Analysis of directional coupler electro-optic switches using effective-index-based matrix method
Introduction
An integrated-optic directional coupler can be used for a variety of applications such as power dividers, switches and switch-matrices, modulators, filters, multiplexers, etc. [1], [2], [3], [4], [5]. The electro-optic effect in substrate materials like LiNbO3 is extensively used for electrically controlled switching [1] and modulation [2] of optical power in directional couplers. Since the electro-optic (EO) effect is preserved during the fabrication of optical waveguides on LiNbO3 substrates by using high temperature thermal indiffusion of titanium [6], the Ti:LiNbO3 EO switches and modulators are quite popular for practical uses. Although the beam propagation method (BPM), a rigorous computer simulation technique based on 2D/3D FEM/FDM [7], can be used for the accurate simulation of the Ti:LiNbO3 waveguides and devices with complex refractive index profiles, a simple analytical effective-index-based matrix method (EIMM) has been successfully developed by the authors [8] for the fast simulation of graded-index channel waveguides and coupled structures with a reasonable accuracy. In the present communication, a brief report on the application of EIMM for the simulation of a Ti:LiNbO3 EO directional coupler switch is presented. The results of our simulation have been compared with the available experimental data [9], [10], [11], [12], [13] and BPM/FEM simulated results obtained from the literatures [7], [14].
Section snippets
Modeling of directional coupler electro-optic switch using EIMM
EIMM has been used for calculating the propagation constant and bending loss of graded-index channel waveguides and modal profiles of single and coupled waveguides [8], [15], [16]. If the medium considered to be made of a number of layers, then the electric field associated with each layer can be represented aswhereEi+ and Ei− are the
Results
A Ti-indiffused Z-cut Y-propagating weakly coupled directional coupler switch is considered here. The input light is TM polarised. Hence, the component of electric field, which will cause equal and opposite change in Δn(x,y) for the two guides, will be Ey(x,y). It may be noted that the coordinates axes (x,y,z) chosen here for analysis do not coincide with the crystal axes (x,y,z) of LiNbO3. Ey(x,y) is the component of applied electric field normal to the surface (along y). x is the lateral
Conclusions
EIMM has been successfully employed in simulating the switching voltages of Ti:LiNbO3 EO directional coupler switches with uniform-electrode and Δβ-reversed-electrode configurations. Since EIMM involves practically no iterations, it runs in standard PCs and the results are obtained almost instantly. Hardly, there is any problem of memory shortage, which is typical for numerical 3D programs. As such, EIMM is significantly faster and requires much less memory than the softwares based on rigorous
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