afack
Newbie level 1
some questions about photonic band calculation ..
the origin reference paper is:
Phys. Rev. B 60, 2610–2618 (1999)
Scattering-matrix treatment of patterned multilayer photonic structures
i try to reproduce its results using matlab.
the first problem is :
no matter which matlab function 'eig' i use, eig(M) or eig(M,\[w^2-k\],'qz')(because M is an asymmetric matrix), to sove the equation 3.7 or 3.8,the resultant eigenvectors automatically satisfy the orthogonality relationship \[\psi_n^T\psi_n'=\delta_{nn'}\],rather than equation (3.9)\[\psi_n^T(w^2-k)\psi_n'=\delta_{nn'}\].
another problem is how to rescale the frequency \[\omega\] and lattice period \[a\]
\[\omega=\omega_{SI}/lightspeed\] ?
\[\omega=\omega_{SI}/(2*\pi*lightspeed)\] ?
\[\omega=\omega_{SI}*a/lightspeed\] ?
\[\omega=\omega_{SI}*a/(2*\pi*lightspeed)\] ?
（the parameters at right hand side of equations are all in SI （international system of units））
and
\[a\] rescales to 1?
help please:grin:
the origin reference paper is:
Phys. Rev. B 60, 2610–2618 (1999)
Scattering-matrix treatment of patterned multilayer photonic structures
i try to reproduce its results using matlab.
the first problem is :
no matter which matlab function 'eig' i use, eig(M) or eig(M,\[w^2-k\],'qz')(because M is an asymmetric matrix), to sove the equation 3.7 or 3.8,the resultant eigenvectors automatically satisfy the orthogonality relationship \[\psi_n^T\psi_n'=\delta_{nn'}\],rather than equation (3.9)\[\psi_n^T(w^2-k)\psi_n'=\delta_{nn'}\].
another problem is how to rescale the frequency \[\omega\] and lattice period \[a\]
\[\omega=\omega_{SI}/lightspeed\] ?
\[\omega=\omega_{SI}/(2*\pi*lightspeed)\] ?
\[\omega=\omega_{SI}*a/lightspeed\] ?
\[\omega=\omega_{SI}*a/(2*\pi*lightspeed)\] ?
（the parameters at right hand side of equations are all in SI （international system of units））
and
\[a\] rescales to 1?
help please:grin:
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