  Integrated photonic devices are poised to play a key role in a wide variety
of applications, ranging from optical interconnects and sensors to quantum
computing. However, only a small library of semi-analytically designed devices
are currently known. In this paper, we demonstrate the use of an inverse design
method that explores the full design space of fabricable devices and allows us
to design devices with previously unattainable functionality, higher
performance and robustness, and smaller footprints compared to conventional
devices. We designed a silicon wavelength demultiplexer that splits
$1300~\mathrm{nm}$ and $1550~\mathrm{nm}$ light from an input waveguide into
two output waveguides, and fabricated and characterized several devices. The
devices display low insertion loss $\left(2 - 4~\mathrm{dB}\right)$, high
contrast $\left(12 - 17~\mathrm{dB}\right)$, and wide bandwidths $\left(\sim
100~\mathrm{nm} \right)$. The device footprint is $2.8 \times 2.8 ~\mathrm{\mu
m}$, making this the smallest dielectric wavelength splitter to date.
