  Integration of photonic chips with atomic, micromechanical, chemical and
biological systems can advance science and open many possibilities in
chip-scale devices and technology. Compact photonic structures for direct
coupling of light between high-index single-mode waveguides and arbitrary
free-space modes spanning hundreds of waves in cross-section would eliminate
bulky optical components and enable integration of photonics into many new
applications requiring wide beams, structured light and centimeter-scale
propagation distances with low diffraction-limited losses. Conventional
fiber-coupling approaches do not scale well for accurate, low-loss coupling
across the extremely large mode scale mismatch ($\approx10^6$ times in modal
area). Here we present an extreme mode converter that can transform the
photonic waveguide mode to the diffraction-limited, free-space Gaussian beam,
with a beam waist of about $160~\mu$m. Using two identical converters, we
demonstrate a grating-to-grating coupling that couples the radiating beam back
to the chip through a mirror reflection in free-space. Operating at 780~nm for
integration with chip-scale atomic vapor cell cavities, our design can be
adapted for visible, telecommunication or other wavelengths. Furthermore, other
types of beams can be implemented by using the 2-stage expansion approach
presented in this paper.
