Local Mode Frequencies Research Articles

Transmission and filtering in photonic circuits: effects of absorption and amplification

We study the effect of absorption and amplification on transmission and filtering in one-dimensional dielectric photonic structures made of dangling side branches grafted periodically along an infinite monomode waveguide with defective branches. The loss and gain are introduced by adding an imaginary part ε″ to the dielectric constant. We show that for reasonable values of ε″, loss and gain affect essentially the transmission at the frequencies of localized modes associated with the defect branch introduced into the periodic structure. The amplitude and the phase of the transmission and reflection coefficients associated with defect modes are discussed as function of ε″ and the size of the structure. The properties of the defect modes in presence of loss and gain can be used as an on/off switching device in a demultiplexer made of the above photonic structures.

A vibrational model of F centres in alkali halides

A model of F-centres in alkali halides, which relates absorption energies in F-bands to the dynamic parameters of host lattices, is proposed. According to this model, the electrons trapped in F-centres are treated as classical particles with a proper mass \(m^{*}=m\varepsilon_{loc}^{4}/\varepsilon_{\infty }^{2}\) , m standing for the actual electron mass, \(\varepsilon_{loc}\) and \(\varepsilon_{\infty }\) for local high frequency and optical dielectric constants, respectively. Hence, by considering the trapped electrons as substitutional impurities of small mass, the dynamics of the lattice is investigated by means of the theory of local modes with the assumption of isotopicity. A simple equation allowing calculation of the local mode frequencies is obtained. Knowledge of the Debye frequency and of transverse and longitudinal mode frequencies at the long wavelength limit is required. With this model, F-band absorption energy is reasonably well accounted for.

Structural and vibrational study of chromium doped elpasolite crystals Cs2NaAlF6

The influence of site-symmetry and electron phonon coupling in Cs2NaAlF6:Cr3+ is probed by correlation of optical and structural measurements. Based on neutron and x-ray analysis the structure is a distorted R3m¯, exhibiting a unique stacking interaction. Selection rules have been used to assign the Raman-active zone-center vibrations. Although local and bulk mode frequencies differ slightly, indicating that the guest Cr3+ ion does not significantly perturb the host structure, vibrational analysis indicates the Cr3+ ion is coupled to the first coordination sphere of the Al–F lattice.

Two-dimensional ultrafast infrared vibrational echo studies of solute–solvent interactions and dynamics

Two-dimensional spectrally resolved ultrafast infrared vibrational echo experiments were used to investigate the nature of solute–solvent interactions in solution. The experiments were performed on (acetylacetonato)dicarbonylrhodium(I) in dibutylphthalate at 150 K. The 2D spectra display features that reflect the 0–1 and 1–2 transitions and the combination band transition of the symmetric (S) and antisymmetric (A) CO stretching modes. Three oscillations in the data arise from the frequency difference between the S and A modes (quantum beats) and the S and A anharmonicities. The novel mechanism that gives rise to the anharmonic oscillations, which is distinct from that of a conventional quantum beat, is described. The frequency of the S/A mode-splitting quantum beats varies for different observation wavelengths across the 0–1 inhomogeneous lines. For either the S or A lines, as the wavelength of observation of the vibrational echo is moved to higher energy, the quantum beat frequency decreases. The change in frequency is related to the nature of the solute–solvent interactions (inhomogeneous broadening) of the S and A transitions. A simple analytical approach is used to determine how a solute vibrational oscillator is influenced by the solvent. Three models of solute–solvent interactions are considered in terms of CO local mode energies and coupling. In one, the transition energies in the S and A lines are anticorrelated either because the inhomogeneous broadening arises from variations in the local mode coupling or the local mode energies are anticorrelated. In the other two, the local mode energies are either correlated or uncorrelated. The results of the model calculations indicate that interactions with the solvent result in local mode frequencies that are strongly correlated.

Solute–solvent interactions: two-dimensional ultrafast infrared vibrational echo experiments

Two-dimensional (time–frequency) ultrafast IR vibrational echo experiments were used to investigate solute–solvent interactions in solution. The experiments were performed on symmetric (S) and antisymmetric (A) CO stretching modes of (acetylacetonato) dicarbonylrhodium(I) in dibutylphthalate (DBP) at 150 K. The two-dimensional (2D) spectrum displays quantum beats at the nominal frequency difference between the S and A modes. However, as the observation wavelength is moved to higher energy, the quantum beat frequency decreases. The change in frequency is related to the nature of the solute–solvent interactions. Model calculations indicate that interactions with the solvent result in CO local mode frequencies that are strongly correlated.

Investigation of two infrared bands at 1032 and 1043 cm−1 in neutron irradiated silicon

We report on infrared (IR) studies of defects in Czochralski-grown silicon (Cz-Si) subjected to fast neutron irradiation and subsequent thermal anneals. We focus mainly on the investigation of the VO4 defect which, in the literature, has been correlated with the pair of bands (1032 and 1043 cm−1) in neutron-irradiated Si and another pair of bands (983 and 1004 cm−1) in oxygen-implanted Si. Semiempirical calculations of the localized vibrational mode frequencies of the VO4 structure support its correlation with the second pair of bands. This correlation is consistent with the ascertainment that the zero point energy of each VOn (n=1,2,3,4) defect is smaller than the zero point energy of the constituent defects VOn−1, Oi, that is: EVOn<EVOn−1+EOi.

Phase diagrams and compression effect on solidus curve of Al-rich Al–Cu alloy

By considering the contributions from the band and local mode frequencies, the temperature- and pressure-dependent mean-square displacement for Al–Cu solid solution is quantitatively obtained. Next, the concentration dependence of the Debye temperature at higher and lower temperatures is estimated. The obtained Debye temperature decreases with the solubility of Cu at low temperatures, but increases at high temperatures. Then, the compression effect on the solidus curves for the Al–Cu solid solution is presented by applying Lindeman's melting law to the alloy systems, and an increase of the solubility exceeding 10 at% Cu in Al is predicted under pressure.

Phase Diagrams of .ALPHA.-Phase Al-Li System.

By taking into account the contributions of the band and local mode frequencies, the temperature- and pressure-dependent mean-square displacement in AI-Li solid solution was quantitatively calculated. Next, the concentration-dependence of the Debye temperature at higher and lower temperatures is estimated. The Debye temperature decreases with increasing the solubility of Li at low temperatures, while it increases at higher temperatures. Then, the compression effect on the solidus curves in the α-phase AI-Li solid solution is expressed by applying Lindeman's melting law to the alloy systems, and an increase of solubility exceeding 20 at. % Li in Al is predicted under pressure.

Vibrational Spectroscopy of GaN:Mg Under Pressure

AbstractThe microscopic structure of Mg-H complexes in GaN has been a subject of intense theoretical and experimental investigation. In order to probe the Mg-H structure, we have studied the effect of hydrostatic pressure on the local vibrational mode (LVM) frequency. At ambient pressure, the LVM frequency is 3125 cm-1, which corresponds to a N-H stretching mode. In this study, Fourier-transform spectroscopy was performed on free-standing GaN:Mg,H samples in a diamond-anvil cell, with nitrogen as a pressure-transmitting fluid. The samples had been removed from their sapphire substrate by the laser-liftoff technique. The LVM frequency was measured, at liquid helium temperatures, for pressures ranging from 0 to 5 GPa. The pressure dependence of the frequency is nonlinear: first it decreases with pressure, then it increases. Comparison with first-principles calculations allows us to derive information about the microscopic structure of the Mg-H complex. The calculated stable configuration indeed gives rise to a frequency shift consistent with experiment. Based on the comparison between theory and experiment, we can exclude the bond-center configuration, which would result in a much larger pressure derivative than experimentally observed.

Phase-slip induced distributed feedback resonator modes with tilted modulation

Transversely bounded λ/4 distributed feedback (DFB) resonator with tilted index modulation is considered. By treating the modulation as a weak perturbation and averaging the wave equation with respect to the transverse field distribution we obtain an effective coupled-wave equations with spatially varying coupling constant. We analyze these equations both analytically and numerically for a specific case of transverse confinement. The evolution of the frequency of the lowest threshold laser mode with the tilt angle is studied. It is demonstrated that the dependence of the frequency of the intra-gap localized mode on the tilt angle originates from the mode-conversion mechanism in the DFB process.

Transformation of soft localized modes in glasses under pressure

Experimentally observed narrowing of spectral holes in a glass under hydrostatic pressure confirms our theoretical finding that the external pressure, in addition to increasing the frequencies of soft localized modes, also reduces their number. This occurs because the majority of soft localized modes in glasses is shown to have a negative cubic anharmonicity. For that reason the applied pressure not only enhances the stiffness of these modes, but also transforms a fraction of them into tunneling two-level systems, whereas the simultaneous reverse transformations of some other two-level systems into soft localized modes are less numerous.

Local vibrational modes of two neighboring substitutional carbon atoms in silicon

Infrared absorption measurements on n-type silicon doped with carbon and irradiated with electrons at room temperature have revealed new absorption lines at 527.4 and $748.7 {\mathrm{cm}}^{\ensuremath{-}1},$ which originate from the same defect. The $748.7\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ line is observed only when the sample is cooled in the dark and the spectrum is measured through a low-pass filter with cutoff frequency below $6000 {\mathrm{cm}}^{\ensuremath{-}1}.$ Light with frequency above $6000 {\mathrm{cm}}^{\ensuremath{-}1}$ removes this line and generates the $527.4\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ line. Comparison with spectra recorded on irradiated silicon doped with ${}^{13}\mathrm{C}$ shows that the two lines represent local vibrational modes of carbon. The annealing behavior of the $748.7\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ line is identical to that of the EPR signal originating from the negative charge state of two adjacent substitutional carbon atoms $({\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{s}{)}^{\ensuremath{-}}.$ The 527.4- and $748.7\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ lines are ascribed to the E modes of ${\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{s}$ in the neutral and negative charge states, respectively. The structure and local vibrational modes of $({\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{s}{)}^{0}$ and $({\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{s}{)}^{\ensuremath{-}}$ have been calculated by ab initio local density functional theory. The calculated structures agree qualitatively with those obtained previously by Hartree-Fock methods, but the calculated Si-C and C-C bond lengths differ somewhat. The calculated local mode frequencies are in good agreement with those observed. The formation of ${\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{s}$ has also been investigated. It is suggested that the center is formed when a vacancy is trapped by the metastable substitutional carbon-interstitial carbon center, ${\mathrm{C}}_{s}\ensuremath{-}{\mathrm{C}}_{i}.$

Modelling of local modes in SixGe1−x and CxSiyGe1−x−y alloys to explore the local clustering of the species

The frequencies of the local vibrational modes due to defects within group IV alloys are affected by the local environment of the defects; therefore by investigating known modes we get an insight into alloy fluctuations near the defects. The local modes are modelled around defects in a range of local alloy arrangements to investigate the effects of clustering alloy species. An interatomic potential has been fitted to phonon frequencies for the pure materials at symmetry points in k-space, to local vibrational modes of lighter elements in otherwise pure local environments and to atomic positions predicted by local density calculations for certain alloy structures. Using this potential, the frequencies of local modes of substitutional carbon are found in SixGe1−x with various values of x. From a stochastic analysis of the local environs to the carbon, the modes are weighted to produce the expected local vibrational spectrum of a SixGe1−x alloy. The experimental local mode line shapes in the alloys deviate sufficiently from those predicted to show that the carbon substitutes preferentially in regions of high silicon content.

Substitutional carbon inSi1−xGex

Local vibrational modes of carbon impurities in relaxed ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ have been studied with infrared absorption spectroscopy in the composition range $0.05l~xl~0.50.$ Carbon modes with frequencies in the range 512\char21{}600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are observed in ${}^{13}{\mathrm{C}}^{+}$-implanted ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ after annealing at 550 \ifmmode^\circ\else\textdegree\fi{}C. Measurements on samples coimplanted with ${}^{12}{\mathrm{C}}^{+}$ and ${}^{13}{\mathrm{C}}^{+}$ show that these modes originate from defects containing a single carbon atom and from the variation of the mode frequencies with composition x, the modes are assigned to substitutional carbon in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}.$ Based on the frequencies obtained from a simple vibrational model, the observed modes are assigned to specific combinations of the four Si and Ge neighbors to the carbon. The intensities of the modes indicate that the combination of the four neighbors deviates from a random distribution. Ab initio local-density-functional cluster theory has been applied to calculate the structure and the local mode frequencies of substitutional carbon with n Ge and $4\ensuremath{-}n$ Si neighbors in a Si and a Ge cluster. The calculated frequencies are \ensuremath{\sim}9% higher than those observed, but the ordering and the splitting of the mode frequencies agree with our assignments.

Localized multibunch modes in accelerators

This paper will explore the possibility of the formation of localized modes in the coupled transverse oscillations of bunches in an accelerator. Such modes are characterized by a large amplitude excitation of one of the bunches, with little or no excitation of the other bunches. They are very similar to intrinsic localized modes predicted to appear in lattice excitations of anharmonic condensed matter systems. The existence of the phenomenon in accelerators requires long-range coupling between the bunches, and quartic terms in the effective potential experienced by the bunches. The discussion in this paper considers the specific cases of a long-range coupling due to the resistive wall impedance, and nonlinearities in the transverse force caused by octupoles. The general equations for the localized mode frequencies and amplitudes are derived. The equations are applied to the specific cases of 9 and 21 equally spaced, equally populated bunches in the Cornell electron storage ring. For both cases, with the currently available octupole strength, and with currents of 8 mA per bunch, localized modes with amplitudes of about 2 mm, and with frequency shifts of $50--100\mathrm{s}{}^{\ensuremath{-}1}$ relative to the linear coupled-bunch mode frequencies, may be possible.

Local vibrational modes of the metastable dicarbon center(Cs–Ci)in silicon

The metastable dicarbon center $({\mathrm{C}}_{s}--{\mathrm{C}}_{i})$ in silicon has been studied by infrared absorption spectroscopy. After electron irradiation of carbon-doped silicon, new infrared absorption lines at 540.4, 543.3, 579.8, 640.6, 730.4, and $842.4 {\mathrm{cm}}^{\ensuremath{-}1}$ are observed. The lines are identified as local vibrational modes of the ${\mathrm{C}}_{s}--{\mathrm{C}}_{i}$ center in its $\mathcal{B}$ form. Illumination of the sample with band-gap light at $\ensuremath{\sim}60 \mathrm{K}$ converts the $\mathcal{B}$ to the $\mathcal{A}$ form, and local modes of the $\mathcal{A}$ form are identified at 594.6, 596.9, 722.4, 872.6, and $953 {\mathrm{cm}}^{\ensuremath{-}1}.$ The observed local mode frequencies of both forms are in excellent agreement with those calculated from ab initio theory. Our findings provide strong support for the atomic structure suggested previously for the two forms.

Localized modes of oscillating structures which lie on the bottom

The phenomenon of wave localization in hydroelastic systems leads to the strength concentration of radiation fields. The linear method considers the process of localization to be the formation of nonpropagation waves (trapped modes phenomenon). The presence of such waves in the total wave packet points to the existance of mixed natural spectrum of differential operators describing the behavior of hydroelastic systems. The problem of liquid and oscillating structure interaction caused by the trapped modes phenomenon has been solved (membranes, dies, plates and different liquid models). The areas of wave localization have been determined. These areas depend on both the parameters of oscillating structures and the liquid waveguide parameters (the linear dimensions of the channel filled with liquid; the height from the bottom to the liquid surface; the liquid density gradient according to the height, etc.). Necessary and sufficient conditions for the low-frequency trapped modes and the high-frequency trapped modes have been found. The wave localization in nonlinear elastic structures interacting with liquid has been studied. Cases of weak and strong nonlinearity have been investigated. It has been shown that the slightly decreasing tail is added to nonlinear localized modes depending on the frequency of linear localized modes. The tail is caused by the interaction of the mode’s continuous spectrum and the localized modes.

Lattice Specific Heat and Debye Temperature of Al-Li Alloy.

The lattice dynamics and thermal properties of α-phase Al-Li alloy by solid-solutioning under pressure are studied using our previous microscopic electronic theory. The phonon frequencies of the band and local modes and the lattice specific heat at constant volume are presented theoretically for the Al1-xLix system. The band and local mode frequencies increase with the solubility of Li, and the specific heat decreases except at low temperatures. The Debye temperature for the AI1-xLix system is estimated from the specific heat at low temperatures and from the average elastic velocity. The Debye temperature decreases as Li content increases.

Intensity sharing between Brillouin and Umklapp scattering in glasses

The interaction between low frequency localized modes and sound waves in glasses is treated in terms of the simplest possible model, namely a single elastic dipole proportional to the displacement of the localized mode. The approximation makes it possible to calculate the contribution of the localized mode to the inelastic coherent neutron or X-ray scattering with relatively small momentum transfer. The connection to the classical second moment sum rule is discussed.

Local modes of transition metal ions (Mn, Fe, Co) in narrow-gap II–VI semiconductors

Optical phonons in mercury chalcogenides doped with selected transition metal ions (TMI) are investigated by infrared reflectivity and Raman scattering measurements performed at temperatures from 5 to 295 K. The results obtained for Hg 1− x Fe x Se, Hg 1− x Co x Se, Hg 1− x Fe x S and Hg 1− x Co x S mixed crystals confirm the chemical trends in the dependence of the local mode frequency on the number of 3d electrons of the TMI, reported previously for the wide-gap, zinc-blende II–VI semiconductors.