Systematic investigation of the principal and first secondary maxima of ultrashort optical pulses focused by a high numerical aperture aplanatic lens

摘要

The electromagnetic field in the focus of an ideal aplanatic lens with high numerical aperture, which is illuminated by an ultrashort optical pulse and plane wave front, is simulated by taking the vectorial Debye integral and the coherent superposition of a frequency spectrum of monochromatic waves. The behavior of the principal maxima and the first secondary maxima as function of the numerical aperture (NA) and the pulse duration T is investigated systematically for light incident with linear polarization. First, one would not expect remarkable deviations from the stationary case. But also this simple system of an ideal aplanatic lens without any chromatic or monochromatic aberrations (of course only simple from the point of theory, but not at all from the point of practical realization) shows some remarkable results. If the NA (in vacuum) tends to the limiting case of 1.0 the maximum value of |E|~2 increases faster than expected from the scalar theory (Airy disc) with a maximum deviation of about 13%. The second effect really comes from very short pulses, i.e. very small values T. Then, the value of |E|~2 compared to the expected linear increase with 1/T decreases slightly (only less than 2%), but systematically for all NAs. Even more interesting is the dependence of the height of the first secondary maxima along the x-axis and y-axis on the NA and 1/T. It can be seen that along both axes the first secondary maxima nearly vanish for very short pulses, i.e. large values 1/T.