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Comp. Phys. Comm. 151 251-264 (2003).
Complex frequency technique for linear and second harmonic optical properties of metallic surfaces
CEMES-CNRS, 29 rue Jeanne Marvig,BP 4347, 31055 Toulouse Cedex 4, F
rance,
and
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Department of Physics and Astronomy, University of Wales, PO Box 913, Cardiff, CF24 3YB, United Kingdom
Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
Department of Physics, School of Chemistry and Physics, Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom
Research Institute for Materials, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Abstract
We describe a complex frequency technique for evaluating the linear
and quadratic dielectric responses of metal surfaces, illustrated
by application to the surface of jellium. The electric
susceptibilities are shorter-range functions of the spatial
coordinates at complex frequency, whereas their general behaviour
is complicated, long-range and highly oscillatory at real frequency.
As a result the linear and the second harmonic electric charges induced by an
optical perturbation are then numerically easier to calculate at complex
frequency. As the functions which characterise the optical behaviour
of the metal surface are analytic in the upper complex frequency
half-plane, the dielectric response at real frequency can be deduced
by analytic continuation from the results at complex frequency.
We illustrate and discuss this approach,
which should be useful for studying more realistic models of a
surface in which the crystal potential is included, and where
a direct calculation of the dielectric response is difficult to obtain
at real frequency.