空芯光子带隙光纤的结构设计和特性研究
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摘要
光子晶体光纤的出现开辟了光纤发展的新时代,并在短时间就展现出了普通光纤无法比拟的优越特性和巨大的发展潜力,近年来已成为光通信领域的一个研究热点。而根据导光机制的不同可将光子晶体光纤分为两大类,一类是全内反射光子晶体光纤,另一类是光子带隙光纤,对于前者的研究较多且理论上已接近成熟,后者的研究偏少且与前者相比后者具有高效耦合特性,低非线性特性和传输窗口可控等特性,因此受到了包括军方在内的各界的广泛关注。
本论文从理论上对空芯光子带隙光纤(HC-PBGFs)的结构设计与特性分析进行了探索性的研究,首先对光子晶体和光子晶体光纤的概念、发展和特性给予介绍,尤其对HC-PBGFs的特性进行了总结,随后建立了理论研究的基础,对HC-PBGFs的纤芯设计、模式特征、色散、非线性和损耗等特性进行了分析,主要工作概括如下:
1.对构成光纤的四种格点结构包括圆化空气孔进行了简要的介绍,利用平面波展开法(PWM)求解电场的本征值方程,得到了折射率比为1.45:1的平面外带隙结构图,并对其进行了较详细的分析,得出占空比越大要求沿传播方向的传播常数越大才能形成光子带隙的结论;利用PWM给出了带隙传播图,并利用该图解释了要想在HC-PBGFs中实现中心缺陷导光,必须同时具备光波频率落入光子带隙范围内和传播模式满足β≤kn_2,这两个条件的结论。
2.详细推导了基于混合棱边/节点元的全矢量有限元(FEM)模型和完全匹配层(PML)边界条件。给出了计算光子晶体光纤磁场矢量的FEM模型。并利用该模型考察了三角格子全内反射光子晶体光纤的色散特性,给出了模式的场能量分布、等高线分布和色散,与已发表文献的结果吻合良好,验证了模型的正确性和有效性。为后续章节提供了理论基础。
3.利用带隙传播图设计了研究的三角格子HC-PBGFs,简要分析了表面模(SMs)形成的原因,并利用全矢量FEM模拟了在不同纤芯截切半径情况下的光纤,得出了消除SMs的光纤纤芯半径的最佳可取范围为R=0.9-1.0A。随后,同样利用带隙结构图设计了研究的圆六边形空气孔按三角格子排列的HC-PBGFs,模拟了不同纤芯外半径和不同石英环相对厚度的光纤,发现石英环的引入既可以抑制SMs也可以激发SMs,关键要看纤芯环厚度的选择;得出了相应的消除SMs的光纤纤芯外半径和石英环相对厚度的可取范围。在最后研究了光纤的薄壁芯环,得出了芯环壁的最佳归一化厚度取值范围为T=0.3-0.6之间。
4.对具有C_(6v)对称的19单元芯HC-PBGFs的模式简并特性进行了分析,对找到的16个模式进行了分类和命名,随后对常用的7单元芯三角格子HC-PBGFs的模场特性、色散特性、基质中的能量分布特性、有效模场面积、非线性系数以及损耗特性进行了较全面的分析,并对材料效应也做了研究,研究发现在计算大占空比的HC-PBGFs的色散时,可以忽略材料色散,而材料效应对非线性系数的贡献是不能忽略的,并得出了对于HC-PBGFs而言其非线性系数很小要比传统单模光纤的非线性系数低大约3个数量级的结论;最后研究了HC-PBGFs的色散可控特性,发现可以通过改变光纤的包层和纤芯的结构参数来实现调节光纤的零色散点和色散斜率,改变空气孔的圆化直径或者芯环的厚度能够控制光纤的色散斜率,改变空气孔的圆化直径、孔间距、基质折射率、芯环厚度以及占空比可调节光纤的零色散点。
5.研究了基于正方格子(SL)的HC-PBGFs的模场行为,发现该种光纤有两个优点一是模式的宽带运行,二是有效的单模运转。随后对SLHC-PBGFs的泄漏损耗进行了全面的分析,发现包层数是影响泄漏损耗的主要因素,圆化直径、孔间距和纤芯直径对泄漏损耗的影响较小,但可以通过调节它们使得在确定的波长下具有最小的泄漏损耗。首次对该种光纤的色散特性进行了分析,经分析发现SL HC-PBGFs的色散特性主要由光纤纤芯和包层结构决定,纤芯直径的和包层环数的变化对色散的影响较小,圆化直径、孔间距和占空比的变化对色散的影响较大;色散特性满足HC-PBGFs的缩放率,且改变这种光纤的结构可以实现对其色散波长和色散斜率的调节。
Advent of photonic crystal fibers(PCFs) opens up a new era of development of optical fibers,which exhibit many unique properties that are not realized in conventional optical fibers and hold great potential,and PCFs have become a research hotspot in the field of optical communications.According to the difference of guiding mechanisms,PCFs can be.divided into two types.One is total internal reflection PCFs(TIR-PCFs),the other is photonic bandgap fibers(PBGFs).More researches concentrate on the former one and matured theory has been developed.But PBGFs posses a few unique properties,such as highly effective coupling,low nonlinear and controllable transmission window, and they have attracted a considerable amount of attention from various fields including army.
The dissertation focuses on structure designs and properties research of hollow-core photonic bandgap fibers(HC-PBGFs) from theory.Firstly,it presents a brief review of photonic crystal and some fundamental concepts,the development and properties of PCFs,especially the properties of HC-PBGFs are summarized.And then,numerical methods and mathematic tools are illustrated in the following chapter,by which properties of HC-PBGFs are analyzed,involving core design,mode characteristics,dispersion,nonlinear,and loss.The primary works could be described as follows:
1.A brief introduction to four types of lattice structure of photonic crystal is presented.By means of plane wave extension method(PWM) to solve the eigenvalue equation of electric field,we come at out of plane bandgap structure diagram with index ratio 1.45:1,and conclude by detailed analysis that more larger air filling fraction is,more larger propagation constants are needed to form photonic bandgap.In addition,from bandgap propagation diagram we can found that guiding light in defect core for HC-PBGFs needs satisfy two conditions:(1) beam frequency lying in range of photonic bandgap,(2) propagation constant of guiding mode abides by the condition ofβ≤kn_2.
2.A full-vector finite element method(FEM) based on hybrid edge/nodal element and perfectly matched layers boundary conditions are deduced in detail. Furthermore,the FEM model of the magnetic field vector for PCFs is given by this method.And we take advantage of the model to investigate the dispersion of triangular lattice TIR-PCF,and corresponding results are in good agreement with that of the literature published,which verifies the correctness and effectiveness of the model.This chapter provides a theoretical basis for the follow-up chapters.
3.Triangular lattice HC-PBGFs to be studied are designed by using the bandgap propagation diagram,the different core radius of the fibers are simulated by full-vector FEM model solver.A brief analysis of the reasons for the formation of surface modes(SMs) is presented,the optimal range of core radius that is free of SMs is R = 0.9-1.0A.And then,we design HC-PBGFs with rounded hexagons air hole arranged by triangular lattice,and simulate the fibers with different outer core radius and different normalized core thickness. By analysis it shows that the introduction of the silica ring can not only inhibit SMs but also induce SMs,whether SMs appear or not depends on the choice of the core ring thickness.The desired range of outer core radius and core ring thickness free of SMs is derived.In the final we investigate thin-wall core ring of the fibers and conclude that the optimal normalized thickness range is T= 0.3-0.6.
4.Mode degeneracy of 19-cell HC-PBGFs with C_(6v) symmetry is discussed in detail and 16 models found are classified and named according to the label of traditional step-index fiber.And then we investigate properties of 7-cell HC-PBGFs,including mode characteristics,dispersion,power fraction in silica,mode effective area,nonlinear coefficient and loss,and together with material effect.By analysis we can conclude that material dispersion can be neglected for HC-PBGFs with high air filling fraction,but the contribution of material effect to nonlinear coefficient can not be ignored,and the nonlinear coefficient of HC-PBGFs is roughly 3 orders of magnitude lower than that of conventional optical fibers.Finally,controllable dispersion property of HC-PBGFs is discussed.By simulating we found that theoretically the zero dispersion wavelength can be tailored by respectively changing rounded diameter of air holes,pitch,refractive index,normalized thickness of core rings, and the ratio of hole diameter to pitch.At the same time the tailoring of dispersion slope can also be realized by changing rounded diameter of air holes or pitch or normalized thickness of core rings.
5.The modal characteristics of HC-PBGFs based on a square lattice with rounded square air holes are investigated,by using a full-vector FEM.And it was found that there are two advantages for this type fiber,one is operating under broad bandgap and another is single mode.And then,the leakage loss was analyzed completely.Simulations show that the number of cladding rings plays a key role to the leakage loss,while the rounded diameter,the core diameter and the hole pitch have a small influence on leakage loss but for a given wavelength the desired lowest leakage loss could be obtained by tuning them.In addition, the dispersion properties of the fibers are investigated for the first time.By simulation,we can found the core diameter and the number of cladding rings have a small influence on dispersion comparing to rounded diameter,hole pitch and air filling fraction.And dispersion property is found to satisfy scaling law of HC-PBGFs,furthermore the desired dispersion wavelength or desired dispersion slope could be obtained by properly changing the structure of the fibers.
本论文从理论上对空芯光子带隙光纤(HC-PBGFs)的结构设计与特性分析进行了探索性的研究,首先对光子晶体和光子晶体光纤的概念、发展和特性给予介绍,尤其对HC-PBGFs的特性进行了总结,随后建立了理论研究的基础,对HC-PBGFs的纤芯设计、模式特征、色散、非线性和损耗等特性进行了分析,主要工作概括如下:
1.对构成光纤的四种格点结构包括圆化空气孔进行了简要的介绍,利用平面波展开法(PWM)求解电场的本征值方程,得到了折射率比为1.45:1的平面外带隙结构图,并对其进行了较详细的分析,得出占空比越大要求沿传播方向的传播常数越大才能形成光子带隙的结论;利用PWM给出了带隙传播图,并利用该图解释了要想在HC-PBGFs中实现中心缺陷导光,必须同时具备光波频率落入光子带隙范围内和传播模式满足β≤kn_2,这两个条件的结论。
2.详细推导了基于混合棱边/节点元的全矢量有限元(FEM)模型和完全匹配层(PML)边界条件。给出了计算光子晶体光纤磁场矢量的FEM模型。并利用该模型考察了三角格子全内反射光子晶体光纤的色散特性,给出了模式的场能量分布、等高线分布和色散,与已发表文献的结果吻合良好,验证了模型的正确性和有效性。为后续章节提供了理论基础。
3.利用带隙传播图设计了研究的三角格子HC-PBGFs,简要分析了表面模(SMs)形成的原因,并利用全矢量FEM模拟了在不同纤芯截切半径情况下的光纤,得出了消除SMs的光纤纤芯半径的最佳可取范围为R=0.9-1.0A。随后,同样利用带隙结构图设计了研究的圆六边形空气孔按三角格子排列的HC-PBGFs,模拟了不同纤芯外半径和不同石英环相对厚度的光纤,发现石英环的引入既可以抑制SMs也可以激发SMs,关键要看纤芯环厚度的选择;得出了相应的消除SMs的光纤纤芯外半径和石英环相对厚度的可取范围。在最后研究了光纤的薄壁芯环,得出了芯环壁的最佳归一化厚度取值范围为T=0.3-0.6之间。
4.对具有C_(6v)对称的19单元芯HC-PBGFs的模式简并特性进行了分析,对找到的16个模式进行了分类和命名,随后对常用的7单元芯三角格子HC-PBGFs的模场特性、色散特性、基质中的能量分布特性、有效模场面积、非线性系数以及损耗特性进行了较全面的分析,并对材料效应也做了研究,研究发现在计算大占空比的HC-PBGFs的色散时,可以忽略材料色散,而材料效应对非线性系数的贡献是不能忽略的,并得出了对于HC-PBGFs而言其非线性系数很小要比传统单模光纤的非线性系数低大约3个数量级的结论;最后研究了HC-PBGFs的色散可控特性,发现可以通过改变光纤的包层和纤芯的结构参数来实现调节光纤的零色散点和色散斜率,改变空气孔的圆化直径或者芯环的厚度能够控制光纤的色散斜率,改变空气孔的圆化直径、孔间距、基质折射率、芯环厚度以及占空比可调节光纤的零色散点。
5.研究了基于正方格子(SL)的HC-PBGFs的模场行为,发现该种光纤有两个优点一是模式的宽带运行,二是有效的单模运转。随后对SLHC-PBGFs的泄漏损耗进行了全面的分析,发现包层数是影响泄漏损耗的主要因素,圆化直径、孔间距和纤芯直径对泄漏损耗的影响较小,但可以通过调节它们使得在确定的波长下具有最小的泄漏损耗。首次对该种光纤的色散特性进行了分析,经分析发现SL HC-PBGFs的色散特性主要由光纤纤芯和包层结构决定,纤芯直径的和包层环数的变化对色散的影响较小,圆化直径、孔间距和占空比的变化对色散的影响较大;色散特性满足HC-PBGFs的缩放率,且改变这种光纤的结构可以实现对其色散波长和色散斜率的调节。
Advent of photonic crystal fibers(PCFs) opens up a new era of development of optical fibers,which exhibit many unique properties that are not realized in conventional optical fibers and hold great potential,and PCFs have become a research hotspot in the field of optical communications.According to the difference of guiding mechanisms,PCFs can be.divided into two types.One is total internal reflection PCFs(TIR-PCFs),the other is photonic bandgap fibers(PBGFs).More researches concentrate on the former one and matured theory has been developed.But PBGFs posses a few unique properties,such as highly effective coupling,low nonlinear and controllable transmission window, and they have attracted a considerable amount of attention from various fields including army.
The dissertation focuses on structure designs and properties research of hollow-core photonic bandgap fibers(HC-PBGFs) from theory.Firstly,it presents a brief review of photonic crystal and some fundamental concepts,the development and properties of PCFs,especially the properties of HC-PBGFs are summarized.And then,numerical methods and mathematic tools are illustrated in the following chapter,by which properties of HC-PBGFs are analyzed,involving core design,mode characteristics,dispersion,nonlinear,and loss.The primary works could be described as follows:
1.A brief introduction to four types of lattice structure of photonic crystal is presented.By means of plane wave extension method(PWM) to solve the eigenvalue equation of electric field,we come at out of plane bandgap structure diagram with index ratio 1.45:1,and conclude by detailed analysis that more larger air filling fraction is,more larger propagation constants are needed to form photonic bandgap.In addition,from bandgap propagation diagram we can found that guiding light in defect core for HC-PBGFs needs satisfy two conditions:(1) beam frequency lying in range of photonic bandgap,(2) propagation constant of guiding mode abides by the condition ofβ≤kn_2.
2.A full-vector finite element method(FEM) based on hybrid edge/nodal element and perfectly matched layers boundary conditions are deduced in detail. Furthermore,the FEM model of the magnetic field vector for PCFs is given by this method.And we take advantage of the model to investigate the dispersion of triangular lattice TIR-PCF,and corresponding results are in good agreement with that of the literature published,which verifies the correctness and effectiveness of the model.This chapter provides a theoretical basis for the follow-up chapters.
3.Triangular lattice HC-PBGFs to be studied are designed by using the bandgap propagation diagram,the different core radius of the fibers are simulated by full-vector FEM model solver.A brief analysis of the reasons for the formation of surface modes(SMs) is presented,the optimal range of core radius that is free of SMs is R = 0.9-1.0A.And then,we design HC-PBGFs with rounded hexagons air hole arranged by triangular lattice,and simulate the fibers with different outer core radius and different normalized core thickness. By analysis it shows that the introduction of the silica ring can not only inhibit SMs but also induce SMs,whether SMs appear or not depends on the choice of the core ring thickness.The desired range of outer core radius and core ring thickness free of SMs is derived.In the final we investigate thin-wall core ring of the fibers and conclude that the optimal normalized thickness range is T= 0.3-0.6.
4.Mode degeneracy of 19-cell HC-PBGFs with C_(6v) symmetry is discussed in detail and 16 models found are classified and named according to the label of traditional step-index fiber.And then we investigate properties of 7-cell HC-PBGFs,including mode characteristics,dispersion,power fraction in silica,mode effective area,nonlinear coefficient and loss,and together with material effect.By analysis we can conclude that material dispersion can be neglected for HC-PBGFs with high air filling fraction,but the contribution of material effect to nonlinear coefficient can not be ignored,and the nonlinear coefficient of HC-PBGFs is roughly 3 orders of magnitude lower than that of conventional optical fibers.Finally,controllable dispersion property of HC-PBGFs is discussed.By simulating we found that theoretically the zero dispersion wavelength can be tailored by respectively changing rounded diameter of air holes,pitch,refractive index,normalized thickness of core rings, and the ratio of hole diameter to pitch.At the same time the tailoring of dispersion slope can also be realized by changing rounded diameter of air holes or pitch or normalized thickness of core rings.
5.The modal characteristics of HC-PBGFs based on a square lattice with rounded square air holes are investigated,by using a full-vector FEM.And it was found that there are two advantages for this type fiber,one is operating under broad bandgap and another is single mode.And then,the leakage loss was analyzed completely.Simulations show that the number of cladding rings plays a key role to the leakage loss,while the rounded diameter,the core diameter and the hole pitch have a small influence on leakage loss but for a given wavelength the desired lowest leakage loss could be obtained by tuning them.In addition, the dispersion properties of the fibers are investigated for the first time.By simulation,we can found the core diameter and the number of cladding rings have a small influence on dispersion comparing to rounded diameter,hole pitch and air filling fraction.And dispersion property is found to satisfy scaling law of HC-PBGFs,furthermore the desired dispersion wavelength or desired dispersion slope could be obtained by properly changing the structure of the fibers.
引文
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