Numerical analysis of optical modes in two-dimensionally ordered polystyrene spheres in attenuated total reflection geometry

We have numerically calculated attenuated total reflection (ATR) signals du e to two-dimensionally ordered (2D) spheres on a glass substrate for both T E- and TM-polarized incident light beams using a finite difference time-dom ain method. The calculated ATR spectra are in good agreement with the exper imental ones reported previously by Lis. From the ATR spectra and the spati al distribution of light intensity, it has been found that the ATR dips are due to the excitation of the optical modes in the 2D spheres. The propagat ion length of the optical modes is confirmed to be comparable to the diamet er of the sphere. It indicates that the optical modes propagate in a variet y of fashions and the light intensity in the 2D spheres takes a maximum val ue at the contact points between the spheres.