We have

[tex]\epsilon(i f, r) = \epsilon_2(i f)[/tex] when [tex]H + h_2(x) \leq z < + \infty[/tex]

[tex]\epsilon(i f, r) = 0[/tex] when [tex]h_1(x) < z < H + h_2(x)[/tex]

[tex]\epsilon(i f, r) = \epsilon_1(i f)[/tex] when [tex]- \infty < z \leq h_1(x)[/tex]

show the corresponding Fourier transform is

[tex]\frac{i}{q_z} \int d^2x e^{iq_\bot \cdot x}[\epsilon_2 e^{iq_z[H+h_2(x)]} - \epsilon_1 e^{iq_z h_1(x)}][/tex]

I've looked in a few books but tbh I have no real idea how to show this...

Any help/suggestions/tips would be much appreciated. Thanks.

[tex]\epsilon(i f, r) = \epsilon_2(i f)[/tex] when [tex]H + h_2(x) \leq z < + \infty[/tex]

[tex]\epsilon(i f, r) = 0[/tex] when [tex]h_1(x) < z < H + h_2(x)[/tex]

[tex]\epsilon(i f, r) = \epsilon_1(i f)[/tex] when [tex]- \infty < z \leq h_1(x)[/tex]

show the corresponding Fourier transform is

[tex]\frac{i}{q_z} \int d^2x e^{iq_\bot \cdot x}[\epsilon_2 e^{iq_z[H+h_2(x)]} - \epsilon_1 e^{iq_z h_1(x)}][/tex]

I've looked in a few books but tbh I have no real idea how to show this...

Any help/suggestions/tips would be much appreciated. Thanks.

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