LIMITATIONS OF GAUGE INVARIANCE

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INCORRECT PREDICTIONS FROM TUNNELING THEORY • A laser field is strong when the electric field is of the order of one atomic unit; that is, when the external field is of the order of magnitude of internal fields in the atom. (Already examined.) • A single parameter – the Keldysh parameter γ – is sufficient for scaling. • Weak fields can be characterized as in the multiphoton domain and strong fields are in the tunneling domain. • A tunneling limit or classical limit will be approached at long wavelengths of the field. • There are no evident upper and lower frequency limits on the dipole approximation. • Higher harmonics are not produced by circularly polarized fields because the photoelectron “walks away” from the atom. 34
PONDEROMOTIVE ENERGY A charged particle in a plane-wave field has a minimal interaction energy with the field. That is, even a particle at rest on average has a minimal interaction energy with the field (sometimes called “quiver energy”). This is the ponderomotive energy U p . KELDYSH GAMMA PARAMETER Based on the tunneling concept, the following classification is nearly universal in the strong-field community: 35
Page 1 and 2: LIMITATIONS OF GAUGE INVARIANCE and
Page 3 and 4: Furthermore… There is another set
Page 5 and 6: ELECTROMAGNETIC POTENTIALS Electric
Page 7 and 8: GAUGE TRANSFORMATION If is any sca
Page 9 and 10: THERE ARE HINTS OF BASIC PROBLEMS F
Page 11 and 12: These equations can be combined to
Page 13 and 14: GAUGE EQUIVALENT - BUT DIFFERENT Th
Page 15 and 16: NEWTONIAN MECHANICS DIFFERS FROM OT
Page 17 and 18: CAUTIONS ABOUT THE “PHYSICAL GAUG
Page 19 and 20: MIXED FIELDS The physical gauge for
Page 21 and 22: ATOMIC UNITS 1; m 1; e 1, or q 1 e
Page 23 and 24: V(r) LASER PHYSICS IN THE LENGTH GA
Page 25 and 26: Intensity (a.u.) Intensity (W/cm 2
Page 27 and 28: QUALITATIVE IMPLICATIONS OF THE VEL
Page 29 and 30: DOMAINS FOR AN ELECTRON IN A PLANE-
Page 31 and 32: VG-LG COMPARISON It has just been s
Page 33: CONTRADICTIONS Much success has bee
Page 41 and 42: ANOTHER FUNDAMENTAL PROBLEM The pon
Page 43 and 44: RIGOROUS DERIVATION OF AN S MATRIX
Page 45 and 46: By hypothesis, the laser pulse is f
Page 47 and 48: The end result of this alternative
Page 49 and 50: TRANSITION MATRIX ELEMENTS ARE NOT
Page 51 and 52: The SFA includes A 2 (t); the HFA h
Page 53 and 54: REVISIT ITEMS FROM THE PREAMBLE •

LIMITATIONS OF GAUGE INVARIANCE

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