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Acta Physica Polonica A

Extreme Nonlinear Optics in Terms of Riccati-Type Equation

R. Parzyński, Agnieszka Pluciñska

Published Dec 1, 2005• 2 citations
Publisher

Abstract

In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.

DOI
10.12693/aphyspola.108.959

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In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the whole scale time of the laser pulse.Very good quality of the iterative method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon--emission spectra from model molecular ions, double quantum wells, atoms, and semiconductors.The method is used to describe novel, carrier-envelope offset phase effects in the region of extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach the laser light frequence.
For Rabi frequencies comparable to, or even larger than, the transition frequency of a two-level system, the regime of extreme nonlinear optics is reached. Here, we give an overview of the radiated light intensity as a function of carrier frequency of light, transition frequency, Rabi frequency, spectrometer frequency, as well as of the shape and duration of the exciting optical pulses. The graphical representations reveal an amazing complexity and beauty of the nonlinear optical response. Analytical results within the ``square-wave approximation'' qualitatively reproduce many of the intricate features of the exact numerical calculations.
Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven 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.