The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.
The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.
A new theoretical approach to the problem of non-linear polarisation of matter is suggested. The density matrix equation for a low-density gas in a strong light field has been solved without using the phenomenological relaxation constants. Use is made of the general Hamiltonian that explicitly involves, besides the interaction of atoms with the external field, also their interactions with each other and with the vacuum electromagnetic field. The equation is solved by the canonical transformation method (a variant of the Bogolyubov-Mitropolski method of averages). It is generalised and used in the more complicated case of interacting multilevel atoms (molecules) in a strong light field. An expression for the cubic susceptibility is obtained, enabling analysis of the resonant saturation in both stationary and non-stationary cases. The proposed method provides correct expressions for the dynamic Stark shifts, amplitudes of multiphoton transitions and of radiational collisions, as well as for effective interatomic interactions caused by photon exchange. The proposed theoretical approach can also be used in studying non-linear optical processes in dense gases, liquids and solids.
An interaction of an atomic/molecular medium with two strong electric fields E L (t) and E M (t) is investigated. The frequency omega L of the first (laser) field E L (t) is close to a transition frequency omega 21 between an upper (2) and a lower (1) atomic levels while the second field E M (t) is of a much lower frequency omega M << omega 21 . The medium is a dipole gas characterized by a nonzero averaged value of electric dipole moment in the states 1 and/or 2. As analytical solution of equations for the density matrix of a dipole atom/molecule interacting with the fields E L (t) and E M (t) is found using the second approximation of the averaging method by Krylov-Bogoliubov-Mitropolskii. The solution obtained is valid in a much broader range of field strengths than an analogous solution that could have been found by the usual time-dependent perturbation theory. Using the solution obtained for the density matrix, polarization of a dipole gas interacting with the fields E L (t) and E M (t) is analytically calculated. This analytical expression for polarization of such media can be utilized for study of various nonlinear optical phenomena. One of the phenomena is a generation of waves at frequencies omega L +or-p omega M and (p+1) omega M (where p=1,2,3,...) in a dipole gas. Another phenomenon is an amplification of the incident wave of the lower frequency omega M due to a stimulated scattering in a dipole gas.
Abstract A general approach to the discussion of optical birefringence phenomena is presented. It is based on the S-matrix approach to photon scattering in a nonrelativistic quantum field theoretical formalism and the Stokes operator description of polarization. The use of a canonically transformed interaction Hamiltonian in combination with diagrammatic perturbation theory enables the response of a system to electromagnetic radiation to be calculated in a straightforward and consistent manner to any order in the perturbation, and the effect of static fields is included easily. As an illustration, the angle of rotation of a beam of plane-polarized light by a solution of optically active molecules is calculated and the intensity dependence of the angle determined. The latter phenomenon should become apparent at high photon flux densities particularly when ω, the frequency of the incident light, or 2ω are similar to electronic excitation frequencies in the optically active molecules.
It is shown that the optical Eabi precession model developed by Feynman, Vernon and Hellwarth for two-level systems can be extended not only to discuss the two-photon resonant coherent interaction, but also to the case of three photons. Using this model and the adiabatic following approximation, the third-order polarization expression in an intense and (or) resonant optical field is obtained, which differs from that obtained by perturbation theory. The saturation phenomena in the third-order resonant non-linear effects are also discussed.
Some typical resonance nonlinear-optics phenomena taking place when light interacts with atoms are considered. The multitude of such phenomena reduces to scattering of the perturbing light, perturbation of the atomic spectrum, excitation of an atom and its ionization. In all these cases the investigations are carried out using the simplest model—an isolated atom in a monochromatic external field. Such a model enables one to give an exact description of many elementary processes. On the other hand it is sufficiently realistic. A detailed investigation is carried out of resonance fluorescence, spontaneous Raman scattering, multiphoton excitation of atoms, resonance shifts and splitting of atomic levels and resonance lonication of atoms. The nature of these processes is investigated as a function of the intensity of the external field, its frequency, a specific atomic spectrum, the nature of polarization of the perturbing field, and the degree of its nonlinearity. The role played by the field of the electromagnetic vacuum is analyzed. Theoretical predictions are compared with the results of many experiments describing resonance processes of the interaction of an intense light field with atoms.
Conceptual problems in quantum optics are investigated by a study of the physical significance of various types of description of the field of a single mode. The descriptions are examined through the effect of the field on matter. Both undamped and damped modes are considered, the descriptions being those of various degrees of precision in classical and quantum-mechanical formalisms. The matter consists of a large number of "molecules," and the interaction is studied by means of low-order perturbation theory. Formal expressions are obtained for the energy interchange between field and molecules in terms of the zeroth-order (uncoupled) operators, with the effect of the commutation properties of the field variables explicitly separated from that of the excitation of the field, in second order. The significance of taking expectation values of the operator results is discussed, and it is concluded that this procedure is justified only when the experiment under consideration involves an averaging process; thus, the molecular variables should be averaged, but not necessarily those of the field. Conditions under which the averaging process is justified are considered, and it is reasoned that, when such a process is not justified, a statistical description of the field can result only in a statistical description of the interaction process. Results of various field descriptions are compared, and it is shown that for induced emission and for spontaneous emission from coherently oscillating molecules, classical and quantum-mechanical fields are equivalent. However, for a self-consistent theory of spontaneous emission from molecules that are not oscillating coherently, the quantum-mechanical commutation properties of the field are essential if the molecules are treated quantum-mecahnically, and the field must be treated classically if the molecules are treated classically; the type of description used for the excitation of the field is inconsequential. Photoelectric emission is examined, and, within the approximation framework used, shown to be accurately described by a classical treatment of the field. It is pointed out that there does not necessarily exist a connection between "photon statistics," that is, the statistics associated with an ensemble of fields, and photocurrent fluctuations in one or more detectors coupled to the same field.