  The current searches for microlensing events towards the galactic bulge can
be used to detect planets around the lensing stars. Their effect is a
short-term modulation on the smooth lightcurve produced by the main lensing
star. Current and planned experiments should be sensitive enough to discover
planets ranging from Jupiter mass down to Earth mass. For a successful
detection of planets, it is necessary to accurately and frequently monitor a
microlensing event photometrically, once it has been "triggered".
  We present a large variety of two-dimensional magnification distributions for
systems consisting of an ordinary star and a planetary companion. We cover
planet/star mass ratios from $m_{pl}/M_* = 10^{-5}$ to $ 10^{-3}$. These limits
correspond roughly to $M_{Earth}$ and $M_{Jup}$, for a typical lens mass of
$M_* = 0.3 M_{\odot}$. We explore a range of star-planet distances, with
particular emphasis on the case of "resonant lensing", a situation in which the
planet is located at or very near the Einstein ring of the lensing star.
  We show a wide selection of light curves - one dimensional cuts through the
magnification patterns - to illustrate the broad range of possible light curve
perturbations caused by planets. The strongest effects are to be expected for
caustic crossings. But even tracks passing outside the caustics can have
considerable effects on the light curves. The easiest detectable (projected)
distance range for the planets is between about 0.6 and 1.6 Einstein radii.
Planets in this distance range produce caustics inside the Einstein ring of the
star. For a lensing star with a mass of about $0.3 M_{\odot}$ at a distance of
6 kpc and a source at 8 kpc, this corresponds to physical distances between
star and planet of about 1 to 3 AU.
