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We report a modulational instability (MI) analysis of a mathematical modelappropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear mediabeyond the so-called slowly varying envelope approximation. Theoreticallypredicted MI properties are found to be in good agreement with numericalsimulation. The study shows the possibility of controlling the generation of MIand formation of solitons in a cascaded quadratic-cubic media in the few cycleregimes. We also find that stable propagation of soliton-like few-cycle pulsesin the medium is subject to the fulfilment of the modulation instabilitycriteria.

Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation