μ-Raman spectroscopy characterization of LiNbO3 femtosecond laser written waveguides

Abstract

In this paper, we present an iterative method which merges experimental l-Raman measurements and numerical simulations to describe femtosecond written waveguides in LiNbO 3 crystals. This method is based on the deformation potential theory, and uses the finite element method to analyze elastic deformations after femtosecond laser micro-explosions in x-cut Mg:LiNbO 3 crystals. The resultant strain and refractive index field after laser interaction were estimated and yielded similar values to those obtained in other works. The LiNbO 3 Raman deformation potential constants were also estimated in this work.

Computation of the expansion parameters of femto-waveguides using a two dimensional μ-Raman map and guided modes

“…17 In that report, the computed horizontal expansion parameters (a i ) are negligible, as in the present case. Similarly, the obtained f/e value computed using the current model (f/e % 0.45) is close to that obtained in the previous report (f/e % 0.6).…”

“…The values of e and f obtained from the current model are around À190 and À90, respectively; in a previous report, 17 they give values of À160 and À100, respectively. The difference between the deformation potential constants obtained in these works is at most 15%.…”

“…11 As mentioned, a numerical model can be used to estimate the residual strain field, and, thus, the refractive index field in femto-waveguides. In the current work, the following general assumptions, validated in a previous work, 17 are implemented. These are elastic material, static expansion, plane strain deformations (e yy ¼ 0), and an orthotropic approximation for the LiNbO 3 compliance matrix.…”

“…(2), dw/dp can be expressed as a linear function of e, f, and the known compliance matrix elements. 17 In Figures 4(a) and 4(b), using Eq. (2), dw/dp num was plotted as a function of b (a ¼ 0) for case (i); and as a function of a (b ¼ 0) for case (ii).…”

“…The most of them are not quantitatively described. So, the result of the whole process from a point of view of the surrounding residual strain field was modeled in literature, 11,15,17 as a pseudoarbitrary mechanical expansion of an ellipse in an "infinite" medium. Consequently, the expansion and geometrical parameters of this model represent, in a first order of approximation, the sum of all the mentioned phenomena.…”