  We consider a recently reported micro-fluidic dye ring laser and study the
full wave nature of TE modes in the cavity by means of finite-element
simulations. The resonance wave-patterns of the cavity modes support a
ray-tracing view and we are also able to explain the spectrum in terms of
standing waves with a mode spacing dk = 2pi/L_eff where L_eff is the effective
optical path length in the cavity.
