Design rules and optimization of electro-optic modulators based on coplanar waveguides

Abstract

Electro-optical traveling wave modulators (EO-TWM) are basic building blocks of the optical communications industry which is leading a revolution in the way we communicate, work and live. As a result, the demand for high-speed data transmission with low driving voltage is continuously growing up with costs that should be kept below a minimum. Besides communications, a growing number of applications for EO-TWM is continuously emerging with equally stringent requirements. This Thesis is concerned with advances in the eld of systematic design and optimization of EO-TWM for coping inverse of the velocity matching constant has been shown to govern the low-loss limit (LL), while in the velocity matching limit (VM), a constant bandwidth times squared-length rule proportional to the inverse of the squared loss constant has been found more appropriate. In this work we provide insights into the trade-o issue in EO-TWM, and a complete picture of the applicable gures of merit for every operative range. Besides the known LL and VM gures of merit, two intermediate ranges, the quasi-low loss (QLL) and the quasi-velocity matching (QVM), have been identi ed. 
 Also novel closed-forms expressions fully accounting for the e ffects of the skin-e ffect electrode loss and optical-electrical wave velocity mismatch, explicitly relating the operative bandwidth and the electrode length in EO-TWM, have been found. Novel bandwidth and electrode-length charts have been created, which constitute a useful tool for the optimization and design of this modulators.
 A graphical interface tool called MZM-GIT has been built integrating the analytical optimization and design strategies developed throughout the Thesis. With the aid of the MZM-GIT, several proposals of optimized MZM designs based on practical structures described in literature, and also based on the industry trends, are made and analyzed. with the industrial demands.
 In EO-TWM, the accumulated electro-optic e ect over the optical wave grows with the co-propagated traveling wave (TW) length, allowing to reduce the required RF driving power. However, in typical electro-optic materials for modulators, among which LiNbO3 stands up, due to the natural mismatch between the velocity of the RF and the optical waves, the modulation bandwidth decreases with the TW length, giving place to a well-known trade-o ff. In typical LiNbO3 substrates, in which this Thesis is focused, this trade-off is seen to mainly depend on the values of the electrical loss constant and the e ective wave velocity mismatch in the TW structure that forms the electrodes, usually a coplanar waveguide (CPW).
 Special emphasis has historically been placed on the optimized design of the CPW in EO-TWM. In this Thesis the study of closed-form expressions for the propagation parameters of CPW as a function of the geometry, has proven useful for the design and optimization procedures sought. Although some interesting approaches to closed-form formulations have been found in literature, none of them completely ful lls the desired requirements of providing a reliable yet simple description of propagation in CPW, appropriate to systematic and easy to follow design rules for EO-TWM, and therefore new simpli ed closed-form expressions for the CPW transmission parameters have been developed. 
 In a second part of the Thesis, the bandwidth-length trade-off has been examined. To date, two bandwidth-length rules have been proposed: a constant bandwidth-length product proportional to the inverse of the velocity matching constant has been shown to govern the low-loss limit (LL), while in the velocity matching limit (VM), a constant bandwidth times squared-length rule proportional to the inverse of the squared loss constant has been found more appropriate. In this work we provide insights into the trade-off issue in EO-TWM, and a complete picture of the applicable fi gures of merit for every operative range. Besides the known LL and VM gures of merit, two intermediate ranges, the quasi-low loss (QLL) and the quasi-velocity matching (QVM), have been identi ed. Also novel closed-forms expressions fully accounting for the e ffects of the skin-eff ect electrode loss and optical-electrical wave velocity mismatch, explicitly relating the operative bandwidth and the electrode length in EO-TWM, have been found. Novel bandwidth and electrode-length charts have been created, which constitute a useful tool for the optimization and design of this modulators. A graphical interface tool called MZM-GIT has been built integrating the analytical optimization and design strategies developed throughout the Thesis. With the aid of the MZM-GIT, several proposals of optimized MZM designs based on practical structures described in literature, and also based on the industry trends, are made and analyzed.