Calculating Optical waveguide geometry with parameters

ooe

Hello all,
is there a way to calculate the width of a waveguide required (slab and ribbed) made of silicon with refractive index 3.47 of 220nm height, using 1550nm laser, based on a variable N-effective (or n1 and n2)?

rather, does there exist a relationship between the width and height of a waveguide in regards to material, wavelength of laser, and the desired effective index? thanks!