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Are there other reasons why monochromatic solutions to Maxwells equations of the form E(z, t) = E(z)exp(-iωt) are good other than its plane wave solutions forming a complete set?

Best,

Niles.

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- Thread starter Niles
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- #1

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Are there other reasons why monochromatic solutions to Maxwells equations of the form E(z, t) = E(z)exp(-iωt) are good other than its plane wave solutions forming a complete set?

Best,

Niles.

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ehild

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[tex] \vec D(t)= \int_{-∞}^0 {K(\tau) \vec E(t-\tau)d\tau} [/tex],

which is the convolution of the electric field the molecule feels with the function K.

The Fourier transform of this convolution is the product of the Fourier transforms of the functions K and E. The Fourier transform of K is called epsilon(ω), the frequency-dependent permittivity or dielectric function.

So the proportionality between P and E or D and E is valid for the Fourier coefficients (Fourier transforms) D(ω)=ε(ω)E(ω). That is why we consider the periodic electric field as a Fourier series, sum of terms E

In case when the time needed for the polarization to reach equilibrium is comparable with the time period of the external electric field, there is a phase difference between D(ω) and E(ω), so ε(ω) is complex. As both E and D are real in the real word, the Fourier components belonging to -ω are equal to the conjugate of the component for ω. E

ehild

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Best,

Niles.

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