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A novel gold-coated PCF polarization filter based on surface plasmon resonance
Optics and Laser Technology 126 (2020) 106125
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
A novel gold-coated PCF polarization filter based on surface plasmon resonance
T
⁎
Xin Yan , Ziheng Guo, Tonglei Cheng, Shuguang Li College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
H I GH L IG H T S
polarization filter we designed is novel and have a high performance. • The loss peak in Y-polarization is much higher than in X-polarization. • The except the innermost layer also influence the loss peak well. • Air-holes • The PCF filter can be widely used in system integration.
A R T I C LE I N FO
A B S T R A C T
Keywords: Photonic crystal fiber Surface plasmon resonance Polarization filter Metal filling Peak loss
In this study, a novel photonic crystal fiber (PCF) polarization filter has been designed. To resonate the surface plasma mode with the core mode, gold is selectively filled in the air holes. Using numerical simulations based on the finite element method, the influence of structural parameters on the filter is analyzed, and a set of rules for designing the PCF polarization filter is determined. The numerical simulation shows that the peak loss in the ypolarization direction at 1.31 μm reaches 1209.57 dB/cm, whereas the peak loss in the x-polarization is close to zero. Working at 1310 nm in the communication band, a new type of PCF is designed using these characteristics.
1. Introduction Photonic crystal fibers (PCFs) are receiving considerable attention from researchers owing to their unique properties compared to traditional fibers [1]. The physical structure of the PCF is primarily responsible for its properties. The PCF cladding comprises periodically arranged air holes is its unique structure. Because of this, PCF has properties such as endlessly single-mode guiding, low loss, high nonlinear effect, high birefringence, controllable dispersion, and large mode area [2–4]. Recently, researchers found that many properties of PCF can be combined with surface plasmon resonance (SPR) effect and applied in many optical devices. Usually, Surface Plasmon Wave (SPW) cannot be excited directly by the incident wave from the dielectric medium. Because the value of SPW wavenumber is higher than the tangent component of incident wave wavevector. Some special coupling method like prism, grating coupling should be used to reach the phase matching condition. However, PCF has a special adjustable structure. By changing the material and geometry, the optical properties of PCF can be changed to achieve the phase matching condition at a certain wavelength. When the coupling condition is satisfied, the
⁎
evanescent wave resonates with the SPW, thus causing most of the energy of the incident light to be absorbed. This effect is known as the SPR. [5,6]. With the continuous integration with SPR theory, PCF has a broader application prospect. Recently, the SPR effect has been widely used in sensors, polarization filters. Lee et al. [7] studied the coupling properties of SPR. The fiber optic devices were designed to have a length of 24.5 mm and an extinction ratio of 45 dB. With further research in SPR effect, many researchers studied new properties of PCF polarization based on SPR. In 2013, Li and Zhao [8] studied the dispersion and polarization properties of dual core and metal-filled PCFs. The paper proved that the polarization properties of output beams can be improved by introducing hybridization of SPR. In 2016, An et al. [9] designed a new high-birefringence PCF and explored the influence of structural parameters on the filter’s performance. In addition to designing the polarization filter, SPR effects have been used to design sensors [10,11] and polarization splitters [12,13]. In this study, the finite element method is used to calculate the performance of the PCF polarization filter based on the SPR effect. The filter simulation works in the single-mode regime and the computation was performed in the whole spectral domain. And the simulation analysis shows that
Corresponding author. E-mail address: [email protected] (X. Yan).
https://doi.org/10.1016/j.optlastec.2020.106125 Received 18 July 2019; Received in revised form 30 November 2019; Accepted 1 February 2020 0030-3992/ © 2020 Published by Elsevier Ltd.
Optics and Laser Technology 126 (2020) 106125
X. Yan, et al.
considered as the weighting factor; ω is the angular frequency of the guided light; ωD and γD are the plasma frequency and damping frequency, respectively; ωD /2π = 2113.6 THz, and γD /2π = 15.92 THz.ΩL and ΓL represent the frequency and spectral width of the Lorentz oscillator, respectively, ΩL /2π = 650.07 THz, and ΓL /2π = 104.86 THz. Furthermore, the mode’s confinement loss can be derived using the following formula [21]:
L = 8.686 ×
where λ is the propagation speed of light and Im(n eff ) is the imaginary part of the effective refractive index. For manufacturing a certain optical fiber, many processes are necessary such as modified chemicalvapor deposition process [16] and laser fabrication [17,18]. Using the above-mentioned methods, it is not difficult to fabricate such types of fibers. In the simulation works, the initial value of mode always can be found near the refractive index of cladding material. Change the initial value gradually, until the fundamental mode is found in the calculation. In this study, PML and scattering boundary condition are used to simulated infinite free space, waves could pass through domain boundary without reflection. When the phase matching condition was attained, the energy of core mode and SPP mode are coupled. The SPP dispersion property can be expressed by the following formula [22]:
Fig. 1. Cross-section of the polarizing filter having an air hole-coated gold layer.
ω Kspp = Re ⎡ ⎢c ⎣
changing the diameter of the air hole, the thickness of the metal layer, filling the air hole with water, change the position and intensity of the loss peak. In this work, it has been defined that the horizontal direction as the x polarization direction and the vertical direction as the y polarization direction in Fig. 1. The loss in the y-polarization direction is as high as 1209.57 dB/cm and that in the x-polarization direction is close to zero, it can be considered to use as a polarization filter.
ε1 ε2 ⎤ ε1 + ε2 ⎥ ⎦
where ε1 is the dielectric constant of metal, ε2 is the dielectric constant of dielectric and ω/c is the wave vector propagating in vacuum. Therefore, the loss of core mode increased at that point. Because of the highly asymmetric structure of the PCF fiber, the strength and position of loss peak are different in X and Y polarization. Consequently, the PCF achieved the effect of polarization filtering. The loss peak at 1310 nm in the communication window exceeds 1000 db/cm, which is difficult to achieve in simulation works. In this study, using the method of controlling variables, the size of air holes and the thickness of the gold layers were changed respectively to make the loss peak achieve its maximum and the wavelength of it reach to 1310 nm. The specific method will be introduced in Section 3. Except of this, the novelty of this paper reflected in the study of the structure of air-holes except the innermost layer.
2. Structure and operation principle Fig. 1 shows a cross-section of a polarizing filter having an air holecoated gold layer. The air holes are hexagonally arranged. Two oversized air holes are coated with gold (the thickness of the gold layer is 37 nm). It can be found that the diameter of the small air holes is d1 = 1.2 μm; The diameters of the air holes that are coated gold and filled with water is d2 = 5.6 μm; The diameters of the air holes on the left and right sides of the core d3 and d 4 are 0.96 and 1.6 μm respectively and the pitch of air holes in cladding are all 2 μm. The thickness of Perfectly Matching layer [19] is 2 μm with the inner diameter 10 μm and outer diameter 12 μm. The special structure of the air hole arrangement determines its unique physical properties. Air hole arrangement affects the physical properties of the fiber in the following ways:
3. Simulation results and analysis In Section 2, the simulation results of the PCF polarization filter were discussed. In this section, some structural parameters of the proposed PCF will changed. With the change of structural parameters, the position and strength of the loss peak changed which can be used to analyze the influence of structural parameters on the performance of the polarization filter.
1. Change the shape of the core 2. Enhanced birefringence effect 3. Increasing the area of SPR effect
3.1. The original structure of the PCF polarization filter
The structure of the innermost layer air holes like d1, d3 effect the shape of the core, and then influence the strength of SPR effect. The bigger air holes in the horizontal direction like d 4 mainly enhance birefringence effect and then change the position of loss peak. Two oversized air holes in vertically direction like d2 increase the area of SPR effect and then influence the strength of SPR effect. The background material of the PCF is SiO2 whose material dispersion can be derived using Sellmeier’s equation [14]. Similarly, gold’s material dispersion is derived using the Drude–Lorentz model [15]:
εm = ε∞ −
2π Im (neff ) × 10 4 λ
Fig. 2 shows the characteristic loss curves of the PCF polarization filter shown in Fig. 1. In this figure, the range of measuring wavelength is from 750 nm to 2000 nm and the modal dispersion characteristics for both polarizations computed with the presence of gold layers. COMSOL was used to calculate the effective refractive index of the certain structure of PCF. The real part of it can be used to characterize dispersion and the loss can be calculated by the imaginary part. The image shows that the loss peak of the y-polarization direction reached 1209.57 dB/cm near the communication band of 1310 nm; moreover, the loss at any position in the X-direction was close to 0. Furthermore, the first-order SPP mode of the y-polarization direction was coupled with the core mode at 1310 nm, which confirms that the SPR effect does occur. It’s very easy to find out in the picture that the effective index of
ωD2 Δε∙Ω2L − 2 ω (ω + jγD ) (ω − Ω2L) − jΓ ωL
where ε∞ = 5.9673 is the dielectric constant of gold; Δε = 1.09 can be 2
Optics and Laser Technology 126 (2020) 106125
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the core mode in Y polarization rapidly changed at around 1.31 μm. That is mainly because a complete coupling happens at phase-matching point which has been proved in the coupling theory [23]. The lower loss peak could also be found in the figure, core mode and the second order SPP mode are coupled here and SPR happened here as well. But according to the coupling theory, an incomplete coupling happened and thus the loss peak is much lower. The distributions of the fundamental mode in X and Y direction are shown in Figs. 3a and 3b, respectively. The figures clearly show the difference in coupling strength between X and Y polarization. Note that the properties of the polarization filter are influenced by multiple parameters, which mainly change the position and strength of the loss peak. Because of the low loss in X polarization, the relationship of the loss peak’s position in X and Y direction are discussed. It’s clearly that the performance of the polarization filter changed as per the structural parameters. 3.2. Changing the diameter of air-holes coated with gold
Fig. 2. Loss characteristic and the dispersion relations between core mode and SPP mode.
To confirm the effect of structural change on the performance of the polarizing filter, we first changed the size of the air hole coated with gold. The performance of the filter which had a super-large hole diameter of d2 = 5.6 μm was compared with other filters, and the diameter of air hole was changed from 5.4 to 5.8 μm. The results of the comparison are shown in Fig. 4. With increase in the diameter of the air hole, the loss peak value of the filter was blue-shifted. However, at 5.6 μm, the loss peak value was the largest, which indicates that the strength of the confinement loss did not monotonically change with increase in the diameter of gold-coated air holes. Thus, the position of the loss peak could be adjusted by controlling the size of the air holes, which have a gold-coated layer. But, there is no definite rule for the influence of the strength of the loss peak. 3.3. Changing the thickness of gold layers The change of the loss peak when the thickness of the gold film is different is also within the range of our calculation. The thicknesses of the gold films were 32, 37, and 42 nm, and the rest of the conditions remained unchanged. Fig. 5 shows that, as the thickness of the gold film increased the loss peak value gradually blue-shifted and the strength of the loss peak decreased. The thickness of the gold layer has a great relationship with the polarization filter’s performance. Fig. 5 also show that thinner gold layers result in more pronounced loss peaks due to a stronger SPR coupling, as it has been previously reported [24,25]. Therefore, changing the thickness of gold layer can make the loss peak as high as possible at the position of communication window. Thus, changing the thickness of the gold layer is one of the best ways to
Fig. 3a. Coupling strength in X-polarization when phase-matching condition happened.
Fig. 3b. Coupling strength in Y-polarization when phase-matching condition happened. Fig. 4. Filter characteristic with different diameter of gold-coated air holes. 3
Optics and Laser Technology 126 (2020) 106125
X. Yan, et al.
Fig. 5. Filter characteristic with different thickness of gold layer.
improve the property of polarization filters.
Fig. 7a. The cross section of PCF with the air holes except innermost layers changed and the peak loss decreased.
3.4. Changing the innermost layer air hole structure 3.5. Changing the structure of air-holes except the innermost layer Changing the structure of the innermost layer air hole is one of the important functions of the adjustment filter. The size of the left and right holes of the innermost air hole was changed from d3 = 0.54 μm to 0.34 μm and 0.74 μm. Fig. 6 shows that the loss peak at 0.54 µm was the lowest, while the loss peaks were 1244.14 and 1380.88 dB/cm when the diameters were 0.34 and 0.74 µm respectively. However, at the wavelength of 1310 nm, the loss peak at a diameter of 0.54 µm was the highest, while the loss peaks were 733.89 and 955.85 dB/cm when the diameters were 0.34 and 0.74 µm, respectively. These results confirm that the structure of the innermost air hole has an effect on the size and location of the loss peak and that a small change can have a considerable impact. One of the primary reasons is that changing the structure of the innermost layer air holes will change the shape and size of the core, the distance between the core and the metal layer changes after that. The distance d3 change to 0.34 μm the core mode become closer to gold layer but if change to 0.74 µm the core mode far away from the gold layer. But no matter far away or approach to the metal layer, the loss peak blue shifted and reduced. The authors’ hypothesis is that the distance between core mode and metal layer has a limit value. When the distance meets the limit value and other conditions remain unchanged, the loss peak and the wavelength of it reach its maximum.
The most influential part of the performance of a PCF filter is the innermost air-hole structure of the PCF, the size of the air holes coated with the gold layer, and the thickness of the gold-coated layer. These factors can significantly change the structure of the core and increase the strength of the core coupling to the SPP mode. However, the outer air holes have little effect on the filter’s performance, and very few studies have examined this aspect. In this section, we will study the effect of the outer air holes except the gold coated and the innermost air-holes on the polarization filter’s performance. Figs. 7a and 7b show two cross-sections of the polarization filter that change the outer air holes. Although the cross-sectional structure seems to be irregular, according to Fig. 7c we can determine that the losses of the filters of structures Figs. 7a and 7b are reduced and increased compared to the filter that does not change the outer air holes. The loss peak of 7(a) is 1086.25 dB/cm, whereas the loss peak of 7(b) is 1319.11 dB/cm. However, the loss peak showed almost no blue shift or red shift,
Fig. 7b. The cross section of PCF with the air holes except innermost layers changed and the peak loss increased.
Fig. 6. Filter characteristic with the diameter of innermost air holes changed. 4
Optics and Laser Technology 126 (2020) 106125
X. Yan, et al.
Fig. 7c. The characteristic of filter with changing the structure of air holes that except innermost layer. Fig. 7e. The cross section of PCF with the second and third layer of air holes changed.
Fig. 8. Filter characteristic with filling water or not in gold coated air holes. Fig. 7d. The cross section of PCF with the second layer of air holes changed.
4. Crosstalk indicating that changing the size of the outer air holes is an effective way to change the peak value of the loss, which has a low impact on the peak position of the loss. Furthermore, the method of changing the outer air holes is not complicated. The strategy of air holes distribution are showed in Figs. 7d and 7e. Continuously changing the size of each air hole from the inner layer to the outer layer can certainly improve the strength of loss. Moreover, because of the symmetrical design of most PCF filters, it is unnecessary to change only one air hole at a time.
Crosstalk reflects the effect of one signal on another and is an important parameter for measuring the polarization filter operating at a particular wavelength. It determines the influence of unwanted polarization modes and thus can characterize the transmission performances. The optical bandwidth is used to analyze the polarization filter’s performance. The bandwidth required for the polarization filter is less than −20 or more than 20 dB. The formula for crosstalk is defined as follows [20]:
3.6. Without water in the gold coated air-holes
CT = 20lg{exp[(α2 − α1)L]}
Because the gold-coated air holes in this study are filled with water, it is a necessary step to compare the performance of the water-filled filter with the unfilled one while ensuring that the rest of conditions remained unchanged. Fig. 8 shows that the strength of the loss peak with water was only 30 dB/cm higher than the loss peak without water, filling water led to a red shift in the loss peak. Filling the air holes with water can help adjust the loss peak; however, it is not a good choice to change the strength of the confinement loss. It seems that water can improve the strength of SPR effect, but it produce very little effect.
where α1 and α2 are the confinement losses of the X and Y polarization directions, respectively, and L represents the fiber length. Fig. 9 shows the crosstalk of the filter designed in this study. As the fiber length increased from 150 to 300 μm, the peak at 1.31 μm increased from 157 to 314 dB, which is much higher than usual polarization filters. When the length of the optical fiber was 150, 200, 250, and 300 µm, the bandwidths of more than 20 dB were 250, 440, 490, and 570 nm, respectively. The simulation revealed that the PCF has a big error tolerance and the fiber can be used in making a polarization filter. 5
Optics and Laser Technology 126 (2020) 106125
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authors thank the national Young 1000 Talent Plan program of China. References [1] J.K. Ranka, R.S. Windeler, A.J. Stentz, Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm, Opt. Lett. 25 (1) (2000) 25–27. [2] T.A. Birks, J.C. Knight, P.S.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (13) (1997) 961–963. [3] K. Hansen, Dispersion flattened hybrid-core nonlinear photonic crystal fiber, Opt. Express 11 (13) (2003) 1503–1509. [4] P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, et al., Ultimate low loss of hollow-core photonic crystal fibers, Opt. Express 13 (1) (2005) 236–244. [5] M. Hautakorpi, M. Mattinen, H. Ludvigsen, Surface-plasmon-resonance sensor based on three-hole microstructured optical fiber, Opt. Express 16 (12) (2008) 8427–8432. [6] M.A. Schmidt, L.N. Prill Sempere, H.K. Tyagi, C.G. Poulton, P. St, J. Russell, Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires, Phys. Rev. B 77 (3) (2008) 033417. [7] H. Lee, M. Schmidt, H. Tyagi, L.P. Sempere, P.S.J. Russell, Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber, Appl. Phys. Lett. 93 (2008) 111102. [8] P. Li, J. Zhao, Polarization-dependent coupling in gold-filled dual-core photonic crystal fibers, Opt. Express 21 (2013) 5232–5238. [9] G. An, S. Li, X. Yan, Z. Yuan, X. Zhang, High-birefringence photonic crystal fiber polarization filter based on surface plasmon resonance, Appl. Opt. 55 (2016) 1262–1266. [10] Y. Chen, H. Ming, Review of surface plasmon resonance and localized surface plasmon resonance sensor, Photo. Sens. 2 (1) (2012) 37–49. [11] C. Zhou, Y. Zhang, L. Xia, D. Liu, Photonic crystal fiber sensor based on hybrid mechanisms: Plasmonic and directional resonance coupling, Opt. Commun. 285 (9) (2012) 2466–2471. [12] S. Zhang, X. Yu, Y. Zhang, P. Shum, Y. Zhang, L. Xia, D. Liu, Theoretical study of dual-core photonic crystal fibers with metal wire, IEEE Photon. J. 4 (4) (2012) 1178–1187. [13] J. Zi, S. Li, G. An, Z. Fan, Short-length polarization splitter based on dual-core photonic crystal fiber with hexagonal lattice, Opt. Commun. 363 (2016) 80–84. [14] H. Lee, M. Schmidt, H. Tyagi, L.P. Sempere, P.S.J. Russell, Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber, Appl. Phys. B 93 (11) (2008) 111102. [15] A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. de la Chapelle, Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method, Phys. Rev. B 71 (8) (2005) 085416. [16] W. Blanc, V. Mauroy, L. Nguyen, B. Shivakiran Bhaktha, P. Sebbah, B.P. Pal, B. Dussardier, Fabrication of rare earth-doped transparent glass ceramic optical fibers by modified chemical vapor deposition, J. Am. Ceram. Soc. 94 (2011) 2315–2318. [17] D. Hunger, C. Deutsch, R.J. Barbour, R.J. Warburton, J. Reichel, Laser micro-fabrication of concave, low-roughness features in silica, arXiv:1109.5047, 2011. [18] L. Xu, F.F. Luo, L.S. Tan, X.G. Luo, M.H. Hong, Hybrid plasmonic structures: design and fabrication by laser means, IEEE J. Sel. Top. Quant. Electron. 19 (2013) 4600309. [19] M. Koshiba, Y. Tsuji, Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems, IEEE J. Lightw. Technol. 18 (5) (2000) 737–743. [20] N. Florous, K. Saitoh, M. Koshiba, A novel approach for designing photonic crystal fiber splitters with polarization-independent propagation characteristics, Opt. Express 13 (19) (2005) 7365–7373. [21] T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, Confinement losses in microstructured optical fibers, Opt. Lett. 26 (2001) 1660–1662. [22] Anatoly V. Zayats, Igor I. Smolyaninov, Alexei A. Maradudin, Nano-optics of surface plasmon polaritons, Phys. Rep. 408 (3–4) (2005) 131–314. [23] Z. Zhang, Y. Shi, B. Bian, J. Lu, Dependence of leaky mode coupling on loss in photonic crystal fiber with hybrid cladding, Opt. Express 16 (2008) 1915–1922. [24] Yujun Wang, Shuguang Li, Hailiang Chen, Min Shi, Yingchao Liu, Ultra-wide bandwidth polarization filter based on gold-coated photonic crystal fiber around the wavelength of 1.55µm, Opt. Laser Technol. 106 (2018) 22–28. [25] Chao Liu, Liying Wang, Lin Yang, Famei Wang, Xu Chunhong, The single-polarization filter composed of gold-coated photonic crystal fiber, Phys. Lett. A 383 (25) (2019).
Fig. 9. Crosstalk of polarization filter on the operable wavelength with the optimal geometric structure.
5. Conclusion In this study, a novel PCF polarization filter is designed with selective gold coating of air holes that are filled with water. When the phase matching condition is satisfied, the SPP first-order mode and the core mode will be coupled. Note that the polarization filter has the following characteristics: a loss peak at 1310 nm, which is the communication window, and a loss peak value that is as high as 1209.57 dB/cm. Note that the loss in the X-polarization direction is close to zero compared with the high-loss Y-polarization direction. We also examined the properties of the air-hole structure of the PCF. Using numerical simulations, the thickness of the gold layer, the diameter of the air hole of the gold-coated layer, the size of the innermost air holes, the filling of water, and the size of the outer air-holes were obtained, and all of these factors influenced the polarization filter’s performance. Thus, by changing the structures, a better polarization filter can be designed. CRediT authorship contribution statement Xin Yan: Investigation. Ziheng Guo: Investigation. Tonglei Cheng: Investigation. Shuguang Li: Investigation. Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted Acknowledgement This research was funded by [National Natural Science Foundation of China] grant number [61775032] and [11604042], [Fundamental Research Funds for the Central Universities] grant number [N170405007] and [N160404009] and [111 project] grant number [B1009]. The
6
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
A novel gold-coated PCF polarization filter based on surface plasmon resonance
T
⁎
Xin Yan , Ziheng Guo, Tonglei Cheng, Shuguang Li College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
H I GH L IG H T S
polarization filter we designed is novel and have a high performance. • The loss peak in Y-polarization is much higher than in X-polarization. • The except the innermost layer also influence the loss peak well. • Air-holes • The PCF filter can be widely used in system integration.
A R T I C LE I N FO
A B S T R A C T
Keywords: Photonic crystal fiber Surface plasmon resonance Polarization filter Metal filling Peak loss
In this study, a novel photonic crystal fiber (PCF) polarization filter has been designed. To resonate the surface plasma mode with the core mode, gold is selectively filled in the air holes. Using numerical simulations based on the finite element method, the influence of structural parameters on the filter is analyzed, and a set of rules for designing the PCF polarization filter is determined. The numerical simulation shows that the peak loss in the ypolarization direction at 1.31 μm reaches 1209.57 dB/cm, whereas the peak loss in the x-polarization is close to zero. Working at 1310 nm in the communication band, a new type of PCF is designed using these characteristics.
1. Introduction Photonic crystal fibers (PCFs) are receiving considerable attention from researchers owing to their unique properties compared to traditional fibers [1]. The physical structure of the PCF is primarily responsible for its properties. The PCF cladding comprises periodically arranged air holes is its unique structure. Because of this, PCF has properties such as endlessly single-mode guiding, low loss, high nonlinear effect, high birefringence, controllable dispersion, and large mode area [2–4]. Recently, researchers found that many properties of PCF can be combined with surface plasmon resonance (SPR) effect and applied in many optical devices. Usually, Surface Plasmon Wave (SPW) cannot be excited directly by the incident wave from the dielectric medium. Because the value of SPW wavenumber is higher than the tangent component of incident wave wavevector. Some special coupling method like prism, grating coupling should be used to reach the phase matching condition. However, PCF has a special adjustable structure. By changing the material and geometry, the optical properties of PCF can be changed to achieve the phase matching condition at a certain wavelength. When the coupling condition is satisfied, the
⁎
evanescent wave resonates with the SPW, thus causing most of the energy of the incident light to be absorbed. This effect is known as the SPR. [5,6]. With the continuous integration with SPR theory, PCF has a broader application prospect. Recently, the SPR effect has been widely used in sensors, polarization filters. Lee et al. [7] studied the coupling properties of SPR. The fiber optic devices were designed to have a length of 24.5 mm and an extinction ratio of 45 dB. With further research in SPR effect, many researchers studied new properties of PCF polarization based on SPR. In 2013, Li and Zhao [8] studied the dispersion and polarization properties of dual core and metal-filled PCFs. The paper proved that the polarization properties of output beams can be improved by introducing hybridization of SPR. In 2016, An et al. [9] designed a new high-birefringence PCF and explored the influence of structural parameters on the filter’s performance. In addition to designing the polarization filter, SPR effects have been used to design sensors [10,11] and polarization splitters [12,13]. In this study, the finite element method is used to calculate the performance of the PCF polarization filter based on the SPR effect. The filter simulation works in the single-mode regime and the computation was performed in the whole spectral domain. And the simulation analysis shows that
Corresponding author. E-mail address: [email protected] (X. Yan).
https://doi.org/10.1016/j.optlastec.2020.106125 Received 18 July 2019; Received in revised form 30 November 2019; Accepted 1 February 2020 0030-3992/ © 2020 Published by Elsevier Ltd.
Optics and Laser Technology 126 (2020) 106125
X. Yan, et al.
considered as the weighting factor; ω is the angular frequency of the guided light; ωD and γD are the plasma frequency and damping frequency, respectively; ωD /2π = 2113.6 THz, and γD /2π = 15.92 THz.ΩL and ΓL represent the frequency and spectral width of the Lorentz oscillator, respectively, ΩL /2π = 650.07 THz, and ΓL /2π = 104.86 THz. Furthermore, the mode’s confinement loss can be derived using the following formula [21]:
L = 8.686 ×
where λ is the propagation speed of light and Im(n eff ) is the imaginary part of the effective refractive index. For manufacturing a certain optical fiber, many processes are necessary such as modified chemicalvapor deposition process [16] and laser fabrication [17,18]. Using the above-mentioned methods, it is not difficult to fabricate such types of fibers. In the simulation works, the initial value of mode always can be found near the refractive index of cladding material. Change the initial value gradually, until the fundamental mode is found in the calculation. In this study, PML and scattering boundary condition are used to simulated infinite free space, waves could pass through domain boundary without reflection. When the phase matching condition was attained, the energy of core mode and SPP mode are coupled. The SPP dispersion property can be expressed by the following formula [22]:
Fig. 1. Cross-section of the polarizing filter having an air hole-coated gold layer.
ω Kspp = Re ⎡ ⎢c ⎣
changing the diameter of the air hole, the thickness of the metal layer, filling the air hole with water, change the position and intensity of the loss peak. In this work, it has been defined that the horizontal direction as the x polarization direction and the vertical direction as the y polarization direction in Fig. 1. The loss in the y-polarization direction is as high as 1209.57 dB/cm and that in the x-polarization direction is close to zero, it can be considered to use as a polarization filter.
ε1 ε2 ⎤ ε1 + ε2 ⎥ ⎦
where ε1 is the dielectric constant of metal, ε2 is the dielectric constant of dielectric and ω/c is the wave vector propagating in vacuum. Therefore, the loss of core mode increased at that point. Because of the highly asymmetric structure of the PCF fiber, the strength and position of loss peak are different in X and Y polarization. Consequently, the PCF achieved the effect of polarization filtering. The loss peak at 1310 nm in the communication window exceeds 1000 db/cm, which is difficult to achieve in simulation works. In this study, using the method of controlling variables, the size of air holes and the thickness of the gold layers were changed respectively to make the loss peak achieve its maximum and the wavelength of it reach to 1310 nm. The specific method will be introduced in Section 3. Except of this, the novelty of this paper reflected in the study of the structure of air-holes except the innermost layer.
2. Structure and operation principle Fig. 1 shows a cross-section of a polarizing filter having an air holecoated gold layer. The air holes are hexagonally arranged. Two oversized air holes are coated with gold (the thickness of the gold layer is 37 nm). It can be found that the diameter of the small air holes is d1 = 1.2 μm; The diameters of the air holes that are coated gold and filled with water is d2 = 5.6 μm; The diameters of the air holes on the left and right sides of the core d3 and d 4 are 0.96 and 1.6 μm respectively and the pitch of air holes in cladding are all 2 μm. The thickness of Perfectly Matching layer [19] is 2 μm with the inner diameter 10 μm and outer diameter 12 μm. The special structure of the air hole arrangement determines its unique physical properties. Air hole arrangement affects the physical properties of the fiber in the following ways:
3. Simulation results and analysis In Section 2, the simulation results of the PCF polarization filter were discussed. In this section, some structural parameters of the proposed PCF will changed. With the change of structural parameters, the position and strength of the loss peak changed which can be used to analyze the influence of structural parameters on the performance of the polarization filter.
1. Change the shape of the core 2. Enhanced birefringence effect 3. Increasing the area of SPR effect
3.1. The original structure of the PCF polarization filter
The structure of the innermost layer air holes like d1, d3 effect the shape of the core, and then influence the strength of SPR effect. The bigger air holes in the horizontal direction like d 4 mainly enhance birefringence effect and then change the position of loss peak. Two oversized air holes in vertically direction like d2 increase the area of SPR effect and then influence the strength of SPR effect. The background material of the PCF is SiO2 whose material dispersion can be derived using Sellmeier’s equation [14]. Similarly, gold’s material dispersion is derived using the Drude–Lorentz model [15]:
εm = ε∞ −
2π Im (neff ) × 10 4 λ
Fig. 2 shows the characteristic loss curves of the PCF polarization filter shown in Fig. 1. In this figure, the range of measuring wavelength is from 750 nm to 2000 nm and the modal dispersion characteristics for both polarizations computed with the presence of gold layers. COMSOL was used to calculate the effective refractive index of the certain structure of PCF. The real part of it can be used to characterize dispersion and the loss can be calculated by the imaginary part. The image shows that the loss peak of the y-polarization direction reached 1209.57 dB/cm near the communication band of 1310 nm; moreover, the loss at any position in the X-direction was close to 0. Furthermore, the first-order SPP mode of the y-polarization direction was coupled with the core mode at 1310 nm, which confirms that the SPR effect does occur. It’s very easy to find out in the picture that the effective index of
ωD2 Δε∙Ω2L − 2 ω (ω + jγD ) (ω − Ω2L) − jΓ ωL
where ε∞ = 5.9673 is the dielectric constant of gold; Δε = 1.09 can be 2
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the core mode in Y polarization rapidly changed at around 1.31 μm. That is mainly because a complete coupling happens at phase-matching point which has been proved in the coupling theory [23]. The lower loss peak could also be found in the figure, core mode and the second order SPP mode are coupled here and SPR happened here as well. But according to the coupling theory, an incomplete coupling happened and thus the loss peak is much lower. The distributions of the fundamental mode in X and Y direction are shown in Figs. 3a and 3b, respectively. The figures clearly show the difference in coupling strength between X and Y polarization. Note that the properties of the polarization filter are influenced by multiple parameters, which mainly change the position and strength of the loss peak. Because of the low loss in X polarization, the relationship of the loss peak’s position in X and Y direction are discussed. It’s clearly that the performance of the polarization filter changed as per the structural parameters. 3.2. Changing the diameter of air-holes coated with gold
Fig. 2. Loss characteristic and the dispersion relations between core mode and SPP mode.
To confirm the effect of structural change on the performance of the polarizing filter, we first changed the size of the air hole coated with gold. The performance of the filter which had a super-large hole diameter of d2 = 5.6 μm was compared with other filters, and the diameter of air hole was changed from 5.4 to 5.8 μm. The results of the comparison are shown in Fig. 4. With increase in the diameter of the air hole, the loss peak value of the filter was blue-shifted. However, at 5.6 μm, the loss peak value was the largest, which indicates that the strength of the confinement loss did not monotonically change with increase in the diameter of gold-coated air holes. Thus, the position of the loss peak could be adjusted by controlling the size of the air holes, which have a gold-coated layer. But, there is no definite rule for the influence of the strength of the loss peak. 3.3. Changing the thickness of gold layers The change of the loss peak when the thickness of the gold film is different is also within the range of our calculation. The thicknesses of the gold films were 32, 37, and 42 nm, and the rest of the conditions remained unchanged. Fig. 5 shows that, as the thickness of the gold film increased the loss peak value gradually blue-shifted and the strength of the loss peak decreased. The thickness of the gold layer has a great relationship with the polarization filter’s performance. Fig. 5 also show that thinner gold layers result in more pronounced loss peaks due to a stronger SPR coupling, as it has been previously reported [24,25]. Therefore, changing the thickness of gold layer can make the loss peak as high as possible at the position of communication window. Thus, changing the thickness of the gold layer is one of the best ways to
Fig. 3a. Coupling strength in X-polarization when phase-matching condition happened.
Fig. 3b. Coupling strength in Y-polarization when phase-matching condition happened. Fig. 4. Filter characteristic with different diameter of gold-coated air holes. 3
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Fig. 5. Filter characteristic with different thickness of gold layer.
improve the property of polarization filters.
Fig. 7a. The cross section of PCF with the air holes except innermost layers changed and the peak loss decreased.
3.4. Changing the innermost layer air hole structure 3.5. Changing the structure of air-holes except the innermost layer Changing the structure of the innermost layer air hole is one of the important functions of the adjustment filter. The size of the left and right holes of the innermost air hole was changed from d3 = 0.54 μm to 0.34 μm and 0.74 μm. Fig. 6 shows that the loss peak at 0.54 µm was the lowest, while the loss peaks were 1244.14 and 1380.88 dB/cm when the diameters were 0.34 and 0.74 µm respectively. However, at the wavelength of 1310 nm, the loss peak at a diameter of 0.54 µm was the highest, while the loss peaks were 733.89 and 955.85 dB/cm when the diameters were 0.34 and 0.74 µm, respectively. These results confirm that the structure of the innermost air hole has an effect on the size and location of the loss peak and that a small change can have a considerable impact. One of the primary reasons is that changing the structure of the innermost layer air holes will change the shape and size of the core, the distance between the core and the metal layer changes after that. The distance d3 change to 0.34 μm the core mode become closer to gold layer but if change to 0.74 µm the core mode far away from the gold layer. But no matter far away or approach to the metal layer, the loss peak blue shifted and reduced. The authors’ hypothesis is that the distance between core mode and metal layer has a limit value. When the distance meets the limit value and other conditions remain unchanged, the loss peak and the wavelength of it reach its maximum.
The most influential part of the performance of a PCF filter is the innermost air-hole structure of the PCF, the size of the air holes coated with the gold layer, and the thickness of the gold-coated layer. These factors can significantly change the structure of the core and increase the strength of the core coupling to the SPP mode. However, the outer air holes have little effect on the filter’s performance, and very few studies have examined this aspect. In this section, we will study the effect of the outer air holes except the gold coated and the innermost air-holes on the polarization filter’s performance. Figs. 7a and 7b show two cross-sections of the polarization filter that change the outer air holes. Although the cross-sectional structure seems to be irregular, according to Fig. 7c we can determine that the losses of the filters of structures Figs. 7a and 7b are reduced and increased compared to the filter that does not change the outer air holes. The loss peak of 7(a) is 1086.25 dB/cm, whereas the loss peak of 7(b) is 1319.11 dB/cm. However, the loss peak showed almost no blue shift or red shift,
Fig. 7b. The cross section of PCF with the air holes except innermost layers changed and the peak loss increased.
Fig. 6. Filter characteristic with the diameter of innermost air holes changed. 4
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Fig. 7c. The characteristic of filter with changing the structure of air holes that except innermost layer. Fig. 7e. The cross section of PCF with the second and third layer of air holes changed.
Fig. 8. Filter characteristic with filling water or not in gold coated air holes. Fig. 7d. The cross section of PCF with the second layer of air holes changed.
4. Crosstalk indicating that changing the size of the outer air holes is an effective way to change the peak value of the loss, which has a low impact on the peak position of the loss. Furthermore, the method of changing the outer air holes is not complicated. The strategy of air holes distribution are showed in Figs. 7d and 7e. Continuously changing the size of each air hole from the inner layer to the outer layer can certainly improve the strength of loss. Moreover, because of the symmetrical design of most PCF filters, it is unnecessary to change only one air hole at a time.
Crosstalk reflects the effect of one signal on another and is an important parameter for measuring the polarization filter operating at a particular wavelength. It determines the influence of unwanted polarization modes and thus can characterize the transmission performances. The optical bandwidth is used to analyze the polarization filter’s performance. The bandwidth required for the polarization filter is less than −20 or more than 20 dB. The formula for crosstalk is defined as follows [20]:
3.6. Without water in the gold coated air-holes
CT = 20lg{exp[(α2 − α1)L]}
Because the gold-coated air holes in this study are filled with water, it is a necessary step to compare the performance of the water-filled filter with the unfilled one while ensuring that the rest of conditions remained unchanged. Fig. 8 shows that the strength of the loss peak with water was only 30 dB/cm higher than the loss peak without water, filling water led to a red shift in the loss peak. Filling the air holes with water can help adjust the loss peak; however, it is not a good choice to change the strength of the confinement loss. It seems that water can improve the strength of SPR effect, but it produce very little effect.
where α1 and α2 are the confinement losses of the X and Y polarization directions, respectively, and L represents the fiber length. Fig. 9 shows the crosstalk of the filter designed in this study. As the fiber length increased from 150 to 300 μm, the peak at 1.31 μm increased from 157 to 314 dB, which is much higher than usual polarization filters. When the length of the optical fiber was 150, 200, 250, and 300 µm, the bandwidths of more than 20 dB were 250, 440, 490, and 570 nm, respectively. The simulation revealed that the PCF has a big error tolerance and the fiber can be used in making a polarization filter. 5
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authors thank the national Young 1000 Talent Plan program of China. References [1] J.K. Ranka, R.S. Windeler, A.J. Stentz, Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm, Opt. Lett. 25 (1) (2000) 25–27. [2] T.A. Birks, J.C. Knight, P.S.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (13) (1997) 961–963. [3] K. Hansen, Dispersion flattened hybrid-core nonlinear photonic crystal fiber, Opt. Express 11 (13) (2003) 1503–1509. [4] P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, et al., Ultimate low loss of hollow-core photonic crystal fibers, Opt. Express 13 (1) (2005) 236–244. [5] M. Hautakorpi, M. Mattinen, H. Ludvigsen, Surface-plasmon-resonance sensor based on three-hole microstructured optical fiber, Opt. Express 16 (12) (2008) 8427–8432. [6] M.A. Schmidt, L.N. Prill Sempere, H.K. Tyagi, C.G. Poulton, P. St, J. Russell, Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires, Phys. Rev. B 77 (3) (2008) 033417. [7] H. Lee, M. Schmidt, H. Tyagi, L.P. Sempere, P.S.J. Russell, Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber, Appl. Phys. Lett. 93 (2008) 111102. [8] P. Li, J. Zhao, Polarization-dependent coupling in gold-filled dual-core photonic crystal fibers, Opt. Express 21 (2013) 5232–5238. [9] G. An, S. Li, X. Yan, Z. Yuan, X. Zhang, High-birefringence photonic crystal fiber polarization filter based on surface plasmon resonance, Appl. Opt. 55 (2016) 1262–1266. [10] Y. Chen, H. Ming, Review of surface plasmon resonance and localized surface plasmon resonance sensor, Photo. Sens. 2 (1) (2012) 37–49. [11] C. Zhou, Y. Zhang, L. Xia, D. Liu, Photonic crystal fiber sensor based on hybrid mechanisms: Plasmonic and directional resonance coupling, Opt. Commun. 285 (9) (2012) 2466–2471. [12] S. Zhang, X. Yu, Y. Zhang, P. Shum, Y. Zhang, L. Xia, D. Liu, Theoretical study of dual-core photonic crystal fibers with metal wire, IEEE Photon. J. 4 (4) (2012) 1178–1187. [13] J. Zi, S. Li, G. An, Z. Fan, Short-length polarization splitter based on dual-core photonic crystal fiber with hexagonal lattice, Opt. Commun. 363 (2016) 80–84. [14] H. Lee, M. Schmidt, H. Tyagi, L.P. Sempere, P.S.J. Russell, Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber, Appl. Phys. B 93 (11) (2008) 111102. [15] A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. de la Chapelle, Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method, Phys. Rev. B 71 (8) (2005) 085416. [16] W. Blanc, V. Mauroy, L. Nguyen, B. Shivakiran Bhaktha, P. Sebbah, B.P. Pal, B. Dussardier, Fabrication of rare earth-doped transparent glass ceramic optical fibers by modified chemical vapor deposition, J. Am. Ceram. Soc. 94 (2011) 2315–2318. [17] D. Hunger, C. Deutsch, R.J. Barbour, R.J. Warburton, J. Reichel, Laser micro-fabrication of concave, low-roughness features in silica, arXiv:1109.5047, 2011. [18] L. Xu, F.F. Luo, L.S. Tan, X.G. Luo, M.H. Hong, Hybrid plasmonic structures: design and fabrication by laser means, IEEE J. Sel. Top. Quant. Electron. 19 (2013) 4600309. [19] M. Koshiba, Y. Tsuji, Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems, IEEE J. Lightw. Technol. 18 (5) (2000) 737–743. [20] N. Florous, K. Saitoh, M. Koshiba, A novel approach for designing photonic crystal fiber splitters with polarization-independent propagation characteristics, Opt. Express 13 (19) (2005) 7365–7373. [21] T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, Confinement losses in microstructured optical fibers, Opt. Lett. 26 (2001) 1660–1662. [22] Anatoly V. Zayats, Igor I. Smolyaninov, Alexei A. Maradudin, Nano-optics of surface plasmon polaritons, Phys. Rep. 408 (3–4) (2005) 131–314. [23] Z. Zhang, Y. Shi, B. Bian, J. Lu, Dependence of leaky mode coupling on loss in photonic crystal fiber with hybrid cladding, Opt. Express 16 (2008) 1915–1922. [24] Yujun Wang, Shuguang Li, Hailiang Chen, Min Shi, Yingchao Liu, Ultra-wide bandwidth polarization filter based on gold-coated photonic crystal fiber around the wavelength of 1.55µm, Opt. Laser Technol. 106 (2018) 22–28. [25] Chao Liu, Liying Wang, Lin Yang, Famei Wang, Xu Chunhong, The single-polarization filter composed of gold-coated photonic crystal fiber, Phys. Lett. A 383 (25) (2019).
Fig. 9. Crosstalk of polarization filter on the operable wavelength with the optimal geometric structure.
5. Conclusion In this study, a novel PCF polarization filter is designed with selective gold coating of air holes that are filled with water. When the phase matching condition is satisfied, the SPP first-order mode and the core mode will be coupled. Note that the polarization filter has the following characteristics: a loss peak at 1310 nm, which is the communication window, and a loss peak value that is as high as 1209.57 dB/cm. Note that the loss in the X-polarization direction is close to zero compared with the high-loss Y-polarization direction. We also examined the properties of the air-hole structure of the PCF. Using numerical simulations, the thickness of the gold layer, the diameter of the air hole of the gold-coated layer, the size of the innermost air holes, the filling of water, and the size of the outer air-holes were obtained, and all of these factors influenced the polarization filter’s performance. Thus, by changing the structures, a better polarization filter can be designed. CRediT authorship contribution statement Xin Yan: Investigation. Ziheng Guo: Investigation. Tonglei Cheng: Investigation. Shuguang Li: Investigation. Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted Acknowledgement This research was funded by [National Natural Science Foundation of China] grant number [61775032] and [11604042], [Fundamental Research Funds for the Central Universities] grant number [N170405007] and [N160404009] and [111 project] grant number [B1009]. The
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