Observation of the Talbot effect for ultrasonic waves

Exact results for scattering on ultrashort plane wave backgrounds

“…2. Despite the complexity of the argument of the logarithm in (13), the exact result is very well approximated by the large a 0 expansion (15) for a 0 > 10.…”

“…when dividing by l.q, when introducing u = n.q/n.l, and so on). Expanding (13) for small a 0 shows that the probability behaves as P 7 18…”

“…This brings us to the question of how the probability (13) behaves at high intensity, or large a 0 . Processes in constant crossed fields (the zero frequency limit of plane waves) can scale with powers of a 2/3 0 [12][13][14][15][16], which has lead to a conjecture that for sufficiently high a 0 the Furry expansion as used here breaks down. If one invokes the "locally constant field approximation" (LCFA) [4] then the power-law scaling generalises to more general fields [37,38], but due to the many shortcomings of the LCFA [37][38][39][40][41][42] it would be desirable to have exact analytic results.…”

“…However, the evaluation of observables still requires intense numerical integration. While various results have been found which allow more efficient calculation [8][9][10], it would be desirable to have exact results when confronting questions of a fundamental nature, such as the limits of perturbation theory in the high intensity regime; it has been conjectured that (Furry picture [11]) perturbation theory in strong fields breaks down for sufficiently high field strengths, due to a power-law scaling of higher loop processes [12][13][14][15][16]. If true, this would invalidate current perturbative or semi-perturabtive approaches to QED in strong backgrounds [17,18].…”

“…Highly symmetric backgrounds such as electromagnetic plane waves [1][2][3], widely used as a first model of intense laser fields [4][5][6][7], may be treated exactly for arbitrarily high field strength, allowing a great deal of analytic progress to be made in the calculation of scattering amplitudes.However, the evaluation of observables still requires intense numerical integration. While various results have been found which allow more efficient calculation [8][9][10], it would be desirable to have exact results when confronting questions of a fundamental nature, such as the limits of perturbation theory in the high intensity regime; it has been conjectured that (Furry picture [11]) perturbation theory in strong fields breaks down for sufficiently high field strengths, due to a power-law scaling of higher loop processes [12][13][14][15][16]. If true, this would invalidate current perturbative or semi-perturabtive approaches to QED in strong backgrounds [17,18].Here we have two objectives.…”