Mode-independent attenuation in evanescent-field sensors

Generally, the total power attenuation in multimode evanescent-field sensor waveguides is nonproportional to the bulk absorbance because the modal attenuation constants differ. Hence a direct measurement is difficult and is additionally aggravated because the waveguide absorbance is highly sensitive to the specific launching conditions at the waveguide input. A general asymptotic formula for the modal power attenuation in strongly asymmetric inhomogeneous planar waveguides with arbitrarily distributed weak absorption in the low-index superstrate is derived. Explicit expressions for typical refractive-index profiles are given. Except when very close to the cutoff, the predicted asymptotic attenuation behavior agrees well with exact calculations. The ratio of TM versus TE absorption has been derived to be (2 - n(0)(2)/n(f)(2)) for arbitrary profiles. Waveguides with a linear refractive-index profile show mode-independent attenuation coefficients within each polarization. Further, the asymptotic sensitivity is independent of the wavelength, so that it should be possible to directly measure the spectral variation of the bulk absorption. The mode independence of the attenuation has been verified experimentally for a second-order polynomial profile, which is close to a linear refractive-index distribution. In contrast, the attenuation in the step-profile waveguide has been found to depend strongly on the mode number, as predicted by theory. A strong spread of the modal attenuation coefficients is also predicted for the parabolic-profile waveguide sensor.