-
为了更好地展现该型光子晶体光纤的光学特性,同时给出了圆形双空气孔单元方形晶格排列型光子晶体光纤(square-lattice based on a lattice structure of double-hole units photonic crystal fiber, SL-DH-PCF)和椭圆形双空气孔单元方形晶格排列型光子晶体光纤(square-lattice based on the elliptical-hole photonic crystal fiber, SL-EH-PCF),并将两者的特性进行了对比。
图 1a中给出的是圆形双空气孔单元方形晶格排列型光子晶体光纤。两相同的圆形空气孔沿纵轴排列,组成空气孔单元。每一个空气孔的半径为R,两空气孔中心之间的间距为H。圆形空气孔单元以方形晶格方式进行排列组成整个光纤横截面,单元之间的间距为晶格间距,记为Λ。移除光纤横截面中心处一组空气孔单元组成光纤的纤芯,其它空气孔单元构成光纤的包层。图 1b中给出的是椭圆形双空气孔单元方形晶格排列型光子晶体光纤。该型光纤和图 1a中给出的光纤的占空比相同。椭圆形空气孔单元以方形晶格方式进行排列组成整个光纤横截面,椭圆形空气孔之间的晶格间距为Λ,椭圆率为η。两光纤空气孔的折射率为1,介质材料的折射率由下列Sellmeier色散公式[3]所决定:
$ \begin{array}{l} {n^2} = 1 + \frac{{0.6961663{\lambda ^2}}}{{{\lambda ^2} - {{\left( {0.0684043} \right)}^2}}} + \\ \frac{{0.4079426{\lambda ^2}}}{{{\lambda ^2} - {{\left( {0.1162414} \right)}^2}}} + \frac{{0.8974794{\lambda ^2}}}{{{\lambda ^2} - {{\left( {9.896161} \right)}^2}}} \end{array} $
(1) Figure 1. a—cross section of the proposed photonic crystal fiber based on a double-hole uint b—cross section of the proposed photonic crystal fiber based on a elliptical-hole uint
式中, n为介质材料的折射率; λ为工作波长,单位为μm。在计算过程中,两光纤的晶格间距设定为Λ=1.0μm。
采用有限元分析法对两光纤的导模进行数值分析。边界条件定为采用完美匹配层。光纤的模双折射[20]定义为:
$ \Delta n = {n_{{\rm{eff}}, y}} - {n_{{\rm{eff}}, x}} $
(2) 式中, neff, y和neff, x分别为光纤y偏振方向和x偏振方向各自基模的有效折射率。光纤的限制损耗[21]可由基模复数有效折射率的虚部求得,求解公式为:
$ L = 8.686 \times \frac{{2{\rm{ \mathsf{ π} }}}}{\lambda }{\rm{Im}}({n_{{\rm{eff}}}}) $
(3) 两偏振方向上的偏振模之间的偏振拍长Lb为:
$ {L_{\rm{b}}} = \frac{\lambda }{{\Delta n}} $
(4) 光纤的色散系数(其单位为ps·km-1·nm-1)可以定义为:
$ D = - \frac{\lambda }{c}\cdot{\rm{ }}\frac{{{{\rm{d}}^2}{\rm{Re}}({n_{{\rm{eff}}}})}}{{{\rm{d}}{\lambda ^2}}} $
(5) 式中, neff为模式的有效折射率,c为光速。
图 2中给出了两型光纤x偏振方向和y偏振方向各自基模的有效折射率随工作波长变化的曲线。其中实心符号曲线表示x偏振方向,空心符号曲线表示y偏振方向。圆形符号曲线表示SL-DH-PCF的两偏振方向有效折射率变化曲线,三角形符号曲线表示SL-EH-PCF的两偏振方向有效折射率变化曲线。两光纤的结构参量为Λ=1.0μm,R=0.2μm, H=0.5μm, η=1.5, 空气占空比都为f=25.13%。结果显示两光纤x偏振方向比y偏振方向具有更高的基模有效折射率。插图为工作波长为λ=1.55 μm时,两型光纤x偏振方向基模的电场分布图(其中左下图为SL-DH-PCF,右上图为SL-EH-PCF)。
Figure 2. Effective index of x-polarized and y-polarized fundamental modes as a function of wavelength
图 3中给出了SL-DH-PCF和SL-EH-PCF两种不同光纤在不同结构参量条件下的双折射特性。其中SL-EH-PCF椭圆空气孔的椭圆率η分别为1.3和1.5。对比文献中介绍的关于SL-EH-PCF的双折射特性,结果显示当SL-DH-PCF的几何结构参量为Λ=1.0μm, R=0.2μm, H=0.5μm时,其高双折射特性要优于椭圆率η分别为1.3和1.5时SL-EH-PCF的高双折射特性。此外发现, SL-DH-PCF的双圆形空气孔单元对该光纤的双折射具有重要的影响作用,特别是双圆形空气孔单元空气孔的半径R。从图 3可以看出, 当H=0.5μm保持不变时,SL-DH-PCF的双折射随着圆形空气孔半径的增大而迅速增大。而当R=0.2μm保持不变时,SL-DH-PCF的双折射随着空气孔单元两孔间距的变化而变化不是太大。
图 4中给出了SL-DH-PCF和SL-EH-PCF两种不同光纤在相同的空气占空比条件下的限制损耗特性。结果显示, SL-DH-PCF在x偏振方向基模的限制损耗和SL-EH-PCF的近似,但在相同的空气占空比条件下,SL-DH-PCF比SL-EH-PCF具有更大的双折射。
图 5中给出了SL-DH-PCF和SL-EH-PCF两种不同光纤在不同结构参量条件下的偏振拍长特性。结果显示, SL-DH-PCF比SL-EH-PCF的偏振拍长要短。当H=0.5μm保持不变时,SL-DH-PCF的偏振拍长随着圆形空气孔半径的变化而变化较大,圆形空气孔半径越大,偏振拍长越短; 而当R=0.2μm保持不变时,SL-DH-PCF的偏振拍长随着双空气孔单元两孔间距的变化而变化不是太大。
图 6中给出了SL-DH-PCF和SL-EH-PCF两种不同光纤在不同结构参量条件下x偏振方向上的色散特性。结果显示, SL-DH-PCF和SL-EH-PCF在波长λ=1550nm处为负色散。
-
图 7中给出了该单偏振单模圆形双空气孔单元方形晶格排列型光子晶体光纤的有效折射率随工作波长变化的曲线。该型光纤包层有4层空气孔单元,即空气孔层数N=4, 其结构参量为Λ=2.3μm,R=0.4μm, H=1.0μm。左下角插图表示x偏振方向的基模电场分布图,右上角插图表示y偏振方向的基模电场分布图,对应的工作波长为λ=1.55μm。
Figure 7. Effective index of x-polarized and y-polarized fundamental modes as a function of wavelength for the proposed PCF
图 8中给出了该型光纤在参量为R=0.4μm,H=1.0μm, Λ分别为2.2μm和2.3μm时, 对应的限制损耗随工作波长变化的曲线。
双孔单元四边形晶格光子晶体光纤特性的研究
Properties of regular-lattice photonic crystal fiber based on a double-hole unit
-
摘要: 为了获得双空气孔单元四边形晶格排列光子晶体光纤的光学特性,采用有限元分析法对该型光纤进行了数值模拟计算,得到了该型光纤的双折射、限制损耗、偏振拍长及色散特性结果。结果表明,与椭圆空气孔方形晶格排列光子晶体光纤相比,在相同的空气占空比条件下,双空气孔单元方形晶格排列光子晶体光纤可以获得更高的双折射特性,达到10-2量级;该型光纤两偏振模的限制损耗差可达103量级。该型光纤易于制造,在光纤通信及光纤传感等领域有一定的应用前景。Abstract: In order to obtain optical characteristics of the photonic crystal fiber with double air holes and quadrilateral lattice arrangement, the finite element method was used to simulate the fiber. The results of birefringence, limiting loss, polarization beat length and dispersion characteristics of the fiber were obtained. The results show that, compared with the elliptical air hole photonic crystal fiber with square lattice arrangement, the double air hole photonic crystal fiber with square lattice arrangement can obtain higher birefringence characteristics, reaching 10-2 orders of magnitude, under the same air duty cycle conditions. The limiting loss difference of the two polarization modes of the fiber can reach 103 order of magnitude. This type of optical fiber is easy to manufacture, and has a certain application prospect in optical fiber communication and optical fiber sensing.
-
Key words:
- fiber optics /
- photonic crystal fiber /
- finite element method /
- birefringence /
- limiting loss
-
-
[1] CHEN D, SHEN L. Highly birefringent elliptical-hole photonic crystal fibers with double defect[J]. Journal of Lightwave Technology, 2007, 25(9): 2700-2705. doi: 10.1109/JLT.2007.902114 [2] CHEN D R, WU G Zh. Highly birefringent photonic crystal fiber based on a double-hole unit[J]. Applied Optics, 2010, 49(9): 1682-1686. doi: 10.1364/AO.49.001682 [3] LIU X A, WU G Zh, CHEN D R, et al. Novel highly bireferingent photonic crystal fiber based on an elliptical hole fiber cladding and a fiber core of double-micro-hole units[J]. Acta Photonica Sinica, 2011, 40(11): 1728-1732(in Chinese). doi: 10.3788/gzxb [4] MUSIDEKE M, YAO J Q, LU Y, et al. High birefringence and high nonlinear octagonal photonic crystal fiber with low confinement loss[J]. Infrared and Laser Engineering, 2013, 42(12): 3373-3379. [5] XU K, LU Sh Y, YANG Y. Research of CO2 gas sensors based on photonic crystal fiber[J]. Laser Technology, 2017, 41(5): 693-696 (in Chinese). [6] ZHANG X D, CHEN N, NIE F K, et al.Dispersion characteristics analysis of photonic crystal fibers based on structure parameters and filling modes[J]. Laser Technology, 2018, 42(1): 48-52 (in Chinese). [7] ZHANG W, LI Sh G, AN G W, et al.Double-cladding rectangular-lattice birefringence photonic crystal fiber with elliptical air holes[J]. Optical & Quantum Electronics, 2015, 47(8): 2649-2657. [8] YANG J F, CHEN M. Design of photonic crystal fiber based on hexagon-lattice circle air hole with high birefringence[J]. Journal of Guilin University of Electronic Technology, 2016, 36(4): 279-283 (in Chinese). [9] ZHOU M H, HUANG Y L. Highly bireferingent photonic crystal fiber based on lattice structure of elliptic layer[J]. Acta Photonica Sinica, 2016, 45(3): 0106002(in Chinese). [10] GU Q Zh, LI Q H. Novel photonic crystal fiber with high bireferingence and low loss[J]. Laser & Optoelectronics Progress, 2017, 54(6): 060603(in Chinese). [11] WANG J Y, CAO Y, LU Y J, et al. A novel high bireferingent photonic crystal fiber based on Schott glass[J]. Acta Photonica Sinica, 2014, 43(7): 0706020(in Chinese). doi: 10.3788/gzxb [12] CAI H J, SHEN Sh J, LIU X Sh.Photonic crystal fiber with Yb3+-doped aluminosilicate glass core[J]. Laser Technology, 2017, 41(5): 759-763(in Chinese). [13] ZHEN H L.Polarization filters based on high birefringence photonic crystal fiber filled with Au[J]. Laser Technology, 2016, 40(1): 1-4(in Chinese). [14] WU X X, FAN W D, LIAO W Y, et al. High bireferingence in graphene structure photonic crystal fiber[J]. Acta Photonica Sinica, 2016, 45(1):0106002(in Chinese). doi: 10.3788/gzxb [15] LIU Y C, LAI Y. Optical birefringence and polarization dependent loss of square- and rectangular-lattice holey fibers with elliptical air holes: numerical analysis[J]. Optics Exppress, 2005, 13(1): 225-235. doi: 10.1364/OPEX.13.000225 [16] WANG L, YANG D X. Highly birefringent elliptical-hole rectangular-lattice photonic crystal fibers with modified air holes near the core[J]. Optics Express, 2007, 15(14): 8892-8897 doi: 10.1364/OE.15.008892 [17] LIAO J F, SUN J Q.High birefringent rectangular-lattice photonic crystal fibers with low confinement loss employing different sizes of elliptical air holes in the cladding[J]. Optical Fiber Technology, 2012, 18(6): 457-461. doi: 10.1016/j.yofte.2012.07.006 [18] SHENG Y, LU J, YAO G F, et al. Analysis of highly bireferingent and confinement loss of elliptical air-holes rectangular photonic crystal fiber[J]. Acta Photonica Sinica, 2014, 43(s1): 0106008(in Chinese). [19] ZHANG X D, NIE F K, LU X L, et al. The characteristic analysis of microstructure photonic crystal fibers based on regular quadrilateral lattice[J]. Optical Instruments, 2017, 39(4): 18-24 (in Chinese). [20] ORTIGOSA-BLANCH A, KNIGHT J C, WADSWORTH W J. Highly birefringent photonic crystal fibers[J]. Optics Letters, 2000, 25(18): 1325-1327. doi: 10.1364/OL.25.001325 [21] NAMIHIRA Y, LIU J J, KOGA T, et al. Design of highly nonlinear octagonal photonic crystal fiber with near-zero flattened dispersion at 1.31μm waveband[J]. Optical Review, 2011, 18(6): 436-440. doi: 10.1007/s10043-011-0082-3