Right-hand circular polarization

Figure 9.15 Second-harmonic intensity as function of rotation angle of quarter waveplate. (a) Transmitted -polarized SH signal, (b) transmitted p-polarized SH signal, (c) reflected -polarized SH signal, and (d) reflected p-polarized SH signal. Left- and right-hand circularly polarized input light is indicated with open and filled circles, respectively.

Fig. 21 Spiral structiu-e formed by seven beam interference central beam is right-handed circularly polarized, and the side beams linearly [32,33]. Simulated by interference of plane waves according to Eq. 2 with side beams comprising an 80° angle with the optical axis (the -field of the central beam is Eo = o/V2(l, i,0), where + corresponds to the right-handedness i = V )...

The handedness, or chirality, inherent in foundational electrodynamics at the U(l) level manifests itself clearly in the Beltrami form (903). The chiral nature of the field is inherent in left- and right-handed circular polarization, and the distinction between axial and polar vector is lost. This result is seen in Eq. (901), where , is a tensor form that contains axial and polar components of the potential. This is precisely analogous with the fact that the field tensor F, contains polar (electric) and axial (magnetic) components intermixed. Therefore, in propagating electromagnetic radiation, there is no distinction between polar and axial. In the received view, however, it is almost always asserted that E and A are polar vectors and that is an axial vector. 

The A potential is a Beltrami field V A A = efcA describing a left-handed circular polarization for e = +1 and a right-handed circular polarization for e = —1. 

The output of CD spectrometers is in two alternative but related types of unit. The difference in absorbance with respect to left- and right-handed circularly polarized... 

Figure B3.5.3 The relation of ellipticity to the differential absorption of circularly polarized radiation. The oscillating radiation sine wave, 01, is proceeding out of the plane of the paper towards the viewer. (A) Plane-polarized radiation is made up of left- and right-handed circularly polarized components, OL and OR, respectively. Absorption by a chromophore in a nonchiral environment results in an equal reduction in intensity of each component, whose resultant is a vector oscillating only in the vertical plane—i.e., plane-polarized radiation. (B) Interaction of the radiation with achiral chromophore leads to unequal absorption, so that combination of the emerging vectors, OL and OR, leads to a resultant that describes an elliptical path as it progresses out of the plane of the paper. The ratio of the major and minor axes of the ellipse is expressed by tan 0, thus defining ellipticity. The major axis of the ellipse makes an angle (q) with the original plane, which defines the optical rotation. This figure thus demonstrates the close relation between optical rotation and circular dichroism.

TE) and transverse magnetic (TM) parts. However, Rumsey [53] detailed a secondary method of solving the same equations that effected a decomposition of the field into left-handed and right-handed circularly polarized parts. For such unique field solutions to the time-harmonic Maxwell equations (e = electric permittivity, p = magnetic permeability) ... 

Analogous g-values may be defined for the degree of circular polarization in emission [or circularly polarized photoluminescence (CPPL)] and circularly polarized electroluminescence (CPEL), eg. gCppL = 2(JL - 1R)/(1L + 1r), where IL and IR denote the intensity of left- and right-handed circularly polarized emission, respectively. CPPL should not be confused with fluorescence-detected CD. 

A circular dichrograph alternately sends left- and right-handed circularly polarized light (LCPL and RCPL) through a sample. If this sample differentially absorbs these two forms of... 

Chirality is an important topic in chemistry and biochemistry, due to the natural occurrence of chiral molecules in living organisms. In circular dichroism (CD) one measures the differential absorption of left- and right-handed circularly polarized light, which for chiral species are different. Therefore, CD has turned out to be a powerful tool which provides information on the electronic and geometric structure of chiral molecules. Since most CD spectra are measured in solution we extended our DRF/TDDFT method to also calculate such properties. As a first example we studied... 

Circular dichroism(CD) is the differential absorption of left- and right-handed circularly polarized light, due to molecules that have optical handedness or optical activity (this happens for most molecules of biological interest—for example, the a helix, [1 sheet, and random coil regions of proteins and the double helix of nucleic acids have recognizable CD spectral signatures). 

Experimentally, the CD intensity is often quantified by the differential molar absorption coefficient Ae = l — r for the absorption of left-handed vs right-handed circular polarized light, where Ae and e are usually in units of L mol 1 cm-1. The conversion from Ae in L moP1 cm-1 to the molar ellipticity in deg cm2 dmoP1 is [0] = (18,0001n(10)/47r)Ae. The connection with quantities that can be calculated from first-principles theory is given by the following equation [35] ... 

A compound is considered optically active if it shows the phenomena of circular birefringence and circular dichroism. These are the manifestations of different refractive indices, /i, and /Ir, and different extinction coefficients, , and Cr, respectively, for left-handed and for right-handed circularly polarized light. Optical activity is therefore closely related to the existence of elliptically and circularly polarized light. 

Circular dichroism is measured using a dichrograph, which modulates a monochromatic beam of light between left-handed and right-handed circular polarization. A difference between and k produces an intensity modulation that can be amplified and displayed. A separate measurement of Ct nd r would be much more exacting because the differences between Sicl and rc7 are usually very small. (The optical densities differ by I0 -10 units.)... 

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