We observe coherent resonant coupling of optical whispering-gallery modes i
n fluorescence from dye doped polymer bispheres with diameters ranging from
2 to 5 mu m. By monitoring the frequencies of fluorescence peaks of indivi
dual spheres, we sort out two spheres with appropriate size matching and br
ing them into contact. Wave optics calculation also gives good agreement wi
th the experiment. By taking into account harmonic coupling of the whisperi
ng-gallery modes, the obtained features of normal mode splitting are well e
xplained by the tight-binding photon picture. [S0031-9007(99)09349-7].