Eigenmodes of laser cavities are studied theoretically and experimentally in two companion papers,
with the aim of making connections between undulatory and geometric properties of light. In this
first paper, we focus on macroscopic open-cavity lasers with localized gain. The model is based on
the wave equation in the paraxial approximation; experiments are conducted with a simple
diode-pumped Nd:YAG laser with a variable cavity length. After recalling fundamentals of laser beam
optics, we consider plano-concave cavities with on-axis or off-axis pumping, with emphasis put on
degenerate cavity lengths, where modes of different order resonate at the same frequency, and
combine to form surprising transverse beam profiles. Degeneracy leads to the oscillation of
so-called geometric modes whose properties can be understood, to a certain extent, also within a ray
optics picture. We first provide a heuristic description of these modes, based on geometric
reasoning, and then show …