Rigorous electromagnetic theory for waveguide evanescent field fluorescence microscopy

Recently, waveguide evanescent field fluorescence (WEFF) microscopy was introduced and used to image and analyze cell-substrate contacts. Here, we establish a comprehensive electromagnetic theory in a seven-layer structure as a model for a typical waveguide-cell structure appropriate for WEFF microscopy and apply it to quantify cell-waveguide separation distances. First, electromagnetic fields at the various layers of a model waveguide-cell system are derived. Then, we obtain the dispersion relation or characteristic equation for TE modes with a stratified media as a cover. Waveguides supporting a defined number of modes are theoretically designed for conventional, reverse, and symmetric waveguide structures and then various waveguide parameters and the penetration depths of the evanescent fields are obtained. We show that the penetration depth of the evanescent field in a three-layer waveguide-cell structure is always lower than that of a seven-layer structure. Using the derived electromagnetic fields, the background and the excited fluorescence in the waveguide-cell gap, filled with water-soluble fluorophores, are analytically formulated. The effect of the waveguide structures on the fluorescence and the background are investigated for various modes. Numerical results are presented for the background and the stimulated fluorescence as functions of the water gap width for various waveguide structures, which can be used to find the water gap width. The results indicate that the background and excited fluorescence increase by increasing the penetration depth of the evanescent field. In addition, we show that for various guided modes of a conventional waveguide, the electric fields in the cell membrane and the cytoplasm are evanescent and they do not depend on the waveguide structure and the mode number. However, for the reverse symmetry and symmetric waveguide structures, the waves are sinusoidal in the cell membrane and the cytoplasm for the highest-order modes.