Light Propagation in Singly and Doubly Periodic Planar Waveguides

Light propagation in singly and doubly periodic planar waveguides is investigated with respect to future applications in integrated optics. The waveguides used in our experiments reveal, in the vicinity of Bragg reflection, a strong difference between the directions of phase and group velocities, the beam steering. A clear graphical representation of the observable propagation effects is given in wave-vector diagrams, showing the directional dispersion of the elementary waves in periodic structures, the Floquet-Bloch waves. The dispersion phenomena were measured with high accuracy, using selective wave excitation. In conjunction with straight tapered transitions to smooth planar waveguides, the periodic structures show a great variety of strong frequency and direction-dependent effects such as lateral beam shifting and focusing with a frequency-variant focal length. Ray optics of Floquet-Bloch waves is used to describe these phenomena. Complex interference patterns observable in the vicinity of Bragg reflection in doubly periodic structures are explained by the superposition of Floquet-Bloch waves. Examples of applications of planar periodic structures as highly selective frequency filters, optical multiplexers as well as frequency-tunable beam narrowing, focusing and expanding devices are given together with measured data.