# Fully Reconfigurable Photonic Filter for Flexible Payloads
## 3 Proposed Structure Analysis
### Tuning Mechanism  
The reconfigurability of filters can be achieved by modifying the effective index n\({}_{\text{eff}}\) of the guided mode. The two primaries are based on the thermo-optic effect [33] and the electro-optic (EO) effect [34].  
The TO effect is exploited through a metal heater, fed by an electric current, and positioned close to the waveguide core. The heat generated as a result of the Joule effect in the metal induces a change in the refractive index of the waveguide, related to the Thermo-Optic Coefficient (TOC) of the material [35]. Due to the remarkably high TOC of silicon (dn/dT = 1.80 \(\times\) 10\({}^{-4}\) a.u. @ C band), the TO tuning method is well-suited for phase shifters. However, temperature change also affects the propagation losses (d\(\alpha\)/dT = 4.39 \(\times\) 10\({}^{-9}\) K\({}^{-1}\) @ C band). Two titanium nitride (TiN) electrodes with thickness t\({}_{\text{H}}\) and width w\({}_{\text{H}}\) have been positioned on top of RRs with a separation of d\({}_{\text{H}}\) from the Si core (as depicted in Figure 2b). Although ticker metal heaters ensure larger efficiency, fabrication constraints limit the thickness (t\({}_{\text{H}}\)) to 100 nm [36; 37]. Moreover, it is essential to avoid the deposition of the metal layer on the coupling region as thermal tuning can impact the coupling coefficient. Therefore, the electrodes are strategically positioned outside the coupling regions, and they show the same tuning lengths for all ring resonators (as illustrated in Figure 2a). The overall electrode length of 25.12 \(\upmu\)m has been chosen, ensuring the absence of electrodes within the coupling region, assumed as 20% of the total resonator length [24].  
The design of the gap between the metal layer and the waveguide (d\({}_{\text{H}}\)) is crucial to avoid absorption losses due to the metal, striking a balance between efficiency and losses. Small values of d\({}_{\text{H}}\) ensure good efficiency with large loss values.  
Another crucial parameter for phase shifters is the response time (\(\uptau\)). This time is typically defined as the duration required to transition from 10% to 90% or from 90% to 10% of the final electrical input square pulse value, corresponding to the rising and falling times, respectively.  
The design of all parameters has been conducted by integrating and harmonizing the capabilities of a thermal solver and an optical mode solver. This synergistic approach enabled the simulations to delve deeply into assessing various facets such as heat distribution, efficiency metrics, and the system's transient response. A temperature of 300 K has been assumed as a boundary condition of the simulation domain. For the thermal simulations, heat capacities and thermal conductivities of 0.8 J/g\({}^{\circ}\)C and 150 W/mK, 0.8 J/g\({}^{\circ}\)C and 1.5 W/mK, and 0.5 J/g\({}^{\circ}\)C and 30 W/mK for silicon, silicon dioxide, and titanium nitride, respectively, have been considered. The design of d\({}_{\text{H}}\) and w\({}_{\text{H}}\) has been conducted, aimed at achieving low power consumption and minimizing the figure of merit (FOM), represented by FOM = P\({}_{\uppi}\cdot\uptau\), where P\({}_{\uppi}\) denotes the power necessary to achieve a phase shift of \(\uppi\). The reduction in w\({}_{\text{H}}\) leads to a decrease in P\({}_{\uppi}\), preserving the value \(\uptau\)[36; 37]. Additionally, P\({}_{\uppi}\) can be reduced by increasing d\({}_{\text{H}}\), thereby enhancing heat insulation rather than conduction. However, the FOM decreases as w\({}_{\text{H}}\) and d\({}_{\text{H}}\) decrease. Therefore, w\({}_{\text{H}}\) = 0.8 \(\upmu\)m and d\({}_{\text{H}}\) = 0.4 \(\upmu\)m have been set with a resulting time response of \(\uptau\) = 9.20 \(\upmu\)s and a P\({}_{\uppi}\) of 11.50 mW. These theoretical results align perfectly with experiments reported in the literature [38].