Electrical & Computer Engineering, Department of


Date of this Version



Optics Express 18:14 (2010), pp. 15155 - 15168


Copyright © 2010 Optical Society of America. Used by permission.


In this paper, interaction of an ultrashort single-cycle pulse (USCP) with a bound electron without ionization is reported for the first time. For a more realistic mathematical description of USCPs, Hermitian polynomials and combination of Laguerre functions are used for two different single cycle excitation cases. These single cycle pulse models are used as driving functions for the classical approach to model the interaction of a bound electron with an applied electric field. A new novel time-domain technique was developed for modifying the classical Lorentz damped oscillator model in order to make it compatible with USCP excitation. This modification turned the Lorentz oscillator model equation into a Hill-like function with non-periodic time varying damping and spring coefficients. Numerical results are presented for two different excitation models and for varying spring and damping constants. Our two driving model excitations provide quite different time response of the bound electron. Different polarization response will subsequently result in relative differences in the time dependent index of refraction.