Actual focal length of a symmetric biconvex microlens and its application in determining the transmitted beam waist position.

The actual focal length of a three-dimensional continuous profile symmetric biconvex microlens with normal monochromatic plane wave illumination is theoretically determined using a full-field separation of variables method in the oblate spheroidal coordinate system. The investigations are performed for microlenses of 5, 10, and 20 wavelength diameters by calculating the electromagnetic field distributions inside of and adjacent to the microlenses. The importance and potential application of the microlens actual focal length in the design of microlens optical systems are demonstrated by showing that for normal monochromatic TEM00 mode Gaussian beam illumination, the transmitted beam waist position through a single microlens, calculated using Self's beam waist position transformation formula [Appl. Opt.22, 658 (1983)] with the microlens actual focal length, closely matches the exact value given by the separation of variables method.