Refractive Index Profile in Special Structure of Optical-Damage-Resistant Mg-Diffused Near-Stoichiometric Ti:Mg:LiNbO$_{3}$ Waveguide

Abstract

Refractive index in special optical-damage-resistant MgO-diffused near-stoichiometric (NS) Ti:LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (Ti:LN) waveguide structure that a number of single-mode strip waveguides are embedded in a planar waveguide is profiled on the basis of the measured mode field profile of strip waveguide. In the NS strip waveguide, the Ti <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> -induced extraordinary index increase studied follows a sum of two error functions in the width direction and a sum of two Gaussian functions in the depth direction. In the NS planar waveguide, the index increase follows a Gaussian function. On the basis of the established index profile model, the mode field profiles were calculated using variational method and compared with the measured data. The results show that the calculated mode sizes are in good agreement with the measured. In addition, the profile characteristics of Ti <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> -concentration in both the strip and planar waveguides were analyzed by secondary ion mass spectrometry and are correlated with the refractive index increase. The result shows that the profile characteristics of the index increase and Ti <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> -concentration are similar for both the strip and planar waveguides and there exists a linear relationship with a slope of ~ 2.0×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 3</sup> (mol%) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> .