_applied sciences_  
_Article_  
**Applicability of the Effective Index Method for the Simulation of X-Cut LiNbO3 Waveguides**  
**[PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 1,2,* and [PERSON] 1**  
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typical curvature radius of about 2-3 cm, which makes it impossible to integrate dozens of basic elements of PICs on the single chip. Around the early 2000s, a technology of producing a thin film of lithium niobate on an insulator (LNOI) was developed (schematic structure of X-cut of LNOI is shown on Figure 1) [11]. It was shown that high-index-contrast waveguides with a step-index type profile could be fabricated on this material platform. These high-index-contrast waveguides based on LNOI can be used for PICs fabrication with many integrated elements with high-frequency modulation rates. Due to this, great attention has been paid to the application of LNOI in integrated photonics; this is confirmed by the large number of published papers on the subject [12; 13; 14; 15; 16; 17; 18; 19].  
The basic process of PICs development includes the simulation of single components, as well as of entire optical circuits [20]. The simulation of arbitrary waveguide structures can be performed using a group of methods based on finite differences and finite elements (FDTD, FDFD, FEMTD) [21; 22; 23], which are widely presented in the commercial software. Moreover, there are other high-accuracy methods for simulation of anisotropic photonic integrated elements, such as the spectral element method [24; 25]. The above methods directly solve [PERSON]'s equations without any approximations and can therefore provide the most accurate result. The main disadvantages of these methods are their long calculation times and their programming complexity [26; 27]. During the simulation process of basic integrated optical elements, hundreds of calculation iterations are performed in order to determine the optimum parameters. Thus, the time of a single calculation iteration becomes critical, and finding ways to speed up and simplify the simulation process is an urgent task.  
The purpose of this study is to evaluate the possibility of applying the effective index method (EIM) for designing an anisotropic high-contrast optical waveguide based on LNOI. EIM is a simple semi-analytical method that allows fast simulation of waveguides with different cross-sections; it could be used to simplify 3D calculations of radiation propagation in integrated optical elements (to perform so-called 2.5D simulation). In addition, EIM might be used for rapid circuit simulation with the S-matrix method [28].  
This paper considers the simulation of the optical anisotropic waveguide on an X-cut LNOI substrate, directed along the Y-crystallographic axis. As far as the authors know, EIM has not been used before for anisotropic waveguides analysis on LNOI substrate. As a result of the simulation, the range of etching depths and slope angles of the sidewalls were determined, for which the difference between the results of calculation by the finite-difference method and by EIM does not exceed 1%. This makes it possible to use EIM to speed up and simplify the simulation process of optical waveguides.  
Since EIM is applicable for the LNOI waveguide analysis, optical radiation losses could be evaluated by the Payne-Lacey model. The model uses the root-mean-square (RMS) roughness and the correlation length for the radiation losses calculation. In the paper, RMS is determined from the line edge roughness (LER) obtained from experiments performed earlier in [29].  
Figure 1: Schematic structure of X-cut LNOI.