  We present a new electromagnetic mode that forms at the interface between two
planar surfaces laid side by side in free space, effectively guiding energy
along an infinitesimal, one-dimensional line. It is shown that this mode occurs
when the boundaries have complementary surface impedances, and it is possible
to control the mode confinement by altering their values correspondingly. The
mode exhibits singular field enhancement, broad bandwidth, direction-dependent
polarization, and robustness to certain defects. As a proof-of-concept,
experimental results in the microwave regime are provided using patterned
conducting sheets. Our proposed effective-medium-based approach is general,
however, thus allowing for potential implementation up to optical frequencies.
Our system is promising for applications including integrated photonics,
sensing, switching, chiral quantum coupling, and reconfigurable waveguides.
