Abstract
A model calculating the laser fields at a flat structureless surface taking into account the surface photoelectric effect is presented. The photon is p or transverse magnetic linearly polarized, continuous and its wave length is long, i.e. λ vac ≥ 12.4 nm. The sharp rise of the electron density at the interface generates an atomic scale spatial dependence of the laser field. In real space and in the temporal gauge, the vector potential A of the laser is obtained as a solution of the classical Ampère-Maxwell and the material equations. The susceptibility is a product of the electron density of the material system with the surface and of the bulk tensor and non-local isotropic (TNLI) polarizability. The electron density is obtained quantum mechanically by solving the Schrödinger equation. The bulk TNLI polarizability including dispersion is calculated from a Drude-Lindhard-Kliewer model. In one dimension perpendicular to the surface the components \hbox{$\mathcal{A}_x(z,\omega)$} 𝒜 x (z,ω) and \hbox{$\mathcal{A}_z(z,\omega)$}𝒜 z (z,ω) of the vector potential are solutions of the Ampère-Maxwell system of two coupled integro-differential equations. The model, called vector potential from the electron density-coupled integro-differential equations (VPED-CIDE), is used here to obtain the electron escape probability from the power density absorption, the reflectance, the electron density induced by the laser and Feibelman’s parameters d ∥ and d ⊥. Some preliminary results on aluminium surfaces are given here and in a companion paper the photoelectron spectra are calculated with results in agreement with the experiment.
Similar content being viewed by others
References
A. Liebsch, Electronic Excitations at Metal Surfaces (Plenum Press, 1997)
S. Hüfner, Photoelectron Spectroscopy (Springer, Berlin, 2003)
W. Schattke, M. Van Hove, F.J. García de Abajo, R. Diez Muino, N. Mannella, Solid-state Photoemission and Related Methods, Theory and Experiment, in Overview of core and valence photoemission, edited by W. Schattke and M.A. Van Hove (Wiley, 2003), pp. 50–115
D. Sarid, W.A. Challener, Modern Introduction to Surface Plasmons (Cambridge University Press, 2010)
G. Raşeev, Eur. Phys. J. D 66, 168 (2012)
G. Mukhopadhyay, S. Lundqvist, Phys. Scr. 17, 69 (1978)
P. Apell, Phys. Scr. 17, 535 (1978)
K.L. Kliewer, Surf. Sci. 101, 57 (1980)
T. Maniv, H. Metiu, J. Chem. Phys. 76, 696 (1982)
P.J. Feibelman, Prog. Surf. Sci. 12, 287 (1982)
P. Apell, A. Ljungbert, S. Lundqvist, Phys. Scr. 30, 367 (1984)
R.R. Gerhardts, K. Kempa, Phys. Rev. B 30, 5704 (1984)
P. Gies, R.R. Gerhardts, T. Maniv, Phys. Rev. B 35, 458 (1987)
K. Kempa, W.L. Schaich, Solid State Commun. 61, 357 (1987)
A.T. Georges, Opt. Commun. 188, 321 (2001)
D. Samuelsen, W. Schattke, Phys. Rev. B 51, 2537 (1995)
E.E. Krasovskii, V.M. Silkin, V.U. Nazarov, P.M. Echenique, E.V. Chulkov, Phys. Rev. B 82, 125102 (2010)
J.A. Heras, Am. J. Phys. 75, 176 (2007)
A. Eguiluz, J.J. Quinn, Phys. Rev. B 14, 1347 (1976)
J.E. Sipe, Surf. Sci. 84, 75 (1979)
F. Forstmann, H. Stenschke, Phys. Rev. Lett. 38, 1365 (1977)
F. Forstmann, Z. Phys. B 32, 385 (1979)
K. Kempa, F. Forstmann, Surf. Sci. 129, 516 (1983)
K.L. Kliewer, R. Fuchs, Phys. Rev. 172, 607 (1968)
K.L. Kliewer, R. Fuchs, Phys. Rev. 181, 552 (1969)
N.D. Mermin, Phys. Rev. B 1, 2362 (1970)
A. Bagchi, N. Kar, R.G. Barrera, Phys. Rev. Lett. 40, 803 (1978)
M. Born, E. Wolf, Principle of Optics, 6th edn. (Pergamon Press, Oxford, 1980)
J.D. Jackson, Classical Electrodynamics, 3rd edn. (John Wiley & Sons, New York, 1998)
N.D. Lang, W. Kohn, Phys. Rev. B 1, 4555 (1970)
C. Kittel, Introduction in Solid State Physics (John Wiley & Sons, New York, 1996)
G. Raşeev, e-J. Surf. Sci. Nanotech. 7, 249 (2009)
G. Raşeev, Mol. Phys. 105, 1769 (2007)
G. Raşeev, D. Bejan, Opt. Commun. 283, 3976 (2010)
D.Y. Smith, B. Segall, Phys. Rev. B 34, 5191 (1986)
R. Sheppard, B. Jordan, E. Grant, J. Phys. D 3, 1759 (1970)
J. Lindhard, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 28, 1 (1954)
K.L. Kliewer, Phys. Rev. B 14, 1412 (1976)
A. Liebsch, Phys. Scr. 35, 354 (1987)
A. Liebsch, Phys. Rev. B 36, 7378 (1987)
L.D. Landau, E.M. Lifshitz, Mécanique Quantique (Mir, Moscow, 1967)
K.L. Kliewer, Phys. Rev. Lett. 33, 900 (1974)
D.R. Penn, Phys. Rev. B 35, 482 (1987)
P. Apell, Phys. Scr. 24, 795 (1981)
A. Zangwill, Physics at Surfaces (Cambridge University Press, Cambridge, 1988)
P.J. Jennings, R.O. Jones, M. Weinert, Phys. Rev. B 37, 6113 (1988)
E.V. Chulkov, V.M. Silkin, P.M. Echenique, Surf. Sci. 437, 330 (1999)
J.V. Lill, G.A. Parker, J.C. Light, Chem. Phys. Lett. 89, 483 (1982)
D.T. Colbert, W.H. Miller, J. Chem. Phys. 96, 1982 (1992)
L. Brugnano, D. Trigiante, Appl. Numer. Math. 18, 79 (1995)
D. Zwillinger, Handbook of Differential Equations (Academic Press, Boston, 1989)
O. Schenk, K. Gärtner, J. Future Gener. Comput. Systems 20, 475 (2004)
O. Schenk, K. Gärtner, Elec. Trans. Numer. Anal. 23, 158 (2006)
H. Ehrenreich, H.R. Philipp, B. Segall, Phys. Rev. 132, 1918 (1963)
E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1985)
E.D. Palik, Handbook of Optical Constants of Solids II (Academic Press, Orlando, 1991)
R.W. Ditchburn, G.H.C. Freeman, Proc. Roy. Soc. Lond. A 294, 20 (1966)
K.S. Yee, IEEE Trans. Antennas Propag. AP-14, 302 (1966)
A. Taflove, IEEE Trans. Electromagn. Compat. EMC-22, 191 (1980)
A.G. Borisov, F.J. García de Abajo, S.V. Shabanov, Phys. Rev. B 71, 075408 (2005)
W. Pernice, F. Payne, D. Gallagher, Opt. Quantum Electron. 38, 843 (2006)
M. Sukharev, J. Sung, K.G. Spears, T. Seideman, Phys. Rev. B 76, 184302 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Raşeev, G. Laser fields at flat interfaces: I. Vector potential. Eur. Phys. J. D 66, 179 (2012). https://doi.org/10.1140/epjd/e2012-20745-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2012-20745-9