COLLIMATING CYLINDRICAL DIFFRACTIVE LENSES - RIGOROUS ELECTROMAGNETICANALYSIS AND SCALAR APPROXIMATION

Practical collimating diffractive cylindrical lenses of 2, 4, 8, and 1 6 discrete levels are analyzed with a sequential application of the tw o-region formulation of the rigorous electromagnetic boundary-element method (BEM). A Gaussian beam of TE or TM polarization is incident upo n the finite-thickness lens. F/4, F/2, and F/1.4 lenses are analyzed a nd near-field electric-field patterns are presented. The near-field wa ve-front quality is quantified by its mean square deviation from a pla nar wave front. This deviation is found to be less than 0.05 free-spac e wavelengths. The far-field intensity patterns are determined and com pared with the ones predicted by the approximate Fraunhofer scalar dif fraction analysis. The diffraction efficiencies determined with the ri gorous BEM are found to be generally lower than those obtained with th e scalar approximation. For comparison, the performance characteristic s of the corresponding continuous Fresnel (continuous profile within a zone but discontinuous at zone boundaries) and continuous refractive lenses are determined by the use of both the BEM and the scalar approx imation. The diffraction efficiency of the continuous Fresnel lens is found to be similar to that of the 16-level diffractive lens but less than that of the continuous refractive lens. It is shown that the vali dity of the scalar approximation deteriorates as the lens f-number dec reases. (C) 1998 Optical Society of America.