Direct measurement of effective indices of guided modes in LiNbO_3 waveguides using the Čerenkov second harmonic

Abstract

Second-harmonic generation in the form of Cerenkov radiation has been used to make direct, contact-free measurements of the effective indices of guided modes in LiNbO(3) channel waveguides. X-cut substrates were used, and channels oriented along the y axis were formed by either proton exchange or titanium indiffusion. For end-fire TE excitation, the Cerenkov harmonic radiates forward at a shallow angle into the substrate, leaves the output facet of the substrate, and appears as bright bands in the far field. These bands are seen to form a one-to-one correspondence with the m lines that are due to guided modes when a prism coupler is simultaneously clamped to the sample surface. The effective indices of the guided modes can be obtained by a simple calculation that involves only the substrate index and the angle at which the Cerenkov harmonic is radiated into the substrate. This technique permits effective index measurements of cladded waveguides where prism coupler measurements cannot be made. Examples of the technique in which index oil is used as a guide overlayer are given.