Waveguide-length Dependence of Cerenkov Second Harmonic Generation in LiNbO₃

Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides

“…To obtain an expression for b 2 , we follow a coupled mode approach similar to that reported in [4] and get 62092, z) = sine…”

“…5). Because of the finite width of the input beam, there is already second-harmonic generated in the waveguidelength behind the edge of the prism [4]. The actual interaction length is approximately the distance measured from the edge of prism (i.e., l 2 ) plus h, which is the input beam-width at the base of the prism.…”

“…beam shape and the intensity profile of the second-harmonic radiation, since this defines the coupling mechanism to be employed to efficiently collect/utilize the radiation. In this paper, we have used coupled-mode theory [3], [4] to study the evolution of the output intensity profile of the second-harmonic radiation in the Cerenkov configuration as a function of propagation distance in planar waveguides. In particular, we have shown that in practical waveguides having finite propagation loss, the intensity profile shows significant difference as comapred to that in the case of lossless propagation.…”

“…The waveguide is assumed to support a single guided TM mode at the pump frequency w. The pump wave generates a nonlinear polarisation at 2o>, which then radiates energy into the continuum of radiation modes of the waveguide, automatically satisfying the phase matching condition: (i(2uj) = 2/3(w), where /3 is the propagation constant. The total second-harmonic field at a particular value of z (i.e., propagation distance) is a superposition of radiation modes with propagation constants around the phase matching value 2/3 (u} where H y is the total magnetic field at 2w, and is expressed as [4] (2)…”