Assuming a metal driven by a femtosecond laser pulse could generate second harmonics, are these harmonics radiative? In other words, do they reach the far-field?
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2 Answers
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One can get second harmonic generation at a metal surface because there the symmetry is broken. This SHG light does propagate to the far field and can be measured, although is usually small. Sipe et al. "Analysis of second-harmonic generation at metal surfaces" Phys. Rev. B. 21 (10) 4389 (1980) (https://journals.aps.org/prb/pdf/10.1103/PhysRevB.21.4389) refer to experiments and discuss the theory. Specifically they state that SHG "sources consist of a bulk current density which extends about a skin depth into the metal, and two 'surface' current densities one normal and one tangential to the surface which extends only a few Fermi wavelengths into the metal. At optical frequencies these latter current densities radiate essentially as a dipole sheet at the surface." By this they mean they act as sources of SHG dipole radiation that radiate into the far field.
Most often these experiments are performed on metal nanoparticles, which have strong localised surface plasmon resonances that enhance the SHG intensity. These metals also have surfaces and, in particular, resonate to produce strong local electric fields. See for example Metzger et al. "Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength" Nano Letters 2015 15 (6), 3917-3922 (https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.5b00747)
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$\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$ Commented Sep 6, 2023 at 9:05
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$\begingroup$ In this case, the metal is structured. The question was directed at a general metal, and that a specific instantiation. $\endgroup$– JQKCommented Sep 6, 2023 at 19:15
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2$\begingroup$ The question does not specify the geometry at all. It just refers to "a metal". But I answered this anyway. As I wrote "One can get second harmonic generation at a metal surface because there the symmetry is broken. This SHG light does propagate to the far field and can be measured, although is usually small." This answers the question. The fact that people also use small metal particles (they are still metals and have surfaces) is a recent advance. Would you prefer not to have this additional information? $\endgroup$ Commented Sep 7, 2023 at 14:06
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Assuming the photo-electric effect isn't ejecting electrons from the metal, then Second Harmonic Generation (SHG) wouldn't happen. SHG can only be created for systems with non-centrosymmetric symmetry due to non-zero hyperpolarizability. The "free" electrons in the metal are symmetric about any point, thus it is a centrosymmetric system.
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$\begingroup$ I agree but I assumed the centrocymmetry is somehow broken. I just want to know what kind of radiation, free electrons could make in a nonlinear response. $\endgroup$ Commented Sep 5, 2023 at 12:25
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$\begingroup$ Not until you get into nonlinear QED regime will you see free electrons create such a response. $\endgroup$– JQKCommented Sep 5, 2023 at 13:28
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1$\begingroup$ Free electrons in metals are not centrosymmetric unless the crystal lattice is centrosymmetric (see pubs.acs.org/doi/10.1021/acs.nanolett.1c01502). Furthermore, that symmetry is broken at interfaces so that SHG in metals becomes possible there too. $\endgroup$– KF GaussCommented Sep 7, 2023 at 14:34
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$\begingroup$ You get SHG from metal surfaces without the ejection of photoelectrons. The broken symmetry comes from the fact that the internal potentials in the metal crystal are different into the surface, i.e. into the bulk metal, compared to out of the surface. In other words the potential that the electrons move in is asymmetric with regard to motion into/out of the surface. Wikipedia has a good discussion of this en.wikipedia.org/wiki/Second-harmonic_generation $\endgroup$ Commented Sep 21, 2023 at 4:59