Inverse Method - Mathematical Formalism

The functions v_N(z) are determined from W by

The functions f(k,z), also referred to as field amplitudes are determined from the Wronskian by

The refractive index, through its dependence on the functions v_N(z), are directly related to the parameters k_m

The refractive index is greater than n0 since the potentials are negative along the entire z axis.

r = 1 implies that n(z) is an even function of z; the absolute magnitude of k_m affects the profile; relative spacing of k_m values affects profile smoothness.