A Precise Photometric Ratio via Laser Excitation of the Sodium Layer I:
  One-photon Excitation Using 342.78 nm Light
  The largest uncertainty on measurements of dark energy using type Ia
supernovae is presently due to systematics from photometry; specifically to the
relative uncertainty on photometry as a function of wavelength in the optical
spectrum. We show that a precise constraint on relative photometry between the
visible and near-infrared can be achieved in upcoming surveys (such as in LSST
at the Vera C. Rubin Observatory) via a mountaintop-located laser source tuned
to the 342.78 nm vacuum excitation wavelength of neutral sodium atoms. Using a
high-power (500 W) laser modified from laser guide star studies, this
excitation will produce an artificial star (which we term a "laser photometric
ratio star," or LPRS) of de-excitation light in the mesosphere that is
observable from the ground at approximately 20 magnitude (i.e., well within the
expected single-image magnitude limit of LSST) at wavelengths in vacuum of
589.16 nm, 589.76 nm, 818.55 nm, and 819.70 nm, with the sum of the numbers of
589.16 nm and 589.76 nm photons produced by this process equal to the sum of
the numbers of 818.55 nm and 819.70 nm photons, establishing a precise
calibration ratio between, for example, the LSST r and z filters. This
technique can thus provide a novel mechanism for establishing a
spectrophotometric calibration ratio of unprecedented precision, from above
most of the Earth's atmosphere, for upcoming telescopic observations across
astronomy and atmospheric physics.
  This article is the first in a pair of articles on this topic. The second
article of the pair describes an alternative technique to achieve a similar,
but brighter, LPRS than the technique described in this paper, by using two
mountaintop-located lasers, at optical frequencies approximately 4 GHz away
from resonances at wavelengths in vacuum of 589.16 nm and 819.71 nm
respectively.
