Accurate modeling of the index profile in annealed proton-exchanged LiNbO 3 waveguides

Abstract

A generalized Gaussian function was used to accurately model the refractive-index profile of planar optical waveguides ill z-cut LiNbO3 fabricated by the annealed proton-exchange technique. The computed waveguide parameters were empirically correlated to the wide range of fabrication conditions through the use of a general power law. In addition, the validity of the conventional simple diffusioii annealing model is investigated in detail.

Estimation of the performance of a 3-dB Y-junction optical coupler with a channel profile of proton-exchanged lithium niobate

“…Along with large index change, PE dramatically modifies the crystal birefringence of the due to the increased difference between the extraordinary and ordinary indices of LN [15]. Proton exchange process leads to a step-function refractiveindex profile with a change in the index [9] given by…”

“…The refractive index profile of such waveguides can be modified, depending on optical needs, by choosing optimal proton-exchange parameters, such as normalized H + fractional concentration, process time and temperature, etc. [9,10]. Therefore, repetitive iterations have been performed to suppress possible imbalance in the structure by determining suitable normalized H + fractional concentration and other parameters of proton-exchange process.…”

Nonlinear Characterization of Waveguide Index Profile: Application to Soft-Proton-Exchange in LiNbO$_3$

“…Initially simple analytical functions have been proposed (e. g. step [12], gaussian [13], exponential [14]) but their prediction capabilities were limited since these functions do not capture the complex dynamics of the diffusion process occurring during both APE and SPE. A more sophisticated generalized Gaussian function has been later introduced [15] resulting in more accurate results. Today, the most precise model simulates M. Neradovoskiy, H. Tronche, D. Chezganov, P. Baldi, T. the kinetics of protons in the substrate by solving a onedimensional nonlinear diffusion equation [1], [5].…”

Análise de guias de ondas ópticos e de microondas pelo Método dos Elementos Finitos.

“…A dependência dos coeficientes de difusão com as concentrações de próton e lítio tem sido estudada por vários autores [140], [142] e [143]. Contudo, não há na literatura dados suficientes sobre a forma da dependência desses coeficientes com as concentrações.…”