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This chapter will compare the models of generation of gas and plasma harmonics, emphasizing symmetry considerations. It will be shown that the picture which is based on the classical considerations of Bloembergen based on the symmetries of the high order susceptibilities, is a simple model and – especially in the case of laser pulses of just a few cycles – both the accurate pulse shape and the geometrical symmetry of the interaction must be taken into account. The aim is to show similarities and differences between harmonic generation in gases and from plasma gradients. In the latter case the range of moderately relativistic intensities will be emphasized in more detail, when the coherent wake emission (CWE) model can be applied which illustrates these symmetry considerations more clearly.

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