  Adiabatic waveguide taper and on-chip wavelength demultiplexer are the key
components of photonic integrated circuits. However, these two kinds of devices
which designed by traditional semi-analytic methods or brute-force search
methods usually have large size. Here, based on regularized digital
metamaterials, we have designed, fabricated and characterized a two-channel
focused wavelength demultiplexer with a footprint of 2.4 x 10 um2. The designed
demultiplexer can directly connect to a grating coupler under the absence of an
adiabatic waveguide taper. The objective first method and modified steepest
descent method are used to design the demultiplexer which splits 1520 nm and
1580 nm light from a 10-um-wide input waveguide into two 0.48-um-wide output
waveguides. Experimental results show that the insertion loss of the upper
(lower) channel of the demultiplexer is -1.77 dB (-2.10 dB) and the crosstalk
is -25.17 dB (-12.14 dB). Besides, the simulation results indicate that the
fabrication tolerance of our devices can reach 20 nm in etching depth and 10 nm
in plane size changing. Benefit From the extensibility of our design method, we
can design other types of ultra-compact 'focused' devices, like mode splitters,
mode converters and power splitters, and we can also design devices with more
complicated functionalities, for example, we have designed a three-channel
focused wavelength demultiplexer.
