-
基于有限元法对多孔光子晶体光纤(PC-PCF)进行数值模拟与仿真。包层外,采用圆形完美匹配层(PML)作为边界条件,厚度占纤维总半径16%。整个仿真过程,定型几何由18176个域单元和2597个边界单元构成完整网格。
为检验PC-PCF保偏性能, 首先研究其双折射特性,计算公式如下[9]:
$ B=\left|n_{x}-n_{y}\right| $
(1) 式中, B为双折射率,nx和ny为x, y方向偏振折射率。
为确保PC-PCF能够高效传输THz波,电磁场应严格限制在纤芯内。光纤模场分布如图 2所示,在光纤单模传输范围内,对光纤进行逆时针方向旋转,旋转角θ为0°~60°,双折射率B=0.0532±0.0001,与先前参考文献中的报道[10-11]相比, 保偏能力更好,几乎不发生变化。双折射率与中心旋转角无关,不需调试特定角度以获得最大双折射,避免因调试而产生误差,在实际应用及操作中具有更优越的稳定性和抗干扰能力。
Figure 2. Mode field distribution of the proposed PCF for core diameter 320μm and operating frequency 0.85THz
纤芯孔隙度P[12]即纤芯气孔面积占纤芯面积百分率,光纤的光场分布和双折射影响如图 3所示。图中模态功率被严格限制在纤芯中,在0.85THz工作频率下,适当调整空隙度值,双折射率高达0.0532,远高于先前参考文献中的[13-16]报道。
为使THz波在纤芯传输更集中,有效模态面积可由下式算出[17]:
$ A_{\mathrm{eff}}=\frac{\left(\iint E^{2} \mathrm{d} x \mathrm{d} y\right)^{2}}{\iint E^{4} \mathrm{d} x \mathrm{d} y} $
(2) 式中, E为电场振幅。图 4中是x,y方向偏振有效模态面积随频率的变化曲线。从图中可明显看出, 随入射频率增加,有效模态面积减小,电磁波传播更趋于纤芯中心。色散是由于光纤传输时延不同而引起的脉冲展宽效应,主要影响系统传输能量大小及传播距离,是光纤一个非常重要的特性,它包括材料色散和波导色散。由于Topas在0.1THz~2THz频段下折射率为常数, 因此该频段下材料色散可以忽略不计,色散主要源于波导色散,可由下式得出[18]:
$ \beta_{2}=\frac{2}{c} \frac{\mathrm{d} n_{\mathrm{eff}}}{\mathrm{d} \omega}+\frac{\omega}{c} \frac{\mathrm{d}^{2} n_{\mathrm{eff}}}{\mathrm{d} \omega^{2}} $
(3) 式中,β2为波导色散, 单位为ps/THz/cm, neff为PCF有效折射率,c为真空中光速, ω是角频率(ω=2πf)。从图 5中可以看出,太赫兹PCF在0.5THz~0.85THz频率范围内呈现出一种相对较低且平坦的色散轮廓,频率增大,色散曲线更加平稳,y向偏振在0.845THz时到达第1个色散零点,临近0.85THz时达到第2个色散零点,整体色散低于先前报道[19-21]。
THz波段下PC-PCF这类多孔微结构纤维,主要传输损耗源于自身材料吸收,通常表现为有效模态损耗(EML),EML是制造THz波导中一个非常重要的特性,是设计高效THz波导主要考虑因素之一,它可以通过下式计算得到[19]:
$ \alpha_{\mathrm{eff}}=\frac{\left(\varepsilon_{0} / \mu_{0}\right)^{1 / 2} \iint_{A_{\mathrm{m}}} n \alpha_{\mathrm{m}}|E|^{2} \mathrm{d} A}{2 \int_{A_{\mathrm{all}}} S_{z} \mathrm{d} A} \mathrm{cm}^{-1} $
(4) 式中, ε0和μ0分别是真空中的介电常数、磁导率, n是Topas材料折射率, E是模态电场, A为面积,Am为介质材料区域,αm是Topas材料吸收损失, 分母是对PCF整体区域Aall进行积分,Sz是坡印亭矢量的z分量。
限制损耗(CL)是光子晶体光纤中通常发生的另一种损耗形式,与有效折射率虚部有关。因为它界定了光波导传输长度范围,是限制THz波在核心区域传播的重要指标之一,可用下式计算得到[20]:
$ {\alpha _{{\rm{CL}}}} = 8.686 \times \frac{{2{\rm{ \mathsf{ π} }}f}}{c}{\mathop{\rm Im}\nolimits} \left( {{n_{{\rm{eff}}}}} \right) \times {10^{ - 2}} $
(5) 式中, f为工作频率,Im(neff)为有效折射率虚部, αCL单位为dB/cm。
不同孔隙度EML随频率变化规律如图 6所示,频率增大,EML也随之增加。相反,限制损耗(CL)则随频率增加而呈下降趋势。0.85THz时,EML低至0.1157/cm,CL为1.47×10-4dB/cm,小于之前报道[21]。可见在固定工作频率下,利用较高空气孔隙度可实现降低EML目的。孔隙度增大,单位气孔所对应纤芯背景材料(Topas)体积减小,大部分模态功率进入多孔,有效材料损失减小。同理,限制损耗随纤芯孔隙度值的增大而增加。
Figure 6. Effective material loss and confinement loss as a function of frequency for different values of core porosity at Dcore=320μm
模态功率分数是PCF的另一个重要性质,即纤维内部不同区域功率分布百分率。在核心空气孔中传播能量大小用功率分数量化表示,功率分数可由下式计算[22]:
$ \eta=\frac{\int_{x} S_{z} \mathrm{d} A}{\int_{A_{\mathrm{all}}} S_{{z}} \mathrm{d} A} $
(6) 式中,η表示模式功率分数, x代表任意核心矩形气孔、背景材料或包层空气孔3个区域之一。图 7是PCF两个正交偏振态,不同区域模态功率作为频率的函数。f=0.85THz时,矩形孔x极化功率约占总功率29.1%, y极化功率约占总功率20.9%,所有能量都被限制在波导内,无任何能量泄露。一部分光能被用于传输;另一部分光能分布于多孔纤维包层区域。
渐近式太赫兹多孔光子晶体光纤模式特性研究
Study on mode characteristics of asymptotic terahertz porous photonic crystal fibers
-
摘要: 为了研究太赫兹波在新型渐近式多孔光子晶体光纤的传输特性, 采用有限元数值分析法进行了数值仿真, 分析了有效模态面积、纤芯孔隙度对有效材料损失及限制损耗、功率分布分数等波导特性的影响。结果表明, 在单模传输范围0.5THz~0.85THz内, 通过在光纤上引入渐近矩形阵列气孔和椭圆空穴, 实现了零色散、0.0532高双折射、有效材料损失为0.1157/cm, 限制损耗低至1.47×10-4dB/cm。此研究可用于制造极化THz波导、滤波器等, 对新一代太赫兹波导实现长距离、高性能传输的研究具有重要意义。Abstract: In order to study transmission characteristics of terahertz wave in new asymptotic porous photonic crystal fibers, finite element numerical analysis method was used for numerical simulation. The effects of effective mode area and core porosity on effective material loss, confinement loss and power distribution fraction were analyzed. The results show that, within the range of 0.5THz to 0.85THz, by introducing an asymptotic rectangular array of holes and elliptical holes into the optical fiber, zero dispersion, high birefringence of 0.0532, effective material loss of 0.1157/cm and confinement loss of 1.47×10-4 dB/cm are achieved. This study can be used to fabricate polarized THz waveguides, filters, etc. It is of great significance to study the long-distance and high-performance transmission of the new generation terahertz waveguides.
-
Key words:
- fiber optics /
- photonic crystal fiber /
- finite element model /
- terahertz /
- dispersion
-
-
[1] AMING A, RAHMAN B M A. Design and characterization low-loss modes in dielectric-coated hollow-core waveguides at THz frequency[J]. Journal of Lightwave Technology, 2018, 36(13):2716-2722. doi: 10.1109/JLT.2018.2820690 [2] WANG C, WU G Zh, ZHOU P, et al. Mode properties of hybrid plasmonic waveguide with an metal nano-rib[J]. Acta Photonica Sinica, 2014, 43(9): 0916001(in Chinese). doi: 10.3788/gzxb20144309.0916001 [3] HSU J M. Systematic design of highly birefringent photonic crystal fibers [J]. Applied Physics, 2017, B123(3):73. [4] ATAKARAMIANS S, SHAHRAAM A V, EBENDORFF-HEIDEPRIEM H, et al. THz porous fibers: Design, fabrication and experimental characterization[J]. Optics Express, 2009, 17(16):14053-14062. doi: 10.1364/OE.17.014053 [5] HASANUZZAMAN G K M, RANA S, HABIB M S. A novel low loss, highly birefringent photonic crystal fiber in THz regime[J]. IEEE Photonics Technology Letters, 2016, 28(8):899-902. doi: 10.1109/LPT.2016.2517083 [6] KAWSAR A, SAWRAD C, KUMAR P B, et al. Ultrahigh birefringence, ultralow material loss porous core sigle-mode fiber for terahertz wave guidance[J]. Applied Optics, 2017, 56(12):3477-3483. doi: 10.1364/AO.56.003477 [7] ZHANG F, WU G Zh, WANG Ch Ch. Influence of surface curvature on mode and sensing characteristics of quartz capillary micro-bottles. Laser Technology, 2018, 42(6): 840-844(in Chinese). [8] CHU Zh Zh, YOU L B, WANG Q Sh, et al. Progress in fabrication of polymer optical fiber gratings[J]. Laser Technology, 2018, 42(1): 11-18(in Chinese). [9] ORTIGOSABLANCH A, KNIGHT J C, WADSWORTH W J, et al. Highly birefringent photonic crystal fibers[J]. Optics Letters, 2000, 25(18):1325-1327. doi: 10.1364/OL.25.001325 [10] WU Zh, SHI Zh, XIA H, et al. Design of highly birefringent and low-loss oligoporous-core THz photonic crystal fiber with single circular air-hole unit[J]. IEEE Photonics Journal, 2016, 8(6):1-11. [11] CHEN N N, LIANG J, REN L, et al. High-birefringence, low-loss porous fiber for single-mode terahertz-wave guidance[J]. Applied Optics, 2013, 52(21):5297-5302. doi: 10.1364/AO.52.005297 [12] HASANUZZAMAN G K M, HABIB M S, ABDUR RAZZAK S M, et al. Low loss single mode porous-core kagome photonic crystal fiber for THz wave guidance[J]. Journal of Lightwave Technology, 2015, 33 (19): 4027-4031. doi: 10.1109/JLT.2015.2459232 [13] CHO M, KIM J, PARK H, et al. Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers[J]. Optics Express, 2008, 16(1):7-12. [14] ISLAM R, HABIB M S, HASANUZZAMAN G K M, et al. Novel porous fiber based on dualasymmetry for low-loss polarization maintaining THz wave guidance[J]. Optics Letters, 2016, 41(3):440-443. doi: 10.1364/OL.41.000440 [15] REN G. Low-loss air-core polarization maintaining terahertz fiber [J]. Optics Express, 2008, 16(18): 13593-13598. doi: 10.1364/OE.16.013593 [16] KIM S E, KIM B H, LEE C G, et al. Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion. [J]. Optics Express, 2012, 20(2):1385-1391. doi: 10.1364/OE.20.001385 [17] LIU M, YUAN H T, SHUM P, et al. Simultaneous achievement of highly birefringent and nonlinear photonic crystal fibers with an elliptical tellurite core[J]. Applied Optics, 2018, 57(22):6383-6387. doi: 10.1364/AO.57.006383 [18] ISLAM M S, FAISAL M, RAZZAK S M A. Extremely low loss porous-core photonic crystal fiber with ul tra-flat dispersion in terahertz regime[J]. Journal of the Optical Society of America, 2017, B34(8):1747-1754. [19] YANG T Y, DING C, ZIOLKOWSKI R W, et al. A scalable THz photonic crystal fiber with partially-slotted core that exhibits improved birefringence and reduced loss[J]. Journal of Lightwave Technology, 2018, 36(16):3408-3417. doi: 10.1109/JLT.2018.2842825 [20] HABIB M A, ANOWER M S. Low loss highly birefringent porous core fiber for single mode terahertz wave guidance[J]. Current Optics and Photonics, 2018, 2(3): 215-220. [21] ATAKARAMIANS S, SHAHRAAM A V, EBENDORFF-HEIDEPRIEM H, et al. THz porous fibers: Design, fabrication and experimental characterization[J]. Optics Express, 2009, 17(16):14053-15062. doi: 10.1364/OE.17.014053 [22] KAIJAGE S F, OUYANG Zh B, JIN X. Porous-core photonic crystal fiber for low loss terahertz wave guiding[J]. IEEE Photonics Technology Letters, 2013, 25(15):1454-1457. doi: 10.1109/LPT.2013.2266412