Fig. 1. (a) Illustration of a TOPS using a metallic heater on top of the waveguide. (b) Cross section of the TOPS. (c) Simulated temperature distribution of the TOPS. (d) Temporal response of the TOPS upon a square electrical signal applied to the heater with (solid blue line) and without (dotted red line) employing pulse pre-emphasis. The considered TOPS comprises a $500\mathrm{nm}\times 220\mathrm{nm}$ Si waveguide with a $2\mu \mathrm{m}\times 100\mathrm{nm}$ Ti heater on top. The gap between the waveguide and the heater is $1\mu \mathrm{m}$. The temperature distribution in the cross section was obtained by solving the conductive heat equation using the COMSOL Multiphysics simulation tool. We considered the thermal constants reported in the literature.²⁰ A nonuniform tetrahedral mesh, with element sizes ranging from 1 to 500 nm, was employed. A conductive heat flux boundary condition with a heat transfer coefficient of $5\mathrm{W}/({\mathrm{m}}^2\mathrm{K})$ was set on the surface. The temperature of the remaining boundaries was fixed at 293.15 K (cold).

Fig. 2. (a) Illustration of a TOPS using a metallic heater on top of the waveguide with thermal isolation by etching the top cladding and buried oxide. (b) Cross section of the free-standing TOPS. (c) Simulated temperature distribution of the free-standing TOPS. The considered TOPS comprises a $500\mathrm{nm}\times 220\mathrm{nm}$ silicon waveguide with a $2\mu \mathrm{m}\times 100\mathrm{nm}$ Ti heater on top. The gap between the waveguide and the heater is $1\mu \mathrm{m}$. The temperature distribution in the cross section was obtained by solving the conductive heat equation using the COMSOL Multiphysics simulation tool. We considered the thermal constants reported in the literature.²⁰ A nonuniform tetrahedral mesh, with element sizes ranging from 1 to 500 nm, was employed. A conductive heat flux boundary condition with a heat transfer coefficient of $5\mathrm{W}/({\mathrm{m}}^2\mathrm{K})$ was set on the boundaries in contact with air. The temperature of the remaining boundaries was fixed at 293.15 K (cold).

Fig. 3. (a) Illustration of a TOPS using a transparent heater directly on top of the waveguide. (b) Cross section of the TOPS. (c) Simulated temperature distribution of the TOPS using an ITO heater. The considered TOPS comprises a $500\mathrm{nm}\times 220\mathrm{nm}$ silicon waveguide with a $2\mu \mathrm{m}\times 100\mathrm{nm}$ ITO heater on top. The gap between the waveguide and the heater is 100 nm. The temperature distribution in the cross section was obtained by solving the conductive heat equation using the COMSOL Multiphysics simulation tool. We considered the thermal constants reported in the literature.²⁰ A nonuniform tetrahedral mesh, with element sizes ranging from 1 to 500 nm, was employed. A conductive heat flux boundary condition with a heat transfer coefficient of $5\mathrm{W}/({\mathrm{m}}^2\mathrm{K})$ was set on the surface. The temperature of the remaining boundaries was fixed at 293.15 K (cold).

Fig. 4. (a) Illustration of a TOPS utilizing a silicon-doped heater, where the heat generation occurs within the doped silicon waveguide. In this configuration, the waveguide is of the rib type, with several silicon-doped heaters arranged in electrical parallel to minimize total resistance. Metallic contacts are linked to the silicon waveguide via silicon-doped strips. (b) Simulated temperature distribution within the TOPS, consisting of a $500\mathrm{nm}\times 220\mathrm{nm}$ silicon waveguide atop a 100-nm-thick slab, with $1\mu \mathrm{m}$-thick ${\mathrm{SiO}}_2$ cladding. Temperature distribution analysis was performed by solving the conductive heat equation with the COMSOL Multiphysics simulation tool, considering the waveguide core as the heat source, based on thermal constants from the literature.²⁰ A nonuniform tetrahedral mesh, with element sizes ranging from 1 to 500 nm, was employed. A conductive heat flux boundary condition, with a heat transfer coefficient of $5\mathrm{W}/({\mathrm{m}}^2\mathrm{K})$, was applied on the surface, while the temperature for all other boundaries was fixed at 293.15 K (cold). (c), (d) Cross-sectional views of the TOPS featuring (c) direct current injection and (d) a pn junction setup.

Fig. 5. (a) Illustration of a TOPS using folded waveguides based on a spiral waveguide with a wide heater on top. (b) Cross section of the folded TOPS. The folded waveguide needs to be designed to avoid cross-coupling between adjacent waveguides.

Fig. 6. (a) Illustration of a TOPS utilizing a multimode waveguide where light is recycled $N$ times through a multipass structure, demonstrating how power consumption decreases as the number of passes increases. (b) Cross section of the TOPS within the multimode waveguide. (c) Depiction of optical mode conversion as a function of the multipass structure’s length. Light enters the structure in the fundamental mode and, after $N$ passes, is converted to the $N$th-order mode before being output from the structure and reverted to the fundamental mode.

Table 1. Summary of basic experimental TOPSs using metallic heaters in SiPh.

Table 2. Summary of basic experimental TOPSs using transparent heaters in SiPh.

Table 3. Summary of basic experimental TOPSs using doped silicon heaters in SiPh.

Table 4. Summary of advanced experimental TOPSs using folded waveguides and metallic heaters in SiPh.

Table 5. Comparison of mainstream and emerging electro-optic technologies for implementing phase shifters in SiPh.