Hi, This is overwhelmingly more of a maths problem than a physics problem, because it's all theoretical. I'll give some background to modle it incase the math's isn't enough. Say you've got a planar structure of thickness 'd', lying on the z plane. Also say the upper and lower surfaces are y = 0 and y = -d, respectively. The structure has scalar potentials inside it as so: As you can see the vector fields cancel out on one side, As it says below, there is a Poisson equation of: BUT I HAVE NO IDEA WHY that is the poission equation, I get that Fiinside is a scalar potential, but why is mok.cos(kx) the vector field?, not like mx+my or something instead? It looks like they've just differentiated mx and that's the vector function, maybe just a coincidence? I also have no idea how that is the general solution? Specifically the homogenious part. I get that for the part of the particular you can solve the Poisson equation of using method of undetermined coefficients with a guess of (Asin(kx) + Bcos(kx)) and just differentiate that twice for del2: (Asin(kx) + Bcos(kx))'' = mok.Cos(kx) therefore: -A.k2sin(kx)-Bk2cos(kx) = mok.Cos(kx) therefore: -A.ksin(kx)-Bkcos(kx) = mo.Cos(kx) and equating coefficients yields: B = - mo/k A = 0 so Yp = - mo/k * Cos(kx) But why does the homogenous part have exponentials and y in them? I thought they'd just be zero. If someone could explain that or even just why the Poisson equation is what they say I'd be greatful. THANKS!!! P.S I also wonder, which point is chosen as x = 0 on the diagram...?