# Rethinking Figure-of-Merits of Liquid Crystals Shielded Coplanar Waveguide Phase Shifters at 60 GHz
## 4 Discussion  
The figure-of-merit (FoM) of LC-based phase-shifting devices is arguably the art of a unified cost-benefit ratio that replaces a set of performance parameters and facilitates benchmarking communication between the UK and global liquid crystals research. For the first time, this work reflects on a mismatching phenomenon between an LC-based phase shifter device's FoM\({}^{\prime}\) and the embedded LC material's FoM\({}^{\prime}\). By computationally analysing 16 types of mainstream mmWave-engineered LCs in a case study with an unconventional LC-based SCPW structure at 60 GHz, GT7-29001 and MDA-03-2838 exhibited the highest FoM\({}^{\prime\prime}\) for devices, surpassing those based on GT5-28004 and TUD-566 (with the highest intrinsic material FoM\({}^{\prime}\)). Geometrical factors were quantified and compared to explain such a discrepancy, underpinned by nonlinear wave-occupied volume effects on the phase shift as well as the line-length effect that was not linearly scalable for the insertion loss. The constraint on existing FoM metrics could partially be remediated by incorporating the mmWave phase-tuning speed, which is remarkably limited by the fall time (FT) [12, 30] of the bulk LC layer where energy is stored. An updated definition of FoM\({}^{\prime\prime\prime}\) can accordingly be adapted in Equation (5), catering to speed-sensitive applications, such as the emerging LC-based flat-panel antenna array for automotive radars. Factoring this into a global benchmark, optimisation insights on material synthesis could be envisioned, e.g., by balancing the polar and non-polar components [18]. \[\text{FoM}^{\prime\prime\prime}=\text{FoM}^{\prime\prime}/\text{FT} \tag{5}\]  
Albeit many open challenges remain (e.g., various nonlinear effects) for formulating a rigorously unified and reliable metric, the value of tailoring a specific FoM is still clear and remains of keen interest to LC researchers and mmWave engineers. It is advisable to keep an eye not only on the generic modalities of phase shift and insertion loss, but also on integrating more specific variables underlying the device operation, e.g., driving voltage, power handling, volume, weight, viscosity, temperature dependence, fabrication cost, and the stability of insertion loss magnitude over different driving voltages, among others. A more comprehensive performance metric can arguably enhance decision-making in navigating LCs for bespoke mmWave applications (e.g., inter-satellite links [31] and satellite internet [32]) beyond the photonics-based display sector. Though the results from this work are exclusively dedicated to LC SCPW phase shifters at 60 GHz, the implications are to a great extent transferrable to the performance evaluation of other LC-based reconfigurable mmWave devices, such as resonators, filters, etc. One of the proposed future work prospects is thus to generalise the characteristic of tunable mmWave components with FoMs of LC materials and LC devices. Another scope of research direction is about leveraging machine learning-related techniques to decipher the complex non-linearities (as discussed above) and aid in reconfigurable device design optimisation with LC materials. The author undertakes the conceptualization, modelling, simulation, experimental verification, data analysis, visualisation, manuscript writing, reviewing, and editing. The author has read and agreed to the published version of the manuscript. This research received no external funding. Sincere thanks to Electrical Engineering Division, Department of Engineering, the University of Cambridge, where part of the insights builds upon the author's previous prototypes of LC SCPW phase shifters [7] developed with extensive academic training support from [PERSON] at the Centre for Photonic Devices and Sensors. Special thanks also go to Imperial College London and University of Southampton, who houses the Ansys Electronics Desktop (AEDT) and dedicated software packages for modelling and data analysis in this work. The author declares no conflict of interest.