LASER PHYSICS 2013 PRAGUE, CZECH REPUBLIC 15 July 2013 OBSERVATION OF RADIATION PRESSURE IN IONIZATION; IMPLICATIONS FOR CIRCULAR POLARIZATION H. R. Reiss Max Born Institute, Berlin, Germany American university, Washington, DC, USA

BRIEF PREVIEW Recent experiments on atomic ionization with circularly polarized laser light are examined to demonstrate very fundamental strong-field physics properties: Length gauge (LG) momentum distributions are too narrow; the Coulomb gauge (CG) performs much better. Radiation pressure effects that were measured cannot be calculated in the context of the LG; it is fundamentally impossible. The physical picture associated with the LG, where ionization occurs in the direction of the electric field, is orthogonal to the actual situation. The widely accepted premise that the zero-frequency limit of a laser field is a constant electric field is fundamentally defective; such a result shows only that the wrong problem was analyzed.

Two recent papers from the Corkum group demonstrated some unusually interesting physics:

Two major issues were examined, using atomic ionization by a circularly polarized laser. The accuracy of the tunneling approximation was assessed. A slight deviation from symmetry was found that was ascribed to the effects of radiation pressure. An attempt to describe this in the context of a tunneling model was made. Neither of these goals was fully achieved.

A re-examination of these issues is reported here, in which some very basic physics problems must be explored and resolved. A general remark: The experiments reported by the Corkum group were performed with remarkable care and accuracy. Disagreement with many of their interpretations are reported here, but this in no way detracts from the impressive experimental effort.

Fig.2(b) from Arissian, et. al.

Purple curve is from the CG SFA Argon, 800 nm, 1.8e14 W/cm2

Magenta curve is from the CG SFA with Radiation Pressure Argon, 800 nm, 1.8e14 W/cm2

Please notice: The theoretical fit to the momentum distribution is near-perfect, as is often the case with the CG SFA. The radiation pressure correction is a bit too large. Also notice: I am calling (my version) of the SFA the “Coulomb gauge “ SFA, not the “velocity gauge” SFA. This requires further explanation. Radiation pressure corrections are very simple to insert without going to a fully relativistic theory. This also requires further explanation.

LENGTH GAUGE AND VELOCITY GAUGE When the “strong form” of the dipole approximation is used, there is full gauge equivalence between the LG and the VG, as shown by Maria Göppert-Mayer in 1931. The STRONG-FORM DIPOLE APPROXIMATION is: This has been extremely useful to the Atomic, Molecular, Optical (AMO) physics community, but it is applicable to laser fields only within a limited range of frequencies and intensities:

Dipole approximation failure AMO OASIS HRR, PRL 101, 043002 (2008)

This is the way “my SFA” is formulated. Note especially the limited scope of the AMO oasis, and that there is no possible approach to zero frequency within the strong-form dipole approximation. The strong-form dipole approximation should be viewed with suspicion, because with no magnetic field there can be no propagating wave, and with no propagation property there can only be limited applicability to laser fields. The Coulomb gauge makes possible a true propagating field behavior, so that |E|=|B| always, but if B has no other obvious manifestations, it can be neglected. This is the way “my SFA” is formulated. See HRR, PRA 42, 1476 (1990).

RADIATION PRESSURE The phase of a propagating wave is Where k is the propagation 4-vector of the field. It is also the energy-momentum 4-vector of the field; that is, the photon energy is  and the photon momentum is k. In the strong-form dipole approximation This is equivalent to saying that the photon has no momentum, with the consequence that there is no radiation pressure. In a relativistic treatment, the complete phase expression must be retained. The Smeenk, et al. paper employs the LG, meaning that the strong-form dipole approximation is being used, and there is no such thing as radiation pressure. This is why they had so much difficulty constructing a theory to explain their results.

RADIATION PRESSURE WITH CIRCULARLY POLARIZED LASERS This is an exaggerated view of the effect of radiation pressure. See HRR, Optics Express 8, 99 (2001).

An accurate expression is known from the relativistic problem for the forward “tilt” of the electron motion [HRR, JOSA B 7, 574 (1990)]: The photoelectron moves in a circular orbit around the ion with the parameters of a free electron in a circularly polarized field. The classical energy of this rotational motion is The final component of radiation pressure momentum in the direction of propagation of the laser beam is This is independent of the identity of the atom being ionized.

CALCULATED RESULTS The Dirac-relativistic SFA (RSFA) was employed to compare with the Arissian, et al. and Smeenk, et al. results, with good agreement. See: HRR PRA 87, 033421 (2013). The calculation using the ad hoc method described in the preceding slides was employed in the nonrelativistic CG SFA to give the results shown earlier:

PHOTOELECTRON TRAJECTORY In strong fields, when Up >> EB , the most probable kinetic energy of the emitted photoelectron is KE = Up , as is well-known. To produce this result, a number of photons given by must be absorbed. Each circularly polarized photon carries one quantum unit ħ of angular momentum, and these are additive, so that the total angular momentum of the photoelectron in its orbit is These are exactly the parameters of a classical free electron in a circularly polarized field, orbiting the ion in a circular trajectory. This can be checked directly from the experiments.

THE PHOTOELECTRON TOROID This is from the Smeenk paper. The image shown is formed by projection onto a screen parallel to the plane formed by the intersecting laser and atomic beams. The laser propagates along the z axis, and px is the radius of the momentum distribution out to the toroid of motion. For 800 nm at 8e14 W/cm2 , the ponderomotive energy is 1.76 a.u., corresponding to a momentum px = 1.87 a.u. This is just the location of the brightest part of the image.

ANOTHER CIRCULAR POLARIZATION TOROID This toroid image is from the photodetachment of F- as reported by Bergues, et al., PRL 95, 263002 (2005); as analyzed by HRR, PRA 76, 033404 (2007). The ponderomotive energy Up = .202 a.u. corresponds to px = .636 a.u., very close to the brightest part of the toroid.

LENGTH-GAUGE – COULOMB-GAUGE CONFLICT LG: The electron responds to the electric field, which is always radial in a circularly polarized field. CG: The electron enters into a circular orbit around the ion. This is perpendicular to the electric field. A change in gauge frequently carries with it a change in physical interpretation. This is an extreme change. All the physical evidence in this problem supports the CG point of view. This should not be surprising. Laser fields are propagating fields that can be described fully within the CG, but only approximately within the LG. Another point of view: in the LG, the force is always along the electric field direction. The problem discussed here is radiation pressure, which is in the propagation direction of the field, perpendicular to the electric field direction.

CLOSING REMARKS The Arissian paper states that: “In adiabatic tunneling the laser field is treated as if it were a static field, time serving only as a parameter.” I concur; this is why the concept of tunneling does not apply to low frequency laser fields. The next sentence states: “It is rigorously valid for long wavelengths (<<1).” This is the seriously incorrect consequence of the first sentence. It is unfortunately widely accepted in the laser community. The title of the Arissian paper contains the phrase: “Direct Test of Laser Tunneling …”. The conclusion is that the test achieves a negative result.