Simplified field wave equations for the nonlinear propagation of extremely short light pulses

We suggest a method to derive the nonlinear wave equations suitable for describing the propagation of light pulses as short as two optical cycles in transparent nonlinear optical media. The equations are suitable for efficient numerical simulation of the propagation of extremely short pulses without the need to resort to any type of envelope approximation, although they contain these as a limiting case. We demonstrate the power of this approach by modeling some recent experiments in which ultrabroadband radiation was generated upon propagating 150 fs duration 390 nm pulses in a deuterium-gas-filled hollow-core waveguide. The calculated spectrum agrees well with the measured spectrum.