  There is currently a strong interest in mirrorless lasing systems, in which
the electromagnetic feedback is provided either by disorder (multiple
scattering in the gain medium) or by order (multiple Bragg reflection). These
mechanisms correspond, respectively, to random lasers and photonic crystal
lasers. The crossover regime between order and disorder, or correlated
disorder, has also been investigated with some success. Here, we report
one-dimensional photonic-crystal lasing (that is, distributed feedback lasing)
with a cold atom cloud that simultaneously provides both gain and feedback. The
atoms are trapped in a one-dimensional lattice, producing a density modulation
that creates a strong Bragg reflection with a small angle of incidence. Pumping
the atoms with auxiliary beams induces four-wave mixing, which provides
parametric gain. The combination of both ingredients generates a mirrorless
parametric oscillation with a conical output emission, the apex angle of which
is tunable with the lattice periodicity.
