  We demonstrate a design for a high-performance $2 \times 2$ splitter meeting
the essential requirements of broadband coupling, support for arbitrary
coupling ratio, ultra low-loss, high fabrication tolerance, and a compact
footprint.
  This is achieved based on a rigorous coupled mode theory analysis of the
broadband response of the bent directional coupler (DC) and by demonstrating a
full coupling model, with measured broadband values of 0.4, 0.5, 0.6, and 0.7.
  As a benchmark, we demonstrate a 0.5:0.5 splitter that significantly reduces
coupling variation from 0.391 in the traditional DC to just 0.051 over an 80 nm
wavelength span.
  This represents a remarkable 7.67 times reduction in coupling variation.
  Further, newly-invented low-loss bends were used in the proposed design
leading to an ultra low-loss design with negligible excess loss ($\mathrm{0.003
\pm 0.013 \ dB}$).
  The proposed 0.5:0.5 silicon strip waveguide-based design is tolerant and
shows consistently low coupling variation over a full 300 mm wafer showcasing a
maximum cross coupling variation of 0.112 over 80 nm wavelength range, at the
extreme edge of the wafer.
  Futhermore, we augmented the wafer mapping with a waveguide width fabrication
tolerance study, confirming the tolerance of the device with a mere 0.061
maximum coupling variation with a waveguide width deviation of $\pm 20$ nm over
80 nm wavelength range.
  These specs make the proposed splitter an attractive component for practical
applications with mass production.
