Fig. 1

a Layout of the thermo-optic waveguide lens (TOWL). b Temperature gradient created by turning on a pair of parallel electrodes spaced over a distance (D) of 90 μm, each with a heating power of 45 mW/mm. c The resulting refractive index distribution in the waveguide center plane (z = 0), forming a parabolic curve along y, i.e., a square law medium. d The corresponding light focusing behavior in TOWL along the propagation direction x. e The variation of the 1 × 1 imaging length L, equivalent to 4f, under different apertures D and heating powers P, allowing TOWL to work as an on-chip tunable lens