Linearized Riccati Equation as a Tool for Nonlinear Optics of Weakly Excited Two-Level Systems

R. Parzyński, T. Kopyciuk Faculty of Physics, A. Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland

Received: October 27, 2019; in final form March 2, 2020

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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.

DOI:10.12693/APhysPolA.137.1080 topics: two-level system, induced electric dipole moment, harmonic generation, Riccati-type equation, nonlinear optics\\vs*{10pt}