I've got this type of diffusion equation below in semi-infinite slab (used for biomedical optics):
$\mu_a\phi(y,z)-D\nabla^2\phi(y,z)=\delta(y)\delta(z)$
$z\in[0,\infty), y\in(-\infty,\infty), \phi<\infty$
EDIT:
I've used the next Fourier Transform:
$\psi(\bar k)=\int\phi(\bar r)exp(-i\bar k \cdot\bar r)d\bar r$
$\phi(\bar r)=\frac{1}{(2\pi)^3}\int\psi(\bar k)exp(i\bar k \cdot\bar r)d\bar k$
and obtained: $\psi(\bar k)=\frac{1}{\mu_a}\cdot(1-\frac{k_y^2+k_z^2}{\mu_{eff}^2})^{-1}$
I'm having troubles with performing the inverse transform and would love to get some help with that.
Thanks.