Voltage-Length Product of X and Z-Cut Ti: LiNbO3 Directional Coupler and BOA Switches: A Comparison

Abstract

The results of the detailed numerical analysis of the voltage-length product of Ti:LiNbO 3 X and Z-cut directional couplers and BOA (or X) switches for λ = 1.3 um are presented. For low-frequency switching, the X-cut devices have been found to have comparable switching voltages, substantially lower than their Z-cut counterparts. For high-frequency applications, both switches with two electrodes, namely the X-cut BOA and the Z-cut directional coupler, exhibit approximately equal voltagelength products.

Model of Ti: LiNbO3 Two-Mode-Interference Polarization-Independent Switch and Polarization Splitter

“…Here, I 0 is the input intensity, Δφ 0 is the built-in phase shift between the modes in the absence of the voltage, and q is the proportionality constant which is related to the voltage-length product ν of the switch [16] by the formula q = -…”

“…1, and arranged so that their efficiencies (the q-factors (3)) are different. To reduce the voltage-length product, the four-electrode arrangement might be used for the X-cut switch [16,17]. Instead of the condition (4) we now obtain two separate conditions for TE and TM polarizations: It is now clear that if…”

“…The explicit general expression for the q-factor is of the form [16] Brought to you by | University of Arizona Authenticated Download Date | 7/6/15 11:05 PM q=ν^Γ ft [e * (x > y) -e°2(x > y)] [Ε < Χ > y)/°] dxd y -Λ, -oo (8) where e s (x,y) and e a (x,y) are the optical field distributions of the symmetric and the antisymmetric modes, n,. is the substrate refractive index, r is the pertinent electrooptic coefficient, and E(x,y) is the distribution of the pertinent component of the electric field induced by the applied voltage U.…”

“…7 where the values of the voltage-length products ν versus the electrode width h of the four-electrode structure are plotted for both TE and TM polarizations. For the calculation of the electric field distribution induced by the electrodes, we used the expression for the periodic interdigital array [16] E y /U = Re{p[sin 2 gp -sin 2 (2pz')]-1 ' 2 }/K(singp), /=y + iJ/^fx, p = u/[2(g + h)], (11) where g is the gap between the electrodes, ε Ε and ε Ε are the components of the (electric) permittivity tensor, and Κ is the complete elliptic integral of the first kind. The curves in Fig.…”

“…For the distribution of applied electric field of electrodes, needed for the calculation of electrooptic overlap integrals, we have used standard expressions obtainable, e.g. by conformal mapping [15,16]. We present the results of a detailed numerical analysis of the polarization-independent X-cut switch for the wavelength of 1.3μιη.…”