Why are coupling coefficients in codirectional coupling in an optical waveguide often real-valued?
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Coupling coefficient between waveguide nnand waveguide mm:
κnm=ωϵ0∬(n2−n2m)e∗n⋅emdxdy∬z^⋅(e∗n×hn+en×h∗n)dxdy,κnm=ωϵ0∬(n2−nm2)en∗⋅emdxdy∬z^⋅(en∗×hn+en×hn∗)dxdy,
where ωω is the angular frequency, nn is the actual index profile, nmnm is the index profile of a given core mm in the absence of the rest of the cores, ee and hh are the normalized vector core modes of the elctric and magnetic fields (respectively), and * the complex conjugate.
Regarding xx,yy,zz: xx and yy represent the cross-sectional plane of the optical waveguide, and the signals propagate in the zz axis.
κnm=ωϵ0∬(n2−n2m)e∗n⋅emdxdy∬z^⋅(e∗n×hn+en×h∗n)dxdy,κnm=ωϵ0∬(n2−nm2)en∗⋅emdxdy∬z^⋅(en∗×hn+en×hn∗)dxdy,
where ωω is the angular frequency, nn is the actual index profile, nmnm is the index profile of a given core mm in the absence of the rest of the cores, ee and hh are the normalized vector core modes of the elctric and magnetic fields (respectively), and * the complex conjugate.
Regarding xx,yy,zz: xx and yy represent the cross-sectional plane of the optical waveguide, and the signals propagate in the zz axis.
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Explanation:
Regarding x,y,z: x and y represent the cross-sectional plane of the optical waveguide, and the signals propagate in the z axis. In this Youtube video, when it comes to codirectional coupling, it is said that the mode coupling coefficients are often real-valued.
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