# some questions about "scattering-matrix method" ..

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#### 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?