SELECTION RULES AND TEMPERATURE DEPENDENCE OF THE FIRST-ORDER RAMAN EFFECT IN CRYSTALS

1956 ◽  
Vol 34 (3) ◽  
pp. 312-338 ◽  
Author(s):  
O. Theimer
Keyword(s):  
Temperature Dependence ◽  
Raman Effect ◽  
Scattered Light ◽  
Low Frequency ◽  
Current Theory ◽  
Selection Rules ◽  
First Order ◽  
Non Linear ◽  
Full Symmetry ◽  
Linear Effects

Starting from the most general scattering formulae, the current theory of the Raman effect in crystals is modified in such a way as to remove the well-known discrepancies between theory and experiment concerning the selection rules for calcite and similar crystals. A distinction is made between electrons in delocalized crystal orbitals and electrons in localized atomic or molecular orbitals and it is shown that only the latter produce a Raman scattering in agreement with the unmodified theory. The general formula for the scattering by delocalized electrons is analyzed and it is found that the magnitude of the components [Formula: see text] of the first-order polarizability (qi normal coordinate of the scattering lattice vibration) depends on the wave vectors Q′ and Q″ of incident and scattered light. The wave vector dependence of the first-order polarizability requires selection rules for the first-order Raman effect which do not correspond to the full symmetry of the scattering crystal but only to the symmetry operations of the group of Q = Q′ – Q″ which leave Q unchanged. These modified selection rules are shown to be compatible with experiment. The influence of mechanical anharmonicity and of polarizability derivatives of higher order on the first-order Raman effect is also discussed. It is found that these non-linear effects offer no satisfactory explanation for the great intensity of forbidden lines in the Raman spectrum of some crystals. Concerning temperature effects the non-linear terms in the intensity formulae are found to be of greater importance and are tentatively suggested as being responsible for the anomalous temperature dependence of low frequency external lattice vibrations.

scholarly journals Detection of non-linear effects in satellite UV/Vis reflectance spectra: Application to the Ozone Monitoring Instrument

2020 ◽  
Author(s):  
Nick Gorkavyi ◽  
Zachary Fasnacht ◽  
David Haffner ◽  
Sergey Marchenko ◽  
Joanna Joiner ◽  
...  
Keyword(s):  
Scattered Light ◽  
Cosmic Ray ◽  
Stray Light ◽  
Ozone Monitoring Instrument ◽  
Data Set ◽  
Monitoring Instrument ◽  
Non Linear ◽  
Linear Effects ◽  
Ozone Monitoring ◽  
Excessive Noise

Abstract. Non-linear effects, such as from saturation, stray light, or obstruction of light, negatively impact satellite measured ultraviolet and visible Earthshine radiance spectra and downstream retrievals of atmospheric and surface properties derived from these spectra. In addition, excessive noise such as from cosmic ray impacts, prevalent within the South Atlantic Anomaly, can also degrade satellite radiance measurements. Saturation specifically pertains to observations of very bright surfaces such as sun glint over water surfaces or thick clouds. Related residual electronic cross-talk or blooming effects may occur in spatial pixels adjacent to a saturated area. Obstruction of light can occur within the zones of solar eclipses as well as from material located outside of the satellite instrument. The latter may also produce unintended scattered light into a satellite instrument. When these effects cannot be corrected to an acceptable level for science quality retrievals, it is desirable to flag the affected pixels. Here, we introduce a new detection method that is based on the correlation, r, between the observed Earthshine radiance and solar irradiance spectra over a 10 nm-spectral range; our Decorrelation Index (DI for brevity) is simply defined as DI=1−r. DI increases with non-linear effects or excessive noise in either radiances (the most likely cause in OMI data) or irradiances. DI is relatively straight-forward to use and interpret and can be computed for different wavelength intervals. We developed a set of DIs for two spectral channels of the Ozone Monitoring Instrument (OMI), a hyperspectral pushbroom imaging spectrometer. For each OMI spatial measurement, we define 14 wavelength-dependent DIs within the OMI visible channel (350–498 nm) and 6 DIs in its ultraviolet 2 (UV2) channel (310–370 nm). As defined, DIs reflect a continuous range of deviations of observed spectra from the reference irradiance spectrum that are complementary to the binary Saturation Possibility Warning (SPW) flags currently provided for each individual spectral/spatial pixels in the OMI radiance data set. Smaller values of DI are also caused by a number of geophysical factors; this allows one to obtain interesting physical results on the global distribution of spectral variations.

scholarly journals On the possibility of precursors of earthquakes in VLF range observed by DEMETER Satellite

2014 ◽  
Vol 1 (1) ◽  
pp. 977-997 ◽  
Author(s):  
D. K. Sondhiya ◽  
S. Kumar ◽  
A. K. Gwal
Keyword(s):  
Ionospheric Plasma ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
Statistical Parameters ◽  
Plasma Parameters ◽  
Demeter Satellite ◽  
Non Linear ◽  
Linear Effects ◽  
Ionospheric Electric Field ◽  
Precursors Of Earthquakes

Abstract. Very Low Frequency (VLF) disturbances in the ionospheric electric field observed by DEMETER satellite prior to three different earthquakes that occurred during the years 2008–2009 have been presented. The electromagnetic wave data has been analyzed for few days before the earthquake with special attention to the variation in spectral characteristics and non-linear effects using the statistical and wavelet based techniques. Results indicate that the earthquake preparation process may disturb the ionospheric plasma and these disturbances can reach the non-linear stage leading to the strong variations in the electromagnetic field and plasma parameters. The enhancement in statistical parameters shows the coherent structure and intermittent phenomenon which is the signature of turbulence. The characteristics features of VLF disturbances have further been studied using the wavelet and bispectral analysis tools which provide useful information on the plasma turbulence.

scholarly journals Quantification and parameterization of non-linearity effects by higher order sensitivity terms in scattered light Differential Optical Absorption Spectroscopy

2016 ◽  
Author(s):  
Jānis Puķīte ◽  
Thomas Wagner
Keyword(s):  
Radiative Transfer ◽  
Optical Absorption ◽  
Absorption Spectroscopy ◽  
Scattered Light ◽  
Higher Order ◽  
Trace Gas ◽  
Optical Absorption Spectroscopy ◽  
Non Linear ◽  
Linear Effects ◽  
Transfer Modelling

Abstract. We address the application of Differential Optical Absorption Spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case, because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well separated paths differing strongly in length and location, like e.g. in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities requiring iterative forward modelling of absorption spectra involving time consuming wavelength by wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a look up table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in presence of a strong absorption background. While the higher order absorption structures can be described as separate fit parameters in the spectral analysis (so called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher or- der absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Temperature Dependent Phononic Response of Few Layered MoS2 Nanosheets

2018 ◽  
Vol 4 (5) ◽  
pp. 546-548
Author(s):  
Sneha Sinha ◽  
Vasant Sathe ◽  
Sunil K. Arora
Keyword(s):  
Temperature Dependence ◽  
Phonon Scattering ◽  
Linear Temperature Dependence ◽  
Mos2 Nanosheets ◽  
Temperature Dependent ◽  
Linear Temperature ◽  
First Order ◽  
Non Linear ◽  
Out Of Plane ◽  
Raman Modes

From the temperature dependent phononic studies of few layered liquid phase exfoliated MoS2 nanosheets we find that the E12g (in-plane) and A1g (out-of-plane) Raman modes follow red shift with increase in temperature and exhibits non-linear temperature dependence in the entire temperature range (80 to 600 K). The first-order temperature coefficients for E12g and A1g modes are found to be -0.0133 cm-1K-1 and -0.0092 cm-1K-1, respectively. The physical origin of the non-linear temperature dependence is analyzed using an analytical model that includes contribution of the thermal expansion and an-harmonic effects to the lattice potential. Our analysis suggests that the non-linear temperature dependence of E12g and A1g modes mainly originates from the an-harmonic contributions from three-phonon and four-phonon scattering.

scholarly journals Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

2016 ◽  
Vol 9 (5) ◽  
pp. 2147-2177 ◽  
Author(s):  
Jānis Puķīte ◽  
Thomas Wagner
Keyword(s):  
Radiative Transfer ◽  
Optical Absorption ◽  
Absorption Spectroscopy ◽  
Scattered Light ◽  
Higher Order ◽  
Trace Gas ◽  
Optical Absorption Spectroscopy ◽  
Non Linear ◽  
Linear Effects ◽  
Transfer Modelling

Abstract. We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer–Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Temperature Dependence of the Air/Water Interface Revealed by Polarization Sensitive Sum-Frequency Generation Spectroscopy

2018 ◽  
Author(s):  
Daniel R. Moberg ◽  
Shelby C. Straight ◽  
Francesco Paesani
Keyword(s):  
Temperature Dependence ◽  
Low Frequency ◽  
Potential Energy Function ◽  
Md Simulations ◽  
Sum Frequency Generation ◽  
Water Molecules ◽  
Water Interface ◽  
Sum Frequency ◽  
Air Water Interface ◽  
Frequency Generation

<div> <div> <div> <p>The temperature dependence of the vibrational sum-frequency generation (vSFG) spectra of the the air/water interface is investigated using many-body molecular dynamics (MB-MD) simulations performed with the MB-pol potential energy function. The total vSFG spectra calculated for different polarization combinations are then analyzed in terms of molecular auto-correlation and cross-correlation contributions. To provide molecular-level insights into interfacial hydrogen-bonding topologies, which give rise to specific spectroscopic features, the vSFG spectra are further investigated by separating contributions associated with water molecules donating 0, 1, or 2 hydrogen bonds to neighboring water molecules. This analysis suggests that the low frequency shoulder of the free OH peak which appears at ∼3600 cm−1 is primarily due to intermolecular couplings between both singly and doubly hydrogen-bonded molecules. </p> </div> </div> </div>

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