Fig. 3
From: Effect of waveguide wall roughness on quantum signal transmission

(a) Shape of the modes \(\:{E}_{1}\left(x\right)\) and \(\:{E}_{2}\left(x\right)\) and their product \(\:{E}_{1}\left(x\right)\)*\(\:{E}_{2}\left(x\right),\) in the ideal slab waveguide. (b) The waveguide with the antisymmetric sinusoidal walls has a nonzero overlap integral. (c) The waveguide has symmetric sinusoidal walls with zero overlap integral. (d) Finite element simulation of the waveguide depicted in (b). (e) Finite element simulation of the waveguide depicted in (c).