Quadratic Electro-optic effects. The effects are induced in a centrosymmetrio nonlinear material by static electric fields produced in an axially symmetric electrodes system as those are used in a Penning trap. Analysis shows that we can get different type of effective lena with materials having different point group symmetry and geometric arrangement. We pay attention especially to those materials having m3m symmetry, which can be used to create effective static cylindrical lens. Estimation shows that with a piece of crystal of several centimetres size and a direct voltage of 104~105 Volts we can obtain a focal length of tens centimetres in the case of line focus.