Reciprocal waveguide coupled mode theory

Yun-Tian Chen; Jing-Wei Wang; Wei-Jin Chen; Jing Xu

doi:10.7498/aps.69.20200194

Journals >Acta Physica Sinica >Volume 69 >Issue 15 >Page 154206-1 > Article

Acta Physica Sinica
Vol. 69, Issue 15, 154206-1 (2020)

Reciprocal waveguide coupled mode theory

Yun-Tian Chen^1,2, Jing-Wei Wang¹, Wei-Jin Chen¹, and Jing Xu^1,2,*

Author Affiliations

¹School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

²Wuhan National Laboratory of Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China

show less

DOI: 10.7498/aps.69.20200194 Cite this Article

Yun-Tian Chen, Jing-Wei Wang, Wei-Jin Chen, Jing Xu. Reciprocal waveguide coupled mode theory[J]. Acta Physica Sinica, 2020, 69(15): 154206-1 Copy Citation Text

show less

Fig. 1. Symmetry relations between the forward and backward propagating modes: (a) Chiral symmetry; (b) time reversal symmetry; (c) parity symmetry.

Download full size | View in the Article

Real part of effective mode indices versus : (a) in core layer 1 and in core layer 2; (b) in core layer 1 and in core layer 2.

Fig. 2. Real part of effective mode indices

versus

: (a)

in core layer 1 and

in core layer 2; (b)

in core layer 1 and

in core layer 2.

Download full size | View in the Article

Fig. 3. Real part and imaginary part of effective mode indices

versus

: (a), (c) Real part of effective mode indices

; (b), (d) imaginary part of effective mode indices

Download full size | View in the Article

Fig. 4. Anisotropic waveguide: (a) The schematic of elliptical waveguide; (b) the real (red line) and imaginary (black line) part of effective modal indices, calculated from fullwave simulation using finite element method, as a function of

; (c) real part of effective mode indices

; (d) imaginary part of effective mode indices

; (e)−(h) the real/imaginary part of

obtained from fullwave simulation is shown for the modes

Download full size | View in the Article

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

Table 1. Symmetric relation of original field and adjoint field in the reciprocal waveguides with

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 ${\bar{ \chi}}({{r}}) = -{\bar{ \chi}}(-{{r}})$

Table 2.

Symmetry relations of original field and adjoint field in the reciprocal waveguides.

互易波导中原始场和伴随场之间的对称关系

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	$\displaystyle\iiint \phi _j ^{\ast} [{\bar{{L} } }{{\phi} }_i-\beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$	$\displaystyle\iiint \sigma \phi _j [{\bar{{L} } }{{\phi} }_i-\beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$	$\displaystyle\iiint \psi _j \cdot [{\bar{{L} } }{{\phi} }_i \!-\! \beta_i {\bar{{B} } }{{\phi} }_i]{\rm{d} }v \!=\! 0$

Table 3. Comparison between CCMT, GCMT and GCMF.

Yun-Tian Chen, Jing-Wei Wang, Wei-Jin Chen, Jing Xu. Reciprocal waveguide coupled mode theory[J]. Acta Physica Sinica, 2020, 69(15): 154206-1

Download Citation

Tools

Save the article for my favorites

Paper Information

微信扫一扫：分享

微信扫一扫：分享