Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses

Via the Richards-Wolf vector diffraction theory, we analyze the three-dimensional intensity distribution of the focal volume that is produced by a strongly focused 750-nm beam of ultrafast, Gaussian-shaped optical pulses (10^-9s>~ pulse width τ>~1fs=10^-15s). Knowledge of the three-dimensional distribution near focus is essential in determining the diffraction-limited resolution of an optical microscope. The optical spectrum of a short pulse is characterized by side frequencies about the carrier frequency. The effect of spectral broadening on the focused intensity distribution is evaluated via the Linfoot’s criteria of fidelity, structural content, and correlation quality and with reference to a 750-nm cw focused beam. Different values are considered for τ and numerical aperture of the focusing lens (0.1<~X_NA<~1.2). At X_NA=0.8, rapid deterioration of the focused intensity distribution is observed at τ=1.2fs. This happens because a 750-nm optical pulse with τ=1.2fs has an associated coherence length of 359.7 nm which is less than the Nyquist sampling interval of 375 nm that is required to sample 750 nm sinusoid without loss of information. The ill-effects of spectral broadening is weaker in two-photon excitation microscope than in its single-photon counterpart for the same focusing lens and light source.