Spectral quantities absorption coefficient

For most treatments, the spectral density, J(a>), Eq. 2.86, also referred to as the spectral profile or line shape, is considered, since it is more directly related to physical quantities than the absorption coefficient a. The latter contains frequency-dependent factors that account for stimulated emission. For absorption, the transition frequencies ojp are positive. The spectral density may also be defined for negative frequencies which correspond to emission. 

We employ the following equations Eq. (142) for the complex susceptibility X, Eq. (141) for the complex permittivity , and Eq. (136) for the absorption coefficient a. In (142) we substitute the spectral functions (132) for the PL-RP approximation and (133) for the hybrid model, respectively. In Table IIIB and IIIC the following fitted parameters and estimated quantities are listed the proportion r of rotators, Eqs. (112) and (127) the mean number m of reflections of a dipole from the walls of the rectangular well during its lifetime x, Eqs. (118)... 

In spectroscopy all of these quantities are usually taken to be defined in terms of the spectral intensity, /(v), so that they are all regarded as functions of wavenumber v (or frequency v) across the spectrum. Thus, for example, the absorption coefficient a(v) at wavenumber v defines the absorption spectrum of the sample similarly T(v) defines the transmittance spectrum. 

Note that the spectral absorptivity, transmissivity, and emissivity of a medium are dimensionless quantities, with values less than or equal to l.The spectral absorption coefficient of a medium (and tlrus Ca, cta, and Ta), in general, vary with wavelength, temperature, pressure, and composition. 

The spectral overlap integral J can be expressed in terms of either wavenumbers or wavelengths (Equation 2.36). The area covered by the emission spectrum of D is normalized by definition and the quantities / and lx are the normalized spectral radiant intensities of the donor D expressed in wavenumbers and wavelengths, respectively. Note that the spectral overlap integrals J defined here differ from those relevant for radiative energy transfer (Equation 2.33). Only the spectral distributions of the emission by D /,P and, are normalized, whereas the transition moment for excitation of A enters explicitly by way of the molar absorption coefficient sA. The integrals J" and Jx are equal, because the emission spectrum of D is normalized to unit area and the absorption coefficients sA are equal on both scales. 

All these quantities are equivalent since they all depend on the same transition matrix element, although their units are not the same. The / value has the advantage of being a dimensionless quantity. With broad band illumination, the appropriate quantities are those which are integrated over the spectral feature, such as the / value or the Einstein coefficient. With narrow band illumination (i.e. a monochromatic source narrower than the spectral feature), it is appropriate to use a quantity which is defined point by point within the line profile, such as the absorption coefficient, the cross section, or the differential oscillator strength df/dE. 

In the following, macroscopic quantities such as the absorption coefficient, refractive index, and coefficient will be related to molecular concepts such as linear polarizability and nonlinear hyperpolarizability. In the derivation, rather simple models will be employed to demonstrate the basic properties of these quantities. It will become apparent why poling of polymers is essential for second-order nonlinear processes such as second-harmonic generation. The spectral dispersion of the coefficients will also be discussed and examples will be given. 

Spectral absorption (transmission) lines are not monochromatic, due to which physical values characterizing transitions of the molecular system from one quantum state to another are also energetically diffused. Therefore, any spectral quantity F (absorption cross section, absorption coefficient, Einstein coefficients, and others) can be of three types F, is the spectral value, Fq is the maximum value corresponding to the frequency Hq, and F = 6F dn is the integral value for the spectral line. The integral and spectral values are related by the following relationship ... 

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