Vacuum Wavenumber Research Articles

Investigation of phase modulation and propagation-route effect from unmatched large-scale structures for Doppler reflectometry measurement through 2D full-wave modeling

To interpret the common symmetric peaks caused by the large-scale structure in the complex S(f) spectrum from the heterodyne Doppler reflectometry (DR) measurement in EAST, a 2D circular-shaped O-mode full-wave model based on the finite-difference time-domain method is built. The scattering characteristics and the influences on the DR signal from various scales are investigated. When the structure is located around the cutoff layer, a moving radial or poloidal large-scale structure k θ ≲ k θ,match (k θ,match is the theoretic wavenumber of Bragg scattering) could both generate an oscillation phase term called ‘phase modulation’, and symmetrical peaks in the complex S(f) spectrum. It was found that the image-rejection ratio A −1/A +1 (A ±1 represents the amplitudes of ±1 order modulation peaks) could be a feasible indicator for experiment comparison. In the case when the structure is near the cutoff layer with the same arrangement as the experiment for the edge DR channel, the curve of A −1/A +1 versus k θ can be divided into three regions, weak asymmetrical range with k θ /k 0 ≲ 0.15 (k 0 is the vacuum wavenumber), harmonics range with 0.15 ≲ k θ /k 0 ≲ 0.4, and Bragg scattering range of 0.4 ≲ k θ /k 0 ≲ 0.7. In the case when the structure is located away from the cutoff layer, the final complex S(f) spectrum is the simple superimposing of modulation and Bragg scattering, and the modulation peaks have an amplitude response nearly proportional to the local density fluctuation, called the ‘propagation-route effect’. Under the H-mode experiment arrangement for the core DR, a critical fluctuation amplitude ∼ 1.3–4.1 ( refers to the pedestal large-scale structure amplitude and Amp(n e,Tur.@MSA) refers to turbulence amplitude at the main scattering area) is needed for the structure in the pedestal to be observed by the core DR measurement. The simulations are well consistent with the experimental results. These effects need to be carefully considered during the DR signal analyses as the injecting beam passes through the plasma region with large-scale structures.

Information system for molecular spectroscopy: 6—systematization of spectral data on deutero-substituted isotopologues of the hydrogen sulfide molecule

Properties of data published on the spectral line parameters for deutero-substituted isotopologues of the hydrogen sulfide molecule (HDS, HD34S, D2S, and D2 34S) are described. Most properties follow from the results of vacuum wavenumber quality analysis. Two applications used for the data quality analysis in W@DIS information system are described. The results of computer-based data quality analysis of vacuum wavenumbers are completed by the expert evaluation of the quality of the same data set. The rotation-vibrational transitions and energy levels of deutero-substituted isotopologues of the hydrogen sulfide molecule are imported into the database; their properties are collected in the knowledge base and available in the W@DIS information system (http://wadis.saga.iao.ru/).

An Algorithm For Computation Of Diatomic Spectra

In principle, an atomic or molecular spectrum would be computed as follows: Upper and lower Hamiltonians would be enumerated in a complete basis, and numerically diagonalized to give the upper and lower energy eigenvalues and eigenvectors. The transition moments for the appropriate operator, e.g., the electric dipole transition moments, would be evaluated from the eigenvectors. The vacuum wavenumbers , i.e., energy eigenvalue differences, would be found for all non-vanishing transition moments. And the line strengths for each spectral line of wavenumber would be determined as sum of the squares of the transition moments over all transitions producing the same . A line list that includes line strengths would be generated by repeating the above computations over the required range of upper and lower total angular momentum quantum numbers. The spectrum from min to max would be separated into a number of pixels, subsequently, the contribution of each line to each pixel is calculated using the line list. We show how this algorithm can be implemented for a diatomic spectrum if the required molecular parameters are available.

Material parameters and microwave properties of a magnetic photonic crystal

Exact dispersion relations are obtained for the main directions of the external magnetic field and the periodicity axis of the magnetic-dielectric structure relative to the propagation direction of eigenwaves. Expressions for the effective permittivity and permeability are obtained within the thin-layer approach. Dependences of the effective permittivity on the layer permeability and effective permeability on the layer permittivity are obtained with corrections proportional to the square of the vacuum wavenumber k02. Microwave properties of the structure are described within the approximation under consideration.

Comparison of the HITRAN and GEISA spectral databases taking into account the restriction on publication of spectral data

It is justified that publication of spectral data should be restricted with respect to expert spectral databases, and restrictions on vacuum wavenumbers used to decompose the information recourses according to the primary published data are described. It is shown that parts of the HITRAN and GEISA expert databases concerning water molecule isotopologues contain outdated data (with inaccurate vacuum wavenumbers).

Molecular Iodine Fluorescence Spectra Generated with Helium-Neon Lasers for Spectrometer Calibration

Gas-phase molecular iodine laser-induced fluorescence (LIF) spectra were recorded out to 815 nm at 1 cm(-1) resolution using green, yellow, and red helium-neon (HeNe) lasers as excitation sources. Nine previously unreported I(2) B←X absorption transitions accessed by these lasers were identified, and specific rovibronic transition assignments were made for two hundred LIF peaks--more than sixty per laser. These I(2) LIF peaks can be used to calibrate the vacuum wavenumber coordinate of spectrometers to better than 0.1 cm(-1) accuracy. In particular, green HeNe excitation of the I(2) R(106) 28-0 transition leads to strong fluorescence well suited for calibration, with a rotational doublet spacing of 15 cm(-1) and a doublet-to-doublet spacing of 190 cm(-1). Calibration by HeNe I(2) LIF may be an especially valuable technique for Raman spectroscopy applications.

Experimental investigation of standing wave interactions with a magnetized plasma in a minimum-B field

Standing waves in the microwave regime are generated by a superposition of forward and backward moving waves induced by reflections from geometrical transitions in the plasma vacuum boundary. The waves are preferentially damped in the weakly collisional (νen∕ω≅10−4) plasma near the launch region (∼3−15cm), where the electron temperature has a higher than average value (Te>Teavg∼12eV). Typical e-folding damping lengths are of the order of 10cm, and depend upon the wave power and plasma collisionality. Fourier spectrum of the standing waves indicates about 23% downshift in the vacuum wave-number due to plasma dispersion. Electron trapping is observed in the potential troughs of the waves.

Standard Reference Material 2036 Near-Infrared Reflection Wavelength Standard

Standard Reference Material 2036 (SRM 2036) is a certified transfer standard intended for the verification and calibration of the wavelength/wavenumber scale of near-infrared (NIR) spectrometers operating in diffuse or trans-reflectance mode. SRM 2036 Near-Infrared Wavelength/Wavenumber Reflection Standard is a combination of a rare earth oxide glass of a composition similar to that of SRM 2035 Near-Infrared Transmission Wavelength/Wavenumber Standard and SRM 2065 Ultraviolet-Visible-Near-Infrared Transmission Wavelength/Wavenumber Standard, but is in physical contact with a piece of sintered poly(tetrafluoroethylene) (PTFE). The combination of glass contacted with a nearly ideal diffusely reflecting backing provides reflection-absorption bands that range from 15% R to 40% R. SRM 2036 is certified for the 10% band fraction air wavelength centroid location, (10%)B, of seven bands spanning the spectral region from 975 nm to 1946 nm. It is also certified for the vacuum wavenumber (10%)B of the same seven bands in the spectral region from 10 300 cm(-1) to 5130 cm(-1) at 8 cm(-1) resolution. Informational values are provided for the locations of thirteen additional bands from 334 nm to 804 nm.

Unidirectional lasing from a microcavity with a rounded isosceles triangle shape

We report that unidirectional lasing emission can be generated from a rounded isosceles triangular microcavity within a low nkD range, where n is the refractive index, k is the vacuum wave number, and D is the characteristic size of the microcavity. It is shown that unidirectional resonance modes have relatively high-Q values and in a nonlinear dynamic model appear as stationary lasing solutions with a low threshold. The formation of a whispering-gallery-type pattern along the rounded part on the symmetry axis is responsible for the unidirectionality of the resonances.

Resonance patterns in a stadium-shaped microcavity

We investigate resonance patterns in a stadium-shaped microcavity around ${n}_{c}kR\ensuremath{\simeq}10$, where ${n}_{c}$ is the refractive index, $k$ the vacuum wave number, and $R$ the radius of the circular part of the cavity. We find that the patterns of high-$Q$ resonances can be classified, even though the classical dynamics of the stadium system is chaotic. The patterns of the high-$Q$ resonances are consistent with ray dynamical considerations and appear as stationary lasing modes with low pumping rate in a nonlinear dynamical model. All resonance patterns are presented in a finite range of $kR$.

Argon I lines produced in a hollow cathode source, 332 nm to 5865 nm

We report precision measurements by Fourier transform spectroscopy of the vacuum wavenumber, line width, and relative signal strength of 928 lines in the Ar I spectrum. Wavelength in air and classification of the transition are supplied for each line. A comparison of our results with other precision measurements illustrates the sensitivity of Ar I wavelengths to conditions in the light source.

Attached and radiated electromagnetic fields of an electric point dipole

The standard dyadic Green function description of the electromagnetic field generated by an electric point dipole is modified (and corrected) so that a rigorous classical theory for the attached and radiated parts of the near field appears. The present propagator formalism follows from analysis of the transverse and longitudinal dipole electrodynamics. Elimination of both the transverse and the longitudinal self-fields leads to a description of the radiated dipole field that enables one to obtain the associated energy flux in the near- and mid-field zones also and that is correctly retarded (with the vacuum speed of light) everywhere in space. The related retarded transverse propagator exists in the time (space) domain, whereas the standard propagator exists only in the frequency (space) domain. As a forerunner to an analysis of the Weyl expansions for the standard, longitudinal self-field and retarded transverse propagators, the plane-wave mode expansions of these propagators are investigated, and contour integrations are specified in such a manner that the rigorous Green function description is regained. It is found that, in order for the retarded transverse propagator description to be consistent in the near-field zone, the Weyl expansion for this propagator has to contain evanescent components not only for wave numbers larger than the vacuum wave number but in the entire angular spectrum. The present theory may influence our view of optical near-field phenomena and (classical) photon tunneling because in both of these fields a proper identification of attached and radiated fields seems needed.

Absolute wave-number measurement of CsD2 resonance line

The absolute wave-number of light from a grating cavity semiconductor laser in resonance at 852 nm with saturated absorption spectra of the first resonance line D2, 62S1/2 → 62P3/2 of atomic 133Cs has been measured with a plane Fabry-Perot interferometer. The vacuum wave-number, after correction for the refractivity of air, was found to be 11 732,3084(3) cm-1. Comparison is made with earlier measurements, and the implications of the result for fundamental constant and gravitational acceleration determination with laser-cooled atoms are discussed.

Molecular optics approach to electromagnetic wave interactions with stratified media

The problem of electromagnetic wave interaction with a stratified dielectric medium is solved in the framework of molecular optics, leading to a new derivation for the refraction and reflection laws at stratified media interfaces. In addition, the solution confirms the Lorentz–Lorenz refractive index formula characterizing the transverse propagation modes and the characteristic frequencies associated with the longitudinal mode. The analytic results presented in this study support the existence of another longitudinal mode propagating with the vacuum wave number within the medium, and they provide a new concept for the Ewald–Oseen extinction theorem. Other new results of this study are that (1) the relation between Fresnel horizontal and vertical reflection coefficients and the relation between the corresponding transmission coefficients are revealed and (2) a new concept is presented for the Brewster angle, and (3) the concept is introduced of multiple reflections in formulating the reflection coefficient at the interface between two different dielectric materials.

The scattering phase shift due to Bragg resonance in one-dimensional fluctuation reflectometry

An explicit integral representation is derived for the tangent of the phase shift due to one-dimensional (1D) scattering of an S-polarized, O-mode, electromagnetic field from a localized wavepacket sitting on top of an inhomogeneous plasma. A Green function technique is used in the derivation together with the Born approximation. The integral representation is evaluated using asymptotic techniques and Bragg resonance is seen to be the dominant mechanism producing the phase shifts due to fluctuations with wavelengths that are short compared to the Airy length. By suitably normalizing the governing differential equation, we have identified the two dominant parameters that control the approximations in our analysis. These are delta n/n0 and kf. The first is the magnitude of the maximum density fluctuation multiplied by the square of the dimensionless length scale that characterizes both the background plasma density profile (with scalelength L) and the incoming microwave field (with vacuum wavenumber k0): delta n/n0 identical to ( delta n/n0)*(k0L)23/. The second is the fluctuation wavenumber normalized to k0 and scaled by the similarly normalized Airy wavenumber: kf identical to (kf/k0)*(k0L)13/. The Born approximation is expected to be valid as long as delta n/n0<1, and the Bragg resonance picture dominates as long as kf>1.

High-resolution spectroscopy of the A 1Π u−X 1Σ +g (6, 1) band in N 2+2

Resonances in the photodissociation spectrum of N 2+ 2 have been further experimentally investigated using a fast ion beam in combination with high-resolution laser spectroscopy. A number of resonances in the photofragmentation cross section belonging to the Q branch of the (6, 1) band of the A 1Π u−X 1Σ + g transition has been recorded. Vacuum wavenumbers of this band as well as molecular constants of the upper state are presented here. Two of the lines of the (6, 1) transition were found to deviate some tenths of a wavenumber from their expected positions, indicating some possible weak perturbation.

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Vacuum wavenumbers of rotational lines with detailed band analysis for excited electronic states of H 35Cl 1

In the present work, rotational assignments and measured line positions are presented for 120 band systems of H 35Cl with 0 ≤ v′ ≤ 2 for Rydberg states, 3 ≤ v′ ≤ 32 for the V 1Σ +(0 +) valence state, and all transitions originating from X 1Σ +(0 +) v″ = 0. Considerable success is made in characterizing the f 3Δ i (3, 2, 1) and i 3Δ i (3, 2, 1) Rydberg states. The line positions of H 37Cl have not been included explicitly, only the magnitude of isotope shifts near the band origins. The line positions of D 35Cl are included for transitions through the v′ = 0 level of the E 1Σ +(0 +) state. The angular momentum and rotational level assignments for the excited electronic state are determined by assessing ground state combination differences for each observed band. In most case, the Ω′ values are established from the first few lines of the various branches. Isotope separation between H 35Cl and H 37Cl assists in providing the vibrational numbering and interstate perturbations.

Waveguide mode deformation in free-electron lasers

The free-electron laser (FEL)-induced modifications to the vacuum waveguide modes are calculated for low-frequency FEL’s. Typically, the mode modifications are large and exhibit complicated axial behaviors. In addition to the wave component with a near vacuum wavenumber, components at two upshifted wavenumbers must be analyzed. Electron beam surface charges and currents are also important. At low gain, effects from all three roots of the FEL dispersion relation must be included. The dominant modification is due to the electron beam space-charge wave.

Full-wave calculations of the O-X mode conversion process

A two-point boundary-value problem has been formulated that describes the conversion between ordinary (O) and extraordinary (X) wave modes in a cold inhomogeneous plasma. Numerical solutions to this problem have been obtained for various values of the WKB parameter k0L; where k0 is the vacuum wavenumber and L the density-gradient scale length. The results are compared with three different theoretical expressions for the O-X mode conversion efficiency derived by others in the WKB limit of k0 L ≫ l. Most of the results presented in this paper are obtained for a collisionless plasma with finite density near the plasma cut-off density. However, some examples are also given of wave propagation from vacuum. In these examples, collision effects are added to the equations in order to remove the singularity otherwise present at the position of the upper hybrid resonance layer.

Absolute frequencies of lasing transitions in nine CO&amp;lt;inf&amp;gt;2&amp;lt;/inf&amp;gt;isotopic species

The band centers, rotational constants, absolute frequencies, and vacuum wavenumbers for12C16O 2 ,13C16O 2 ,12C18O 2 ,13C18O 2 ,12C16O18O,14C16O 2 , and14C18O 2 have been simultaneously computed from 590 beat frequency measurements between pairs of adjacent 00\deg1-[10\deg0,02\deg0] I and II band CO 2 laser transitions. The input data included the 56 beat frequencies measured between adjacent12C16O 2 rotational lines by Petersen et al. The absolute frequencies are directly related to the cesium frequency standard via the 29 442 483.315 (0.025) MHz 10.18 μm I-R (30) and the 32 134 266.891 (0.024) MHz 9.33 μm II-R(10) transitions in12C16O 2 which were measured by Evenson et al. The results described in this paper will provide the means for setting up easily reproducible secondary frequency standards in the 8.9-12.3 \mu m wavelength band.