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熔锥型宽带耦合器是利用带宽拓展技术改变器件的波长特性,使得在其带宽范围内均能满足分光精度的要求,且符合低附加损耗、低偏振损耗特点。为了使两根光纤不对称,普遍的做法是采用预处理的方式将其中一根光纤变细,再将具有半径差的两根光纤熔融拉锥。
图 1是非对称耦合器在某一拉伸长度下归一化光功率随波长变化的图像[10-12]。A点处斜率最大,B点处斜率最小,在AB点各取±5%的光功率变化范围,所对相应的带宽Δλ1明显小于Δλ2。A点附近功率随波长变化对波长变化最敏感,而在曲线转折点B处对波长变化不敏感。由此可知, 想要得到宽带耦合器,就要寻找一个合适的曲线转折点B,即输出光功率的某个极值点。
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传统利用半径不同制造的宽带耦合器需要预拉伸,这种方式的优点是成本低,只用一盘光纤就可以制作;缺点是成品率低,经过预处理的光纤很脆,再经过扭绞后很难耦合且容易断裂。为了避免预处理造成后续工艺的困难,作者提出了一种利用折射率不同、但半径相同的两根光纤制作宽带耦合器的方法。
熔锥型光纤耦合器的融合区可分为3个部分:中间耦合区W(光纤包层的半径为b)和两边的锥形区L/2,如图 2所示。光功率的转移主要存在于耦合区。耦合区可视为两个平行光纤组成的复合波导。对于两根光纤略有差异的非对称光纤耦合器,利用耦合模方程可以求得两根光纤中耦合区的光功率:
$ \left\{\begin{array}{l}{P_{1}=1-F^{2} \sin ^{2}\left[\int_{0}^{L} \frac{C(z)}{F} \mathrm{d} z\right]} \\ {P_{2}=F^{2} \sin ^{2}\left[\int_{0}^{L} \frac{C(z)}{F} \mathrm{d} z\right]}\end{array}\right. $
(1) 式中,C(z)为耦合系数;F是两光纤间转移功率的大小与总输出功率的比值,称之为功率转移比。
$ C(z)=\left(\beta_{+}-\beta_{-}\right) / 2 $
(2) 式中,β+为复合波导中叠加同向模的传播常数,β-为复合波导中叠加反向模的传播常数。
$ F^{2}=\frac{1}{1+\frac{w \nu^{4}}{2 \pi} \mathrm{K}_{0}^{2}(w) \frac{d}{b} \exp \left(2 w \frac{d}{b}\right)\left(\frac{\Delta r}{b}\right)^{2}} $
(3) 式中,d为两纤芯间距,b是较细光纤的半径(见图 2),Δr是两根光纤的半径差,U是纤芯横向传播常数,w是包层横向衰减常数,ν是孤立光纤的归一化频率,K0和K1是零阶和1阶修正第2类Bessel函数。两光纤的传播常数差为[14]:
$ \begin{array}{c} \mathit{\Delta }\beta = \frac{1}{b}\frac{{{U^2}}}{\nu }\frac{1}{{{{(2\mathit{\Delta })}^{\frac{1}{2}}}}} \times \\ \left\{ {\left( {\frac{{{w^2}}}{{{U^2}}} + \frac{{{{\rm{K}}_0}^2(w)}}{{{{\rm{K}}_1}^2(w)}}} \right)\frac{{\Delta {n_{{\rm{co}}}}}}{{{n_{{\rm{co}}, 1}}}} + 2\mathit{\Delta }\frac{{{{\rm{K}}_0}^2(w)\Delta r}}{{{{\rm{K}}_1}^2(w)b}}} \right\} \end{array} $
(4) 当ν=2.4时,由(4)式可得芯径差异和折射率差异相当的条件是:
$ \frac{{\Delta r}}{b} \cong - \frac{{1.4}}{\mathit{\Delta }}\frac{{\Delta {n_{{\rm{co}}}}}}{{{n_{{\rm{co}}, 1}}}} $
(5) 式中,Δ是相对折射率差,Δnco是纤芯折射率差,nco, 1是较低纤芯折射率。半径相同纤芯折射率不同的非对称耦合器取Δr=0,将(5)式代入(3)式,可以得到纤芯折射率差与功率转移比的关系式:
$ \begin{array}{c} {F^2} = \\ \frac{1}{{1 + \frac{{w{\nu ^4}}}{{2{\rm{ \mathsf{ π} }}}}{{\rm{K}}_0}^2(w)\frac{d}{b}\exp \left( {2w\frac{d}{b}} \right){{\left( {\frac{{1.4}}{\Delta }} \right)}^2}{{\left( {\frac{{\Delta {n_{{\rm{co}}}}}}{{{n_{{\rm{co}}, 1}}}}} \right)}^2}}} \end{array} $
(6) 从(1)式和(6)式可以看到, F以二次方的形式决定了耦合器输出端的功率幅值,是一个极其重要的参量。以上公式中,若Δnco=0,则F参量值为1,对应标准耦合器;反之,若F≠1,对应非对称耦合器。
无损传输时,光纤任意位置横截面上应满足能量守恒。假设每根光纤中的模场近似看成三角分布,归一化后半径相同光纤耦合器基模近似表示为[15]:
$ \left\{ {\begin{array}{*{20}{l}} {{\varphi _1} = \sqrt {6/{\rm{ \mathsf{ π} }}} \left( {1 - {r_1}/b} \right){b^{ - 1}}}\\ {{\varphi _2} = \sqrt {6/{\rm{ \mathsf{ π} }}} \left( {1 - {r_2}/b} \right){b^{ - 1}}} \end{array}} \right. $
(7) 式中,r1和r2是考察点f(x, y)到两根光纤中心的距离,如图 3所示。
耦合模理论将两熔锥光纤之间的功率耦合视作复合波导内两基模场之间干涉的结果[16],这两个三角形近似场有部分叠加,其最低次模取为叠加的同相模;第2个最低次模应取为叠加的反向模。传播模Φ±满足亥姆霍兹方程,从而可导出传播常数β±的变分表达式:
$ \begin{array}{c} \beta _ \pm ^2 = k_0^2n_1^2 + \\ \frac{{\left[ {k_0^2\left( {n_{{\rm{co}}, 1}^2 + n_{{\rm{co}}, 2}^2 - 2n_1^2} \right){I_2} - 12{b^{ - 2}}} \right]\left( {1 \pm {I_3}} \right)}}{{2 \pm 2{I_1}}} \end{array} $
(8) 式中,
$ \left\{ {\begin{array}{*{20}{l}} {{I_1} = \int\limits_S {{\varphi _1}} {\varphi _2}{\rm{d}}x{\rm{d}}y}\\ {{I_2} = \frac{{6{a^2}}}{{{b^2}}}\left( {1 + \frac{{{a^2}}}{{2{b^2}}} - \frac{{4{a^2}}}{{3b}}} \right)}\\ {{I_3} = \frac{1}{{{\rm{ \mathsf{ π} }}{b^2}}}\int\limits_S {\cos } \theta {\rm{d}}x{\rm{d}}y} \end{array}} \right. $
(9) 式中,k0为真空中的波数,a为纤芯半径,nco, 1为较低纤芯折射率,nco, 2为另一根纤芯折射率,n1为包层折射率,S为两根光纤的重叠面积。
以下数值模拟中均取纤芯半径a=4.15μm,包层半径(见图 2中光纤包层的半径b)b=62.5μm,包层折射率n1=1.4633,波长λ=1550nm。根据(1)式、(2)式、(6)式、(8)式、(9)式,用MATLAB数值模拟非对称耦合器腰区的光场分布。一根纤芯折射率nco, 1=1.4677, 另一根纤芯折射率nco, 2取为1.4679和1.467935, 分别对应图 4a和图 4b。P1是直通臂的光功率,P2是耦合臂的光功率,P0是耦合器总输入光功率。可以看出,耦合进副光纤的光功率随着纤芯折射率差异的增大而变小,如此便可选择两根具有合适纤芯折射率差的光纤,将功率转移比调节到想要制作的耦合器的分束比,得到宽带耦合器。半径差非对称耦合器和折射率差非对称耦合器从效果上看是一致的,都是通过一定方式让本征模传播常数不同从而达到光功率交换不完全的目的。
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通过改变光纤折射率差可以得到不同功率转移比的耦合器。对于确定的分束比有两种情况,一种是功率转移比大于50%,另一种是小于50%。以分束比是3:7为例,根据(1)式、(2)式、(6)式、(8)式和(9)式,取nco, 1=1.4677;图 5是耦合区输出光功率随拉伸长度的变化曲线。图 5a是直通臂输出光功率达到30%,取nco, 2=1.46787;图 5b是耦合臂输出光功率达到30%,取nco, 2= 1.468。
根据(1)式、(2)式、(6)式、(8)式和(9)式,以波长为自变量,输出光功率为因变量,取D点拉伸长度L=15.4mm,E点拉伸长度L=16.2mm,用MATLAB软件数值模拟耦合器带宽范围, 如图 6所示。图 6a对应D点的宽带; 图 6b对应E点的宽带。
Figure 6. a—bandwidth of alternating type 3:7 coupler b—bandwidth of non-alternating type 3:7 coupler
由图 6可知,耦合区交替的3:7分束比带宽为160nm,耦合区不交替的3:7分束比带宽为230nm。由此猜测,在功率转移比小于50%的基础上当两输出端口光功率相差越大时,带宽越大。
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实际制作熔锥型宽带耦合器的过程中分束比会出现偏差,此时可以改变其它影响因素对分束比进行调整。在耦合区域,复合波导由两平行熔锥光纤相互重叠组成。在某一拉伸长度下,耦合区横截面积尺寸可视为恒定,两光纤的纤芯间距d保持不变。定义α为熔融度,其大小反应两熔锥光纤之间的相对位置,则其计算公式为:
$ \alpha=(2 b-d) /[2(2-\sqrt{2}) b] $
(10) 取nco, 1=1.4677,nco, 2=1.46794。根据(6)式、(10)式可以得到不同归一化频率ν下功率转移比F随熔融度α的关系图,如图 7所示。
由图 7可知,在某一归一化频率ν下,熔融度越大,功率转移比F越大,光能量交换的越充分。功率转移比上升速率呈现出先快后慢的趋势。随着熔融度的增大,两根光纤纤芯间距减小,功率转移比上升速率变慢并趋近于某一定值。归一化频率ν越大,熔融度变化对分束比的调整愈发明显。ν可以通过拉伸长度和温度来调节。因此,当分束比与预期偏差过大时,可以适当改变熔融度来调整。
熔锥型宽带光纤耦合器的研究
Study on fused biconical taper broadband couplers
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摘要: 为了探究非对称耦合器的特性, 利用具有折射率差异的两根光纤制作了宽带耦合器。采用数值计算模拟了不同折射率差光纤耦合器的光场分布以及输出光功率随拉伸长度的变化曲线, 并分析了两种宽带耦合器的带宽差异以及熔融度对功率转换比的影响; 采用光束传播法, 通过仿真模拟得到了理论带宽。结果表明, 耦合的功率转换比随两根光纤的不对称情况而变化, 功率转换比调节到耦合器分束比的大小时, 耦合器带宽最宽; 熔融度对宽带耦合器分束比有一定的调节作用; 3dB光纤耦合器在C+L波段波长响应平缓, 带宽范围达到150nm; 分束比3:7和1:9的耦合器带宽范围分别是210nm和330nm; 分束比1:99的耦合器带宽范围是420nm。此研究结果对制作非对称宽带耦合器提供了参考依据。Abstract: To explore characteristics of asymmetric couplers, a broadband coupler was fabricated by using two optical fibers with different refractive index. The distribution of optical field of fiber couplers with different refractive index differences and the curve of output optical power with stretching length were simulated by numerical calculation. Bandwidth difference between two broadband couplers and the influence of melting degree on power conversion ratio were analyzed. The theoretical bandwidth was obtained by simulation based on the beam propagation method. The results show that, the coupling power conversion ratio varies with the asymmetry of two optical fibers. When the power conversion ratio is adjusted to the splitting ratio of the coupler, the bandwidth of the coupler is the widest. The melting degree can regulate the beam splitting ratio of broadband couplers. The wavelength response of 3dB fiber coupler in C+L band is gentle. The bandwidth range is 150nm. The bandwidth ranges of couplers with beam splitting ratios of 3:7 and 1:9 are 210nm and 330nm, respectively. The bandwidth range of the coupler with beam splitting ratio of 1:99 is 420nm. The results provide a reference for the fabrication of asymmetric broadband couplers.
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Key words:
- fiber optics /
- broadband coupler /
- beam propagation method /
- refractive index difference /
- asymmetric
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