The magneto-optical effects in ultrathin layers are intensively investigated among other for their applications in magneto-optical storage media. In particular, the measurements based on the linear or quadratic Kerr effect require highly homogeneous outer magnetic fields. In our case this one is generated using the so called Malthese Cross, which consists of 4 poles and square yoke. We solve the shape optimization problem which aims at optimal shapes of the pole heads such that the resulting magnetic field is as homogeneous as possible. We establish the corresponding constrained optimization problem which is solved by the Sequential Quadratic Programming method. The underlying linear magnetic field problem is discretized by Finite Element Methods. Multigrid methods are used to solve the direct field problem. The magnetic field of the initial design is compared to measured values. Finally, improvements of homogeneity of the optimized device are discussed.

* This work has been supported by the Austrian Science Fund -- 'Fonds zur Foerderung der wissenschaftlichen Forschung' -- within the SFB F013 ''Numerical and Symbolic Scientific Computing''.