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Summary form only given. Self-phase modulation (SPM) of optical pulses is one of the most important effects in ultrafast nonlinear optics and the physical cause of a variety of phenomena such as optical solitons, spectral broadening, etc. While the nonlinear propagation of pulses with a duration of many cycles is rather well studied, the physical phenomena in the ultrashort (few-cycle and sub-cycle regime) are yet not well understood. In this region, the widely used approximate methods, such as truncated Taylor series approximation to dispersion and the slowly varying envelope approximation (SVEA), are no longer adequate to describe the pulse propagation. In the present talk we investigate this regime and study the possibility to extend the method of pulse compression into the optical subcycle regime. We solve the exact Maxwell equations without the use of the SVEA and apply a global approach to dispersion with a modified Sellmeyer expansion. In such a way dispersion effects, infrared losses due to vibrational modes, as well as other higher-order effects such as self-steepening due to intensity-dependent group velocity, are adequately taken into account. With the help of this approach the character and the limitation of ultrawide spectral broadening by SPM and the frequency-dependence of the phase (chirp) during propagation are explored. We show that pulses with a duration of 0.5 fs or approximately half of a cycle can be generated by SPM, whereby chirp compensation can be achieved using a liquid-crystal spatial light modulator.