Single element laser beam shaper

1. A system for shaping a laser beam from a non-uniform spatial profile to a flat-top or uniform spatial profile comprising:

an input laser beam having an input energy density and a maximum beam radius;

a system magnification factor;

a lens including a first and second aspheric surface;

a central ray having a central optical path length;

a plurality of arbitrary rays having an optical path length equal to said central optical path length;

said first aspheric surface having a curvature profile defined by the equation:

Z =( n 2 2 −n 0 2 ) −1 {[( n 1 n 2 −n 0 2 ) z+n 2 C]±n 0 [( C+n 1 γ 1 n 2 z ) 2 +( n 2 2 −n 0 2 )( R−r ) 2 ] 1/2 }  (4);

and

said second aspheric surface having a curvature profile defined by the equation:

z ′={( R−r )( Z−z )±γ 1 ( R−r )[( Z−z ) 2 +( R−r ) 2 ] 1/2 }/[(γ 1 2 −1)( Z−z ) 2 +γ 1 2 ( R−r ) 2 ]  (6)

where n 0 is the refraction index of the medium, n 1 is the refraction index of said first aspheric surface, n 2 is the refraction index of said second aspheric surface, r and z are the radial and axial values at said first aspheric surface, R and Z are the radial and axial values at said second aspheric surface, C is a constant determined at the condition where the optical path length of said arbitrary rays are equal to said optical path length of said central ray, and γ 1 =n 1 /n 2 .

2. The system of claim 1 wherein the index of refraction between said first and second aspheric surfaces is greater than the index of refraction beyond said first and second aspheric surfaces.

3. The system of claim 2 wherein said lens is constructed of fused silica.

4. The system of claim 1 wherein

said laser beam includes a wavelength; and

said curvature profile of said first aspheric surface has a horizontal axial component.