  The scaling of electromagnetic apertures is a long-standing question that has
been investigated for at least six decades but has still not been resolved
[1-5]. The size of single aperture cavities, bounded by the existence of
higher-order transverse modes, fundamentally limits the power emitted by
single-mode lasers or the brightness of quantum light sources. The
free-spectral range of existing electromagnetic apertures goes to zero when the
size of the aperture increases, and the demonstration of scale-invariant
apertures or lasers has remained elusive. Here, we report open-Dirac
electromagnetic apertures that exploit a subtle cavity-mode-dependent scaling
of losses in reciprocal space. For cavities with a quadratic dispersion, the
complex frequencies of modes converge towards each other with the size of
cavities, making cavities invariably multimode. Surprisingly, for a class of
cavities with linear dispersion, we discover that, while the convergence of the
real parts of cavity modes towards each other is delayed (it still quickly goes
to zero), the normalized complex free-spectral range converge towards a
constant governed by the loss rate of distinct Bloch bands. We show that this
unconventional scaling of the complex frequency of cavity modes in open-Dirac
electromagnetic apertures guarantees single-mode operation of large cavities.
We experimentally demonstrate that single-mode lasing of such cavities is
maintained when the cavity is scale up in size. We name such sources Berkeley
Surface Emitting Lasers (BerkSELs). We further show that the far-field emitted
by the proposed single-mode BerkSELs corresponds to a topological singularity
of charge two, in full agreement with our theory. Open-Dirac apertures open new
avenues for light-matter interaction and basic science in open-wave systems
with applications in classical and quantum communications, sensing, and
imaging.
