Coupling of Planar Waveguide Modes in All-Dielectric Multilayer Structures: Monitoring the Dependence of Local Electric Fields on the Coupling Strength

Except for a few cases to which sophisticated techniques are applicable, it is difficult to observe experimentally local electric fields or near fields associated with excitation of electromagnetic modes supported by building blocks of nanostructures. Although elucidating the behavior of the local electric fields or near fields is very useful to develop potential applications of the nanostructures, in many cases, their behaviors have been only speculated from simulations based on the electromagnetic theory. Here, we develop a simple technique that allows us to study experimentally the average behavior of the local electric fields inside two planar waveguide layers interacting with each other in all-dielectric multilayer structures. The study is made possible by doping the two waveguide layers with two different fluorophores. Fluorescence intensities detected at two different wavelengths allow us to study separately the behaviors of the local electric fields inside each waveguide layer. Angle-scan fluorescence excitation spectra are measured for two different series of multilayer samples by exciting the samples in an attenuated total reflection geometry. The line shapes observed are in good agreement with theoretical ones calculated based on the electromagnetic theory, confirming that the experimental fluorescence excitation spectra reflect well the average behaviors of the local electric fields. Applying the developed technique, we investigate systematically the changes in the local electric fields inside the waveguide layers caused by the change in the strength of coupling between the two waveguide modes. In one series of the samples, a gradual transition in the behavior of the local electric fields, from a Fano-resonant behavior to a double-peak behavior, is demonstrated with increasing the coupling strength. In another series of the samples, the coupling strength is widely changed and the formation of the coupled modes in a strong coupling regime is clearly observed. The observed changes in the local electric fields can be reproduced very well by simple analytical calculations based on a coupled oscillator model. The model is helpful to gain physical insights into the coupling of the waveguide modes, which cannot be obtained by the electromagnetic calculations.