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EM Lasing Medium Green's Function

Consider electromagnetic waves polarized in the direction propagating in one dimension in an active laser medium with current density J(x)J(x). Maxwell's equation for the zz-component of the electric field of these waves then reads

(d2dx2κ2)Ez(x)=J(x) \left(\dfrac{d^2}{dx^2} - \kappa^2 \right) E_z (x) = J(x)

for κ\kappa some constant. Suppose there is a source at x=0x= 0 and that there is a conducting mirror far away so that effectively Ez(0)=1E_z (0) = 1 and Ez()=0E_z (\infty) = 0 are the boundary conditions. Find the Green's function G(x,y)G(x,y) for x<yx<y that will allow for determination of the electric field anywhere in space.

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