  Mode-division multiplexing offers a promising solution to increase the data
capacity for optical communications. Waveguide mode conversion is essential for
on-chip mode-division multiplexing. Previously reported mode converters have
been limited to the conversion from a fundamental mode to one particular
high-order mode. It is challenging to simultaneously satisfy the phase matching
conditions during multiple mode conversion processes. Here, we propose a
scalable design method that overcomes this limitation and realizes the
simultaneous conversion of multiple modes via an all-dielectric two-dimensional
metastructure on a silicon waveguide by shallow etching with hexagonal
patterns. As an example, we experimentally demonstrate a multi-mode converter
that simultaneously converts the TEi modes to the TEi+3 (i = 0, 1, 2) modes.
The length of the multi-mode converter is 16.2 micron. The TE0-TE3, TE1-TE4,
and TE2-TE5 mode conversions exhibit low insertion losses (0.4 to 1.0 dB) and
reasonable crosstalk values (-14.1 to -16.5 dB) at 1538 nm.
