Sketch of the cross-section of a rectangular waveguide (450 nm x 220 nm). The waveguide consists of a silicon core (dark gray) on top of a silicon-dioxide layer (light-gray). Marcatili's method is sketched. The four outer quadrants are neglected. The standing waves in the core of the waveguide are sketched (blue and purple curves) and the exponentially decaying waves outside the waveguide are also sketched (blue and purple curves). The refractive index n of each of the regions is indicated.