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Abstract

Mode coupling is a common phenomenon in waveguides. The mode coupling among different guided modes in fiber-optic communication can cause crosstalk, and the mode coupling of guided mode and radiated mode can reduce the power of the guided mode. Application of mode coupling can guide the design of optical devices such as couplers and beam splitters with specific functions, which have been widely used in fiber optic communication and fiber sensing. So it is important to analyze how waveguide modes are coupled. The coupled-mode theory is a common method of studying mode coupling in waveguides. It provides not only an intuitive picture of how the photonic modes are hybridized, but also a quantitative assessment of how the hybridization among those relevant modes evolves. In recent years, non-Hermitian waveguides, represented by parity-time symmetrical structures, have become a research hotspot. However the conventional coupled-mode theory no longer works in this case. In this review, we briefly summarize the development history of coupled-mode theory and introduce the representative work in reciprocal waveguide coupled-mode theory in detail. Then the relationship among several coupled-mode theories is analyzed and their applications are briefly introduced.

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Authors and contacts

Corresponding author:Xu Jing,jing_xu@hust.edu.cn

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	$\beta_i$对应的模式	$-\beta_i$对应的模式
$({\bar{{L}}}, {\bar{{B}}})$	$\left[\beta_i, {{\phi}}_i\right]$	$\left[-\beta_i, {{\psi}}_i\right]$
$({\bar{{L}}}^{\rm{a}}, {\bar{{B}}}^{\rm{a}})$	$\left[\beta_i, {{\psi}}_i\right]$	$\left[-\beta_i, {{\phi}}_i\right]$

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对称关系	算符	对称性关系	约束条件
手征对称	${\sigma}$	${{{\psi}}}_i({{r}}) = {\bar{\sigma}}{{{\phi}}}_i({{r}})$	${{{\varepsilon}}}_{\rm r}^{zt} = {{{\varepsilon}}}_{\rm r}^{tz} = 0$, ${{{\mu}}}_{\rm r}^{zt} = {{{\mu}}}_{\rm r}^{tz} = 0$和${\bar{ \chi}} = 0$
时间反演对称	${\cal{T}}$	${{{\psi}}}_i({{r}}) = {\bar{\sigma}}({{{\phi}}}_i({{r}}))^*$	${\bar{{{\varepsilon}}}}_{\rm r}$, ${\bar{{{\mu}}}}_{\rm r}$和${\bar{ \chi}}$是实数
宇称对称	${\cal{P}}$	${{{\psi}}}_i({{r}}) = {\bar{\sigma}}{{{\phi}}}_i(-{{r}})$	${\bar{{{\varepsilon}}}}_{\rm r}({{r}}) = {\bar{{{\varepsilon}}}}_{\rm r}(-{{r}})$, ${\bar{{{\mu}}}}_{\rm r}({{r}}) = {\bar{{{\mu}}}}_{\rm r}(-{{r}})$和 ${\bar{ \chi}}({{r}}) = -{\bar{ \chi}}(-{{r}})$

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模式耦合理论	传统模式耦合理论(CCMT)	手征对称模式耦合理论(GCMT)	广义模式耦合理论(GCMF)
耦合模式展开式形式	$\varPhi =\displaystyle \sum a_i\phi _i$	$\varPhi = \displaystyle\sum a_i\phi _i$	$\varPhi = \displaystyle\sum a_i\phi _i ^+ +b_i \psi _i ^-$

守恒量	光功率守恒 $\nabla \left({{{{E}}} _1 \times {{{H}}} _2 ^{\ast}} + {{{E}}} _2 ^{\ast} \times {{{H}}}_1\right) = 0$	作用量守恒 $\nabla \left({{{{E}}} _1 \times {{{H}}} _2 } + {{{E}}} _2 \times {{{H}}}_1\right) = 0$	作用量守恒 $\nabla \left({{{{E}}} _1 \times {{{H}}} _2 } + {{{E}}} _2 \times {{{H}}}_1\right) = 0$
测试函数	$\phi _j ^{\ast} $	$\sigma \phi _j$	$ \psi _j ^+$, $\psi _j ^-$
本征方程	${\bar{{L}}}{{\phi}}_i = \beta_i {\bar{{B}}}{{\phi}}_i $	${\bar{{L}}}{{\phi}}_i = \beta_i {\bar{{B}}}{{\phi}}_i $	${\bar{{L}}}{{\phi}}_i = \beta_i {\bar{{B}}}{{\phi}}_i$
测试函数进行测试	$\displaystyle\iiint \phi _j ^{\ast} [{\bar{{L} } }{{\phi} }_i-\beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$	$\displaystyle\iiint \sigma \phi _j [{\bar{{L} } }{{\phi} }_i-\beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$	$\displaystyle\iiint \psi _j \cdot [{\bar{{L} } }{{\phi} }_i \!-\! \beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$

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Vol. 69, Issue 15 - 2020-08-05

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