  We present a new method for building sequences of solvable profiles of the
electromagnetic (EM) admittance in lossless isotropic materials with 1D graded
permittivity and permeability (in particular profiles of the optical
refractive-index). These solvable profiles lead to analytical closed-form
expressions of the EM fields, for both TE and TM modes. The Property-and-Field
Darboux Transformations method, initially developed for heat diffusion
modelling, is here transposed to the Maxwell equations in the optical-depth
space. Several examples are provided, all stemming from a constant
seed-potential, which makes them based on elementary functions only. Solvable
profiles of increasingly complex shape can be obtained by iterating the process
or by assembling highly flexible canonical profiles. Their implementation for
modelling optical devices like matching layers, rugate filters, Bragg gratings,
chirped mirrors or 1D photonic crystals, offers an exact and cost-effective
alternative to the classical approaches
