Maxwell-Bloch equations

Maxwell-Bloch equations) The Maxwell-Bloch equations provide an even more sophisticated model for a laser. These equations describe the dynamics of the electric field E, the mean polarization P of the atoms, and the population inversion ) ... 

Laser model) As mentioned in Exercise 3.3.2, the Maxwell-Bloch equations for a laser are... 

The main features of SF, such as excitation intensity dependence, emission pulse shortening, and time delay, can be described within a simplified semiclassical approach, which uses Maxwell-Bloch equations while neglecting the dipole-dipole interaction [113,114]. It was shown by Bonifacio and Lugatio [113] that in a mean field approximation the system of noninteracting emitters is described by the damped pendulum equations with two driving terms, as given below ... 

It has been known since 1975 that chaotic behavior is possible in some lasers under specific conditions, due to the similarity between the Lorenz equations (which predict chaos in fluids) and the semiclassical Maxwell-Bloch equations describing single mode lasers including the ef-... 

The modulation dynamics of semiconductor injection lasers can be described by the following rate equations for the laser, which are derived fi om the Maxwell-Bloch equations after adiabatically eliminating the atomic polarization ... 

Studying moderately thin samples, the molecular time constants can be directly obtained from the experimental data without the need of computer simulations. This situation is termed nearly-free induction decay (NFID) which is related to the case of free induction decay in very thin samples. Some numerical results are depicted in Fig. 1. A specific experimental situation is considered with resonant, weak input pulses of Gaussian shape and duration tp (FWHM) and two values of the normalized propagation length, ai 0.2 and aJl 1. Here a denotes the conventional absorption coefficient at the maximum of the absorption band. The intensity of the transmitted pulse is evaluated from Maxwell-Bloch equations for homogeneous line broadening. 

In this part, we show how ultrashort pulses on resonant intersubband (IS) transitions propagate nonlinearly in multiple symmetric double quantum wells (QWs). A -type modulation-doped multiple QWs sample consisting of N are equally spaced electronically uncoupled symmetric double semiconductor GaAs/AlGaAs QWs with separation d, as shown in Fig. 13. There are only two lower energy subbands contribute to the system dynamics, W = 0 for the lowest subband with even parity and = 1 for the excited subband with odd parity. The Fermi level is below the n = subband minimum, so the excited subband is initially empty. This is succeeded by a proper choice of the electron sheet density. The nonlinear propagation of ultrashort pulses on resonant IS transitions in multiple semiconductor quantum wells is described by the fiill Maxwell-Bloch equations ... 

The full Maxwell-Bloch equations are solved by using the iterative predictor-corrector finite-diference time-domain method[76,77,78]. In what follows, we assume that the system is initially in the lowest subband. We consider a hyperbolic secant functional form for the initial... 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

The Bloch equations by themselves cannot describe spontaneous emission, because they contain the effect of the electromagnetic field on the molecule but not vice versa. To include the effect of the molecules on the radiation field within the semiclassical formalism that led to these equations we should supplement them by a description of the radiation field using the Maxwell equations in the presence of the molecular sources, as described in Appendix 3A (see Eq. (3.75). For our present purpose we can however make a shortcut. We know that one result of Eq. (3.75) is that an oscillating dipole emits radiation, so we can obtain the intensity of emitted radiation by calculating the expectation value P(Z) of the oscillating dipole induced in the system and evaluate the emission intensity (energy per unit time) from the classical formula... 

This chapter approached the X-ray difi action on perfect crystals in terms of semi-classical dynamical theory (Maxwell equations + the shape of the wave Bloch functions associated to the fields propagated in the crystal), with the accent on the calculation of the intensities associated to the transmitted and diffracted waves in the two waves approximation the diffraction associated to the production of a single diffracted wave respecting the transmitted one. 

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