  We designed Si-based all-dielectric 1 $\times$ 2 TE and TM power splitters
with various splitting ratios and simulated them using the inverse design of
adjoint and numerical 3D finite-difference time-domain methods. The proposed
devices exhibit ultra-high transmission efficiency above 98 and 99\%, and
excess losses below 0.1 and 0.035 dB, for TE and TM splitters, respectively.
The merits of these devices include a minor footprint of 2.2 $\times$ 2.2
$\mu$m $\times$ $\mu$m and a broad operating bandwidth of 200 nm with a center
wavelength of $\lambda$ = 1.55 $\mu$ m.
