Interference of integrated Floquet-Bloch waves

The interference of scalar optical Floquet-Bloch waves in periodically stratified media is discussed in detail. Two main types of interference are identified and fully analyzed: normal and exchange interference, producing, respectively, real and virtual spatial fringes. In the paper considerable use is made of a reciprocal-space representation of the Floquet-Bloch waves (the wave-vector diagram), first introduced in the dynamical theory of x-ray diffraction. Experimental observations of the interference of integrated versions of the Floquet-Bloch waves, made in corrugated planar ${\mathrm{Ta}}_2$ ${\mathrm{O}}_5$ waveguides, are included by way of illustration.