Center Wavenumber Research Articles

The propagation of transient wave packets in highly dissipative media

AbstractThe group velocity of a wave packet is defined in terms of the central wave number. Because of scale‐dependent dissipation, the central wave number migrates to lower values as transient wave packets propagate through dissipative media. The importance of this effect is greater the broader the bandwidth of the wave packet is or the more localized it is spatially. For modest localization, the migration of the central wave number significantly accelerates the vertical motion of wave packets and allows propagation to significantly greater altitudes before packets are substantially dissipated. Wave packets may experience significant attenuation due to dispersion before they begin to experience strong viscous dissipation.

Studies of spectral modification and limitations of the modified paraxial equation in laser wakefield simulations

Laser pulses propagating through plasma undergo spectral broadening through local energy exchange with driven plasma waves. For propagation distances on the order of the energy depletion length, spectral shifts can be comparable to the laser central frequency and wavenumber, a result of approximate action conservation. Here, we examine the local spectral shift, energy depletion, and action conservation of nonlinear laser pulses using the modified paraxial simulation code WAKE. Breakdown of the modified paraxial equation (MPE), which is based on the assumption of slow temporal variation of the pulse envelope, is monitored via consideration of the wave action. Although action is theoretically conserved for the continuous MPE, we observe that for large red shifts, action decays for the discrete implementation. Numerical analysis of the propagation algorithm verified the observed behavior. Increasing resolution improves action conservation up to a time, which is identified to be the validity limit for the MPE. Increased resolution also leads to increased simulation times and eliminates the strength of the MPE solver–efficiency.

Anomalous and negative reflection of Lamb waves in mode conversion

Mode conversion is an important feature of wave propagation used in ultrasonic nondestructive testing with Lamb waves. When a wave packet with a given central frequency, and a correspondent central wavenumber, impinges on the free edge of a plate, the reflected wave generally is a weighed combination of all the possible modes compatible with the given frequency. Under particular conditions, only one wave packet is reflected with a distinct central wavenumber compared to the incident one. In such a case, according to Snell's law, the reflection angle is different from the incident one (anomalous reflection). In this article, experimental results are presented on anomalous reflection on a free edge of a thin plate of a Lamb wave packet; moreover, experimental results are reported on a Lamb wave packet that is reflected at an angle lying on the same side, with respect to the normal direction, of the impinging wave (negative reflection). Negative reflection of Lamb waves has been obtained through mode conversion taking place at the free edge of a thin plate of constant thickness: More precisely, a symmetric $S1$ Lamb mode has been converted into the same mode but with phase velocity antiparallel to group velocity, so obtaining the so-called backward-propagating Lamb wave packet.

Estimation of phase shifts linked only to the coating for a dielectric mirror

The wavefront is an important characteristic for a dielectric mirror. Its measurement is usually performed with interferometers. We introduce a new method to evaluate only the coating wavefront distortion due to nonuniform thickness errors by using a reflectometer. This method uses some reflectance or transmittance maps at a wavenumber σ(m) for which the reflectance or transmittance factor variation is high. These variations are translated into some central wavenumber σ(c) variations, which enables the determination of a phase map from experimental treatment.

MicroRaman spectroscopy of diamond and graphite in Almahata Sitta and comparison with other ureilites

Abstract–This work is the first detailed study of carbon phases in the ureilite Almahata Sitta (sample #7). We present microRaman data for diamond and graphite in Almahata Sitta, seven unbrecciated ureilites, and two brecciated ureilites. Diamond in Almahata Sitta was found to be distinct from that in unbrecciated and brecciated ureilites, although diamond in unbrecciated and brecciated ureilites is indistinguishable. Almahata Sitta diamond shows a peak center range of 1318.5–1330.2 cm−1 and a full width at half maximum (FWHM) range of 6.6–17.4 cm−1, representing a shock pressure of at least 60 kbar. The actual peak shock pressure may be higher than this due to postshock annealing, if shock synthesis is the source of ureilite diamonds. Diamond in unbrecciated and brecciated ureilites have peak center wave numbers closer to terrestrial kimberlite diamond, but show a wider range of FWHM than Almahata Sitta. The larger peak shift observed in Almahata Sitta may indicate the presence of lonsdaleite. Alternatively, the lower values in brecciated ureilites may be evidence of an annealing step either following the initial diamond‐generating shock or as a consequence of heating during reconsolidation of the breccia. Graphite in Almahata Sitta shows a G‐band peak center range of 1569.1–1577.1 cm−1 and a G‐band FWHM range of 24.3–41.6 cm−1 representing a formation temperature of 990 ± 120 °C. Amorphous carbon was also found. We examine the different theories for diamond formation in ureilites, such as chemical vapor deposition and shock origin from graphite, and explore explanations for the differences between Almahata Sitta and other ureilites.

Equidistant Five Wavenumbers Selection for NIR Spectroscopy Analysis of Glucose in Human Serum

Using Fourier transform near-infrared (FTNIR) transmission spectroscopy and multiple linear regression (MLR) method of the equidistant wavenumbers combination, the quantitative analysis models of human serum glucose were established, and discrete wavenumbers combination was optimized. The optimal models were found in the five equidistant wavenumbers combinations with 7 and 40 gaps.The center wavenumber of the optimal models with 40 gaps in the first overtone region and combination region were 7970 and 5880 cm-1 respectively, and the corresponding RMSEP were 0.371 and 0.389 mmol/L respectively. While the center wavenumber of the optimal models with 7 gaps in the combination region and first overtone region were 5795 and 8041 cm-1 respectively, and the corresponding RMSEP were 0.395 and 0.407 mmol/L respectively. The above four models had a good prediction effect, and could provide basis for designing minitype special NIR spectroscopy instrument.

Theoretical Design of a Wedged Output Coupler Coated by Capacitive Strip-Grating for Optically Pumped Terahertz Lasers

An output coupler for optically pumped terahertz laser consisting of capacitive strip-grating and wedged high-resistivity silicon substrate is designed theoretically and its transmittance performance is also discussed. The etalon effects frequently occurring in previous experiments are effectively suppressed, and thus a flat and accurate transmittance spectrum is obtained in a narrow wavenumber interval of 2 cm−1 near a particular center wavenumber. Furthermore the transmittance sensitivity to the slight shift of substrate thickness is also completely eliminated. The wedged output coupler is easy to fabricate and its substrate may be used repeatedly to meet various transmittance requirements.

Dual cantilever enhanced photoacoustic detector with pulsed broadband IR-source

The cantilever enhanced photoacoustic (CEPA) trace gas detection was combined with an electrically modulated broadband infrared (EMBIR) source. The high sensitivity of the detection method was further improved by using two cantilever sensors on the opposite walls of the photoacoustic cell in order to suppress noise. Methane (CH 4) gas was used to demonstrate the sensitivity of the method yielding a detection limit of 0.5 ppm with 5 s sample integration time employing an optical filter with a center wavenumber 2950 cm −1. The achieved result is very good with a low power infrared source and enables the utilization of the benefits of such a source: low price and power consumption, easily controlled and simple electrical modulation of the radiation intensity and absence of the mechanical chopper and its noise. The structure of the source enables a relatively high pulse rate to be used as the modulating frequency. Optical filters can be used to select the wavenumber region for the selective detection of different gases.

An equality about the velocity derivative skewness in turbulence

We study velocity derivative skewness S of incompressible homogeneous isotropic turbulence. By using exact relations of isotropic turbulence and various typical models of second-order structure function DLL(r) and energy spectrum E(k), it is found that −S=C(kc/kd)2 when Taylor-microscale Reynolds number Rλ is high. Here, C is a coefficient, kc is the center wavenumber of energy dissipation spectrum, and kd is the Kolmogorov wavenumber. Therefore, the problem of Reynolds number dependence of S becomes the problem of Reynolds number dependence of kc/kd. In the inertial range, we have scaling DLL(r)∼rζ2 and E(k)∼k−(ζ2+1), ζ2 is the second-order inertial-range scaling exponent. Equality −S=C(kc/kd)2 is valid in the case of ζ2>2/3 (intermittency models of Kolmogorov’s 1962 theory) as well as in the case of ζ2=2/3 (Kolmogorov’s 1941 theory).

Eikonal simulations for the formation and the maintenance of atmospheric gravity wave spectra

The atmospheric gravity wave energy spectra often show power law dependencies with wavenumbers and frequencies. A simple mechanism involving off‐resonant scale‐separated interactions is proposed for their formation, namely the refraction of the wave packets in pseudorandom shears encountered during their vertical propagation. In the Boussinesq and rotating frame approximation the evolution of the spectral distribution of wave action is calculated within the eikonal formalism, i.e., via the simulation of the ray paths for an ensemble of elementary wave packets. The energy spectra are then easily built from the wave action spectra. Experiments are conducted where wave packets propagate away from Dirac delta function, or spectrally uniform sources at low altitudes, in realistic atmospheric background flows. The energy spectra show dependencies with the vertical wavenumber m and horizontal wavenumber k that are consistent with the most widely recognized empirical spectral models. A specific focus is given on the vertical evolution of the vertical wavenumber spectrum. The spectrum shows an invariant scaling as N2/m3 at large wavenumbers. It possesses a central wavenumber whose value depends on the total wave energy and is controlled by the statistics of the background mean flow. Similarly, the wave packet azimuths show an increasingly strong anisotropy resulting from the wave mean flow interaction at critical levels.

Dynamics of magnetostatic wave solitons in the vicinity of frequency cut-off

Nonlinear dynamics of one-dimensional pulses of exchangeless backward volume magnetostatic waves propagating in thin ferrite films with a thickness 2 l=(3–10) μm is studied numerically. The Whitham's approach of taking into account the exact wave dispersion is utilized. It has been found that in the case of small wave numbers (0.02< k 0 l⩽0.05), even under a validity of quasi-stationary approximation, a commonly used polynomial approximation for the wave dispersion gives only rough description for nonlinear pulse dynamics. The reason is a presence of cut-off at higher frequencies. For greater wave numbers ( k 0 l⩾0.1), the nonlinear wave dynamics coincides with results obtained earlier in the parabolic approximation for the wave dispersion. Two-dimensional dynamics of nonlinear pulses is also investigated briefly in the full dispersion approach. The collapse-like phenomena have been found there when the central wave number is chosen as k 0 l⩾0.04.

Atmospheric gravity wave spectra: A stochastic approach

The evolution of the spectral distribution of atmospheric gravity wave energy, pseudomomentum, and action with altitude is calculated. We apply the eikonal, or ray, formalism to the description of the off‐resonant interaction between scale‐separated waves where the wave action is projected on elementary wave packets distributed in a position‐wave number phase space. We then integrate the ray equations in random vertical shears of horizontal winds. Using stochastic theory, we derive the universal form of the energy‐spectrum dependence on the vertical wave number which results from the vertical propagation away from a stationary source. This spectrum varies with altitude and possesses the main features of observed spectra or their related empirical descriptions. An asymptotic limit at large wave number (tail) is formed for arbitrary sources, scaling as N2m−3 (where N is the Brunt‐Väisälä frequency and m is the vertical wave number). A knee in the spectrum appears at a central wave number m* as the wave field propagates upward. Whereas the tail limit remains approximatively constant, m* decreases with altitude to account for the increase of the wave energy. If, as a proxy for dissipation, we impose a complete loss of action for waves whose wave numbers are larger than a given threshold mc, there is still a large spectral range where the asymptotic limit N2m−3 remains unchanged. With such a proxy, energy and pseudomomentum deposition can be estimated from the particle statistics. This provides the first steps toward a new parameterization of the wave‐induced drag on the mean flow that is required in general circulation models.

Sequence of water thermodynamic singularities in Raman spectra

Anomalies at 0, 4, 19, 36 and 76 °C are experimentally detected in the temperature dependences of envelope widths de and central wavenumber νe of the water Raman spectrum in the wavenumber range around 3450 cm−1. The statistical two-oscillatory model relates these parameters to variations in entropy ΔS and hydrogen bond concentration Δc as Δde ∝ exp(ΔS) and Δνe ∝ Δc. The comparison of the experimental and model temperature dependences of νe and de points to the possibility of structure phase transitions in water, the hydrogen bond concentration being an order parameter. Copyright © 2000 John Wiley & Sons, Ltd.

ＡＳＴＥＲ／ＴＩＲによる海面温度推定における８．３μｍバンドの有効性とその最適中心波長の検討

An effectiveness of the 8.3 [μm] band in the ASTER/TIR (Advanced Spaceborne Thermal Emission and Reflection radiometer / Thermal Infrared Radiometer) on Sea Surface Temperature (SST) estimation is evaluated together with a re-evaluation of SST estimation accuracy for ASTER/TIR by using MODTRAN 3.7 rather than LOWTRAN 7. It is found that SST estimation error for MODTRAN 3.7 is 3 to 9 [%] better than that for LOWTRAN 7 because the atmospheric transparency of the atmospheric window bands are increased by around 2 [%] while the transparency of the water vapor absorption band is decreased by approximately 3 [%] due to the fact that the wavenumber step of MODTRAN 3.7 is better than that of LOWTRAN 7 (1 [cm-1] for MODTRAN 3.7, 5 [cm-1] for LOWTRAN 7) . Furthermore, it is found that 1.5 to 39.2 [%] of improvement on SST estimation can be achieved by adding band 10 to the rest of ASTER/TIR bands (11 to 14) . The band 10 is getting 59.3 [%] more effective on SST estimation by shifting to larger wave number by 25 [cm-1] from the current center wave number.

Solitons in media with random dispersive perturbations

A statistical approach of the propagation of solitons in media with spatially random dispersive perturbations is developed. Applying the inverse scattering transform several regimes are put into evidence which are determined by the mass and the velocity of the incoming soliton and also by the correlation length of the perturbation. Namely, the mass of the soliton is almost conserved if it is initially large. If the initial mass is too small, then the mass decays with the length of the system. The decay rate is exponential in case of a white noise perturbation, but the mass will decrease as the inverse of the square root of the length if the central wave number of the soliton lies in the tail of the spectrum of the perturbation.

Measurement of stress distribution inside crystals by multi-channel Raman scattering tomography

We have developed the method of obtaining distribution of the stress in the crystal by using a multi channel Raman scattering apparatus. It is difficult to obtain the presence of the stress from the amount of the Raman shift because it is small though the Raman-spectrum shifts by the stress. We have shown that the Raman intensity ratio on both sides (± a few cm −1) of the center wave number of the Raman spectrum was sensitive in the peak wave number shift. We developed an apparatus which measured the intensity distribution on both sides of the peak at the same time, and obtained intensity ratio distribution. The stress distribution in the neighborhood of a dislocation wall in the ZnSe crystal was obtained as an example of applying this method.

Ultraviolet Interstellar Linear Polarization. III. Features

Astro-2 has revealed a broad, weak spectral feature in the ultraviolet interstellar linear polarization for two lines of sight, confirming the original detection toward HD 197770 and adding HD 147933-4. These are the only two polarization features found in some 30 lines of sight now observed. Both features are centered close to 2175 A, the position of the ubiquitous ultraviolet extinction bump. Two possibilities are considered for the source of the polarization feature: changes in the mass distribution of the aligned silicate grains responsible for the continuum polarization, and alignment of the small graphite grains responsible for the extinction bump. While the former approach meets with some success for the HD 197770 feature, it is not possible to produce a feature as clearly peaked as in HD 147933-4. The central wavenumbers and widths of both polarization features correspond closely to those of the corresponding extinction bump. Taken together, it seems the graphite grains are a more likely source of the polarization features. Both polarization features have amplitudes that are very small compared to the amount of excess extinction present in the 2175 A bump, implying poor polarization efficiency. Many other lines of sight have been observed with sufficient signal-to-noise ratios such that features should have been clearly detected if the same polarization efficiency applied, and so real variations in the alignment or shape of the grains responsible seem to occur from one line of sight to another. The weak alignment might be caused by unusually low concentrations of paramagnetic impurities in rapidly spinning small grains.

Fourier Transform Infrared Spectrum and Rotational Structure of the A-Type 730 cm −1 Band of p-Fluorotoluene

Fourier transform infrared spectrum of the A-type 730 cm −1 band of p-fluorotoluene recorded in the region 716 to 744 cm −1 with a resolution of 0.002 cm −1 has been analyzed using Watson′s A-reduction Hamiltonian in the I r representation. The upper state (ν = 1) rotational and centrifugal distortion constants and the center wavenumber of the band have been obtained by the least-squares fit of 935 rovibrational transitions for the m = 0 state of the methyl rotor (ν 6 = 4.77 cm −1). The maximum J and K a values were 41 and 21, respectively; the inclusion of transitions with higher K a values did not affect the fitted constants. The values are compared with the ones obtained earlier for the C-type 819 cm −1 band of p-fluorotoluene.

Ground‐based remote sensing of methane height profiles with a tunable diode laser heterodyne spectrometer

Height distributions of methane in the troposphere and stratosphere were derived from high resolution absorption spectra observed with a ground‐based tunable diode laser heterodyne spectrometer. The center wavenumber of the measured methane absorption line is 1223.1561 cm−1. In the retrieval of methane height profiles, a volume mixing ratio of methane was assumed to have a constant value in the troposphere and to decrease with a constant rate in the stratosphere. The tropospheric mixing ratio and the decreasing rate in stratosphere were derived to be 1.7±0.1 ppmv and −0.06 ppmv/km, respectively, for measurements at Tsukuba (36.0°N, 140.1°E) on December 17 and 20, 1991.

A stochastic approach to the theory of nonlinear wave trains near marginal stability

By employing the turbulent theoretical approach of Alber, Davidson and Roy and Bhakta the dynamical evolution of the wave spectrum of nonlinear wavetrains near marginal stability is derived, starting from a derivative nonlinear Schrödinger equation, extended with a quintic nonlinearity, called the EDNLS-equation. The stability of three homogeneous background spectral densities (the delta-, the normal- and the uniform distribution), is investigated in the linear regime. The most important findings in that respect as as follows: First, the delta-distribution instability criterion deviates by a numerical factor from the one presented in Flå and Wyller for the modulational instability in the EDNLS-equation. Secondly, the growth rate of this instability result in the limit of small, but finite spectral width limit is equivalent with the turbulence theory result based on the derivative nonlinear Schrödinger equation up to modulo translation in the central wave number.