Illumination apparatus for forming an output beam, the apparatus comprising: (a) a light source adapted to emit a source beam of linearly-polarized light in a downstream direction along an optical axis, said source beam having a polarization direction transverse to said optical axis; and (b) a fixed birefringent plate having first and second regions with different rotational properties such that said first region of said plate intercepts a first portion of said source beam and said second region intercepts a second portion of said source beam, said first and second regions altering the polarization of said first and second portions of said source beam by different amounts so as to form an altered beam having a central portion with a first polarization direction and a peripheral portion with a second polarization direction transverse to said first polarization direction, said peripheral portion surrounding said central portion, said central portion having a first intensity distribution relative to said optical axis, said peripheral portion having a second intensity distribution relative to said optical axis; and (c) at least one polarization-selective element mounted downstream from said birefringent plate, said at least one polarization-selective element having a transmission axis and being operative to allow transmission of light having a polarization direction parallel to such transmission axis and to prevent transmission of light having a polarization direction perpendicular to such transmission axis.