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In this paper we will follow the common convention of using complex values for the time dependent electric fields, with the implicit understanding that one should add the complex conjugate of the expressions to obtain the physical field. In the frequency domam, this convention implies that the value of Ẽ(ω) should be replaced by Ẽ(ω) + Ẽ(-ω).
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As discussed in Ref. 11, we need to use both Eq. (1) and its complex conjugate. Since only the term oscillating as exp(-iωt) will cause significant excitation (the rotating wave approximation), for positive frequencies (by the present phase convention), we will retain only the complex conjugate term.
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