Template:Incident potential for two dimensions
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Incident potential
The incident potential is a wave of amplitude [math]\displaystyle{ A }[/math] in displacement travelling in the positive [math]\displaystyle{ x }[/math]-direction. We would only see this in the time domain [math]\displaystyle{ \Phi(x,z,t) }[/math] however, in the frequency domain the incident potential can therefore be written as
[math]\displaystyle{ \phi^{\mathrm{I}}(x,z) =e^{-k_{0}x}\chi_{0}\left( z\right). }[/math]
The first term in the expansion of the diffracted potential for the region [math]\displaystyle{ x \lt 0 }[/math] is given by
[math]\displaystyle{ a_{0}e^{k_{0}x}\chi_{0}\left( z\right). }[/math]
