Optical phonon dispersion

In the following sections, we first show the phonon dispersion relation of CNTs, and then the calculated results for the Raman intensity of a CNT are shown as a function of the polarisation direction. We also show the Raman calculation for a finite length of CNT, which is relevant to the intermediate frequency region. The enhancement of the Raman intensity is observed as a function of laser frequency when the laser excitation frequency is close to a frequency of high optical absorption, and this effect is called the resonant Raman effect. The observed Raman spectra of SWCNTs show resonant-Raman effects [5, 8], which will be given in the last section. 

The Dispersion of Long-Wave Polar Optical Phonons in Diatomic... 

Fig. 3. Dispersion curves of the long-wavelength optical phonons, photons, and polaritons in the centre of BZ 1. In order to demonstrate the connection with the dispersion effects in the region 107 < k < 10 cm-1, the branches of an LO and an LA phonon in this region have been added in a different linear scale. The figures correspond to a cubic lattice with two atoms in the unit cell 3S)...

In this chapter some of the presently known optical properties of zinc oxide are reviewed. In particular, the anisotropic dielectric functions (DFs) of ZnO and related compounds from the far-infrared (FIR) to the vacuum-ultraviolet (VUV) spectral range are studied. Thereupon, many fundamental physical parameters can be derived, such as the optical phonon-mode frequencies and their broadening values, the free-charge-carrier parameters, the static and high-frequency dielectric constants, the dispersion of the indices of refraction within the band-gap region, the fundamental and above-band-gap band-to-band transition energies and their excitonic contributions. 

The optical-phonon threshold at low temperature is not as sharp as experimental spectra show. The bidimensional exciton model does not account for the specific dispersions of excitons and phonons in anthracene. 

AIN exists in two types the hexagonal (wurtzite structure) and the cubic (zincblende structure). The former is more stable, and has been investigated in more detail. The wurtzitic AIN has two formula units per unit cell (4 atoms per cell) and 9 optical branches to the phonon dispersion curves [1] ... 

Axe JD, Flarada J, Shirane G (1970) Anomalous acoustic dispersion in centrosymmetric crystals with soft optic phonons. Phys Rev B 1 1227... 

Here T is the temperature of acoustic phonons (thermostat), T is the temperature of optical phonons (284), the anharmonicity constant k is much less than 1, and flq is the frequency of acoustic phonons it is possible to assume ilq = (10 2 to 10 1)flDebye. The coupling between the optical and acoustic phonons is strongest near f>Debye 1 and because of this, for sufficiently large anharmonicity, k > 10 2 even at T = T", the last exponential multiplier can be approximated by the exponent below, with the dispersion being neglected ... 

In compound crystals, the ujn values considered are wlo, the frequency of the longitudinal optical phonons on the high-energy (h-e) side, and wto, the frequency of the transverse optical phonons, on the low-energy side. The dielectric constant at frequencies above c lo is denoted as while that below wto is denoted as s (the index s represents static, despite the fact that s shows a small dispersion between the value just below ujto and the one at radiofrequencies1). It can be seen from expressions (3.14) and (3.15) that above ujo, the ionic contribution decreases such that qo is smaller than s. Typical values are given in Table 3.1. 

Subsequently, a peak in the RSL spectra, similar to the one observed by Krishnan, was not found in some crystals, such as silicon and germanium, which have the same type of structure as diamond and have even stronger anharmonicity than diamond. This encouraged Tubino and Birman (33) to improve the accuracy of the calculations of the structure of the phonon bands in crystals with a diamond-type structure. It was shown as a result of comprehensive investigations that the dispersion curve of the above-mentioned optical phonon in diamond has its highest maximum not at k = 0, but at k 0. The result of these calculations indicates that the peak experimentally observed in the RSL spectra of diamond falls within the region of the two-phonon continuum. It cannot correspond to a biphonon and is most likely related to features of the density of two-particle (dissociated) states. 

Now we have two (2) phonon dispersion curves, a so-called optical branch and a lower energy acoustical branch. The standing waves are better understood in terms of the actual displacement the atoms undergo ... 

After considerable work, it was determined that the hosts which work best in this application are those in which vlbronic coupling is minimized. This was established by determining and comparing the phonon dispersion branches of the various compounds. It was found that those hosts which have low energy optical branches in the phonon spectrum function best for up-conversion phosphor applications. Note that this is akin to minimizing ground state perturbation at the activator site proper choice of host. The best hosts were found to be ... 

The obtained results show that the lattice dynamics of very small ZnSe NCs is similar to that of bulk ZnSe crystal in the case that dispersion curves of the main optical phonon frequencies are still correct. It is confirmed by the data obtained in... 

In the two-particle picture (Fig. 1), the optical absorption by excitons involves the conversion of a photon into an exciton, the absorption occurring at a place where phonon dispersion curve intersects the exciton dispersion curve, meeting... 

Figure 7. Bulk phonon dispersion curves for KBr and RbCl in their <100> and <111> high-symmetry directions. Both crystals have fee lattices and rocksalt structures. Note that the transverse branches, labeled TA (transverse acoustic) and TO (transverse optical), are doubly degenerate in these directions. (Adapted from Fig. 3 of Ref. 32.)...

Figure 16. Surface phonon dispersion curves for LiF(OOl). The calculated bulk bands are indicated by the vertical-striped regions. The surface localized modes are shown by heavy solid lines, whereas the resonances lying within bulk bands are given by thinner solid lines. The mode label S refers to the Rayleigh wave, to the longitudinal resonance, Sg to the crossing resonance, and S2, S3, and S4 to optical modes. (Reproduced from Fig. 2 of Ref. 58, with permission of Elsevier Science Publishers.)...

Figure 18. Surface phonon dispersion for RbCl(OOl). The shaded regions correspond to the surface projected density of states, with the darker shades representing higher state densities. The Rayleigh wave, crossing resonance, and optical mode are indicated by RW, CR, and 2, respectively. (Reproduced from Ref. 119.)...

---