Optical continuum

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

Figure 8.16 (a) IR and (b) Raman spectra for the mineral calcite, CaC03. The estimated density of vibrational states is given in (c) while the deconvolution of the total heat capacity into contributions from the acoustic and internal optic modes as well as from the optic continuum is given in (d). 

Figure 3J Schematic representation of a vibrational spectrum of a crystalline phase. Dotted curves acoustic branches and optical continuum. Solid line total spectrum, and 0) 2 Einstein oscillators. Reprinted with permission from Kieffer (1979c), Review of Geophysics and Space Physics, 17, 35-39, copyright 1979 by the American Geophysical Union.

In the optical continuum, frequency distribution is approximately constant (see figure 3.7) ... 

The corresponding vibrational function in the optical continuum frequency field has the form... 

Because the dispersed acoustic function 3.69, the optic continuum function 3.71, and the Einstein function 3.73 may be tabulated for the limiting values of undi-mensionalized frequencies (see tables 1, 2, 3 in Kieffer, 1979c), the evaluation of Cy reduces to the appropriate choice of lower and upper cutoff frequencies for the optic continuum (i.e., X/ and limits of integration in eq. 3.71), of the three... 

The densities of vibrational states for the two potentials (Fig. 15) are actually very similar, exeept for a somewhat wider gap for RIMl between the two peaks at higher frequencies, corresponding to inner modes of CO3. As for the Kieffer s model, the cut off frequencies of acoustic modes were derived from elastic constants by the Voigt-Reuss-Hill approximation[38], amounting to 51, 66 and 90 cm"i. An optic continuum ranging from 113 to 287 cm was used, and four Einstein oscillators at 708,867, 1042 and 1470 cm with appropriate weights represented the internal optical modes. The... 

Luminosity profile decomposition has been applied to the optical continuum images eind the NIR J, H and E images of NGC 5252. A multicomponent model that takes into account the contribution of a point source, the bulge and the disk has been used for fitting the observed luminosity profiles. Details of the fitting technique are given in Kotilainen et al. (1992). 

Knox W H, Downer M C, Fork R L and Shank C V 1984 Amplified femtosecond optical pulses and continuum generation at 5 kHz repetition rate Qpt. Lett. 9 552-4... 

The continuum model with the Hamiltonian equal to the sum of Eq. (3.10) and Eq. (3.12), describing the interaction of electrons close to the Fermi surface with the optical phonons, is called the Takayama-Lin-Liu-Maki (TLM) model [5, 6], The Hamiltonian of the continuum model retains the important symmetries of the discrete Hamiltonian Eq. (3.2). In particular, the spectrum of the single-particle states of the TLM model is a symmetric function of energy. 

Optic cavitation It is produced by photons of high intensity light (laser) rupturing the liquid continuum. 

For 2PA or ESA spectral measurements, it is necessary to use tunable laser sources where optical parametric oscillators/amplifiers (OPOs/OPAs) are extensively used for nonlinear optical measurements. An alternative approach, which overcomes the need of expensive and misalignment prone OPO/OPA sources, is the use of an intense femtosecond white-light continuum (WLC) for Z-scan measurements [71,72]. Balu et al. have developed the WLC Z-scan technique by generating a strong WLC in krypton gas, allowing for a rapid characterization of the nonlinear absorption and refraction spectra in the range of 400-800 nm [72]. 

Grant, D. M., Elson, D. S., Schimpf, D., Dunsby, C., Requejo-Isidro, J., Auksorius, E., Munro, I., Neil, M. A. A., French, P. M. W. Nye, E., Stamp, G. and Courtney, P. (2005). Optically sectioned fluorescence lifetime imaging using a Nipkow disk microscope and a tunable ultrafast continuum excitation source. Opt. Lett. 30, 3353-5. 

Ranka, J. K., Windeler, R. S. and Stentz, A. J. (2000). Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm. Opt. Lett. 25, 25-7. 

In the case of scintillation noise, however, we cannot do either of those things. By the physical picture we set up to describe the situation, the situation can in fact occur that the obstruction would completely block the optical beam and allow zero energy through, yet since it represents a continuum of values we do not see a justification to arbitrarily reject those readings. Therefore we cannot see a clear path to trying to determine the noise performance of such a system, since it will inevitably come out as infinite in all cases. 

In the continuum and semicontinuum models of es, long-range forces due to distant solvent molecules are usually represented by the optical and static dielectric constants. In a true continuum model, the continuity is extended to the origin or to the surface of the cavity. In some sense, the continuum and semicontinuum models both contain both short- and long-ranged interactions. The main difference is that in the semicontinuum model, the molecules in the first shell(s) are structured. 

The optical absorption of the solvated electron, in the continuum and semicontinuum models, is interpreted as a Is—-2p transition. Because of the Franck-Condon principle, the orientational polarization in the 2p state is given... 

The bulk of stellar radiation comes from the surface layers or atmosphere of a star, more particularly the photosphere , which is defined as the region having optical depths for continuum radiation between about 0.01 and a few. The optical depth ti is measured inwards from the surface and represents the number of mean free paths of radiation travelling vertically outwards before it escapes from the star. It is related to the geometrical height z above some arbitrary layer by... 

---