An electromagnetic radiation is basically considered to be a transverse wave propagating through an accessible media whether it is an optical fibre or a thin film depending on its propagating conditions. In analyzing its propagation, utilized specific cross-section areas have become an important base of understanding its extinction parameters. The term cross-section in this work applies only to boundary conditions within which particles interact within electromagnetic spectra through absorption or scattering. In such small volume contextual framework, nanotechnology reconsiders scattering cross-section coefficients. In this work, two different degenerate states were modeled and analyzed using a developed model of a laser cavity containing a media of length, L, with a gain of, k, per unit length which were mirrored to represent the upper and a lower level manifolds inhomogeneous broadening Stark levels respectively. The model developed created an impression that a laser medium is a coherent ensemble of particles or atoms whose bandwidth depends on how a laser is constructed .
An electromagnetic radiation is basically considered to be a transverse wave propagating through an accessible media whether it is an optical fibre or a thin film depending on its propagating conditions. In analyzing its propagation, utilized specific cross-section areas have become an important base of understanding its extinction parameters. The term cross-section in this work applies only to boundary conditions within which particles interact within electromagnetic spectra through absorption or scattering. In such small volume contextual framework, nanotechnology reconsiders scattering cross-section coefficients. In this work, two different degenerate states were modeled and analyzed using a developed model of a laser cavity containing a media of length, L, with a gain of, k, per unit length which were mirrored to represent the upper and a lower level manifolds inhomogeneous broadening Stark levels respectively. The model developed created an impression that a laser medium is a coherent ensemble of particles or atoms whose bandwidth depends on how a laser is constructed .
The interaction of intense laser fields with matter is accompanied by a multitude of phenomena, ranging from the generation of coherent radiation across various spectral ranges (from terahertz to soft X-rays) to the creation of beams of accelerated charged particles and micromodification of the volume and surface of various samples.To describe this diversity of phenomena, several theoretical approaches have been developed to date.These approaches utilize different approximations to address this complex nonlinear problem, allowing for the explanation of specific aspects of such interactions.The developed theoretical frameworks consider the interaction at both microscopic and macroscopic levels; at the microscopic level, they investigate the characteristics of single atoms interacting with laser fields, while at the macroscopic level, they analyze nonlinear susceptibilities that describe the nonlinear polarization of the medium during the propagation of laser radiation through it.This work presents an overview of methods describing some of the most commonly employed theoretical approaches to model the response of a medium at a microscopic (quantum-mechanical) level, as well as various methods for controlling the properties of generated coherent radiation.A model for the gas medium is described that accounts for both the response characteristics of individual atoms and allows for consideration of phase and quasiphase matching effects during radiation generation.The influence of medium parameters on the efficiency of generation and polarization properties of generated radiation is analyzed under both phase and quasi-phase matching conditions.A detailed description of an analytical method for calculating the nonlinear susceptibility of a gas medium is provided.The obtained values of nonlinear susceptibility for arbitrary orders may be useful in numerical calculations concerning the propagation of laser radiation in matter.Various channels for radiation generation are analyzed as parameters of the laser field are varied.
Abstract : Computational methodologies were developed to treat rigorously (1) transverse boundary in an inverted (amplifying) media; (2) to treat quantum fluctuations in an initial boundary condition in the light-matter interactions problem; (3) construct a two-laser three-level code to study light control by light effect; (4) construction of a data base that (a) would manage the production of different types of laser calcualtions: cylindrical, cylindrical with atomic frequency broadening, cartesian geometry; (all of the above with quantum mechanical initiation), (b) allow parametric comparison within the same type of calculations, by establishing a unifying protocol of software storage, of the various refinements of the model could be contrasted among themselves and with experiment; (5) construct an algorithm for counterbeam transient studies for optical bistability and optical oscillator studies. (A) Transverse propagation effects in an inverted medium were studied. Special care had to be taken to treat the boundary reflection conditions. If ill-posed, they can obscure the emergence of any new physical results. The two transverse effects considered are (1) the 'spatial averaging' associated with the inial atomic inversion density being radially dependent (since the pump which inverts the sample has typically a Gaussian-like profile); and (2) the 'diffraction coupling' (which permits the various parts of the cylindrical cross-section to communicate, interact and emit at the same time). The first effect is important for large Fresnel numbers, whereas the second predominant for small Fresnel numbers.
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schrödinger equation proposed by Hudson and Parthasarathy, we show that such models can be generalized to include other processes into the interaction. In the case of a two-level atom we construct a model on the basis of some physical requirements, the main being a balance equation on the fluxes of the ingoing and outgoing photons; in this model the atom-field interaction turns out to be due either to absorption/emission processes either to direct scattering processes, which simulate the interaction due to virtual transitions to the levels which have been eliminated from the description. To see the effects of the new terms, we consider both direct and heterodyne detection of the fluorescence light emitted by an atom stimulated by a monochromatic coherent laser and we deduce from these two detection schemes the expressions of the total, elastic and inelastic electromagnetic cross sections and the spectral distribution of the fluorescence light. The total cross section, as a function of the frequency of the stimulating laser, can present not only a Lorentzian shape, but the full variety of Fano profiles; intensity dependent widths and shifts are obtained. The fluorescence spectrum can present complicated shapes, according to the values of the various parameters; when the direct scattering is not important the usual symmetric triplet structure of the Mollow spectrum appears (for high intensity of the stimulating laser), while a strong contribution of the direct scattering process can distort such a triplet structure or can even make it to disappear.
We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.
Abstract Laser radiation is an intense coherent light field that is characterized by its high monochromatic brightness and high photon degeneracy. Thus, it is capable of generating various stimulated scattering effects and a series of multiphoton excitation-induced opto-physical and opto-chemical effects. There are two parallel theoretical regimes. The first regime is the semiclassical theory that treats light as a classical electromagnetic field described by Maxwell’s equations. The second regime is the quantum electrodynamic theory, which treats light as an assembly of photons obeying Bose–Einstein statistics. Both regimes can be complementarily adopted to describe the interaction of light radiation with matter.