Single-pulse nuclear echo signals in magnetically ordered media

An analytical expression for the amplitude of a single-pulse nuclear echo signal generated in magnetically ordered materials is obtained taking into account the inhomogeneous broadening of the spectroscopic transition and the inhomogeneous distribution of the gain with an average value of greater than unity. It is shown that, in this signal, summation of the oscillations of nuclear magnetic moments with equal amplitudes and phases occurs at each instant of time. The cause of the effective suppression of the nuclear magnetic moment oscillations in the initial portion of the free precession signal is revealed analytically. The dependence of the amplitude of the one-pulse echo signal on the strength of an external alternating magnetic field, the pulse duration, and the width of the gain distribution is determined. The results obtained are compared with the experimental data for a Co₂MnSi ferromagnetic polycrystalline sample.     

Pulsed nuclear magnetic resonance signals in magnetically ordered materials

We have obtained an analytical expression for nuclear precession and nuclear echo signals generated in magnetically ordered materials upon resonant excitation of the nuclear subsystem by two pulses of identical amplitude but different durations. We show that in a nuclear subsystem with inhomogeneous broadening of the spectroscopic transition and an inhomogeneous gain distribution, the two-pulse precession and echo signals are split into four and nine components respectively. We have analytically established a correlation between the macroscopic parameters of the components of the two-pulse signals (relative amplitudes, signal formation times) and the microscopic parameters of the magnetically ordered media (inhomogeneous half-width of the spectral line, half-width of the gain distribution function, average gain). The theoretically calculated formation times for the components of the nuclear precession and nuclear echo signals agree with the experimental data obtained for the alloy FeNiCo (70% Co). __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 4, pp. 529–538, July–August, 2008.     

Resonant excitation of single-pulse nuclear spin echo in magnetically ordered media

An analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of the spectroscopic transition and non-uniform distribution of the enhancement factor. The signal has been shown to result from superimposing the nuclear magnetic moment oscillations of the same amplitude and phase that arise upon termination of a radio-frequency pulse. The cause for the effective suppression of oscillations of nuclear magnetic moments in the initial phase of the free precession signal has been determined analytically. The single-pulse echo signal amplitude has been found as a function of the external variable magnetic field strength, the exciting pulse duration, the inhomogeneous NMR line broadening, and the distribution width of the enhancement factor. The results have been compared with experimental data observed in a Co₂MnSi ferromagnetic polycrystalline sample. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 387–394, May–June, 2009.     

Selective saturation in strongly inhomogeneous magnetic fields

The possibility to produce selective saturation by nuclear magnetic resonance (NMR) sequences of low-power radio-frequency pulses in strongly inhomogeneous magnetic fields is explored. The saturation of parts of the sensitive volume is produced by a particular pulse sequence with reduced amplitude distribution and the spectrum of the recorded signal is compared with the simulated spectrum. The spectra of the recorded free induction decays and echo signals are in good agreement with the simulated spectra of the pulse sequence, which demonstrates the effect of the selective saturation. The results obtained are an important step towards the development of new mobile and lowpower NMR equipments operating with inhomogeneous magnetic fields.     

Secondary Nuclear Spin Echo Signals in Thin Yttrium Iron Ferrite Garnet Films

The results are presented of experimental and theoretical study of the phenomenon of secondary nuclear spin echo in magnetically ordered materials in which the formation of additional echo signals is due to dynamic hyperfine coupling. Numerical simulation of the effect of the amplitude (ω1) and the durations of the first (t1) and the second (t2) exciting pulses on the echo signals is performed. It is found that the maximum amplitude of the secondary echo is formed under the conditions ω1t1 = 0.5π and ω1t2 ≈ 0.6π. It is shown that secondary echo signals can be observed upon inhomogeneous excitation of the spectral line ω1 ≤ Δω, where Δω is the inhomogeneous spectral line width. At a temperature of T = 4.2 K, additional double-pulse spin 3τ-echo signals from iron nuclei are experimentally observed in an epitaxial yttrium ferrite garnet film enriched with 57Fe magnetic isotope to 96%. The experimentally observed phase relationships between the primary and secondary echo signals, as well as the dependence of the echo signal amplitude on the amplitude and duration of the exciting pulses, are in good agreement with the results of numerical simulation of the dynamics of nuclear magnetization with regard to the dynamic hyperfine coupling. It is shown that the secondary echo exhibits the effect of spectral line narrowing, and the amplitude of the secondary echo is proportional to the nuclear magnetic resonance (NMR) enhancement factor in magnets, η. In the case of 57Fe NMR in an yttrium iron garnet (YIG) film, the amplitude of the 3τ-echo is two to three orders of magnitude smaller than the amplitude of the primary 2τ-echo, which corresponds to η ≈ 440. The detection of weak secondary echo signals proves to be possible due to the use of a phase-coherent NMR spectrometer with digital quadrature detection at the carrier frequency and signal accumulation.     

Effect of the Excitation Radiation Coherence on Oscillations of the Photon Echo Intensity

The physical reasons for observing the splitting of optical lines several orders of magnitude smaller than the spectral width of a laser pulse are investigated. A theory of coherent and incoherent photon echo (PE) in an external static magnetic field and in the presence of a pulsed magnetic field, which causes oscillations of the PE intensity, is elaborated. It is shown that the periods of oscillations in the echo intensity, the echo duration, and the dimensions of the regions in the inhomogeneous line, where the excited ions are coherent, do not depend on the degree of coherence of the laser pulse and on the external static magnetic field. As follows from the theory, in the case of the coherent excitation of the echo, the amplitude of the intensity oscillations is independent of the external static magnetic field if the inhomogeneous line is symmetric. It is shown that the amplitude of the oscillations at the incoherent excitation of the echo is equal to the autocorrelation function of the distribution function of the transition frequency along the inhomogeneous line with the argument equal to the Zeeman splitting of the optical line in the external magnetic field. In this case, the experimental values of the oscillation amplitude are in good agreement with the calculated values of the autocorrelation function for the total inhomogeneous line in LuLiF₄:Er³⁺ (⁴I_15/2?F_9/2 transition). In the same way, the autocorrelation function has been obtained for YLiF₄:Er³⁺ on the same transition.     

The nutation spin echo and its use for localized NMR

A suitably matched combination of unidirectional gradient pulses of the radio frequency amplitude B(1) and of the main magnetic field B(0) produces an unconventional type of spin echo, the nutation echo. The echo signal becomes volume selective if the gradients to be matched are inhomogeneously distributed in space. An example is a combination of a constant B(0) gradient and the inhomogeneous B(1) gradient of a surface coil. We suggest a method for localized NMR on this basis. Nutation echoes can also be used to map the spatial distribution of B(1) gradients of an arbitrary radio frequency coil geometry with the aid of a small probe sample. Copyright 2000 Academic Press.     

Beatings in the Spin Echo Signal in Media Having a Doublet Structure of the Spectrum

We have obtained an analytical expression for the twopulse echo signal arising in nonresonant excitation of a condensed medium with a nonuniformly broadened spectrum of doublet structure by two pulses of an electromagnetic field of different durations and of the same amplitude. It is shown that in the case where the differences between the carrying frequency of exciting pulses and the central frequencies of the spectral lines differ considerably, beatings are formed in the signal of the twopulse echo. The rate of decay of the amplitude of these beatings is found to depend only on the time of reversible and irreversible relaxation, and their circular frequency is determined by the shift of the spectral lines relative to each other. A technique for separate determination of the inhomogeneous width of the lines and time of the irreversible transverse relaxation is suggested which is based on the analysis of the twopulse echo signal beatings.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Effects of inhomogeneous distribution of Si–Nc and Er ions on optical amplification in Si–Nc Er doped fiber

In this article, the effects of Si–Nc and Er³⁺ ions distribution parameters including inhomogeneous and homogeneous distribution profile are studied on the optical parameters such as gain, population inversion and Si–Nc induced losses. We have shown that by increasing of the concentration of Si–Nc particles the net gain and induced Si–Nc losses increased in homogeneous and inhomogeneous distributions. In practice, the homogeneous distribution of Er ions and Si–Nc is hard to be realized. Therefore, the inhomogeneous distributions of ions cased to perturb state in mode shape of optical signal then the investigations of those effects are important for high speed optical communications. In this article, a method for evaluation of the effects of inhomogeneous distribution of impurities on performance of optical amplifier is developed and the managing of the gain with use of suitable distribution functions is proposed.     

Foliage echoes: a probe into the ecological acoustics of bat echolocation

The research reported here aims at understanding the biosonar system of bats based on the properties of its natural inputs (ecological acoustics). Echoes from foliages are studied as examples of ubiquitous, natural targets. The echo properties and their qualitative relationship to plant architecture are described. The echoes were found to be profoundly stochastic and in general neither Gaussian nor stationary. Consequently, features useful for discrimination of such target classes will be confined to estimated random process parameters. Several such statistical signal features which are sufficiently invariant to allow a classification of the used example plants were identified: the characteristic exponent and the dispersion of an alpha-stable model for the amplitude distribution, a crest factor defined as the ratio of maximum squared amplitude and signal energy, the dispersion of the first threshold passage distribution, the structure of the correlation matrix, and a nonstationarity in sound channel gain. Discrimination error probability could be reduced by combining features pairwise. The best combination was the crest factor and the correlation coefficient of a log-linear model of the time-variant sound channel gain; it yielded an estimated Bayes risk of 6.9% for data pooled from different views.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.     

Estimation of efficiency of vertical antenna arrays in underwater sound channels

The gain of the vertical antenna array in a randomly inhomogeneous ocean waveguide is numerically simulated on the assumption that the useful signal is generated by a finite set of mutually uncorrelated discrete spectrum modes and is received against the ocean noise background. It is shown that the choice of themost effective weight distribution of the array and the thus obtained gain strongly depend on both the modal spectra of the signal and noise and the number and position of the receiving elements in the channel. The critical factor is the mutual orthogonality of the waveguide modes at the array input, which indicates the possibility of specially arranging the elements for the known (expected) mode spectrum of the signal.     

NMR-microscopy with TrueFISP at 11.75T

The purpose of this paper is to demonstrate that a fully balanced gradient echo technique (TrueFISP) can be used for microscopic experiments at high static magnetic field strengths. TrueFISP experiments were successfully performed on homogeneous and inhomogeneous objects at 11.75T. High-resolution TrueFISP images were obtained from phantoms, plants, formalin-fixed samples, and from an isolated beating rat heart with an in-plane resolution of 78 micro m and a slice thickness of 500 micro m. The signal-to-noise ratio (SNR) gain of TrueFISP compared to conventional gradient echo or spin echo sequences will allow faster acquisition times or an improvement in spatial resolution for microscopic experiments.     

Multipower spectrum of small-scale ionospheric turbulence

We consider the problem of diagnostics of the local structure of small-scale ionospheric turbulence using the multifractal analysis of received signals from the Earth’s orbital satellites after the radio sounding of the inhomogeneous ionosphere by these signals. In particular, it is shown that analysis of the multifractal structure of the received-signal amplitude records by the method of multidimensional structural functions allows one to determine the indices of the multipower local spectra of the small-scale ionospheric turbulence, which are inherent in it due to the nonuniform spatial distribution of small-scale fluctuations of the electron number density. It is noted that information on the multipower spectrum of small-scale ionospheric turbulence is not available for the conventional radio scintillation method based on the classical spectral analysis of received signals during the remote radio sounding of the ionosphere. At the same time, the method of multidimensional structural functions is efficient under conditions of actual nonstationarity of the process of scattering of the HF radio waves by the randomly inhomogeneous ionospheric plasma. The method of multidimensional structural functions is used for the multifractal processing of received signals of orbital satellites during special experiments on radio sounding of the midlatitude ionosphere under natural conditions and its modification by high-power HF radio waves. First data on the indices of the multipower local spectra of small-scale ionospheric turbulence are obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 1, pp. 14–22, January 2009.     

Photon Echo from Localized Excitons in Semiconductor Nanostructures

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

Investigation of gain recovery for InAs/GaAs quantum dot semiconductor optical amplifiers by rate equation simulation

The gain recoveries in quantum dot semiconductor optical amplifiers (QD SOAs) are numerically studied by rate equation simulation. Similar to the optical pump-probe experiment, the injection of double 150 fs optical pulses is used to simulate the gain recovery of a weak continuous signal under different injection levels, inhomogeneous broadenings, detuning wavelengths, and pulse signal energies for the QD SOAs. The obtained gain recoveries are then fitted by a response function with multiple exponential terms to determine the response times. The gain recovery can be described by three exponential terms with the time constants, which can be explained as carrier relaxation from the excited state to the ground state, carrier captured by the excited state from the wetting layer, and the supply of the wetting layer carriers. The fitted lifetimes decrease with the increase of the injection currents under gain unsaturation, slightly decrease with the decrease of inhomogeneous broadening of QDs, and increase with the increase of detuning wavelength between continuous signal and pulse signal and the increase of the pulse energy.