Advances in ultrafast lasers permit one to measure field strengths
E(t,x) for x fixed for terahertz lasers. Similarly one can measure
the spectrum, which is the Fourier transform of the field with respect
to t. Experimentally, one observes that the D.C. component (the
Fourier transform evaluated at zero frequency), equal to the time
integral of the electric field, is vanishing small for all signals.
In this talk we show that this is true in the far field for all
solutions of Maxwell's equations and it is not true for general
solutions of the scalar wave equation. The difference is explained by
the fact that though each component of the field satisfies the scalar
wave equation, for Maxwell's equations the spatial integral of the
partial time derivative of E(t,x) vanishes identically, while for the
wave equation this spatial integral need not vanish. These conserved
integrals give the leading contribution to the time integrated far
field. This is joint work with G. Mourou.
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