[ E x E y ] = [ A x cos ( ω t + ϕ ( r ) ) A y cos ( ω t + ϕ ( } ) ] [ x y z v ] {\displaystyle {\begin{bmatrix}E_{x}\\E_{y}\end{bmatrix}}={\begin{bmatrix}A_{x}\cos(\omega t+\phi (\mathbf {r} ))\\A_{y}\cos(\omega t+\phi (\rbrace )\end{bmatrix}}{\begin{bmatrix}x&y\\z&v\end{bmatrix}}}
λ 0 = ( 31.3 ± 1.99 ) m m {\displaystyle \lambda _{0}=(31.3\pm 1.99)\mathrm {mm} }
L {\displaystyle L}
L = λ 0 2 m ( m = 1 , 2 , … ) {\displaystyle L={\frac {\lambda _{0}}{2}}m\ (m=1,\ 2,\ \ldots )} ( [ − 2 sin ( Θ ) cos ( Θ ) cos ( ϕ 1 − ϕ 2 ) 4 ( cos 2 ( ϕ 1 − ϕ 2 ) − 1 ) sin 2 ( Θ ) cos 2 ( Θ ) + 1 + 2 sin 2 ( ϕ 1 ) cos 2 ( Θ ) + 2 cos 2 ( Θ ) cos 2 ( ϕ 1 ) − 1 2 sin ( Θ ) cos ( Θ ) cos ( ϕ 1 − ϕ 2 ) 4 ( cos 2 ( ϕ 1 − ϕ 2 ) − 1 ) sin 2 ( Θ ) cos 2 ( Θ ) + 1 − 2 sin 2 ( ϕ 1 ) cos 2 ( Θ ) − 2 cos 2 ( Θ ) cos 2 ( ϕ 1 ) + 1 1 1 ] , [ ( − 1 4 ( − cos ( 4 Θ ) + 1 ) cos ( 2 ϕ 1 − 2 ϕ 2 ) + cos ( 4 Θ ) + 3 + 1 2 ) 2 0 0 ( 1 4 ( − cos ( 4 Θ ) + 1 ) cos ( 2 ϕ 1 − 2 ϕ 2 ) + cos ( 4 Θ ) + 3 + 1 2 ) 2 ] , [ − 4 sin 2 ( Θ ) sin ( ϕ 2 ) cos ( ϕ 2 ) + 4 sin ( ϕ 1 ) cos 2 ( Θ ) cos ( ϕ 1 ) − ( cos ( 4 Θ ) − 1 ) cos ( 2 ϕ 1 − 2 ϕ 2 ) + cos ( 4 Θ ) + 3 + 4 sin 2 ( Θ ) cos 2 ( ϕ 2 ) + 4 cos 2 ( Θ ) cos 2 ( ϕ 1 ) − 2 1 4 sin 2 ( Θ ) sin ( ϕ 2 ) cos ( ϕ 2 ) + 4 sin ( ϕ 1 ) cos 2 ( Θ ) cos ( ϕ 1 ) − ( cos ( 4 Θ ) − 1 ) cos ( 2 ϕ 1 − 2 ϕ 2 ) + cos ( 4 Θ ) + 3 − 4 sin 2 ( Θ ) cos 2 ( ϕ 2 ) − 4 cos 2 ( Θ ) cos 2 ( ϕ 1 ) + 2 1 ] ) {\displaystyle \left(\left[{\begin{matrix}-{\frac {2\sin {\left(\Theta \right)}\cos {\left(\Theta \right)}\cos {\left(\phi _{1}-\phi _{2}\right)}}{{\sqrt {4\left(\cos ^{2}{\left(\phi _{1}-\phi _{2}\right)}-1\right)\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\Theta \right)}+1}}+2\sin ^{2}{\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}+2\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}-1}}&{\frac {2\sin {\left(\Theta \right)}\cos {\left(\Theta \right)}\cos {\left(\phi _{1}-\phi _{2}\right)}}{{\sqrt {4\left(\cos ^{2}{\left(\phi _{1}-\phi _{2}\right)}-1\right)\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\Theta \right)}+1}}-2\sin ^{2}{\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}-2\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}+1}}\\1&1\end{matrix}}\right],\quad \left[{\begin{matrix}\left(-{\frac {1}{4}}{\sqrt {\left(-\cos {\left(4\Theta \right)}+1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+{\frac {1}{2}}\right)^{2}&0\\0&\left({\frac {1}{4}}{\sqrt {\left(-\cos {\left(4\Theta \right)}+1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+{\frac {1}{2}}\right)^{2}\end{matrix}}\right],\quad \left[{\begin{matrix}-{\frac {4\sin ^{2}{\left(\Theta \right)}\sin {\left(\phi _{2}\right)}\cos {\left(\phi _{2}\right)}+4\sin {\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}\cos {\left(\phi _{1}\right)}}{{\sqrt {-\left(\cos {\left(4\Theta \right)}-1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+4\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{2}\right)}+4\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}-2}}&1\\{\frac {4\sin ^{2}{\left(\Theta \right)}\sin {\left(\phi _{2}\right)}\cos {\left(\phi _{2}\right)}+4\sin {\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}\cos {\left(\phi _{1}\right)}}{{\sqrt {-\left(\cos {\left(4\Theta \right)}-1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}-4\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{2}\right)}-4\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}+2}}&1\end{matrix}}\right]\right)}
δ ϕ {\displaystyle \delta \phi }
ω 0 {\displaystyle \omega _{0}}
ω = c k {\displaystyle \omega =ck}
ω = c k 2 + ( m π a ) 2 + ( n π b ) 2 {\displaystyle \omega =c{\sqrt {k^{2}+{\Bigl (}{\frac {m\pi }{a}}{\Bigr )}^{2}+{\Bigl (}{\frac {n\pi }{b}}{\Bigr )}^{2}}}}
ω = c k 2 + ( n π b ) 2 {\displaystyle \omega =c{\sqrt {k^{2}+{\Bigl (}{\frac {n\pi }{b}}{\Bigr )}^{2}}}}
x {\displaystyle x}
λ 0 − 2 + λ − 2 = n 2 ( 2 b ) − 2 {\displaystyle \lambda _{0}^{-2}+\lambda ^{-2}=n^{2}(2b)^{-2}}
λ 0 − 2 = ( ( 2 b ) − 1 ) 2 + ( λ − 1 ) 2 {\displaystyle \lambda _{0}^{-2}=((2b)^{-1})^{2}+(\lambda ^{-1})^{2}}
n = 1 {\displaystyle n=1}
n {\displaystyle n}
m {\displaystyle m}
b {\displaystyle b}
a {\displaystyle a}
ω {\displaystyle \omega }
λ {\displaystyle \lambda }
λ 0 {\displaystyle \lambda _{0}}
k {\displaystyle k}
ω m , n {\displaystyle \omega _{m,n}}
ω n c u t o f f {\displaystyle \omega _{n}^{\mathrm {cutoff} }}
ω ≥ ω n c u t o f f = n π b {\displaystyle \omega \geq \omega _{n}^{\mathrm {cutoff} }={\frac {n\pi }{b}}}
ω 1 c u t o f f ≤ ω < ω 2 c u t o f f , ω = 2 π c λ 0 {\displaystyle \omega _{1}^{\mathrm {cutoff} }\leq \omega <\omega _{2}^{\mathrm {cutoff} },\ \omega =2\pi {\frac {\mathrm {c} }{\lambda _{0}}}}
ω n c u t o f f = c n π b {\displaystyle \omega _{n}^{\mathrm {cutoff} }=\mathrm {c} {\frac {n\pi }{b}}}
ω m , n = ( m π a ) 2 + ( n π b ) 2 {\displaystyle \omega _{m,n}={\sqrt {{\Bigr (}{\frac {m\pi }{a}}{\Bigr )}^{2}+{\Bigl (}{\frac {n\pi }{b}}{\Bigr )}^{2}}}}
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![{\displaystyle \left(\left[{\begin{matrix}-{\frac {2\sin {\left(\Theta \right)}\cos {\left(\Theta \right)}\cos {\left(\phi _{1}-\phi _{2}\right)}}{{\sqrt {4\left(\cos ^{2}{\left(\phi _{1}-\phi _{2}\right)}-1\right)\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\Theta \right)}+1}}+2\sin ^{2}{\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}+2\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}-1}}&{\frac {2\sin {\left(\Theta \right)}\cos {\left(\Theta \right)}\cos {\left(\phi _{1}-\phi _{2}\right)}}{{\sqrt {4\left(\cos ^{2}{\left(\phi _{1}-\phi _{2}\right)}-1\right)\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\Theta \right)}+1}}-2\sin ^{2}{\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}-2\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}+1}}\\1&1\end{matrix}}\right],\quad \left[{\begin{matrix}\left(-{\frac {1}{4}}{\sqrt {\left(-\cos {\left(4\Theta \right)}+1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+{\frac {1}{2}}\right)^{2}&0\\0&\left({\frac {1}{4}}{\sqrt {\left(-\cos {\left(4\Theta \right)}+1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+{\frac {1}{2}}\right)^{2}\end{matrix}}\right],\quad \left[{\begin{matrix}-{\frac {4\sin ^{2}{\left(\Theta \right)}\sin {\left(\phi _{2}\right)}\cos {\left(\phi _{2}\right)}+4\sin {\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}\cos {\left(\phi _{1}\right)}}{{\sqrt {-\left(\cos {\left(4\Theta \right)}-1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}+4\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{2}\right)}+4\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}-2}}&1\\{\frac {4\sin ^{2}{\left(\Theta \right)}\sin {\left(\phi _{2}\right)}\cos {\left(\phi _{2}\right)}+4\sin {\left(\phi _{1}\right)}\cos ^{2}{\left(\Theta \right)}\cos {\left(\phi _{1}\right)}}{{\sqrt {-\left(\cos {\left(4\Theta \right)}-1\right)\cos {\left(2\phi _{1}-2\phi _{2}\right)}+\cos {\left(4\Theta \right)}+3}}-4\sin ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{2}\right)}-4\cos ^{2}{\left(\Theta \right)}\cos ^{2}{\left(\phi _{1}\right)}+2}}&1\end{matrix}}\right]\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e84080900b7ace38547793b5b4bb0f1a441bfc6)
