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Study on photonic crystal fiber filter with two large gold layer air-holes based on surface plasma resonance
Optik 149 (2017) 220–228
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Study on photonic crystal fiber filter with two large gold layer air-holes based on surface plasma resonance Junjun Wu a,b , Shuguang Li a,∗ , Xili Jing a , Chao Dou a,c , Qiang Liu a a b c
Key Laboratory for Microstructural Material Physics, College of Science, Yanshan University, Qinhuangdao, China College of Qing gong, North China University of Science and Technology, Tangshan 063009, Hebei, China Department of Basic Education, Tangshan University, Tangshan 063009, Hebei, China
a r t i c l e
i n f o
Article history: Received 19 July 2017 Received in revised form 13 September 2017 Accepted 13 September 2017 Keywords: Photonic crystal fiber Polarization filter Surface plasma resonance
a b s t r a c t We design a crystal photonic fiber (PCF) polarization filter with asymmetric structure and two large air-holes coated with gold film. The influence of the thickness of metal layers and the diameter of large air-holes on the filtering characteristic is investigated using finite element method (FEM). In calculations, the sixth and the third order surface plasma modes (SPM) are presented. The resonance positions are well separated by the asymmetry of the structure in vertical direction. The loss of unwanted polarization is 829 and 1267 times than that of wanted polarization at 1.48 and 1.55 m respectively. When the fiber length is 3 mm, the crosstalk is 1055 dB and 927 dB for 1.48 and 1.55 m. The bandwidth with crosstalk better than 20 dB can reach to 1000 nm, covering almost all communication band. What’s more, gold excitation of SPR and silver excitation of SPR are compared and studied. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fiber (PCF) is also called microstructure optical fiber or porous fiber. The holes are arranged periodically and their magnitude of size is similar to the light wavelength. The fiber core can be solid or hollow core. Compared with the traditional optical fiber, it has many advantages, such as flexible control, low loss, large mode area and so on [1], which have attracted many scholars’ attention and research, such as dispersion compensation [2], polarization filtering [3,4], sensing characteristics [5,6] and other aspects. Because of its flexibility and controllability, PCF is widely used in the design of optical fiber devices. Some functional materials like metal [7–9], liquid [10], molecular gas [11], or semi-conductor [12] are filled in the core or cladding of PCF to achieve more demanded functions, especially the filling of metal. The combination of PCF technology and surface plasma resonance (SPR) is a hot research topic in recent years. When the metal surface is exposed to light and meet certain conditions, a surface plasma element can be generated. Once the transmission constants of surface plasma and fiber core match, coupling phenomena will occur, which make the PCF device based SPR has better characteristics. Such as the PCF polarization filter, SPR can greatly improve the limited loss that improves the filtering characteristics. There is a lot of coverage on it:In 2016, Zi J [13] proposed a polarization filter with two large diameter gold coated air holes, when fiber length is 1 mm, extinction ratio can reach 396 dB at 1.31 m. In 2016 Yogalakshmi [14] designed and analysed a photonic crystal fiber based polarization filter using surface plasmon resonance. The loss can reach 348.55 and 302 dB/cm for y-polarized and x-polarized light at 1.52 and 1.56 m respectively for single gold wire.
∗ Corresponding author. E-mail address: [email protected] (S. Li). http://dx.doi.org/10.1016/j.ijleo.2017.09.048 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
J. Wu et al. / Optik 149 (2017) 220–228
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Fig. 1. The designed PCF filter model structure.
In 2016, An G [15] proposed high birefringence photonic crystal fiber polarized filter filled with metal wires which can selectively filter out the polarized light in one direction by adjusting the wire diameter. In 2016, Zhen H [16] obtained symmetrical high birefringence photonic crystal fiber filled with Au. The core mode loss in x-direction light could reach 473 dB/cm, however the core mode loss of y-direction light was almost not affected by the surface plasma polarized mode at the wavelength of 1.55 m. In 2016, Liu [17] studied that the gold wires are selectively filled into the cladding air holes of PCF, the loss of x-polarized mode is 443.36 dB/cm at 1.31 m, and the corresponding loss of y polarization mode is 2.24 dB/cm. G Wang [18] studied PCF polarized filtering with nanoscale gold film, the confinement loss in x direction can reach 857.80 dB/cm at the resonance wavelength. When the length of fiber is longer than 30 m, the extinction ratio is better than 20 dB at the wavelength 1.31 m. In this paper, we design a single polarized PCF filter with two large air-holes. The loss in x-polarized direction is much larger than that in y-polarized direction. The loss in x-polarized direction is 405.50 dB/cm and 356.49 dB/cm at the communication wavelength 1.48 and 1.55 m, but the corresponding loss in y-polarized direction is only 0.32 dB/cm and 0.43 dB/cm. The loss in x direction is 1267 and 829 times of y direction. When the fiber length is 3 mm, the crosstalk is 927 dB and 1055 dB respectively. The designed filter has perfect filtering performance better than Refs. [14], [17] and [22]. Operable bandwidth can reach to 1000 nm and is wider than Ref. [20]. 2. Model structure and theoretical knowledge Fig. 1 is the designed PCF filter model, which is a square rotation of 45◦ . There are two large air holes coated with gold layer. The rest small holes are divided into two kinds of different sizes. The asymmetric structure can make the resonant positions of two vertical directions are well separated even without high birefringence. This view has been presented by Zhang in Ref. [19]. The SPR effect can greatly improve the loss of x direction light and improve the filtering performance. In the model, the diameter of the big gold layer hole is D. The thickness of gold later is t. The smaller holes diameter is d1 and holes spacing is 1 . The diameter of the smallest air holes is d2 , holes spacing is 2 . What’s more, we employ full vector finite element method (FV-FEM) for simulating both core mode and SPP mode, which is a powerful software that is recognized as the most suitable for solving fiber complex cross section structures. To improve the calculation accuracy, the scattering boundary conditions and the perfect matching layer of several micrometers are set to absorb the energy radiated outward. The fiber material is silicon. Besides, the dispersion of silicon and metal are considered in simulation. The refractive index of silicon is calculated by Sellmeier equation. The dielectric constant of gold is determined by Lorentz-Drude model [20]: εm = ε∞ −
2 ωD
ω(ω − iD )
−
ε · ˝L2 (ω2
− ωL2 ) − iL ω
(1)
In the formula, ε∞ is the high frequency dielectric constant, ε is the weighted coefficient, ω is the guiding optical angular frequency, ωD is the plasma frequency and D is damping frequency, ˝L represents the oscillator strength of the Lorenz oscillator, and L is the frequency spectrum width of the Lorenz oscillator. The mode loss is an important optical fiber indicator and can be calculated by the formula [21]: Loss =
20 2 × Im (neff ) × 104 dB/cm ln(10)
Im (neff) is the imaginary part of the effective refractive index.
(2)
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Fig. 2. (a) the electric field distribution of x-polarized core mode (b) y-polarized core mode (c) surface plasma polarization mode (d) the grid graph of the proposed PCF filter by finite element method.
Fig. 2 shows up the electric field distribution of (a) x-polarized core mode (b) y-polarized core mode (c) SPM (d) the grid graph of the proposed PCF filter by the FEM which is composed of 40748 grid elements when D = 5.92 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m. The coupling theory plays an important role in the SPR filter. When the SPP mode and core mode are in phase matching, they will couple and accompanied by energy transfer. In our work, the coupling between the sixth order SPP or the third order SPP and the core modes can be explained by a series of coupled equations. At first, the dispersion relation of SPP can be expressed by Ref. [22]:
nm =
εεm − ε + εm
(m − 1) d
2 (3)
Here, m, ε, εm , d respectively represent the order for SPP, the dielectric constants of silicon glass and metal, and the diameter of nanometer wire. From this formula (3), each SPP order can be obtained. Secondly, the coupled-mode equations are: dE1 = iˇ1 E1 + ikE2 dz
(4)
dE2 = iˇ2 E2 + ikE1 dz
(5)
E1 , E2 , ˇ1 , ˇ2 respectively represent the mode fields and propagation constants of core mode and SPP mode. and z is coupling strength and propagation length. Assuming the propagation constant of the coupling mode is ˇ. E1 and E2 can be written as follows: E1 = A exp(iˇz)
(6)
E2 = B exp(iˇz)
(7)
We take them into (4) and (5) then getˇ: ˇ± = ˇave ±
ı2 + k2
(8)
here ˇave = (ˇ1 + ˇ2 )/2, ı = (ˇ1 − ˇ2 )/2. For the two modes, ˇ1 and ˇ2 are complex. So ı can be written as ı = ır + iıi . The real parts of propagation constants of core and SPP mode are same if phase matching condition is satisfied, thus ır = 0 and get ı2 + k2 = − ıi 2 + k. When ıi < k, ˇ+ and ˇ- have different real parts and same imaginary parts, then a complete coupling will happen. When ıi > k, the real part s of ˇ+ and ˇ- are equal, the imaginary parts of ˇ+ and ˇ- are different, an incomplete coupling will happen. In our paper, a complete coupling between core mode and 6th SPP or 3rd SPP occurs. Fig. 3 is the dispersion relation and the loss curve of filtering for 1.48 m. The black solid, red solid and purple dotted lines are effective index of refraction of x-PM, y-PM, and SPP respectively. The blue solid and blue dotted line are the loss of x-PM, y-PM. It can be seen from Fig. 3 that the loss of x-PM is much stronger than that in y-PM. The loss value of x-PM and
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Fig. 3. The dispersion relation and the loss curve of filtering for 1.48 m when coated with gold layer.
y-PM is 405.50 dB/cm and 0.32 dB/cm respectively at communication band 1.48 m, where the Re(neff) lines of x-PM and SPP intersect. The inner illustration is the 6th SPP which couples to the core mode. 3. Simulation results and discussion At first we study the influence of metal layer thickness. Keeping the diameter of all the holes unchanged: D = 5.92 m, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m. The thickness of the gold layer is t = 18, 20, 22, 24 nm. Fig. 4(a) shows the relationship between the loss and wavelength with different thicknesses. Fig. 4 (b) is the resonance wavelength curve with different thickness. We find that the resonance position moves to the shorter wavelength, but the resonance intensity has almost no change with the increase of the thickness. The thickness of the metal layer has little effect on the resonance strength in this polarization filter model.
Fig. 4. (a) The relationship between the loss and wavelength (b) the resonance position curve with different gold layer thickness, when D = 5.92 m, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m.
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Fig. 5. (a) the relationship between the loss and wavelength and (b) the resonance strength and resonance position curve with different diameter of the large hole, when d1 = 1.8 m, d2 = 1.0 m and same gold layer t = 20 nm.
Fig. 6. (a) The loss curve (a) and crosstalk curve (b) with wavelength change in PCF filter for 1.55 m when D = 5.7 m, gold layer t = 20 nm, d1 = 1.8 m, d2 = 1.0 m.
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Fig. 7. (a) The loss curve and (b) the crosstalk curve with wavelength change in PCF filter for 1.55 m when D = 5.92 m, gold layer t = 20 nm, d1 = 1.8 m, d2 = 1.0 m.
Secondly the effect of large diameter hole is discussed. The diameter of large holes are D = 5.7, 5.8, 5.92 m. We maintain the rest holes diameter and the thickness of the gold film unchanged: d1 = 1.8 m, d2 = 1.0 m, t = 20 nm, Fig. 5(a) shows the relationship between loss and wavelength with different diameter. Fig. 5(b) is the curve of the resonance strength and resonance position with the change of the large air holes diameter. We find that the resonance position moves to the shorter wavelength and the resonance intensity increases with the increase of diameter. Because with the increase of the diameter of large air-holes, the distance between the metal layer and the core is closer, and the interaction and energy transfer between the two modes is more likely to occur. As the resonant position can be changed by adjusting the large holes diameter or the gold film thickness, we achieve single wavelength filter for 1.55 m and 1.48 m by adjusting the structure parameters. 1.55 m filter parameters: D = 5.7 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m. 1.48 m filter parameters: D = 5.92 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m. In order to embody the exc- ellent filtering performance, the crosstalk (CT) value is calculated. The CT value reflects the impact of a signal to another signal. It is an important measure of polarization filter and can be calculated by [21] CT = 20 ∗ lg exp[(˛2 − ˛1 )L]
(9)
Fig. 6(a) shows that the loss of x-direction light is 356.49 dB/cm at 1.55 m, while the loss of y direction light is only 0.43 dB/cm and is almost zero in the figure. The loss in x direction is 829 times than that of y direction which shows good filtering performance. As can be seen from Fig. 6(b), when the fiber length L = 1 mm, 2 mm, 3 mm, the values of CT are 309 dB, 618 dB, 927 dB,respectively. Fig. 7(a) is the loss curve and crosstalk curve with wavelength change in filter for 1.48 m. It shows the loss of x-direction light is 405.50 dB/cm at 1.48 m, however the loss of y-direction light is only 0.32 dB/cm and is almost zero in the figure. The loss in x direction is 1267 times than that of y direction which shows good filtering performance. As can be seen from Fig. 7(b), when the fiber length L = 1 mm, 2 mm, 3 mm, the values of CT are 352 dB, 703 dB, 1055 dB,respectively. In this part the influence of d1 is studied. Due to the influence on filter characteristics is mainly determined by the two loops of holes near fiber core, so here we only change the size of four holes near the fiber core. The original diameter d1 is 1.8 m and now is changed to 1.6 m. Fig. 8(a) is the loss curve before and after the change. We find that they are almost completely coincident. The effect of small hole is very small. At the same time, the situation of only one big circular hole is compared, while they have same holes diameters and gold layer thickness. Fig. 8(b) is the result of the comparison. It is
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Fig. 8. (a) The comparison results of four smaller holes near the fiber core when D = 5.7 m, gold layer t = 20 nm. (b) The comparison results of only one large holes when D = 5.78 m, gold layer t = 20 nm.
found that the resonance positions are almost the same, but the resonance strength with two large gold layer air holes is much stronger than that of one large gold layer hole. In the front part, the proposed PCF coated with gold layer is studied and the communic- ation band filter is realized. Next, we change the gold layer in the optimized structure into silver layer, and explore the differences. The dielectric constant of silver can be obtained from [20]. Fig. 9(a) is the dispersion and loss curve depend on wavelength when coated with Ag layer when t = 20 nm, D = 5.92 m, d1 is 1.8 m, and d2 is 1.0 m. Compared with that coated with Au layer, the resonant position changes from 1.55 m to 1.54 m, and the loss changes from 356.49 dB/cm to 355.61 dB/cm. Fig. 9(b) is the dispersion and loss depend on wavelength when coated with Ag layer when t = 20 nm, D = 5.7 m. Comparing with that coated with Au layer, the resonant position changes from 1.48 m to 1.47 m, and the loss changes from 405.00 dB/cm to 406.24 dB/cm. Fig. 10 displays the loss contrast between filter coated with Au layer and that with Ag layer with the same model parameter at the communication band 1.48 m and 1.55 m. Fig. 11 displays the crosstalk contrast between filter coated with Au layer and that with Ag layer with same model parameter. The crosstalk peak value changes from 927 dB to 925 dB at 1.55 m, and changes from 1055 dB to 1057 dB at 1.48 m. There is only a slight change in the designed PCF, which is unlike that mentioned in [23] that the SPR excited Au is much stronger than excited Ag. It is worth mentioning that the two PCF filters coated with Au or Ag layer all have good filtering characteristics. However, considering that gold has better ductility and oxidation resistance than silver, we advise to use gold layer to excite SPP. It can be seen that the proposed filter displays perfect filtering performance through the above calculation and discussion. About the manufacture of the filter, we can use the mature stack − draw technology. Additionally, the deposition of the metallic layer through the PCF can be achieved by sputtering technique, high pressure chemical vapor deposition technology or electroplating. Therefore, our proposed filter can be implemented in reality. 4. Conclusion In our work, a PCF filter of square asymmetric structure with two large air-holes coated with gold layer is designed and simulated. The res- ults show that the designed filter has perfect filtering performance. The resonant positions of x and y direction are well separated using the asymmetry of structure. Moreover, the loss of unwanted polarization is much larger than that of wanted polarization direction. The loss in x direction is 829 times and 1267 times than that of y
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Fig. 9. The dispersion and loss depend on wavelength when coated with Ag layer (a) when t = 20 nm, D = 5.7 m (b) when t = 20 nm, D = 5.92 m.
Fig. 10. The loss contrast between filter coated with gold layer and that with silver layer with same model parameter at communication band 1.48 m and 1.55 m.
Fig. 11. The crosstalk contrast between filter coated with gold layer and that with silver layer with same model parameter at communication band 1.48 m and 1.55 m.
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J. Wu et al. / Optik 149 (2017) 220–228
direction at communication band 1.55 m and1.48 m respectively. What’s more, the proposed filter has high extinction and wide bandwidth. When the fiber length is 3 mm, the crosstalk can reach 927 dB and 1055 dB at 1.55 m and 1.48 m respectively.The bandwidth of which crosstalk better than 20 dB can reach to 1000 nm, covering almost all communication bands. In addition, the gold layer in optimized structure of the communication window is changed into silver layer. It is found that both of them can perform filtering perfectly, and the calculation results are basically the same without obvious difference. As for the difference between SPR excited gold and excited silver in different structures is worthy of further study. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 61475134, 61505175) and Key Program of the Natural Science Foundation of He Bei Province (Grant No. F2017203193). References [1] J. Li, S. Li, et al., Soliton and four-wave mixing effects induced by the third-order dispersion in a photonic crystal fiber with femtosecond pulses pumping at normal-dispersion regime, IEEE Photonics J. 7 (2015) 3200211. [2] S. Gowre, S. Mahapatra, S.K. Varshney, P.K. Sahu, Dispersion characteristics of all-glass photonic crystal fibers, Optik 124 (18) (2013) 3730–3733. [3] P. Li, Q. Li, Y. Zhang, W. Song, Study on polariza- tion characteristics of photonic crystal fiber with lateral pressure, Nat. Sci. J. Habin Norm. Univ. (2016) 01. [4] H. Jiang, E. Wang, K. Xie, Z. Hu, Dual core photo- nic crystal fiber for use in fiber filters, IEEE Photonics J. 8 (2) (2016) 1–8. [5] N. Ayyanar, D. Vigneswaran, et al., Hydrostatic pressure sensor using high birefringence photonic crystal fibers, IEEE Sens. J. 17 (3) (2017) 650–656. [6] Z.L. Liu, G.S. Zhao, W. Wang, L.T. Hou, X.T. Zhao, Characteristics of a large negative dispersion and low confinement losses PCF, Semicond. Optoelectr. (2008). [7] Y. Lu, C.J. Hao, et al., Surface plasmon resonance sensor based on polymer photonic crystal fibers with metal nanolayers, Sensors 13 (1) (2013) 956. [8] S. Zhang, X. Yu, Y. Zhang, S. Ping, Theoretical study of dual-core photonic crystal fibers with metal wire, IEEE Photonics J. 4 (4) (2012) 1178–1187. [9] D. Cui, H. Chen, Surface platinum metal plasma resonance photonic crystal fiber sensor, International Conference on Optoelectronics and MicroelecTronics Technology and Application (2017) 102441. [10] B. Sun, Z. Zhang, W. Wei, C. Wang, Unique temperature dependence of selectively liquid crys- tal filled photonic crystal fibers, IEEE Photonics Technol. Lett. 28 (12) (2016) 1. [11] Andrew Jones, A.V. Vasudevan Nampoothiri, et al., Mid-IR Fiber Lasers Based on Molecular Gas Filled Hollow-Core Photonic Crystal Fiber, OSA, 2011. [12] O.N.L.A. Kozina Mel’nikov, Determination of the possibility of controlling the optical properties of dielectric photonic-crystal fibers with semiconductor inclusions, Opt. Spectrosc. 114 (6) (2017) 899–903. [13] Zi, S. Li, H. Chen, J. Li, H. Li, Photonic crystal fiber polarization filter based on surface plasmon polaritons, Plasmonics 11 (1) (2016) 65–69. [14] Yogalakshmi, S. Selvendran, A. Sivanantha, Raja Design and analysis of a photonic crystal fiber based polarization filter using surface plasmon resonance, Laser Phys. 26 (5) (2016) 056201. [15] G. An, et al., High-birefringence photonic crystal fiber polarization filter based on surface plasmon resonance, Appl. Opt. 55 (6) (2016) 1262. [16] H.L. Zhen, Polarization filters based on high biref- ringence photonic crystal fiber filled with Au, Acta Opt. Sin. 9 (3) (2016). [17] Q. Liu, S. Li, J. Li, X. Wang, Tunable fiber polarization filter by filling different index liquids and gold wire into photonic crystal fiber, J. Lightwave Technol. 34 (10) (2016). [18] G. Wang, et al., A kind of broadband polarization filter based on photonic crystal fiber with nano-scale gold film, Plasmonics (2016) 1–6. [19] H. Li, S. Li, H.L. Chen, A polarization filter based on photonic ctystal fiber with asymmetry around gold-coated holes, Plasmonics 11 (2016) 103–108. [20] Z. Fan, S. Li, Q. Liu, Plasmonic polarization filter based on dual-core photonic crystal fiber with elliptical metallic nanowires, Plasmonics (2016), http://dx.doi.org/10.1007/s11468-016-0211-8. [21] G.P. Agrawal, Nonlinear Fiber Optics, Academic, San Diego, CA, USA, 1989. [22] G. An, S. Li, W. Zhang, Z.K. Fan, A polarization filter of gold-filled photonic crystal fiber with regular triangular and rectangular lattices, Opt. Commun. 331 (2014) 316–319. [23] Z. Fan, S. Li, Q. Liu, Plasmonic polarization beam splitter based on dual-core photonic crystal fiber, Plasmonics 10 (2015) 1283–1289.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Study on photonic crystal fiber filter with two large gold layer air-holes based on surface plasma resonance Junjun Wu a,b , Shuguang Li a,∗ , Xili Jing a , Chao Dou a,c , Qiang Liu a a b c
Key Laboratory for Microstructural Material Physics, College of Science, Yanshan University, Qinhuangdao, China College of Qing gong, North China University of Science and Technology, Tangshan 063009, Hebei, China Department of Basic Education, Tangshan University, Tangshan 063009, Hebei, China
a r t i c l e
i n f o
Article history: Received 19 July 2017 Received in revised form 13 September 2017 Accepted 13 September 2017 Keywords: Photonic crystal fiber Polarization filter Surface plasma resonance
a b s t r a c t We design a crystal photonic fiber (PCF) polarization filter with asymmetric structure and two large air-holes coated with gold film. The influence of the thickness of metal layers and the diameter of large air-holes on the filtering characteristic is investigated using finite element method (FEM). In calculations, the sixth and the third order surface plasma modes (SPM) are presented. The resonance positions are well separated by the asymmetry of the structure in vertical direction. The loss of unwanted polarization is 829 and 1267 times than that of wanted polarization at 1.48 and 1.55 m respectively. When the fiber length is 3 mm, the crosstalk is 1055 dB and 927 dB for 1.48 and 1.55 m. The bandwidth with crosstalk better than 20 dB can reach to 1000 nm, covering almost all communication band. What’s more, gold excitation of SPR and silver excitation of SPR are compared and studied. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Photonic crystal fiber (PCF) is also called microstructure optical fiber or porous fiber. The holes are arranged periodically and their magnitude of size is similar to the light wavelength. The fiber core can be solid or hollow core. Compared with the traditional optical fiber, it has many advantages, such as flexible control, low loss, large mode area and so on [1], which have attracted many scholars’ attention and research, such as dispersion compensation [2], polarization filtering [3,4], sensing characteristics [5,6] and other aspects. Because of its flexibility and controllability, PCF is widely used in the design of optical fiber devices. Some functional materials like metal [7–9], liquid [10], molecular gas [11], or semi-conductor [12] are filled in the core or cladding of PCF to achieve more demanded functions, especially the filling of metal. The combination of PCF technology and surface plasma resonance (SPR) is a hot research topic in recent years. When the metal surface is exposed to light and meet certain conditions, a surface plasma element can be generated. Once the transmission constants of surface plasma and fiber core match, coupling phenomena will occur, which make the PCF device based SPR has better characteristics. Such as the PCF polarization filter, SPR can greatly improve the limited loss that improves the filtering characteristics. There is a lot of coverage on it:In 2016, Zi J [13] proposed a polarization filter with two large diameter gold coated air holes, when fiber length is 1 mm, extinction ratio can reach 396 dB at 1.31 m. In 2016 Yogalakshmi [14] designed and analysed a photonic crystal fiber based polarization filter using surface plasmon resonance. The loss can reach 348.55 and 302 dB/cm for y-polarized and x-polarized light at 1.52 and 1.56 m respectively for single gold wire.
∗ Corresponding author. E-mail address: [email protected] (S. Li). http://dx.doi.org/10.1016/j.ijleo.2017.09.048 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
J. Wu et al. / Optik 149 (2017) 220–228
221
Fig. 1. The designed PCF filter model structure.
In 2016, An G [15] proposed high birefringence photonic crystal fiber polarized filter filled with metal wires which can selectively filter out the polarized light in one direction by adjusting the wire diameter. In 2016, Zhen H [16] obtained symmetrical high birefringence photonic crystal fiber filled with Au. The core mode loss in x-direction light could reach 473 dB/cm, however the core mode loss of y-direction light was almost not affected by the surface plasma polarized mode at the wavelength of 1.55 m. In 2016, Liu [17] studied that the gold wires are selectively filled into the cladding air holes of PCF, the loss of x-polarized mode is 443.36 dB/cm at 1.31 m, and the corresponding loss of y polarization mode is 2.24 dB/cm. G Wang [18] studied PCF polarized filtering with nanoscale gold film, the confinement loss in x direction can reach 857.80 dB/cm at the resonance wavelength. When the length of fiber is longer than 30 m, the extinction ratio is better than 20 dB at the wavelength 1.31 m. In this paper, we design a single polarized PCF filter with two large air-holes. The loss in x-polarized direction is much larger than that in y-polarized direction. The loss in x-polarized direction is 405.50 dB/cm and 356.49 dB/cm at the communication wavelength 1.48 and 1.55 m, but the corresponding loss in y-polarized direction is only 0.32 dB/cm and 0.43 dB/cm. The loss in x direction is 1267 and 829 times of y direction. When the fiber length is 3 mm, the crosstalk is 927 dB and 1055 dB respectively. The designed filter has perfect filtering performance better than Refs. [14], [17] and [22]. Operable bandwidth can reach to 1000 nm and is wider than Ref. [20]. 2. Model structure and theoretical knowledge Fig. 1 is the designed PCF filter model, which is a square rotation of 45◦ . There are two large air holes coated with gold layer. The rest small holes are divided into two kinds of different sizes. The asymmetric structure can make the resonant positions of two vertical directions are well separated even without high birefringence. This view has been presented by Zhang in Ref. [19]. The SPR effect can greatly improve the loss of x direction light and improve the filtering performance. In the model, the diameter of the big gold layer hole is D. The thickness of gold later is t. The smaller holes diameter is d1 and holes spacing is 1 . The diameter of the smallest air holes is d2 , holes spacing is 2 . What’s more, we employ full vector finite element method (FV-FEM) for simulating both core mode and SPP mode, which is a powerful software that is recognized as the most suitable for solving fiber complex cross section structures. To improve the calculation accuracy, the scattering boundary conditions and the perfect matching layer of several micrometers are set to absorb the energy radiated outward. The fiber material is silicon. Besides, the dispersion of silicon and metal are considered in simulation. The refractive index of silicon is calculated by Sellmeier equation. The dielectric constant of gold is determined by Lorentz-Drude model [20]: εm = ε∞ −
2 ωD
ω(ω − iD )
−
ε · ˝L2 (ω2
− ωL2 ) − iL ω
(1)
In the formula, ε∞ is the high frequency dielectric constant, ε is the weighted coefficient, ω is the guiding optical angular frequency, ωD is the plasma frequency and D is damping frequency, ˝L represents the oscillator strength of the Lorenz oscillator, and L is the frequency spectrum width of the Lorenz oscillator. The mode loss is an important optical fiber indicator and can be calculated by the formula [21]: Loss =
20 2 × Im (neff ) × 104 dB/cm ln(10)
Im (neff) is the imaginary part of the effective refractive index.
(2)
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Fig. 2. (a) the electric field distribution of x-polarized core mode (b) y-polarized core mode (c) surface plasma polarization mode (d) the grid graph of the proposed PCF filter by finite element method.
Fig. 2 shows up the electric field distribution of (a) x-polarized core mode (b) y-polarized core mode (c) SPM (d) the grid graph of the proposed PCF filter by the FEM which is composed of 40748 grid elements when D = 5.92 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m. The coupling theory plays an important role in the SPR filter. When the SPP mode and core mode are in phase matching, they will couple and accompanied by energy transfer. In our work, the coupling between the sixth order SPP or the third order SPP and the core modes can be explained by a series of coupled equations. At first, the dispersion relation of SPP can be expressed by Ref. [22]:
nm =
εεm − ε + εm
(m − 1) d
2 (3)
Here, m, ε, εm , d respectively represent the order for SPP, the dielectric constants of silicon glass and metal, and the diameter of nanometer wire. From this formula (3), each SPP order can be obtained. Secondly, the coupled-mode equations are: dE1 = iˇ1 E1 + ikE2 dz
(4)
dE2 = iˇ2 E2 + ikE1 dz
(5)
E1 , E2 , ˇ1 , ˇ2 respectively represent the mode fields and propagation constants of core mode and SPP mode. and z is coupling strength and propagation length. Assuming the propagation constant of the coupling mode is ˇ. E1 and E2 can be written as follows: E1 = A exp(iˇz)
(6)
E2 = B exp(iˇz)
(7)
We take them into (4) and (5) then getˇ: ˇ± = ˇave ±
ı2 + k2
(8)
here ˇave = (ˇ1 + ˇ2 )/2, ı = (ˇ1 − ˇ2 )/2. For the two modes, ˇ1 and ˇ2 are complex. So ı can be written as ı = ır + iıi . The real parts of propagation constants of core and SPP mode are same if phase matching condition is satisfied, thus ır = 0 and get ı2 + k2 = − ıi 2 + k. When ıi < k, ˇ+ and ˇ- have different real parts and same imaginary parts, then a complete coupling will happen. When ıi > k, the real part s of ˇ+ and ˇ- are equal, the imaginary parts of ˇ+ and ˇ- are different, an incomplete coupling will happen. In our paper, a complete coupling between core mode and 6th SPP or 3rd SPP occurs. Fig. 3 is the dispersion relation and the loss curve of filtering for 1.48 m. The black solid, red solid and purple dotted lines are effective index of refraction of x-PM, y-PM, and SPP respectively. The blue solid and blue dotted line are the loss of x-PM, y-PM. It can be seen from Fig. 3 that the loss of x-PM is much stronger than that in y-PM. The loss value of x-PM and
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Fig. 3. The dispersion relation and the loss curve of filtering for 1.48 m when coated with gold layer.
y-PM is 405.50 dB/cm and 0.32 dB/cm respectively at communication band 1.48 m, where the Re(neff) lines of x-PM and SPP intersect. The inner illustration is the 6th SPP which couples to the core mode. 3. Simulation results and discussion At first we study the influence of metal layer thickness. Keeping the diameter of all the holes unchanged: D = 5.92 m, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m. The thickness of the gold layer is t = 18, 20, 22, 24 nm. Fig. 4(a) shows the relationship between the loss and wavelength with different thicknesses. Fig. 4 (b) is the resonance wavelength curve with different thickness. We find that the resonance position moves to the shorter wavelength, but the resonance intensity has almost no change with the increase of the thickness. The thickness of the metal layer has little effect on the resonance strength in this polarization filter model.
Fig. 4. (a) The relationship between the loss and wavelength (b) the resonance position curve with different gold layer thickness, when D = 5.92 m, d1 = 1.8 m, d2 = 1.0 m, 1 = 2 m, 2 = 1.5 m.
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Fig. 5. (a) the relationship between the loss and wavelength and (b) the resonance strength and resonance position curve with different diameter of the large hole, when d1 = 1.8 m, d2 = 1.0 m and same gold layer t = 20 nm.
Fig. 6. (a) The loss curve (a) and crosstalk curve (b) with wavelength change in PCF filter for 1.55 m when D = 5.7 m, gold layer t = 20 nm, d1 = 1.8 m, d2 = 1.0 m.
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Fig. 7. (a) The loss curve and (b) the crosstalk curve with wavelength change in PCF filter for 1.55 m when D = 5.92 m, gold layer t = 20 nm, d1 = 1.8 m, d2 = 1.0 m.
Secondly the effect of large diameter hole is discussed. The diameter of large holes are D = 5.7, 5.8, 5.92 m. We maintain the rest holes diameter and the thickness of the gold film unchanged: d1 = 1.8 m, d2 = 1.0 m, t = 20 nm, Fig. 5(a) shows the relationship between loss and wavelength with different diameter. Fig. 5(b) is the curve of the resonance strength and resonance position with the change of the large air holes diameter. We find that the resonance position moves to the shorter wavelength and the resonance intensity increases with the increase of diameter. Because with the increase of the diameter of large air-holes, the distance between the metal layer and the core is closer, and the interaction and energy transfer between the two modes is more likely to occur. As the resonant position can be changed by adjusting the large holes diameter or the gold film thickness, we achieve single wavelength filter for 1.55 m and 1.48 m by adjusting the structure parameters. 1.55 m filter parameters: D = 5.7 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m. 1.48 m filter parameters: D = 5.92 m, t = 20 nm, d1 = 1.8 m, d2 = 1.0 m. In order to embody the exc- ellent filtering performance, the crosstalk (CT) value is calculated. The CT value reflects the impact of a signal to another signal. It is an important measure of polarization filter and can be calculated by [21] CT = 20 ∗ lg exp[(˛2 − ˛1 )L]
(9)
Fig. 6(a) shows that the loss of x-direction light is 356.49 dB/cm at 1.55 m, while the loss of y direction light is only 0.43 dB/cm and is almost zero in the figure. The loss in x direction is 829 times than that of y direction which shows good filtering performance. As can be seen from Fig. 6(b), when the fiber length L = 1 mm, 2 mm, 3 mm, the values of CT are 309 dB, 618 dB, 927 dB,respectively. Fig. 7(a) is the loss curve and crosstalk curve with wavelength change in filter for 1.48 m. It shows the loss of x-direction light is 405.50 dB/cm at 1.48 m, however the loss of y-direction light is only 0.32 dB/cm and is almost zero in the figure. The loss in x direction is 1267 times than that of y direction which shows good filtering performance. As can be seen from Fig. 7(b), when the fiber length L = 1 mm, 2 mm, 3 mm, the values of CT are 352 dB, 703 dB, 1055 dB,respectively. In this part the influence of d1 is studied. Due to the influence on filter characteristics is mainly determined by the two loops of holes near fiber core, so here we only change the size of four holes near the fiber core. The original diameter d1 is 1.8 m and now is changed to 1.6 m. Fig. 8(a) is the loss curve before and after the change. We find that they are almost completely coincident. The effect of small hole is very small. At the same time, the situation of only one big circular hole is compared, while they have same holes diameters and gold layer thickness. Fig. 8(b) is the result of the comparison. It is
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Fig. 8. (a) The comparison results of four smaller holes near the fiber core when D = 5.7 m, gold layer t = 20 nm. (b) The comparison results of only one large holes when D = 5.78 m, gold layer t = 20 nm.
found that the resonance positions are almost the same, but the resonance strength with two large gold layer air holes is much stronger than that of one large gold layer hole. In the front part, the proposed PCF coated with gold layer is studied and the communic- ation band filter is realized. Next, we change the gold layer in the optimized structure into silver layer, and explore the differences. The dielectric constant of silver can be obtained from [20]. Fig. 9(a) is the dispersion and loss curve depend on wavelength when coated with Ag layer when t = 20 nm, D = 5.92 m, d1 is 1.8 m, and d2 is 1.0 m. Compared with that coated with Au layer, the resonant position changes from 1.55 m to 1.54 m, and the loss changes from 356.49 dB/cm to 355.61 dB/cm. Fig. 9(b) is the dispersion and loss depend on wavelength when coated with Ag layer when t = 20 nm, D = 5.7 m. Comparing with that coated with Au layer, the resonant position changes from 1.48 m to 1.47 m, and the loss changes from 405.00 dB/cm to 406.24 dB/cm. Fig. 10 displays the loss contrast between filter coated with Au layer and that with Ag layer with the same model parameter at the communication band 1.48 m and 1.55 m. Fig. 11 displays the crosstalk contrast between filter coated with Au layer and that with Ag layer with same model parameter. The crosstalk peak value changes from 927 dB to 925 dB at 1.55 m, and changes from 1055 dB to 1057 dB at 1.48 m. There is only a slight change in the designed PCF, which is unlike that mentioned in [23] that the SPR excited Au is much stronger than excited Ag. It is worth mentioning that the two PCF filters coated with Au or Ag layer all have good filtering characteristics. However, considering that gold has better ductility and oxidation resistance than silver, we advise to use gold layer to excite SPP. It can be seen that the proposed filter displays perfect filtering performance through the above calculation and discussion. About the manufacture of the filter, we can use the mature stack − draw technology. Additionally, the deposition of the metallic layer through the PCF can be achieved by sputtering technique, high pressure chemical vapor deposition technology or electroplating. Therefore, our proposed filter can be implemented in reality. 4. Conclusion In our work, a PCF filter of square asymmetric structure with two large air-holes coated with gold layer is designed and simulated. The res- ults show that the designed filter has perfect filtering performance. The resonant positions of x and y direction are well separated using the asymmetry of structure. Moreover, the loss of unwanted polarization is much larger than that of wanted polarization direction. The loss in x direction is 829 times and 1267 times than that of y
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Fig. 9. The dispersion and loss depend on wavelength when coated with Ag layer (a) when t = 20 nm, D = 5.7 m (b) when t = 20 nm, D = 5.92 m.
Fig. 10. The loss contrast between filter coated with gold layer and that with silver layer with same model parameter at communication band 1.48 m and 1.55 m.
Fig. 11. The crosstalk contrast between filter coated with gold layer and that with silver layer with same model parameter at communication band 1.48 m and 1.55 m.
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direction at communication band 1.55 m and1.48 m respectively. What’s more, the proposed filter has high extinction and wide bandwidth. When the fiber length is 3 mm, the crosstalk can reach 927 dB and 1055 dB at 1.55 m and 1.48 m respectively.The bandwidth of which crosstalk better than 20 dB can reach to 1000 nm, covering almost all communication bands. In addition, the gold layer in optimized structure of the communication window is changed into silver layer. It is found that both of them can perform filtering perfectly, and the calculation results are basically the same without obvious difference. As for the difference between SPR excited gold and excited silver in different structures is worthy of further study. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 61475134, 61505175) and Key Program of the Natural Science Foundation of He Bei Province (Grant No. F2017203193). References [1] J. Li, S. Li, et al., Soliton and four-wave mixing effects induced by the third-order dispersion in a photonic crystal fiber with femtosecond pulses pumping at normal-dispersion regime, IEEE Photonics J. 7 (2015) 3200211. [2] S. Gowre, S. Mahapatra, S.K. Varshney, P.K. Sahu, Dispersion characteristics of all-glass photonic crystal fibers, Optik 124 (18) (2013) 3730–3733. [3] P. Li, Q. Li, Y. Zhang, W. Song, Study on polariza- tion characteristics of photonic crystal fiber with lateral pressure, Nat. Sci. J. Habin Norm. Univ. (2016) 01. [4] H. Jiang, E. Wang, K. Xie, Z. Hu, Dual core photo- nic crystal fiber for use in fiber filters, IEEE Photonics J. 8 (2) (2016) 1–8. [5] N. Ayyanar, D. Vigneswaran, et al., Hydrostatic pressure sensor using high birefringence photonic crystal fibers, IEEE Sens. J. 17 (3) (2017) 650–656. [6] Z.L. Liu, G.S. Zhao, W. Wang, L.T. Hou, X.T. Zhao, Characteristics of a large negative dispersion and low confinement losses PCF, Semicond. Optoelectr. (2008). [7] Y. Lu, C.J. Hao, et al., Surface plasmon resonance sensor based on polymer photonic crystal fibers with metal nanolayers, Sensors 13 (1) (2013) 956. [8] S. Zhang, X. Yu, Y. Zhang, S. Ping, Theoretical study of dual-core photonic crystal fibers with metal wire, IEEE Photonics J. 4 (4) (2012) 1178–1187. [9] D. Cui, H. Chen, Surface platinum metal plasma resonance photonic crystal fiber sensor, International Conference on Optoelectronics and MicroelecTronics Technology and Application (2017) 102441. [10] B. Sun, Z. Zhang, W. Wei, C. Wang, Unique temperature dependence of selectively liquid crys- tal filled photonic crystal fibers, IEEE Photonics Technol. Lett. 28 (12) (2016) 1. [11] Andrew Jones, A.V. Vasudevan Nampoothiri, et al., Mid-IR Fiber Lasers Based on Molecular Gas Filled Hollow-Core Photonic Crystal Fiber, OSA, 2011. [12] O.N.L.A. Kozina Mel’nikov, Determination of the possibility of controlling the optical properties of dielectric photonic-crystal fibers with semiconductor inclusions, Opt. Spectrosc. 114 (6) (2017) 899–903. [13] Zi, S. Li, H. Chen, J. Li, H. Li, Photonic crystal fiber polarization filter based on surface plasmon polaritons, Plasmonics 11 (1) (2016) 65–69. [14] Yogalakshmi, S. Selvendran, A. Sivanantha, Raja Design and analysis of a photonic crystal fiber based polarization filter using surface plasmon resonance, Laser Phys. 26 (5) (2016) 056201. [15] G. An, et al., High-birefringence photonic crystal fiber polarization filter based on surface plasmon resonance, Appl. Opt. 55 (6) (2016) 1262. [16] H.L. Zhen, Polarization filters based on high biref- ringence photonic crystal fiber filled with Au, Acta Opt. Sin. 9 (3) (2016). [17] Q. Liu, S. Li, J. Li, X. Wang, Tunable fiber polarization filter by filling different index liquids and gold wire into photonic crystal fiber, J. Lightwave Technol. 34 (10) (2016). [18] G. Wang, et al., A kind of broadband polarization filter based on photonic crystal fiber with nano-scale gold film, Plasmonics (2016) 1–6. [19] H. Li, S. Li, H.L. Chen, A polarization filter based on photonic ctystal fiber with asymmetry around gold-coated holes, Plasmonics 11 (2016) 103–108. [20] Z. Fan, S. Li, Q. Liu, Plasmonic polarization filter based on dual-core photonic crystal fiber with elliptical metallic nanowires, Plasmonics (2016), http://dx.doi.org/10.1007/s11468-016-0211-8. [21] G.P. Agrawal, Nonlinear Fiber Optics, Academic, San Diego, CA, USA, 1989. [22] G. An, S. Li, W. Zhang, Z.K. Fan, A polarization filter of gold-filled photonic crystal fiber with regular triangular and rectangular lattices, Opt. Commun. 331 (2014) 316–319. [23] Z. Fan, S. Li, Q. Liu, Plasmonic polarization beam splitter based on dual-core photonic crystal fiber, Plasmonics 10 (2015) 1283–1289.