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双Sagnac环滤波器结构如图1所示,由三个3 dB耦合器(OC),两个偏振控制器(PC),两段长度不同的保偏光纤(PMF)和少模光纤(FMF)组成。对于单个Sagnac环路,当入射光从1端口进入OC1后被分为两束光,一束光经过3端口沿顺时针(正向)传输,另一束光经过4端口沿逆时针(逆向)传输,然后分别通过PC和PMF(或FMF),最后回到耦合器相干输出。
当入射光经过3 dB耦合器OC时,根据光波导理论,OC1,OC2,OC3的传输矩阵为:
$$ {T_{{\rm{OC}}}} = \frac{{\sqrt 2 }}{2}\left[ {\begin{array}{*{20}{c}} 1&j \\ j&1 \end{array}} \right] $$ (1) 当正向传输光经过PMF时,由于其应力双折射效应,PMF传输矩阵为:
$$ {T_{{\rm{PMF}}}} = \left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&{{e^{j\dfrac{{2\pi L\Delta n}}{\lambda }}}} \end{array}} \right] $$ (2) 式中:
$\Delta n = \left| {{n_{\rm{f}}} - {n_{\rm{s}}}} \right|$ 为PMF快慢轴的有效折射率差;L为PMF的长度;$\lambda $ 为入射光的波长。FMF的模式在FMF中的传播速度不同,产生的相位延迟不同,故其传输矩阵[15]可以由相位延迟器表示:
$$ {T_{{\rm{FMF}}}} = \left[ {\begin{array}{*{20}{c}} {{e^{{{ - j2\pi {n_{1{\rm{eff}}}}{L_{\rm{F}}}} / \lambda }}}}&0 \\ 0&{{e^{{{j2\pi {n_{2{\rm{eff}}}}{L_{\rm{F}}}} / \lambda }}}} \end{array}} \right] $$ (3) 式中:
${n_{1{\rm{eff}}}}$ 和${n_{2{\rm{eff}}}}$ 分别为少模光纤中两个模式的等效折射率差;${L_{\rm{F}}}$ 为FMF的长度;$\lambda $ 为入射光的波长。当入射光经过PC1后,光的偏振方向会旋转
$\theta $ 角度,故正向传输光经过PC时,其传输矩阵为:$$ {T_{{\rm{PC}}}} = \left[ {\begin{array}{*{20}{c}} {\cos \theta }&{\sin \theta } \\ {\sin \theta }&{ - \cos \theta } \end{array}} \right] $$ (4) 光波在Sagnac环传输一周后,反向经过OC1的传输矩阵为其逆矩阵,即:
$$ T_{{\rm{OC}}1}^{\rm{B}} = {\left( {{T_{{\rm{OC}}1}}} \right)^{ - 1}} $$ (5) 同理PMF、FMF、PC的反向传输矩阵为其逆矩阵
$T_{{\rm{PMF}}}^{\rm{B}}$ 、$T_{{\rm{FMF}}}^{\rm{B}}$ 、$T_{{\rm{PC}}}^{\rm{B}}$ 。对于图1所示双Sagnac环路,1端口光场为
${E_1}$ ,3、4端口光场为${E_3}$ 和${E_4}$ ,可描述为:$$ \left[ {\begin{array}{*{20}{c}} {{E_3}} \\ {{E_4}} \end{array}} \right] = {T_{{\rm{OC1}}}}\left[ {\begin{array}{*{20}{c}} {{E_1}} \\ {{E_2}} \end{array}} \right] $$ (6) 而
${E_3}$ 和${E_4}$ 被3 dB耦合器OC2和OC3分成相等的两束光,即当光正向从OC2和OC3传输时,有${E_5} = {E_6} = \dfrac{{{E_3}}}{2}$ ,${E_7} = {E_8} = \dfrac{{{E_4}}}{2}$ 。光在双环内顺时针和逆时针传输一周后,端口5、6、7、8的光场为:$$ E_{\rm{5}}^{'} = T_{{\rm{PC}}2}^{\rm{B}}T_{{\rm{FMF}}}^{\rm{B}}{E_7} $$ (7) $$ E_{\rm{6}}^{'} = T_{{\rm{PC}}1}^{\rm{B}}T_{{\rm{PMF}}}^{\rm{B}}{E_8} $$ (8) $$ E_7^{'} = {T_{{\rm{FMF}}}}{T_{{\rm{PC}}2}}{E_5} $$ (9) $$ E_8^{'} = {T_{{\rm{PMF}}}}{T_{{\rm{PC}}1}}{E_6} $$ (10) 光在双Sagnac环传输一周后,在耦合器OC2和OC3处相干输出的透射光场和反射光场分别为:
$$ \left[ {\begin{array}{*{20}{c}} {{E_{{\rm{TOC}}2}}} \\ {{E_{{\rm{ROC}}2}}} \end{array}} \right] = T_{{\rm{OC}}2}^{\rm{B}}\left[ {\begin{array}{*{20}{c}} {E_5^{'}} \\ {E_6^{'}} \end{array}} \right] $$ (11) $$ \left[ {\begin{array}{*{20}{c}} {{E_{{\rm{TOC}}3}}} \\ {{E_{{\rm{ROC}}3}}} \end{array}} \right] = T_{{\rm{OC}}3}^{\rm{B}}\left[ {\begin{array}{*{20}{c}} {E_7^{'}} \\ {E_8^{'}} \end{array}} \right] $$ (12) 因耦合器OC2和OC3的入射端均只使用一个端口,故对于OC1的端口3、4的逆向光场为:
$$ E_3^{''} = {E_{{\rm{ROC}}2}} $$ (13) $$ E_4^{''} = {E_{{\rm{ROC}}3}} $$ (14) 最后,滤波器透射光场和反射光场可以由下式表示:
$$ \left[ {\begin{array}{*{20}{c}} {E_{\rm{T}}^{''}} \\ {E_{\rm{R}}^{''}} \end{array}} \right] = T_{{\rm{OC}}1}^{\rm{B}}\left[ {\begin{array}{*{20}{c}} {E_3^{''}} \\ {E_4^{''}} \end{array}} \right] $$ (15) 其主要是PMF、FMF、PC和OC组合结果。
Switchable multi-wavelength fiber laser utilizing double Sagnac loop filter
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摘要: 提出了一种基于双Sagnac环滤波器的可切换多波长掺铒光纤激光器,该滤波器由基于保偏光纤和少模光纤的Sagnac环并联构成,结构简单,利用其梳状滤波特性,实现了掺铒光纤激光器的多波长输出。采用传输矩阵法详细分析了双Sagnac环的传输特性,进一步搭建了线性腔掺铒光纤激光器,实验中通过调节偏振控制器,改变腔内偏振态,在室温下得到稳定可切换的单、双、三波长激光输出,且激光器输出波长的位置可调。研究结果表明,输出激光波长的边模抑制比大于34 dB,稳定性测量中波长漂移量小于0.05 nm,具有良好的稳定性,可应用于波分复用及全光通信系统等领域。Abstract: A switchable multi-wavelength erbium-doped fiber laser based on double Sagnac loop filter was proposed. The parallel double Sagnac loop filter was consisted of polarization-maintaining fiber and few-mode fiber. Its structure was simple. And the multi-wavelength output of erbium-doped fiber laser was realized by the comb filter property. Adoptting transmission matrix method, the characteristics of double Sagnac loop were analyzed in detail. When using the double Sagnac comb filter in linear cavity laser system, a switchable multi-wavelength fiber laser with stable single-, dual-, and triple-wavelength outputs can be obtained at room temperature by adjusting the polarization controllers and changing the polarization state in the cavity. At the same time the lasing wavelength locations also can be switched. The results show that the side mode suppression ratio (SMSR) of the output wavelength is more than 34 dB. In the test of the stability, the maximum wavelength shift of output wavelength is less than 0.05 nm, which has stable output and can be applied in fields such as wavelength division multiplexing and all-optical communication systems.
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