Frequencies Of Longitudinal Modes Research Articles

Polarization self-modulation in a coaxially end-pumped orthogonally polarized laser

A scheme of orthogonally polarized laser (OPL) with polarization self-modulation (PSM) in the coaxial end-pumping configuration is proposed in this work. The gain medium consisted of two Nd:YVO4 crystals with orthogonal optical axes, and a quarter-wave plate served as a polarization-switching device. By rotating the electric vector during each cavity round trip, frequency degeneration and correlated operation of two polarization components were achieved. The polarization eigenstates in two orthogonal directions were analyzed using the Jones matrix and eigenequation. The spectral distribution was also briefly discussed based on thermal effects. The results showed that two eigenmodes located at 45° and 135° to the crystal axis, respectively, with a frequency difference equaled to half the free spectral range of the resonator. In the experiments, it was found for the first time that the modulation of eigenstates can be realized by adjusting pump parameters (including pump power, beam size, focusing position, and pump wavelength) and cavity anisotropy, which enables the manipulation of degree of polarization (DOP) and monitoring the resonator properties. Overall, tuning the laser polarization eigenstate offers a flexible method to switch the operational states of the OPL, including the longitudinal mode frequency difference, DOP, polarization angle, etc. It is believed this scheme provides a valuable reference to realize compact, high-beam-quality, and robust OPLs for applications such as dual-frequency light source development, precision measurement and polarization control.

Phononic origin of the infrared dielectric properties of RE2O3 (RE = Y, Gd, Ho, Lu) compounds

Understanding the phononic origin of the infrared (IR) dielectric properties of yttria (Y2O3) and other rare-earth sesquioxides (RE2O3) is a fundamental task in the search of appropriate RE2O3 materials that serve particular IR optical applications. We herein investigate the IR dielectric properties of RE2O3 (RE = Y, Gd, Ho, Lu) using density functional theory-based phonon calculations and Lorentz oscillator model. The abundant IR-active optical phonon modes that are available for effective absorption of photons result in high reflectance of RE2O3, among which four IR-active modes originated from large distortions of REO6 octahedra are found to contribute dominantly to the phonon dielectric constants. Particularly, the present calculation method by considering one-phonon absorption process is demonstrated with good reliability in predicting the IR dielectric parameters of RE2O3 at the far-IR as well as the vicinity of mid-IR region, and the potential cutoff frequency/wavelength of its applicability is disclosed as characterized by the maximum frequency of IR-active longitudinal phonon modes. The results deepen the understanding on IR dielectric properties of RE2O3, and aid the computational design of materials with appropriate IR properties.

Temporal dynamics of surface phonon polaritons in polar dielectric nanoparticles with nonlocality

Surface phonon polaritons (SPhPs) supported by polar dielectrics have been a promising platform for nanophotonics in mid-infrared spectral range. In this work, the temporal dynamic behavior of polar dielectric nanoparticles without (or with) spatial dispersion/nonlocality driven by the ultrashort Gaussian pulses is carried out. We demonstrate that three possible scenarios for the temporal evolutions of the dipole moment including ultrafast oscillations with the decay, exponential decay, and keeping a Gaussian shape exist, when the pulse duration of the incident field is much shorter than, similar to, and much longer than the localized SPhP lifetime. Once the nonlocal effect is considered, the oscillation period becomes large slightly, and the exponential decay turns fast. Furthermore, nonlocality-induced novel temporal behavior is found such as the decay with long-period oscillations when the center frequency of the incident pulse lies at the frequency of adjacent longitudinal resonant modes. The positive and negative time-shifts of the dielectric response reveal that the excitation of the dipole moment will be delayed or advanced. These temporal evolutions can pave the way towards potential applications in the modulation of ultrafast signals for the mid-infrared optoelectronic nanodevices.

Thickness-Dependent Terahertz Permittivity of Epitaxially Grown PbTe Thin Films

The exceptional thermoelectric properties of PbTe are believed to be associated with the incipient ferroelectricity of this material, which is caused by strong electron–phonon coupling that connects phononic and electronic dynamics. Here, we have used terahertz time-domain spectroscopy measurements to generate complex permittivity spectra for a set of epitaxially grown PbTe thin films with thicknesses between 100 and 500 at temperatures from 10K to 300K. Using a Drude–Lorentz model, we retrieved the physical parameters of both the phononic and electronic contributions to the THz permittivity. We observed a strong decrease, or softening, of the transverse optical phonon mode frequency with decreasing temperature, determining a thickness-independent negative ferroelectric-transition critical temperature, while we found a thickness-dependent anharmonic phonon decay lifetime. The electronic contribution to the permittivity was larger in thinner films, and both the carrier density and mobility increased with decreasing temperature in all films. Finally, we detected a thickness-dependent longitudinal optical phonon mode frequency, indicating the presence of plasmon–phonon coupling.

Propagation modeling and guided waves in a ZnO piezoelectric planar resonator: open-circuit and short-circuit cases

This paper presents an application of Legendre polynomial approach to solve the wave propagation in a piezoelectric ZnO planar resonator subjected to stress-free boundary conditions and excited using two thin electrodes connected to an electrical source. The method is able to take into account the boundary conditions, the presence of electrical source and the different dissimilarities of the physical properties. Resonance frequencies of longitudinal modes are calculated in case of an open and short-circuit brunch. Dispersion characteristics are also calculated such as mechanical displacement and stress profiles for different resonance frequencies. The electromechanical coupling coefficient is also calculated.

Assessment of thrust chamber stability margins to high-frequency oscillations based on mathematical modeling of coupled ‘injector – rocket combustion chamber’ dynamic system

High-frequency instability of a liquid-propellant rocket engine (LRE) during static firing tests is often accompanied by a significant increase in dynamic loads on the combustion chamber structure, often leading to a chamber destruction. This dynamic phenomenon can also be extremely dangerous for the dynamic strength of a liquid-propellant rocket engine. The calculation of acoustic combustion product oscillation parameters is important in the design and static firing tests of such rocket engines. The determination of the oscillation parameters (natural frequencies and stability margins such as oscillation decrement) is one of the problems solved in the LRE design period as part of the development of measures to ensure the engine stability. The main aim of the paper is to develop a numerical approach to determining the parameters of acoustic oscillations of combustion products in liquid-propellant rocket engines combustion chambers taking into account the features of combustion space configuration and the variability of gaseous medium physical properties depending on the axial length of the chamber, acoustic impedance in critical throat and dissipation effects (damping experimental values) in the shell structure and the gas media in the chamber. The approach is based on mathematical modeling of the coupled ‘chamber shell structure – gas’ dynamic system by using the finite element method and the CAE (Computer Aided Engineering) system. The developed approach testing and further analysis of the results for the RD 253 engine using nitrogen tetroxide and unsymmetrical dimethylhydrazine as a propellant pair were carried out. The dynamic system shapes and frequencies of longitudinal, tangential and radial modes are determined. The results of mathematical modeling of the dynamic system indicate a satisfactory agreement of the calculated decrements of the first longitudinal oscillation mode and third tangential oscillation mode with the experimental decrements obtained by hot-fire tests data. From system harmonic analysis of the thrust chamber, it follows that the dynamic pressure gain factor of the gas media in the chamber at the first longitudinal mode frequency is 1.6 times greater than the system dynamic gain in the tangential mode. At the same time, the oscillation decrement for the system tangential mode is 2 times smaller than that of the first longitudinal mode. This means that the thrust chamber tangential mode is more dangerous and can lead to rocket engine combustion instability. The effect of the injector on the high-frequency stability of the combustion chamber and the possibility of partial suppression of combustion chamber thermoacoustic oscillations by adjusting the high-frequency dynamics of the injector are shown theoretically.

Infrared dielectric functions and Brillouin zone center phonons of α−Ga2O3 compared to α - Al2O3

We determine the anisotropic dielectric functions of rhombohedral $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ by far-infrared and infrared generalized spectroscopic ellipsometry and derive all transverse optical and longitudinal optical phonon mode frequencies and broadening parameters. We also determine the high-frequency and static dielectric constants. We perform density functional theory computations and determine the phonon dispersion for all branches in the Brillouin zone, and we derive all phonon mode parameters at the Brillouin zone center including Raman-active, infrared-active, and silent modes. Excellent agreement is obtained between our experimental and computation results as well as among all previously reported partial information from experiment and theory. We also compute the same information for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, the binary parent compound for the emerging alloy of $\ensuremath{\alpha}$-(${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{)}_{2}{\mathrm{O}}_{3}$, and use results from previous investigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)] to compare all properties among the two isostructural compounds. From both experimental and theoretical investigations, we compute the frequency shifts of all modes between the two compounds. Additionally, we calculate overlap parameters between phonon mode eigenvectors and discuss the possible evolution of all phonon modes into the ternary alloy system and whether modes may form single-mode or more complex mode behaviors.

A Method for Estimating Ground Internal Conditions Using Ground Coupled Longitudinal Vibration Modes of Vibratory Piles

Sediment disasters cause landslide deaths, house damage, and traffic network shutdowns. Many local authorities specified the sediment disaster warning area and created a hazard map. However, the hazard map is based on an offline approach, which is insufficient for providing evacuation guidance for residents. Therefore, adaptive upgrading of hazard maps is required. The previous hazard map is based on a survey of the slope dimension and does not consider the soil internal parameter (i.e., soil cohesion, eigen friction angle). Thus, the sensing technology of the soil internal state is important to detect disaster signs. This study proposes a method for sensing the internal state of soil based on the natural frequencies of longitudinal vibration modes of elastic piles coupled to the ground. The internal state of the soil is defined by the adhesion force and the natural friction angle. This paper presents an integrated analysis of the natural frequencies of longitudinal expansion and contraction obtained from field experiments and soil test results obtained from compression tests.

Influence of Transmission Lines on Dynamic Characteristics of Transmission Tower

The influence of transmission lines on dynamic characteristics of transmission tower should not be ignored due to the heavy quality of transmission lines. The finite element models of independent tower and transmission tower-line system are established by ANSYS. The modal analysis is carried out to study the influence of transmission lines on dynamic characteristics of transmission tower. Meanwhile, it is verified by experimental modal analysis. Results show that, the tower-line coupling effect has a great influence on dynamic characteristics of transmission tower. The coupling effect strengthens the vibration intensity. In terms of frequencies, it mainly affects longitudinal bending mode and torsional mode frequencies of transmission tower, but has little effect on transverse bending mode frequency. Therefore, the influence of tower-line coupling effect must be considered in vibration reduction design of transmission tower-line system.

Evaluation of the high-frequency oscillation parameters of a liquid-propellant rocket engine with an annular combustion chamber

The high-frequency instability (HF instability) of a liquid-propellant rocket engine (LPRE) during static firing tests is often accompanied by a significant increase in dynamic loads on the combustion chamber structure, often leading to the chamber destruction. This dynamic phenomenon can also be extremely dangerous for the dynamic strength of a liquid-propellant rocket engine with an annular combustion chamber. Computation of the parameters of acoustic combustion product oscillations is important in the design and static firing tests of such rocket engines. The main aim of this paper is to develop a numerical approach to determining the parameters of acoustic oscillations of combustion products in annular combustion chambers of liquid-propellant rocket engines taking into account the features of the configuration of the combustion space and the variability of the physical properties of the gaseous medium depending on the axial length of the chamber. A numerical approach is proposed. The approach is based on mathematical modeling of natural oscillations of a “shell structure of an annular chamber – gas” coupled dynamic system by using the finite element method. Based on the developed finite-element model of coupled spatial vibrations of the structure of the annular combustion chamber and the combustion product oscillations, the oscillation parameters of the system under consideration (frequencies, modes, and effective masses) for its dominant acoustic modes, the vibration amplitudes of the combustion chamber casing, and the amplitudes of its vibration accelerations can be determined. The operating parameters of the liquid-propellant rocket engine potentially dangerous for the development of thermoacoustic instability of the working process in the annular combustion chamber can be identified. For the numerical computation of the dynamic gains (in pressure) of the combustion chamber, a source of harmonic pressure excitation is introduced to the finite element model of the dynamic system “shell structure of an annular configuration – gas” (to the elements at the start of the chamber fire space). The developed approach testing and further analysis of the results were carried out for an engine with an annular combustion chamber (with a ratio of the outer and inner diameters of 1.5) using liquid oxygen – methane as a propellant pair. The system shapes and frequencies of longitudinal, tangential and radial modes are determined. It is shown that the frequency of the first acoustic mode in the case of a relatively low stiffness of the combustion chamber casing walls can be reduced by 40 percent in comparison with the frequency determined for a casing with rigid walls.

Raman and Infrared Studies of CdSe/CdS Core/Shell Nanoplatelets

The vibrational spectroscopy of semiconductor nanostructures can provide important information on their structure. In this work, experimental Raman and infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell nanoplatelets calculated from first principles using the density functional theory. The calculations confirm the two-mode behavior of phonon spectra of nanostructures. An analysis of the experimental spectra reveals the absence of modes with a high amplitude of vibrations of surface atoms, which indicates their strong damping. Taking into account the difference in the damping of different modes and their calculated intensities, all bands in the spectra are unambiguously identified. It is found that the frequencies of longitudinal optical modes in heterostructures are close to the frequencies of LO phonons in bulk strained constituents, whereas the frequencies of transverse modes can differ significantly from those of the corresponding TO phonons. It is shown that an anomalous thickness dependence of CdS TO mode is due to a noticeable surface relaxation of the outer Cd layer in the nanostructure.

Study the electronic and spectroscopic properties of ALxB7-XN7 Wurtzoids as a function of size and concentration using density functional theory

Electronic properties including (bond length, energy gap, HOMO, LUMO and density of state) as well as spectroscopic properties such like infrared, Raman scattering, force constant, reduced mass and longitudinal optical mode as a function of frequency are based on size and concentration of the molecular and nanostructures of aluminum nitride ALN, boron nitride BN and Al x B 7-X N 7 as nanotubes has calculated using Ab –initio approximation method dependent on density functional theory and generalized gradient approximation. The geometrical structure are calculated by using Gauss view 05 as a complementary program. Shows the energy gap of ALN, BN and Al x B 7-X N 7 as a function of the total number of atoms , start from smallest molecule to reached to Nano structure wurtzoid, wurtzoid2c and triwurtzoid, these values are compared with the experimental bulk value of ALN and BN (6.2 eV and 6.4 eV) respectively. Longitudinal optical mode frequency, force constant and reduced mass are presented which are agreement with experimental results.

Consistency of splitting frequency difference with longtudinal modes spacing variation in Zeeman dual-frequency laser

Phase anisotropy in laser resonant cavity will bring about an influence on laser frequency and polarization, such as laser frequency splitting, of which the frequency difference is determined by their introduced phase retardation. For a helium-neon laser with a small phase retardation in the cavity, the two split modes are very close to each other whose burned holes are overlapped. Then only one mode oscillates while the other is always in lock-in state due to strong mode competition, which forms hidden frequency split. Meanwhile the spacing between adjacent longitudinal modes deviates from original value and produces a certain variation equal to twice the hidden splitting frequency difference. As a result the longitudinal modes spacing variation is dominated by the phase retardation. On the other hand, by applying transverse magnetic field to a laser tube along the polarization direction, the neon atoms will undergo transverse Zeeman effect and be divided into two groups to provide the gain for polarized light beams parallel to the magnetic field and perpendicular to the magnetic field respectively. Then the laser mode competition is greatly weakened so that the two split modes can oscillate simultaneously to obtain the frequency difference. In order to make profound study of the consistency between longitudinal mode spacing variation and splitting mode frequency difference in the presence of transverse magnetic field, the samples of tilted quartz plate or half wave plate is placed into laser cavity to produce phase retardation. By the two mentioned methods, the splitting frequency difference varying with phase retardation of samples is deduced to make a comparison. Two measurements show that the average relative deviation is less than 1%, while the experimental results accord with theoretical analyses quite well. In this way splitting frequency difference of Zeeman dual-frequency laser can be determined accurately, and a new method to measure the phase retardation of half wave plate is provided.

Ultrasonic guided waves reflection from simple dent in pipe for defect rate estimation and parameters determination of axisymmetric wave generation source

In this paper, the reflection of ultrasonic guided waves from simple dent in pipes has been investigated using finite element method and the relationship between reflection coefficient of these waves and deformation rate has been determined. Also, the effect of the parameters of wave generation source on the generated wave field has been investigated using normal modes expansion method. At first, ultrasonic guided waves propagation has been studied in an intact pipe to obtain multiple modes using of displacement potential method. The characteristic equation has been solved using a matlab code in order to draw the dispersion curves of phase and group velocities in different frequencies for longitudinal modes, and it is observed that mode L(0,2) is a suitable mode for inspection in a range of frequency 200-300 kHz. The single sided dent is created in pipe using a plasticity analysis with the aid of finite element simulation and then L(0,2) mode is generated in pipe. By Investigation of the reflection of this mode from dent, the relationship between reflection coefficient and deformation rate is specified and it has been observed that this relationship is almost linear by curve fitting. Also, it has been observed in case of partial loading by wave generation source that is a transducer with a specified axial length and circumferential coverage angle, a combination of different modes such as L(0,2) mode is generated in pipe, if using a axisymmetric wave generation source including 8 segments 45 degree, only L(0,2) symmetric mode is generated.

Modulation Properties of an Extended Cavity Diode Laser and Dynamic Mode Splitting

We have found a fine structure in the frequency dependence of modulation efficiency of a diode laser (DL) with a strong selective optical feedback. The FM response of an extended cavity diode laser (ECDL) to the microwave current modulation has two peaks whose frequencies are close to the intermode frequency of the laser longitudinal modes. The frequency splitting of the peaks depends on the power of laser radiation and on the difference between the frequency of operating ECDL mode and the frequency of the closest DL mode. We have observed similar splitting in AM noise spectra with the same type of dependencies on power and aforementioned frequency detuning. The peculiarity of the AM noise spectrum has been observed and explained previously by nonlinear interaction of fields in the active region of a DL that results in the frequency splitting of the modes. This dynamic splitting of the laser cavity modes explains the specific features of the modulation characteristics.

Intermode beating mode-locking: Toward compact 2 µm short-pulse all-fiber lasers

Abstract We have successfully applied intermode beating mode-locking (IBML) for short pulse generation in compact Tm3+-doped double clad fiber lasers (TDFLs). This IBML technique is implemented by longitudinal-mode frequency matching between pump source and laser oscillator without extra mode-locker. Here, the achieved IBML TDFLs can respectively generate 2056.47 nm, 2003.88 nm and 1963.79 nm short pulses. Their output characteristics have been respectively investigated. The IBML technique enables the large pulse energy of ~20.8 nJ with pulse repetition rate of ~9.6 MHz. This work may open a new route for next-generation of high performance mid-infrared short-pulse all-fiber laser sources.

Feedback in Plasma Maser

A change in the operation mode of a plasma maser with a pulse duration of 40 ns from a noise amplifier to a feedback self-oscillator at a power level of up to 10 MW has been experimentally demonstrated for the first time. In the noise-amplifier mode, the radiation power is distributed almost uniformly in a frequency range from 3 to 9 GHz. In the self-oscillator mode, the emission spectrum contains characteristic frequencies of longitudinal oscillation modes of plasma—beam cavity.

Probing NaCl at High Pressure through Optical Studies and Ab Initio Calculations

The optical constants of sodium chloride in a wide pressure range were determined from the analysis of the reflectance and transmittance spectra of a minute quantity of NaCl powder placed in diamond anvil cells. The so-called “reststrahlen band” dominates the far-infrared reflectance spectra shifting from 150 cm–1 to 500 cm–1 at 100 GPa. For the 0–17.5 GPa pressure range, measurements allow accurate determination of both transverse and longitudinal mode frequencies. Higher pressure measurements reveal the B1 → B2 structural transition around 30 GPa and provide frequencies for the transverse and longitudinal modes. This spectroscopic signature on a sample smaller than 100 μm using light of a wavelength close to this dimension was observed, thanks to the high brilliance synchrotron source. In addition, ab initio calculations performed for the 0–200 GPa range predict the TO and LO frequencies. They are validated by the excellent agreement with the experiment.

Raman Scattering in Lithium Niobate and Lithium Tantalate Single Crystals and Ceramics

We have found conditions for high-speed measurements of Raman spectra of lithium niobate and lithium tantalate single crystals and ceramics. To measure Raman spectra, we used 180° scattering geometry and a minispectrometer equipped with an array detector. The Raman spectra obtained at two distinct orientations of the single crystals relative to the excitation beam direction have been shown to have different frequencies of transverse and longitudinal optical modes. The Raman spectra of the ceramics are mainly contributed by transverse optical modes.

New effects of the electron–phonon interaction in dielectrics: (50th anniversary of the Institute of Spectroscopy, Russian Academy of Sciences)

We have studied the electron–phonon interaction (EPI) in multiferroic PrFe3(BO3)4 applying reflection methods in far-infrared (terahertz) spectral range and theoretical simulations. A specific feature of PrFe3(BO3)4 is that the 4f-electron excitation of the Pr3+ ion falls into a range between the longitudinal (LO) and transverse (TO) phonon mode frequencies. Simultaneously, inversion of the electronic oscillator occurs: its LO frequency becomes smaller than the TO frequency. With lowering temperature, a coupled electron–phonon mode emerges, and a new effect is observed: the reststrahlen band corresponding to a nondegenerate phonon mode splits. Yet another effect caused by the EPI is the appearance of a gap in the spectrum of electronic excitations of a stoichiometric rare-earth easy-axis antiferromagnet placed into an arbitrarily weak external magnetic field directed along the easy magnetization axis.