-
高功率光纤激光器在散热、效率和输出光束质量方面所具有的优势[1-2]，使其广泛应用于医疗、工业和国防等领域。近年来，高功率光纤激光器受到了学者们的广泛关注，其激光输出功率已经超过了10 kW[3]。然而，非线性效应[4]限制了光纤激光器输出功率的进一步提高。增大模场面积能有效降低非线性效应[5]。传统光纤通过增加纤芯直径可以增大模场面积，但也造成光纤中传输模式增多，抗弯曲性能变差，从而影响光纤的传输质量。因此，最大的挑战是在保持单模工作状态下增加光纤的模场面积，同时保证光束质量不受影响[6]。
近年来，人们提出了多种具有良好弯曲稳定性的光纤结构以实现在大模场中的单模传输。如光子晶体光纤(PCFs)[7-11]、低数值孔径(NA)阶跃光纤[12-13]、布拉格光纤[14]、多下陷层光纤[15-16]等。但这些光纤都存在一些问题，光子晶体光纤结构复杂，而且需要纯硅包层，制造工艺难以实现。更重要的是，含有空气孔的PCF在实际中还存在一些缺陷，空气孔的存在会导致光纤容易开裂，熔接过程中空气孔的塌陷会导致光束质量变差、稳定性降低。低NA阶跃光纤通过降低截止波长可实现单模操作，增加纤芯直径虽然有助于降低NA，但在实际制备过程中，生产NA小于0.06的光纤是难以制造的[17]。布拉格光纤在增加模场面积方面表现出良好的性能，但光纤中高折射率环会与纤芯产生不必要的耦合。
文中提出了一种具有多下陷层和梯形折射率环的新型光纤结构。多下陷层的结构使光纤具有较低的弯曲损耗，梯形折射率环的设计使光纤在1550 nm的波长和20 cm的弯曲半径下具有2313.67 μm2的模场面积。与传统光纤相比，带有梯形折射率环的光纤可以获得更显著的模场面积。同时，梯形折射率环可以作为一个谐振环与光纤的HOMs产生谐振耦合，使设计的光纤可以实现单模传输。此外，该光纤的结构是对称的，不同的弯曲方向不会影响光纤的性能。
-
图1(a)为光纤的二维横截面示意图，中心的黑色部分表示光纤的核心，外围的绿-黑-绿部分是梯形折射率环，绿色部分是折射率渐变区域，黑色部分是折射率平坦区域，其折射率与纤芯相同。图中多下陷层的部分为蓝色，与包层相同折射率的部分用灰色表示。图1(b)显示了光纤的折射率分布。纤芯和梯形折射率环的平坦区域的折射率为n1，包层的折射率为n2，而下陷层的折射率为n3。高折射率纤芯的半径为r，纤芯到梯形折射率环的距离为t，渐变区的半径为d，平坦区的宽度为t1，梯形折射率环到下陷层的距离为t2，下陷层的宽度为d1，而下陷层之间的距离为t3。
图 1 (a)光纤二维横截面示意图；(b)光纤折射率分布
Figure 1. Schematic diagram of fiber 2D cross-section; (b) Fiber refractive index distribution
梯形折射率环平坦区域的折射率与纤芯的折射率相同。公式(1)可以定义左侧(nl)和右侧(nr)的渐变部分的折射率分布。
$$ \begin{gathered} {n_l} = {\Delta _l} \times (x - {d_0}) + {n_1}\begin{array}{*{20}{c}} {}&{} \end{array} \\ (r + t < x < r + t + d) \\ {\Delta _l} = (n_1 - n_2)/d \\ {d_0} = r + t + d \\ {n_r} = {\Delta _r} \times (x - {d_2}) + {n_2}\begin{array}{*{20}{c}} {}&{} \end{array} \\ (r + t + d + {t_1} < r + t + 2d + {t_1}) \\ {\Delta _r} = ({n_2} - {n_1})/d \\ \end{gathered} $$ (1) 式中：n1为梯形折射率环的最高折射率；n2为梯形折射率环的最低折射率；Δl和Δr为梯度区域内折射率的相对变化率；d0为平坦区域的起始位置点；d2为梯形折射率环的终点位置点。纤芯的半径为55 μm，光纤的半径r1=200 μm。笔者使用COMSOL Multiphysics商业软件来进行数值模拟。采用映射网格和自由三角形网格对设计结构进行网格划分，网格顶点13666、三角形单元22230、单元数24630，平均网格质量达到0.9088，求解自由度达到了175995，如图2所示。
图 2 所提出横截面的网格划分
Figure 2. Mesh generation of cross-section of proposed fiber
当FM的两个偏振方向之间较高的弯曲损耗低于0.1 dB/m，同时HOMs的不同偏振方向之间最低的弯曲损耗高于1 dB/m时，可以认为其实现了单模工作。同时，损耗比是指HOMs与FM的比值。损耗比越高，光纤的弯曲性能越好[13]。
为计算光纤的弯曲损耗，将弯曲结构的折射率转换为直光纤的等效表示，t弯曲的影响可以表示为[18]：
$$ n_{eq}^2(r,\theta ) = {n^2}(r) \times \left(1 + \dfrac{{2r}}{{\rho R}}\cos \theta \right) $$ (2) 式中：r为光纤的坐标轴，原点为光纤的中心；ρ为弹性光学系数，其值为1.2~1.28；θ为弯曲方位角；R为光纤的弯曲半径。文中根据文献[19]的推荐，将ρ设为1.25。
模场面积可以反映光纤内部功率密度的大小，计算模场面积为：
$$ {A_{eff}} = \frac{{{{\left(\displaystyle\iint {|E{{(x,y)}^2}|} \times {{\rm{d}}x}{{\rm{d}}y}\right)}^2}}}{{\displaystyle\iint {|E{{(x,y)}^4}|} \times {{\rm{d}}x}{{\rm{d}}y}}} $$ (3) 式中：E(x,y)表示光纤中的横向电场分量。
当稀土掺杂光纤用于激光工作时，由于量子缺陷会产生热负载。热负荷下的折射率可计算为[20]：
$$ {n_T}\left(q,r\right) = \left\{ {\begin{array}{*{20}{l}} {{n_1} + \dfrac{{qr_c^2\beta }}{{4{k_{si}}}}\left[ {1 + \dfrac{{2{k_{si}}}}{{{h_1}}} + 2\ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{a}{c}\right) - {{\left(\dfrac{r}{{r_c^2}}\right)}^2}} \right]\begin{array}{*{20}{c}} {} \end{array}0 < r < {r_1}\begin{array}{*{20}{c}} {} \end{array}{r_1} + t + d < r < {r_1} + t + d + {t_1}} \\ {{n_1} + \dfrac{{qr_c^2\beta }}{{4{k_{si}}}}\left[ {1 + \dfrac{{2{k_{si}}}}{{{h_1}}} + 2\ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{a}{c}\right) - {{\left(\dfrac{r}{{r_c^2}}\right)}^2}} \right]\begin{array}{*{20}{c}} {} \end{array}{r_1} < r < {r_1} + {t_1}\begin{array}{*{20}{c}} {} \end{array}{r_1} + t + 2d + {t_1} < r < {r_1} + t + 2d + {t_1} + {t_2}} \\ {\left({\Delta _l}\left(r - {d_0}\right) + {n_1}\right) + \dfrac{{qr_c^2\beta }}{{4{k_{si}}}}\left[ {1 + \dfrac{{2{k_{si}}}}{{{h_1}}} + 2\ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{c}{b}\right) - {{\left(\dfrac{r}{{r_c^2}}\right)}^2}} \right]\begin{array}{*{20}{c}} {} \end{array}{r_1} + t < r < {r_1} + t + d} \\ {\left({\Delta _l}\left(r - {d_2}\right) + {n_1}\right) + \dfrac{{qr_c^2\beta }}{{4{k_{si}}}}\left[ {1 + \dfrac{{2{k_{si}}}}{{{h_1}}} + 2\ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{c}{b}\right) - {{\left(\dfrac{r}{{r_c^2}}\right)}^2}} \right]\begin{array}{*{20}{c}} {} \end{array}{r_1} + t + d + {t_1} < r < {r_1} + t + 2d + {t_1}} \\ {{n_2} + \dfrac{{qr_c^2\beta }}{{2{k_{si}}}}\left[ {\dfrac{{2{k_{si}}}}{{{h_1}}} + \ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{a}{c}\right)} \right]\begin{array}{*{20}{c}} {} \end{array}{\rm cladding}\begin{array}{*{20}{c}} {} \end{array}{r_c} < r < b} \\ {{n_3} + \dfrac{{qr_c^2\beta }}{{2{k_{si}}}}\left[ {\dfrac{{2{k_{si}}}}{{{h_1}}} + \ln \left(\dfrac{b}{{{r_c}}}\right) + 2\dfrac{{{k_{si}}}}{{{k_{ac}}}}\ln \left(\dfrac{a}{c}\right)} \right]\begin{array}{*{20}{c}} {} \end{array}{ {\rm{Low}}\text{-}{\rm{index}}}\begin{array}{*{20}{c}} {} \end{array}{\rm in}\begin{array}{*{20}{c}} {} \end{array}{\rm cladding}\begin{array}{*{20}{c}} {} \end{array}{r_c} < r < b} \end{array}} \right. $$ (4) -
为了研究梯形折射率环和多下陷层结构的光纤弯曲性能，固定设置折射率为n1=1.44，n2=1.4395，n3=1.439，并对相关参数r、t、d、t1、t2、d1、t3进行参数化扫描，总结不同结构对光纤弯曲性能的影响，选择较优的结构参数。文中提出的光纤原始参数为r=30 μm，t=14 μm，d=4 μm，t1=4 μm，t2=22 μm，d1=12 μm，t3=17 μm。
首先，文中讨论了通过改变r值，即纤芯半径对光纤弯曲性能的影响。当其他参数保持不变时，r值在25~32 μm范围内变化。如图3(a)所示，随着r的增加，FM的弯曲损耗持续下降。当t分别为25 μm和32 μm时，对应的FM的弯曲损耗为0.027334 dB/m和0.00855 dB/m，弯曲损耗提高了一个数量级。然而，HOMs的弯曲损耗也不断下降，它从t=25 μm时的4.549815 dB/m下降到t=32 μm时的1.455636 dB/m，减少了68%。按照这个变化趋势，r继续增加，所提出的光纤将不能满足单模操作的要求。所以，弯曲损耗的改善是以牺牲单模操作为代价的。图3(b)显示了光纤的模场面积和损耗比随r的变化趋势，随着r
的增加，弯曲光纤的模场面积逐渐变大，损耗比先增加后减少。当r=32 μm时，模场面积达到最大，最大值为2007.42 μm2，损耗比为170。当r=28 μm时，模场面积为1898.02 μm2，损耗比达到最大值243。笔者选择r=28 μm，舍弃模场面积，使设计的光纤具有更好的弯曲性能。 
图 3 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积和高基频损耗比随r的变化
Figure 3. (a) Bending loss of FM and HOMs; (b) Mode field area of FM and variation of high-fundament loss ratio with r
-
纤芯到梯形折射率环的距离以及梯形折射率环到多下陷层的距离分别用t、t2表示，t的变化范围是12~20 μm，t2的范围是20~26 μm。从图4(a)可看出，当t=20 μm时，FM的弯曲损耗大于0.1 dB/m，不符合单模工作的要求。随着t和t2的减少，FM的弯曲损耗持续下降。当t=12 μm、t2=20 μm时，FM的弯曲损耗达到最小值0.007735 dB/m。这是因为t和t2的增加，间接降低了纤芯的折射率，导致纤芯与包层之间的折射率差减小，不利于改善光纤的弯曲损耗。HOMs的弯曲损耗总是随着t和t2的增加先增加后减少。当t=14 μm、t2=26 μm时，HOMs的弯曲损耗为10.08 dB/m，较大的损耗有利于光纤的单模工作，弯曲损耗随着FM和包层模式之间的耦合达到峰值。图4(b)为模场面积随t和t2的变化曲线。模场面积随着t的增大先减小后增大，且与t2呈正比关系。t的增大间接降低了纤芯的折射率，纤芯与包层的折射率差减小，不利于增加光纤的模场面积。t继续增大，纤芯的直径变大，模场面积克服了折射率差的影响。当t=18 μm、t2=24 μm时，在满足单模工作的前提下，模场面积达到2018.61 μm2。图4(c)显示了光纤的损耗比，这表明了光纤的弯曲性能。当t=14 μm、t2=24 μm时，损耗比高达342，同时，此处光纤的模场面积为1907.49 μm2，这种结构参数的光纤具有更好的弯曲性能。
图 4 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c) 高基频损耗比随t和t2的变化
Figure 4. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with t and t2
-
通过改变d和t1，研究梯形折射率环结构对光纤性能的影响。如图5所示，d和t1都在2~5 μm的范围内变化。图5(a)显示了FM和HOMs的弯曲损耗随d和t1的变化情况，从图5(a)中可以看出，当d=5 μm、t1=5 μm时，FM的弯曲损耗为0.132385 dB/m，大于0.1 dB/m，除此以外，其他范围内都满足单模工作的要求。随着d和t1的增加，HOMs的弯曲损耗先增加后减少。梯形折射环起到了耦合环的作用，HOMs与耦合环之间的谐振耦合效应增强，HOMs的弯曲损耗增大；随着t1的增加，耦合效果下降，HOMs损耗降低。当t1为3 μm，d=｛2，3，4，5｝时，FM损耗从0.002047 dB/m增加到0.0213 dB/m；HOMs损耗分别为2.2847 dB/m、7.3798 dB/m、6.347 dB/m与7.95 dB/m。
图 5 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c)损耗比随t1和d的变化
Figure 5. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with t1 and d
图5(b)为光纤模场面积的变化曲线，模场面积随着d和t1的增加而扩大，参数越大，变化越明显。当d保持5 μm不变，t1为3 μm时，模场面积为1894.555 μm2；t1为4 μm时，模场面积为2307.317 μm2，增幅为22%。图5(c)显示了光纤损耗比随d和t1的变化曲线。在t1=5 μm，d=4 μm时，损耗比达到46，此时光纤的模场面积为2312.71 μm2。
-
通过改变t3和d1的尺寸，分析研究了多下陷层对光纤性能的影响。图6所示为FM和HOMs的弯曲损耗随t3和d1的变化情况，d1的变化范围为10~16 μm，t3的变化范围为16~19 μm。当d1=16 μm时，HOMs的弯曲损耗小于1 dB/m，不能进行单模传输。当d1增大、t3减小时，包层的等效折射率减小，纤芯和包层的折射率差变大，有利于改善光纤的弯曲损耗。当t保持16 μm不变，d1从10 μm增加到16 μm时，FM的弯曲损耗从0.078083 dB/m降低到0.009186 dB/m。图6(b)显示了光纤模场面积的变化趋势。如上所述，光纤的模场面积随着t3的增加而增加，随着d1的增加而减小。不过，这种影响还不明显，下陷层结构对改变光纤模场面积几乎没有作用。当t3=19 μm、d1=12 μm时，在其他参数不变的情况下，光纤的模场面积达到最大值2314.98 μm2。图6(c)中显示了光纤损耗率的变化情况，当t3=18 μm、d1=12 μm时，损耗比达到最大值63。
图 6 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c)高基频损耗比随d1和t3的变化
Figure 6. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with d1 and t3
-
表1显示了不同结构的折射率环对光纤的弯曲损耗和模场面积的影响。由电模式场分布可知，梯形折射率环和三角形折射率环都有一个折射率渐变区域，可以与弯曲光纤的HOMs耦合得更充分。HOMs向包层溢出，弯曲损耗也随之增加，使得所提出的光纤能够满足单模操作的需要。梯形折射率环的弯曲损耗为0.056868 dB/m，三角形折射率环的弯曲损耗为0.010790 dB/m。然而，三角形折射率环结构的模场面积并不理想，其值为1699.19 μm2。通过比较这三种结构可知梯形折射率环更具优越性。
表 1 不同结构的折射率环的光纤性能比较
Table 1. Performance comparison of fibers with different structures of refractive index ring
Classification Diagram Bending
loss of FM/
dB·m−1Bending
loss of HOM/
dB·m−1Mode field area/
μm2Trapezoid 
0.056868 3.584245 2313.67 Rectangle 
0.045282 0.090814 1904.19 Triangle 
0.010790 5.790616 1699.19 图7显示了不同结构的谐振环所对应的FM和HOMs的电模式场分布。由图可知，矩形折射率谐振环的FM都集中在环上，没有集中在纤芯，是不符合实际情况的；三角形折射率谐振环虽然具有较低的FM损耗，但是对有效摸场面积影响较大，对比分析可知，梯形折射率谐振环更具有优势。
图 7 (a1)~(c1) 梯形、矩形、三角形谐振环结构的FM电场模式分布；(a2)~(c2) 梯形、矩形、三角形谐振环结构的HOMs电场模式分布
Figure 7. (a1)-(c1) Electric mode field distribution of FM when the refractive index ring are trapezoidal, rectangular, Triangle; (a2)-(c2) Electric mode field distribution of HOMs when the refractive index ring are trapezoid, rectangular, triangle
图8(a)显示了FM和HOMs的弯曲损耗随下陷层数量的变化情况。只有当下陷层数量为2时，光纤才能进行单模操作。随着下陷层数的增加，纤芯和包层之间的折射率差异增加，光纤的弯曲损耗得到了改善。图8(b)显示了光纤的模场面积和损耗比的变化情况，当下陷层数量为0和1时，光纤的模场面积分别为2601.758 μm2和2311.248 μm2。多下陷层的结构将模场限制在纤芯中，当下陷层的数量继续增加时，模场面积基本上保持不变。
图9为不同下陷层对应FM与HOMs的电场分布，随着下陷层层数的增加，芯层与包层折射率差越来越大，限制光的能力逐渐增强，导致FM与HOMs的损耗逐渐减小；随着下陷层的层数继续增加，光能所受限制也会增强，但只限制在芯层，所以FM的有效摸场面积保持不变。
图 8 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积和弯曲损耗比随下陷层数量的变化
Figure 8. (a) Bending loss of FM and HOMs; (b) Mode field area of FM and bending loss ratio with the number of trenches
图 9 (a1)~(d1) 0层-3层下陷层结构对应的FM电场分布图；(a2)~(d2) 0层-3层下陷层结构对应的HOMs电场分布图
Figure 9. (a1)-(d1) Electric field distribution of FM with 0 type trench to 3 types trenches; (a2)-(d2) Electric field distribution of HOMs with 0 type trench to 3 types trenches
-
光纤FM、HOMs与有效模场面积随热载荷变化趋势如图10所示，从图中可知，随着热载荷的增加，光纤FM、HOMs与有效模场面积均会减小。
FM从0.0568 dB/m减小到0.0099 dB/m；HOMs从3.5842 dB/m减小到0.0942 dB/m；有效模场面积从2313.67 μm2减小到2021 μm2。当Q为9.5 W/m时，HOMs小于1 dB/m，此时光纤不能实现单模传输。
图 10 光纤FM、HOMs与有效模场面积随热载荷变化趋势
Figure 10. Change trend of FM, HOMs and effective mode field area with thermal load
-
文中提出了一种具有大模场面积的新型抗弯曲光纤，采用全矢量有限元法分析了不同结构参数对光纤弯曲特性与模式特性的影响。梯形折射率环作为一个谐振环能与HOMs发生谐振耦合，滤掉高阶模式，有利于获得更大的模场面积。包层中下陷层数增加，增强了纤芯和包层之间的有效折射率差，减少了光纤的弯曲损耗。研究结果表明，在波长为1550 nm、弯曲半径为20 cm时，FM弯曲损耗为0.056868 dB/m，HOMs的损耗为3.584245 dB/m，损耗比为63，模场面积为2313.67 μm2，可实现单模工作。分析了不同的热载荷对光纤FM、HOMs与有效模场面积的影响，当热载荷Q小于9.5 W/m，光纤均能实现单模传输，符合高功率光纤激光器的要求。
Structural design of bending-resistant all-solid fiber with large mode field
-
摘要: 提出了一种具有对称结构的大模场面积和低弯曲损耗的新型结构光纤，运用全矢量有限元法结合完美匹配层边界条件分析了光纤特性。该光纤由纤芯中的梯形折射率环和包层中的多层下陷层组成，仿真结果显示该光纤具有低弯曲损耗大模场单模传输的特性。对比分析了梯形谐振环、矩形谐振环、三角形谐振环结构光纤的弯曲损耗以及电场模式分布，实验结果显示梯形折射率环更具优越性。多层下陷层结构将模场限制在纤芯中，下陷层的数量大于2时模场面积基本上保持不变。研究结果表明，在波长为1 550 nm、弯曲半径为20 cm时，基模（FM）弯曲损耗只有0.056 868 dB/m，而高阶模（HOMs）损耗为3.58 dB/m，有效模场面积可达2313.67 μm2。该光纤对弯曲方向不敏感，在高功率光纤激光器放大器等光通信器件领域具有广阔的发展前景。Abstract:
Objective Compared with traditional solid-state lasers and gas lasers, high-power lasers have a series of advantages such as high stability, flexibility, good beam quality, and energy concentration. In recent years, the output power of fiber lasers has increased to 10 kW. There are important applications in mechanical, medical, communication, sensing, and other fields. However, fiber lasers are usually limited by nonlinear effects such as stimulated Brillouin scattering, stimulated Raman scattering, and four-wave mixing with increasing output power. The massive intensity of the optical field inside the high-power fiber laser usually causes specific damage to the fiber core. Traditionally, the method to avoid core burning is to enlarge the effective mode field area by increasing the fiber diameter. However, it leads to an increase in the output modes and generates mode competition to compromise both the output quality of the beam and bending resistance. Therefore, it is necessary for fibers to achieve a large mode field area with the single-mode operation. For the purpose, a novel fiber with a large mode field area, low bending loss and symmetric is designed in this paper. Methods A novel fiber with a large mode field area, low bending loss and symmetric structure is designed in this paper. The proposed fiber consists of a trapezoidal refractive index ring in the core and a multi-trench in the cladding (Fig.1). COMSOL Multiphysics commercial software based on the full vector finite element method is chosen to study the bending properties of the designed fiber. Mapped mesh and free triangle mesh are used to mesh the proposed structure (Fig.2). The bending loss and single-mode operation are used to evaluate the bending properties. The numerical simulation was carried out by changing the fiber related structure, and the optimal structure is verified by thermal load. Results and Discussions The bending loss and electric field mode distribution of trapezoidal refractive index ring, rectangular refractive index ring and triangular refractive index ring are compared and analyzed. The experimental results show that trapezoidal refractive index ring has more advantages (Tab.1, Fig.7). The structure of multi-trench in the cladding limits the mode field in the core of fiber. When the number of trenches is greater than 2, the mode field area basically remains the same (Fig.8, Fig.9). The results show that when the wavelength is 1 550 nm and the bending radius is 20 cm, the bending loss of fundamental mode is only 0.056 868 dB/m, while that of high order modes is 3.58 dB/m. The mode field area is 2 313.67 μm2, which meets the requirements of high-power fiber laser (Fig.6). As the thermal load increases, the bending loss of fundamental mode, high order modes and effective mode field area all decrease. When Q is 9.5 W/m, the bending loss of high order modes is less than 1 dB/m, at which time the fiber cannot achieve the single-mode operation (Fig.10). Conclusions A novel bending-resistant fiber with large mode field area is proposed. The effects of different structural parameters on bending properties and mode properties are analyzed by the full vector finite element method. The trapezoidal refractive index ring as a resonant ring can fully couple with modes and filter out high order modes, which is beneficial to obtain a larger mode field area. The increase in the number of trenches in the cladding enhances the effective refractive index difference between the core and the cladding, which reduces proposed fiber bending loss. The results show that at a wavelength of 1 550 nm and a bending radius of 20 cm, the bending loss of fundamental mode is only 0.056 868 dB/m and the bending loss of high order modes is 3.58 dB/m, with a loss ratio of 63 and a mode field area of 2 313.67 μm2 for single-mode operation. The effects of different thermal loads on fundamental mode, high order modes and effective mode field area are analyzed. When the thermal load Q is less than 9.5 W/m, proposed fiber can achieve a stable single-mode operation. The fiber is insensitive to bending and has a broad development prospect in the field of optical communication devices such as high-power fiber laser amplifiers. -
图 1 (a)光纤二维横截面示意图；(b)光纤折射率分布
Figure 1. Schematic diagram of fiber 2D cross-section; (b) Fiber refractive index distribution
图 3 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积和高基频损耗比随r的变化
Figure 3. (a) Bending loss of FM and HOMs; (b) Mode field area of FM and variation of high-fundament loss ratio with r
图 4 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c) 高基频损耗比随t和t2的变化
Figure 4. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with t and t2
图 5 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c)损耗比随t1和d的变化
Figure 5. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with t1 and d
图 6 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积；(c)高基频损耗比随d1和t3的变化
Figure 6. (a) Bending loss of FM and HOMs; (b) Mode field area of FM; (c) Variation of high-fundament loss ratio with d1 and t3
图 7 (a1)~(c1) 梯形、矩形、三角形谐振环结构的FM电场模式分布；(a2)~(c2) 梯形、矩形、三角形谐振环结构的HOMs电场模式分布
Figure 7. (a1)-(c1) Electric mode field distribution of FM when the refractive index ring are trapezoidal, rectangular, Triangle; (a2)-(c2) Electric mode field distribution of HOMs when the refractive index ring are trapezoid, rectangular, triangle
图 8 (a) FM和HOMs的弯曲损耗；(b) FM的模场面积和弯曲损耗比随下陷层数量的变化
Figure 8. (a) Bending loss of FM and HOMs; (b) Mode field area of FM and bending loss ratio with the number of trenches
图 9 (a1)~(d1) 0层-3层下陷层结构对应的FM电场分布图；(a2)~(d2) 0层-3层下陷层结构对应的HOMs电场分布图
Figure 9. (a1)-(d1) Electric field distribution of FM with 0 type trench to 3 types trenches; (a2)-(d2) Electric field distribution of HOMs with 0 type trench to 3 types trenches
图 10 光纤FM、HOMs与有效模场面积随热载荷变化趋势
Figure 10. Change trend of FM, HOMs and effective mode field area with thermal load
表 1 不同结构的折射率环的光纤性能比较
Table 1. Performance comparison of fibers with different structures of refractive index ring
Classification Diagram Bending
loss of FM/
dB·m−1Bending
loss of HOM/
dB·m−1Mode field area/
μm2Trapezoid 0.056868 3.584245 2313.67 Rectangle 0.045282 0.090814 1904.19 Triangle 0.010790 5.790616 1699.19 
下载: 导出CSV
-
[1] Nilsson J, Payne D N, Jeong Y, et al. High-power fiber lasers [J]. Science, 2011, 332(6032): 921-922. doi: 10.1126/science.1194863 [2] Zervas M N, Codemard C A. High power fiber lasers: A review [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2014, 20(5): 219-241. doi: 10.1109/JSTQE.2014.2321279 [3] Dawson J W, Messerly M J, Beach R J, et al. Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power [J]. Optics Express, 2008, 16(17): 13240-13266. doi: 10.1364/OE.16.013240 [4] Smith A V, Smith J J. Overview of a steady-periodic model of modal instability in fiber amplifiers [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2014, 20(5): 1-12. [5] Jain D, Jung Y, Barua P, et al. Demonstration of ultra-low NA rare-earth-doped step-index fiber for applications in high power fiber lasers [J]. Optics Expres, 2015, 23(6): 7407-7415. doi: https://doi.org/10.1364/OE.23.007407 [6] Naderi S, Dajani I, Madden T, et al. Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations [J]. Optics Express, 2013, 21(13): 16111-16129. doi: 10.1364/OE.21.016111 [7] Liu E, Liang S, Liu J. Double-cladding structure dependence of guiding characteristics in six-fold symmetric photonic quasi-crystal fiber [J]. Superlattices & Microstructures, 2019, 130: 61-67. doi: https://doi.org/10.1016/j.spmi.2019.03.011 [8] Liu E, Tan W, Yan B, et al. Robust transmission of orbital angular momentum mode based on a dual-cladding photonic quasi-crystal fiber [J]. Journal of Physics D Applied Physics, 2019, 52(32): 325110. doi: 10.1088/1361-6463/ab2369 [9] Li C, Yan B, Liu J. Refractive index sensing characteristics in a D-shaped photonic quasi-crystal fiber sensor based on surface plasmon resonance [J]. Journal of the Optical Society of America A, 2019, 36(10): 1663. doi: 10.1364/JOSAA.36.001663 [10] She Y L, Zhou D J, Chen X Y, et al. Study on ultralow bending loss of bend-insensitive single-mode optical fiber [J]. Optical Fiber Technology, 2019, 50: 225-232. [11] She Y L, Zhou D J, Chen X Y. Optimization design of bending performance for ultralow loss hole assisted fiber [J]. Infrared and Laser Engineering, 2019, 48(9): 0918006. (in Chinese) doi: 10.3788/IRLA201948.0918006 [12] She Y L, Zhang W T, Liang G L, et al. Optimal design of large mode area All-Solid-Fiber using a gray relational optimization technique [J]. Optik - International Journal for Light and Electron Optics, 2021, 242(11): 167188. doi: https://doi.org/10.1016/j.ijleo.2021.167188 [13] She Yulai, Zhou Dejian, Chen Xiaoyong, et al. Bend-resistant low bending loss and large mode area single-mode fiber with low NA [J]. Optical Fiber Technology, 2019, 51: 101-106. doi: 10.1016/j.yofte.2019.05.006 [14] Song H, Liu Y, Shen B J, et al. Partially inscribed Bragg gratings suppressing high-order modes in high-power large-mode-area fiber oscillators [J]. Optik - International Journal for Light and Electron Optics, 2020, 220: 165217. doi: 10.1016/j.ijleo.2020.165217 [15] Ma S S, Ning T G, Pei L, et al. Bend-resistant leaky multi-trench fiber with large mode area and single-mode operation [J]. PLoS ONE, 2018, 13(8): 0203047. [16] Kurade B M, Ayyanar N, Raja G T, et al. Asymmetric-clad multi-trench fibers with large-mode-area and controlled leakage loss [J]. Optical Fiber Technology, 2019, 48: 235-241. doi: 10.1016/j.yofte.2019.01.017 [17] Tünnermann A, Schreiber T, Röser F, et al. The renaissance and bright future of fibre lasers [J]. Journal of Physics B Atomic Molecular & Optical Physics, 2005, 38(9): S681. doi: 10.1088/0953-4075/38/9/016 [18] Jain D, Sahu J K. Large mode area single trench fiber for 2 μm operation [J]. Journal of Lightwave Technology, 2016, 34(14): 3412-3417. doi: 10.1109/JLT.2016.2569664 [19] Jain D, Baskiotis C, Sahu J K. Bending performance of large mode area multi-trench fibers [J]. Optics Express, 2013, 21(22): 26663-26670. doi: 10.1364/OE.21.026663 [20] Ma S S, Ning T G, Li J, et al. Design and analysis of a modified segmented cladding fiber with large mode area [J]. Optics & Laser Technology, 2017, 88: 172-179. doi: 10.1016/j.optlastec.2016.08.014 -
点击查看大图
计量
- 文章访问数: 231
- HTML全文浏览量: 39
- PDF下载量: 25
- 被引次数: 0
