utilizing the ER, and it can be calculated by the ratio of X polarization output power to Y. The calculation expression of ER is as follows [35]:

Dispersion Relation
The structural parameters are optimized by genetic algorithm, and the optimal parameters of microstructured optical fiber (MOF) filter are obtained with d 1 = 1.7 µm, d 2 = 1.6 µm, d 3 = 1.75 µm, and t = 31.3 nm. Figure 2 displays the relationship between the loss (left Y axis) and Re(n eff ) (right Y axis) of X and Y polarization of the core. From Figure 2, the Re(n eff ) decreases with increasing wavelength; however, the Y polarization Re(n eff ) curve of the core has an inflection point around 1.55 µm. Meanwhile, the loss of Y polarization increases and then decreases with the increase of wavelength. The maximum occurs at 1.55 µm, and the value is 665.97 dB/cm, which also indicates that the core and surface plasma polarization (SPP) mode is coupled in Y polarization. For X polarization, the change of the loss value is not obvious with increasing wavelength, and the loss is only 0.17 dB/cm at 1.55 µm. This also shows that there is no obvious coupling between the core and SPP mode. Besides, the loss ratio is 3917.47, which also indicates that the single polarization MOF filter of 1.55 µm wavelength is implemented. The light in Y polarization is consumed due to high loss, and only the light in X polarization travels through the fiber core.

Dispersion Relation
The structural parameters are optimized by genetic algorithm, and the optimal parameters of microstructured optical fiber (MOF) filter are obtained with d1 = 1.7 μm, d2 = 1.6 μm, d3 = 1.75 μm, and t = 31.3 nm. Figure 2 displays the relationship between the loss (left Y axis) and Re(neff) (right Y axis) of X and Y polarization of the core. From Figure 2, the Re(neff) decreases with increasing wavelength; however, the Y polarization Re(neff) curve of the core has an inflection point around 1.55 μm. Meanwhile, the loss of Y polarization increases and then decreases with the increase of wavelength. The maximum occurs at 1.55 μm, and the value is 665.97 dB/cm, which also indicates that the core and surface plasma polarization (SPP) mode is coupled in Y polarization. For X polarization, the change of the loss value is not obvious with increasing wavelength, and the loss is only 0.17 dB/cm at 1.55 μm. This also shows that there is no obvious coupling between the core and SPP mode. Besides, the loss ratio is 3917.47, which also indicates that the single polarization MOF filter of 1.55 μm wavelength is implemented. The light in Y polarization is consumed due to high loss, and only the light in X polarization travels through the fiber core.  Figure 3a displays the change of Re(neff) of Y polarization of the core and second SPP mode. The illustration shows the electric field distribution of the core and second SPP mode at different wavelengths. From Figure 3a, at the short wavelength, the field of the core is limited to the core, and that of second SPP is confined to the surface of the gold film. The mode field of the core begins to transfer to the surface of the gold film with increasing wavelength. At the inflection point of the curve-in other words, at 1.55 μm-the core and second SPP mode have the same mode field strength, which is referred to as the resonance wavelength. The energy returns to the core and the surface of the gold film at the long wavelength. Figure 3b shows the losses of Y polarization of the core and second SPP mode. From Figure 3b, the losses of the core and second SPP mode at 1.55 μm are equal when the condition of phase-matching is met, which indicates that the complete coupling has occurred [24].  Figure 3a displays the change of Re(n eff ) of Y polarization of the core and second SPP mode. The illustration shows the electric field distribution of the core and second SPP mode at different wavelengths. From Figure 3a, at the short wavelength, the field of the core is limited to the core, and that of second SPP is confined to the surface of the gold film. The mode field of the core begins to transfer to the surface of the gold film with increasing wavelength. At the inflection point of the curve-in other words, at 1.55 µm-the core and second SPP mode have the same mode field strength, which is referred to as the resonance wavelength. The energy returns to the core and the surface of the gold film at the long wavelength. Figure 3b shows the losses of Y polarization of the core and second SPP mode. From Figure 3b, the losses of the core and second SPP mode at 1.55 µm are equal when the condition of phase-matching is met, which indicates that the complete coupling has occurred [24].  Figure 4 displays the loss of the core varies with d1 = 1.2, 1.4, 1.6, 1.8 μm, d2 = 1.6 μm, d3 = 1.75 μm, and t = 31.3 nm. As d1 increases, the resonance wavelength moves towards the longer wavelength, which can be seen from Figure 4. That is why the Re(neff) of the core decreases, and that of second SPP is basically unchanged, which causes the phase matching point to red-shift. The resonance intensity increases and then decreases when d1 increases. The Re(neff) of the core is close to second SPP with increasing d1, which makes the coupling enhance and more energy of the core be transferred to second SPP. That causes the resonance intensity to increase. However, the further increase of d1 will cause the core to struggle to limit the light, which will weaken the coupling and make the resonance intensity reduce.   Figure 5, the resonance wavelength moves towards the shorter wavelength as d2 increases. The structures around the core and gold film are changed with increasing d2, which causes the Re(neff) of both the core and second SPP to change. The Re(neff) of second SPP is greatly reduced, but the variation of the Re(neff) of the core is very small, which causes the phase matching point to blue-shift. The resonance intensity augments and then reduces as d2 increases. That is why increasing d2 causes the area of the silica bridge between the core and gold film to decrease, which will weaken the coupling.  As d 1 increases, the resonance wavelength moves towards the longer wavelength, which can be seen from Figure 4. That is why the Re(n eff ) of the core decreases, and that of second SPP is basically unchanged, which causes the phase matching point to red-shift. The resonance intensity increases and then decreases when d 1 increases. The Re(n eff ) of the core is close to second SPP with increasing d 1 , which makes the coupling enhance and more energy of the core be transferred to second SPP. That causes the resonance intensity to increase. However, the further increase of d 1 will cause the core to struggle to limit the light, which will weaken the coupling and make the resonance intensity reduce.  Figure 4 displays the loss of the core varies with d1 = 1.2, 1.4, 1.6, 1.8 μm, d2 = 1.6 μm, d3 = 1.75 μm, and t = 31.3 nm. As d1 increases, the resonance wavelength moves towards the longer wavelength, which can be seen from Figure 4. That is why the Re(neff) of the core decreases, and that of second SPP is basically unchanged, which causes the phase matching point to red-shift. The resonance intensity increases and then decreases when d1 increases. The Re(neff) of the core is close to second SPP with increasing d1, which makes the coupling enhance and more energy of the core be transferred to second SPP. That causes the resonance intensity to increase. However, the further increase of d1 will cause the core to struggle to limit the light, which will weaken the coupling and make the resonance intensity reduce.   Figure 5, the resonance wavelength moves towards the shorter wavelength as d2 increases. The structures around the core and gold film are changed with increasing d2, which causes the Re(neff) of both the core and second SPP to change. The Re(neff) of second SPP is greatly reduced, but the variation of the Re(neff) of the core is very small, which causes the phase matching point to blue-shift. The resonance intensity augments and then reduces as d2 increases. That is why increasing d2 causes the area of the silica bridge between the core and gold film to decrease, which will weaken the coupling.   Figure 5, the resonance wavelength moves towards the shorter wavelength as d 2 increases. The structures around the core and gold film are changed with increasing d 2 , which causes the Re(n eff ) of both the core and second SPP to change. The Re(n eff ) of second SPP is greatly reduced, but the variation of the Re(n eff ) of the core is very small, which causes the phase matching point to blue-shift. The resonance intensity augments and then reduces as d 2 increases. That is why increasing d 2 causes the area of the silica bridge between the core and gold film to decrease, which will weaken the coupling.  Figure 6 displays the loss of the core varied with d3 = 1.4, 1.5, 1.6, 1.7 μm, d1 = 1.7 μm, d2 = 1.6 μm, and t = 31.3 nm. The resonance wavelength moves towards the longer wavelength with increasing d3, which can be viewed from Figure 6. The structure around the core is not affected with the increase of d3, but that of the gold film changes. This also makes the Re(neff) of the core mode change very little; nevertheless, the change of the Re(neff) of second SPP mode is very big, which causes the phase matching point to red-shift. Besides, the distance between the core and gold film decreases with increasing d3. That will make the coupling strengthen and cause the resonance intensity to rise.   Figure 7, the resonance wavelength moves towards the shorter wavelength as t increases. Although increasing t does not affect the structure around the core, that of the gold film changes. The change of the Re(neff) of second SPP has a big reduction, but that of the core changes very little, which causes the phase matching point to blue-shift. Besides, the coupling weakens, so the resonance intensity decreases.   Figure 6. The structure around the core is not affected with the increase of d 3 , but that of the gold film changes. This also makes the Re(n eff ) of the core mode change very little; nevertheless, the change of the Re(n eff ) of second SPP mode is very big, which causes the phase matching point to red-shift. Besides, the distance between the core and gold film decreases with increasing d 3 . That will make the coupling strengthen and cause the resonance intensity to rise.  Figure 6 displays the loss of the core varied with d3 = 1.4, 1.5, 1.6, 1.7 μm, d1 = 1.7 μm, d2 = 1.6 μm, and t = 31.3 nm. The resonance wavelength moves towards the longer wavelength with increasing d3, which can be viewed from Figure 6. The structure around the core is not affected with the increase of d3, but that of the gold film changes. This also makes the Re(neff) of the core mode change very little; nevertheless, the change of the Re(neff) of second SPP mode is very big, which causes the phase matching point to red-shift. Besides, the distance between the core and gold film decreases with increasing d3. That will make the coupling strengthen and cause the resonance intensity to rise.   Figure 7, the resonance wavelength moves towards the shorter wavelength as t increases. Although increasing t does not affect the structure around the core, that of the gold film changes. The change of the Re(neff) of second SPP has a big reduction, but that of the core changes very little, which causes the phase matching point to blue-shift. Besides, the coupling weakens, so the resonance intensity decreases.   Figure 7, the resonance wavelength moves towards the shorter wavelength as t increases. Although increasing t does not affect the structure around the core, that of the gold film changes. The change of the Re(n eff ) of second SPP has a big reduction, but that of the core changes very little, which causes the phase matching point to blue-shift. Besides, the coupling weakens, so the resonance intensity decreases.  Both the ER and the bandwidth with ER less than −20 dB also increase gradually as L increases, which can be seen from Figure 8. When L is 1, 2, 3, and 4 mm, respectively, the corresponding ER is −66.58 dB, −133.16 dB, −199.74 dB, and −266.32 dB. When L is 1 mm, the ER less than −20 dB is the wavelength range from 1.49 to 1.63 μm, and the bandwidth is up to 140 nm. When L increases to 4 mm, the realized filtering wavelength range is from 1.40 μm to a longer wavelength, which shows that the designed MOF filter achieves broadband filtering.  Table 1 displays the comparison results of the designed filter with those previously reported. The high loss ratio and the wide filtering bandwidth are desired parameters in wavelength-division multiplexing (WDM) and coherent optical fiber communication systems. From Table 1, when the fiber length is 4 mm, the loss ratio and filtering bandwidth of the designed filter is 3917.47 and more than 900 nm, respectively. That indicates that the proposed microstructured optical fiber (MOF) filter has a larger loss ratio and wider filtering bandwidth, which is superior to others.  Both the ER and the bandwidth with ER less than −20 dB also increase gradually as L increases, which can be seen from Figure 8. When L is 1, 2, 3, and 4 mm, respectively, the corresponding ER is −66.58 dB, −133.16 dB, −199.74 dB, and −266.32 dB. When L is 1 mm, the ER less than −20 dB is the wavelength range from 1.49 to 1.63 µm, and the bandwidth is up to 140 nm. When L increases to 4 mm, the realized filtering wavelength range is from 1.40 µm to a longer wavelength, which shows that the designed MOF filter achieves broadband filtering.  Figure 8 displays the ER varied with L = 1, 2, 3, 4 mm and the structure parameters d1 = 1.7 μm, d2 = 1.6 μm, d3 = 1.75 μm, and t = 31.3 nm. Both the ER and the bandwidth with ER less than −20 dB also increase gradually as L increases, which can be seen from Figure 8. When L is 1, 2, 3, and 4 mm, respectively, the corresponding ER is −66.58 dB, −133.16 dB, −199.74 dB, and −266.32 dB. When L is 1 mm, the ER less than −20 dB is the wavelength range from 1.49 to 1.63 μm, and the bandwidth is up to 140 nm. When L increases to 4 mm, the realized filtering wavelength range is from 1.40 μm to a longer wavelength, which shows that the designed MOF filter achieves broadband filtering.  Table 1 displays the comparison results of the designed filter with those previously reported. The high loss ratio and the wide filtering bandwidth are desired parameters in wavelength-division multiplexing (WDM) and coherent optical fiber communication systems. From Table 1, when the fiber length is 4 mm, the loss ratio and filtering bandwidth of the designed filter is 3917.47 and more than 900 nm, respectively. That indicates that the proposed microstructured optical fiber (MOF) filter has a larger loss ratio and wider filtering bandwidth, which is superior to others.  Table 1 displays the comparison results of the designed filter with those previously reported. The high loss ratio and the wide filtering bandwidth are desired parameters in wavelength-division multiplexing (WDM) and coherent optical fiber communication systems. From Table 1, when the fiber length is 4 mm, the loss ratio and filtering bandwidth of the designed filter is 3917.47 and more than 900 nm, respectively. That indicates that the proposed microstructured optical fiber (MOF) filter has a larger loss ratio and wider filtering bandwidth, which is superior to others.

Analysis of the Tolerance
The polarization microstructured optical fiber (MOF) filters generally can be made through two steps. Firstly, the designed pentagonal MOF is fabricated by ultrasonic punching [36]. The ultrasonic wave is used to make the required air holes in the silica glass rod to obtain the fiber preform. Then, the preform goes into the fiber drawing tower and pulls to make the pentagonal MOF under the conditions of the suitable pressure and temperature. Secondly, the gold film is plated into the specific air hole by wet chemical deposition or high pressure chemical vapor deposition method [37,38]. It is inevitable that the structure parameters of the fiber changed slightly during fiber drawing. Figure 9 and Table 2 display the ER varied with wavelength when d 1 , d 2 , d 3 , and t change ±1%. From Figure 9, the change of d 2 have a slight effect on the ER, while the changes of d 1 , d 3 , and t have little effect on the ER. The ER curves with ±1% deviations of the structural parameters d 1 , d 2 , d 3 , and t are almost overlapping. From Table 2, when d 1 , d 2 , d 3 , and t change ±1%, the minimum ER and bandwidth with ER less than −20 dB is −58.42 dB and 120 nm with the 100 µm fiber length, respectively. That indicates the proposed filter still has the large loss ratio and wide filtering bandwidth as the tiny deformation occurs, which illustrates that good filtering performance can also be realized. This shows that the MOF filter has good fabrication tolerance.

Analysis of the Tolerance
The polarization microstructured optical fiber (MOF) filters generally can be made through two steps. Firstly, the designed pentagonal MOF is fabricated by ultrasonic punching [36]. The ultrasonic wave is used to make the required air holes in the silica glass rod to obtain the fiber preform. Then, the preform goes into the fiber drawing tower and pulls to make the pentagonal MOF under the conditions of the suitable pressure and temperature. Secondly, the gold film is plated into the specific air hole by wet chemical deposition or high pressure chemical vapor deposition method [37,38]. It is inevitable that the structure parameters of the fiber changed slightly during fiber drawing. Figure 9 and Table 2 display the ER varied with wavelength when d1, d2, d3, and t change ±1%. From Figure 9, the change of d2 have a slight effect on the ER, while the changes of d1, d3, and t have little effect on the ER. The ER curves with ±1% deviations of the structural parameters d1, d2, d3, and t are almost overlapping. From Table 2, when d1, d2, d3, and t change ±1%, the minimum ER and bandwidth with ER less than −20 dB is −58.42 dB and 120 nm with the 100 μm fiber length, respectively. That indicates the proposed filter still has the large loss ratio and wide filtering bandwidth as the tiny deformation occurs, which illustrates that good filtering performance can also be realized. This shows that the MOF filter has good fabrication tolerance.

Conclusions
A new broadband gold-coated pentagonal microstructured optical fiber (MOF) filter is put forward in this paper. The mode-coupling characteristic and the influence of d1, d2, d3, and t on the properties of the filter are researched by using FEM. The resonance wavelength and resonance intensity are greatly influenced by d1, d2, d3, and t. When d1 = 1.7 μm, d2 = 1.6 μm, d3 = 1.75 μm, and t = 31.3 nm, the core and second SPP are completely coupled in Y polarization direction. The large loss ratio is realized at 1.55 μm, and the value is 3917.47. When L is 4 mm, the ER is −266.32 dB, and in the wavelength range greater than 1.40 μm, the ER is less than −20 dB, which also shows that the designed filter has a wider filtering bandwidth. Besides, the designed filter has a better fabrication tolerance. Thus, the filter can be widely used in WDM and coherent optical fiber communication systems.
Author Contributions: C.W. wrote the manuscript, and all authors contributed to the completion of the manuscript. All authors have read and agreed to the published version of the manuscript.

Conclusions
A new broadband gold-coated pentagonal microstructured optical fiber (MOF) filter is put forward in this paper. The mode-coupling characteristic and the influence of d 1 , d 2 , d 3 , and t on the properties of the filter are researched by using FEM. The resonance wavelength and resonance intensity are greatly influenced by d 1 , d 2 , d 3 , and t. When d 1 = 1.7 µm, d 2 = 1.6 µm, d 3 = 1.75 µm, and t = 31.3 nm, the core and second SPP are completely coupled in Y polarization direction. The large loss ratio is realized at 1.55 µm, and the value is 3917.47. When L is 4 mm, the ER is −266.32 dB, and in the wavelength range greater than 1.40 µm, the ER is less than −20 dB, which also shows that the designed filter has a wider filtering bandwidth. Besides, the designed filter has a better fabrication tolerance. Thus, the filter can be widely used in WDM and coherent optical fiber communication systems.