Hello, I come from a solid-state physics background and have just started using meep, forgive me if this is obvious. I am trying to use meep to simulate the (classical part of the) interaction of few-cycle laser pulses with metal targets. To give some numbers, at 800 nm central laser wavelength (period 2.7 fs) the pulse duration would be of the order of 6 fs.
For such short pulses, it is expected that the so-called carrier-envelope phase (shift between the maximum of the carrier frequency and the envelope function) plays a vital role for the outcome of experiments. However, if I try to simulate the propagation of an ultra-short pulse in vacuum, I find that contrary to my expectations, the carrier-envelope phase does not stay constant. This remains true even for very high resolutions (say, 5 nm = 1/160 wavelength). In fact, the rate of change appears to converge to around 0.2 * pi/2 (that is, 1/5 of the phase difference between a sine and a cosine pulse) per micron propagation distance. The effect persists in 2d as well as in 3d, my simulation box size is around 7x5x5 microns and I have tried to put the source as far away from the pml (1 micron on each side) as possible. The spatial width of the source does not have an appreciable effect (FWHM around 2 microns), so I do not think this is due to focusing. The carrier envelope phase is extracted from the simulation by recording the E field in several points at different distances from the source and then fitting with a source function with free parameters, E(r_0, t) = A cos( omega t + phi) * sin^2( 2pi* (t-t0)/(tau)), which matches the recorded functions perfectly (chi <1%) but with phi dependent on the distance to the source. Is this a problem with the "numerical dispersion" and that ultra-short pulses are unfortunately ideal to probe numerical dispersion? Or is this far above what you would expect, and the simulation is not converged in some other way? Does anyone have experience with the simulation of ultrashort pulses with meep? I appreciate your comments and ideas. Thank you for your time, Best regards, Georg Wachter Institute for Theoretical Physics Vienna University of Technology Wiedner Hauptstr. 8-10, A-1040 AUSTRIA
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