http://iopscience.iop.org/article/10.1088/2399-6528/aa8cfe
The Unidirectional Pulse Propagation Equation (uppe) is often used to compute the forward component of ultrashort light pulses in nonlinear materials. While its accuracy has frequently been reported for many applications in ultrafast optics, its validity can be questionable for ionizing pulses, in particular in the frequency domain below the electron plasma frequency
. Inaccuracy of the upper model in this frequency range may be detrimental to, e.g., a correct description of laser-driven terahertz emission. Here we demonstrate, analytically and numerically, that over long enough propagation paths, the one-dimensional solutions of both uppe and the full wave equation match in the entire spectrum, including the spectral range 
. Our findings confirm the reliability of the uppe solutions for a wide class of propagation problems.
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