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Imaging electron motion with attosecond time resolution

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Problems<br />

Problem #2:<br />

Discrete points violate causality<br />

Im[χ(k,ω)] must be defined on continuous ω interval. Periodicity incompatible <strong>with</strong><br />

causality.<br />

Solution:<br />

Analytic continuation (interpolate)<br />

Side effects:<br />

• χ(x,t) defined forever. Vanishes for t < 0.<br />

• Repeats <strong>with</strong> period T = 2π/∆ω = 13.8 femtoseconds<br />

• ∆ω plays role of rep rate

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