Bandwidth–length trade-off figures of merit for electro-optic traveling wave modulators

Abstract

Closed-form expressions explicitly relating modulation bandwidth and active length in electro-optic traveling wave modulators are presented which fully account for skin-effect electrode loss and optical-electrical wave velocities mismatch. Four Optical modulators based on the electro-optic (EO) Pockels effect are basic building blocks of optical systems, with applications continuously growing up. As compared to lumped electrode configurations, bounded by a fundamental sensitivity-bandwidth limit, traveling wave (TW) configurations allow pushing the limit by optimization of the TW structure and provide extended modulation bandwidth with reduced drive power [1,2]. In EO-TW modulators (EO-TWM) the Pockels electrically induced optical phase shift accumulates with the copropagated distance (L) and therefore, the modulation drive voltage, usually quantified as the voltage required for a π phase shift, V π , is reduced proportionally to increases in L [3]. However, as it is well known, this comes at the expense of a corresponding reduction in operative bandwidth (B), which in typical EO-TWM based on coplanar waveguides (CPWs) over LiNbO 3 substrates stems mainly from the combined action of two basic mechanisms, namely the skin-effect electrode loss and the optical-electrical wave velocity mismatch. When trying to elucidate the expected B reduction that a specific L increase could have, a constant BL product rule proportional to the inverse of the velocity matching (VM) constant (ν) has been shown to govern the low-loss (LL) limit [4], while in the VM limit, a constant BL 2 rule proportional to the inverse of the square of the loss constant (α) has been found more appropriate [5]. To the best of our knowledge, no simple B-L rules have been derived for the intermediate ranges in which both α and ν are relevant, nor have the LL and VM limits been quantified in a general way.In this Letter we present closed-form expressions that fully account for the effects of skin-effect electrode loss and optical-electrical wave velocities mismatch and that explicitly and in a biunivocal way relate the operative bandwidth and the electrode length in EO-TWM. From these, four B-L trade-off figures of merit are identified with different validity ranges which are seen to depend both on the TW cross-sectional parameters (i.e., skineffect constant and optical-electrical velocity mismatch) and on the target B and L values.In order to analyze the B-L relationship, we begin by considering the electrical modulation frequency response of an impedance matched EO-TWM in the presence of skin-effect electrical loss in the conducting electrodes of length L and optical-electrical velocity mismatch [6] Mf e

Heterogeneous microring and Mach-Zehnder modulators based on lithium niobate and chalcogenide glasses on silicon

“…The lower V π .L affords a lower drive voltage, and therefore lower drive power. It also permits smaller device lengths, which not only reduce the device footprint, but can also potentially increase the theoretical modulation bandwidth achievable [24,25]. This is expected based on theoretical studies showing that for the same bandwidth-length product, higher modulation bandwidth is attainable in devices with shorter lengths [25].…”

“…It also permits smaller device lengths, which not only reduce the device footprint, but can also potentially increase the theoretical modulation bandwidth achievable [24,25]. This is expected based on theoretical studies showing that for the same bandwidth-length product, higher modulation bandwidth is attainable in devices with shorter lengths [25]. Once this platform is fully developed, it can potentially offer significantly faster data transmission compared to commercially available lithium niobate modulators.…”

Analytical tool for the design and optimisation of high‐speed lithium niobate thin‐film Mach–Zehnder modulator

“…Once B , V π or B − V π are aimed, the first step is to obtain several sets of α 0 − ν values which allow to reach the targeted performance. For this purpose, the analytical equations for B and L obtained in [10] are used.…”

“…The expressions of L and B given in [10] can be rewritten as being where the constants , …”

“…Towards achievement of the above‐mentioned goals, it is important to bear in mind that in MZM the parameters B , V π and L are closely related through figure of merit trade‐offs, which basically depend of the optical–electrical waves velocity mismatch and the electrode loss. At the same time, it is also important to maintain a good impedance matching to driving sources [10].…”