The discussion centers on the representation of a laser beam's electric field strength using complex conjugates, specifically $$\widetilde{E}(t) = Ee^{-iwt} + c.c$$ as noted in Boyd's "Nonlinear Optics". The real part of the complex electric field is indeed the time-dependent E-field, expressed as $$\tilde E(t)= 2E\cos(\omega t)$$, where ##2E## denotes an arbitrary amplitude. The absence of division by 2 in the original expression is clarified as a standard representation rather than a mathematical necessity.
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BvU said:It's simply a representation of a time-dependent E-field. Your ##\tilde E(t)## is real, by the way:$$\tilde E(t)= 2E\cos(\omega t)$$and that ##2E## is some arbitrary amplitude.
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