Comparative analysis of absorbance calculations for integrated optical waveguide configurations by use of the ray optics model and the electromagnetic wave theory

Focusing on the use of planar waveguides as platforms for highly sensitive attenuated total reflection spectroscopy of organic thin films, we extend the ray optics model to provide absorbance expressions for the case of dichroic layers immobilized on the waveguide surface. Straightforward expressions are derived for the limiting case of weakly absorbing, anisotropically oriented molecules in the waveguide-cladding region. The second major focus is on the accuracy of the ray optics model. This model assumes that the introduction of absorbing species, either in the bulk cladding or as an adlayer on the waveguide surface, only causes a small perturbation to the original waveguide-mode profile. We investigate the accuracy of this assumption and the conditions under which it is valid. A comparison to an exact calculation by use of the electromagnetic wave theory is implemented, and the discrepancy of the ray optics model is determined for various waveguide configurations. We find that in typical situations in which waveguide-absorbance measurements are used to study organic thin films (k_ln_l ≤ 10¹⁰⁻¹, h/λ ≈ 10⁻²) the discrepancy between the ray optics and the exact calculations is only a few percent (23%).