Linearized Riccati equation as a tool for nonlinear optics of weakly excited two-level systems

Authors:

• Ryszard Parzyński,
• Tomasz Kopyciuk

Abstract

Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laser-driven two-level system is used to calculate analytically the induced electric dipole moment. The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances. For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency. © 2020 Polish Academy of Sciences. All rights reserved.