Elsevier

Optics Communications

Volume 219, Issues 1–6, 15 April 2003, Pages 157-163
Optics Communications

Analysis of directional coupler electro-optic switches using effective-index-based matrix method

https://doi.org/10.1016/S0030-4018(03)01270-7Get rights and content

Abstract

The effective-index-based matrix method (EIMM) has been used to simulate the characteristics of integrated-optic directional coupler switch (both the uniform-Δβ and reversed-Δβ types) based on electro-optic (EO) effect. The characteristics are derived from the distributions of optical power and electrical modulating field within the device. The analysis was focused on directional coupler switching devices made by the diffusion of titanium in lithium niobate (Ti:LiNbO3) substrates and incorporation of suitable electrodes. The simulated results are found to match well with available experimental results and other numerical simulation results obtained from the literatures. Although the computations are performed for Ti:LiNbO3 waveguides, the model is applicable to arbitrary graded-index waveguides with the known refractive index profile and electro-optic coefficient. EIMM is found computationally well efficient and considerably faster than beam propagation method (BPM).

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 asEi=ui+Ei+ejΔiexpjωt−Kicosθix−βz+uiEiejΔiexpjωt+Kicosθix−βz,whereΔ12=0,Δ3=K3d2cosθ3,Δ4=K4cosθ4(d2+d3),Δi=Kicosθi(d2+d3+⋯+di−1),Ki=K0ni=(ω/c)ni,βi=Kisinθi.Ei+ 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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