A resonator is provided having a waveguide with a first boundary, a second boundary parallel to the first boundary, a first end, a second end, and a waveguide cavity at least partly between the first boundary and the second boundary. A first grating, having a period of distance a, is at the first boundary of the waveguide, and a second grating, having a period of distance a, is at the second boundary of the waveguide. The first and second boundaries are separated by a constant distance d. The first boundary may have a periodic profile aligned with a periodic profile of the second boundary. The periodic profile of the first boundary and the second boundary may be a sinusoidal profile, a square profile, or profile of another shape. The resonator may be suitable for use in a distributed feedback laser.