Analytical and numerical solutions to the guided poloidal Alfv¿n wave equation in a dipole field are developed, including the effects of realistic and asymmetric finite ionospheric conductivities. We show that when the ionospheric Pedersen conductivity in one hemisphere is less than a critical value, then quarter-wavelength harmonic modes become possible. We present solutions using realistic plasma density variations along the field line and illustrate how the electric and magnetic fields of a field-aligned half-wavelength harmonic mode change as the ionospheric conductivities are made increasingly asymmetric and the wave develops into a quarter-wavelength mode. Further, we show how over a small critical range of ionospheric Pedersen conductivities, the wave damping rates and frequencies change rapidly as this transition from half- to quarter-wavelength mode occurs. We also show that the phase difference between the electric and magnetic field components is strongly dependent upon the distance along the magnetic field line, upon the asymmetry in the ionospheric Pedersen conductivities, and significantly upon which hemisphere has its footprint in the ionosphere whose conductivity is close to critical. This has important implications for inferring the field-aligned harmonic mode of standing ULF pulsations when using single satellite data.