Theoretical analysis of integrated collimating waveguide lens

An integrated collimating waveguide lens is analyzed for applications which require the focusing of an optical beam onto the waveguide of a planar lightwave circuit. The lens has a refractive index profile which is parabolically graded as a function of height to focus light in the vertical plane, and has a convex front face to focus light in the horizontal plane. Analysis based on the propagation of a Gaussian field is used to design a lens pair which minimizes the optical loss for a given propagation length. The beam propagation method is used to identify fabrication tolerances which may have impact on the performance of the lens pair. The lens pair has application in micro-optoelectromechanical (MOEM) switches based on planar optical waveguide circuits.