Comp. Phys. Comm. 151 251-264 (2003).

Complex frequency technique for linear and second harmonic optical properties of metallic surfaces

L. Calmels

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

J. E. Inglesfield

Department of Physics and Astronomy, University of Wales, PO Box 913, Cardiff, CF24 3YB, United Kingdom

S Crampin

Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom

E. Arola

Department of Physics, School of Chemistry and Physics, Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom

Th. Rasing

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.