Paraxial theory of sum-frequency generation by side-walk alignment and   phase-matching in uniaxial crystals
  A formalism in terms of Hertz potentials is presented describing sum-frequency generation in a uniaxial non-linear crystal. A scheme is proposed consisting in aligning the side-walk propagation of extraordinary waves in combination with phase-matching. Simplified paraxial equations describing this situation are obtained. Particular attention is paid to the generation of second harmonics. 
Shahen Hacyan
physics.optics