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).     

Exceptionally narrow homogeneous linewidth in erbium-doped glasses

We show that rare-earth (RE-) doped glasses can have homogeneous linewidths as narrow as 287 kHz at (4)He temperatures. This is far narrower than others reported in glasses in the same temperature range and is suitable for precise spectral hole burning and spatial-spectral holographic applications. It is known that cw spectral hole burning linewidth measurements of RE ions in glasses are hindered by the presence of spectral diffusion but, even in glasses, application of a magnetic field can freeze out RE spin-spin interactions responsible for spectral diffusion and isolate the remaining contribution of two-level systems (TLSs). The Er(3+):2G2S glasses have unusually low TLS contributions, making it possible to study the real homogeneous linewidth using photon echo measurements. The contribution from TLSs is only 170 T(1.3) kHz when subjected to a field of 5 T.     

Effect of magnetic field on tunneling systems in glasses

The effect of a magnetic field on two-level tunneling systems in dielectric glasses originates from the magnetic-field-induced rotation of nuclear spins and the ensuing rearrangement of ordered regions (clusters) in the glass structure. This process accounts for the observed variation of both the spontaneous-polarization echo amplitude and the dielectric constant in a magnetic field at low temperatures. The proposed theory is compared with experiment.     

Evidence for magnetic field induced changes of the phase of tunneling states: spontaneous echoes in (KBr)(1-x)(KCN)(x) in magnetic fields

Recently it was discovered that, in contrast to expectations, the low-temperature dielectric properties of some multicomponent glasses depend strongly on magnetic fields. The low-temperature dielectric response of these materials is governed by atomic tunneling systems. We now have investigated the influence of magnetic fields on the coherent properties of atomic tunneling states in a crystalline host in two-pulse echo experiments. As in glasses, we observe a very strong magnetic field dependence of the echo amplitude. Moreover, for the first time we have direct evidence that the magnetic fields change the phase of coherent tunneling systems.     

Low-temperature photon echo study of 2-MTHF glass under high pressure

A high-pressure photon echo study of the low-temperature dynamics of rhodamine 640 in a 2-methyltetrahydrofuran (2-MTHF) molecular glass is reported. High pressure is found to decrease the homogeneous dephasing rate comparably to the volume compression ratio. The pressured-induced line narrowing is also qualitatively similar to high-pressure hole burning results reported for a 2-MTHF glass doped with bacteriochlorophyll a. The results are consistent with a pressure-induced decrease in the number of tunneling two-level systems (TLSs) that may be associated with collapsible void space in the molecular glass. Comparable high-pressure photon echo studies of organic polymer glasses over the same low-temperature range do not show line narrowing at high pressure, suggesting an intrinsic difference in the nature of TLSs for molecular versus polymer glasses.     

Novel isotope effects observed in polarization echo experiments in glasses

In recent years unexpected magnetic field effects have been observed in dielectric measurements on insulating glasses at very low temperatures. Polarization echo experiments have indicated that atomic tunneling systems are responsible for these effects and that the nuclear properties of the tunneling particles are of importance. Subsequently, it was suggested that the magnetic field effects are caused by tunneling systems carrying a nuclear quadrupole moment. Now we have studied the isotope effect in echo experiments on fully deuterated and ordinary glycerol clearly showing the crucial role of the nuclear quadrupole moments for the magnetic field effects. In addition, we have observed a new effect in the decay of spontaneous echoes in zero magnetic field for the deuterated samples which can be explained in terms of a quantum beating involving the quadrupole levels.     

Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF4:Er3+ and YLiF4:Er3+

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF₄:Er³⁺ and YLiF₄:Er³⁺. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment ?? and makes it possible to determine the difference of the g factors of the ground and excited ⁴ F _9/2(I) states of the Er³⁺ ion in the LuLiF₄ the YLiF₄ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.     

Oscillations of the photon echo intensity in a pulsed magnetic field: Zeeman splitting in LiLuF<Subscript>4</Subscript>:Er<Superscript>3+</Superscript>

A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF₄:Er³⁺ and LiYF₄:Er³⁺. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ～2 G at a duration of 30 ns. The Zeeman splitting in this field is ～10 MHz, which is much less than the laser spectral width (0.15 Å ～ 9 GHz). The g factor of the ⁴ F _9/2(I) excited state of the Er³⁺ ion in the LiLuF₄ matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.     

Electric dipole echo in solid solutions

A theory of microwave electric dipole echo in solid solutions is formulated in the example of (KBr)_1–x(KCN)_x. The behavior of the echo is attributed to tunneling CN^– molecules, which are treated as analogs of two-level systems in glasses. A concentration-dependent density of states of the two-level system is used in the calculations. The difference between the behavior of the echo signal in solid solutions and the behavior of the echo in glasses and spin systems is indicated. New echo signals associated with asymmetry of the double-well potential are found.Branch of the Institute of Solid-State and Semiconductor Physics, Academy of Sciences of Belarus, Vitebsk. Physicotechnical Institute, Kazan Science Center, Russian Academy of Sciences, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 49–58, July, 1993.     

Magnetic Field Dependent Tunneling of Atoms and Molecules in Non-Magnetic Disordered Solids

The low-temperature properties of disordered solids, such as glasses or crystals with certain substitutional defects are governed by atomic tunneling systems. Until recently it was believed that the dielectric properties of insulating materials devoid of magnetic impurities should not—or only very weakly—depend on external magnetic fields. In contrast, new experiments on glasses and crystalline defect systems show a pronounced magnetic field dependence of the dielectric properties of such materials at ultra-low temperatures. In particular, the low-frequency dielectric susceptibility and the amplitude of polarization echoes appear to be strongly affected by magnetic fields. These very surprising findings clearly indicate that atomic tunneling systems can couple to magnetic fields. We summarize the available data and discuss the possible origin of these intriguing phenomena.     

介质球的各向异性瑞利散射

基于电磁场的多尺度理论,研究了各向异性介质球内、外电场的规律,导出了各向异性目标散射场的表达式,得到了各向异性介质目标散射振幅、散射截面等的解析表达式,并对其正确性进行了检验.仿真结果表明:各向异性介质球的散射具有偶极辐射的特点,介电常量越大,产生的偶极矩也愈大,散射也越强.其结果可为各向异性目标监测、各向异性光散射研究等提供理论支持.     

Theoretical description of the spectroscopic properties of rare earth ions in crystals

In this article the present state of knowledge of the theory of one- and two-photon processes observed in rare earth ions in crystals is presented. The conclusions are based on the results of ab initio calculations performed for various ions across the lanthanide series. The model applied for the calculations is based on the Rayleigh–Schrödinger perturbation theory, and the amplitude of a certain electric dipole transition is expressed in terms of effective operators. The radial integrals of the effective operators are defined by the perturbed functions that contain the perturbing influence of single excitations from the 4f shell to all one-electron states of a given symmetry, discrete and continuum. In this approach the interactions between the 4f^N and the excited configurations via the crystal field potential, the electron correlation operator and the spin–orbit interaction operator are discussed; it is believed that the presented theory contains the most important physical mechanisms responsible for the f↔f electric dipole transitions. Two alternative formulations of the theory of one-photon electric dipole transitions are presented. Consequently, the transition amplitude is defined within the standard theory based on the length formula and within a new approach which is based on the velocity form of the electric dipole radiation operator.     

Enhanced transverse relaxation in porous media due to internal field gradients

We present a detailed comparison between the theoretically computed spin echo decay of a fluid-saturated periodic porous medium with strong internal field gradients and that obtained from various approximations using the free diffusion formula which is strictly valid only for infinite uniform fluids. The theoretical computation of the spin echo amplitude was carried out by using the diffusion eigenstates in Fourier representation, and the internal field gradients induced by magnetic susceptibility contrast were calculated by using a two-component composite theory. The comparison allows us to have an assessment of the regime of validity of various approximations for a periodic porous medium where a rigorous theoretical computation of the enhanced transverse relaxation due to magnetic susceptibility contrast induced field heterogeneity is possible.     

Paramagnetic tunneling systems and their contribution to the polarization echo in glasses

Startling magnetic effects on the spontaneous polarization echo in some silicate glasses at low and ultralow temperatures have been reported in the last decade or so. Though some progress in search of an explanation has been made by considering the nuclear quadrupole dephasing of tunneling particles, here we show that the effect of a magnetic field can be understood quantitatively by means of a special tunnel mechanism associated with paramagnetic impurities. For the Fe(3+)-, Cr(3+)-, and Nd(3+)-contaminated glasses we provide reasonable fits to the published data as a function of applied magnetic field and temperature.     

Performance parameters for highly-focused electromagnetic waves

New performance parameters are presented for electromagnetic focusing systems of high numerical aperture. The field in the focal region is expanded into either electric/magnetic dipole components, or transverse electric/magnetic components. The treatments can be applied to the important case of electric dipole waves, where the focused polarization distribution is the same as that of an electric dipole. For the limiting case of a system of unity numerical aperture, the transverse focus for a focused electric dipole field is sharpened up by 19% compared with an aplanatic system with plane-polarized input, while at the same time the focal intensity for a given input power is increased by 17%. This should be contrasted with using a pupil filter, in which case, as the focal spot is made smaller the focal intensity also decreases. Pure TE polarization results in an even smaller central lobe. Other inhomogeneous polarizations can also be investigated as linear combinations of electric/magnetic or TE/TM components.     

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.     

Fano resonances in heterogeneous dimers of silicon and gold nanospheres

We theoretically investigate the optical properties of dimers consisting of a gold nanosphere and a silicon nanosphere. The absorption spectrum of the gold sphere in the dimer can be significantly altered and exhibits a pronounced Fano profile. Analytical Mie theory and numerical simulations show that the Fano profile is induced by constructive and destructive interference between the incident electric field and the electric field of the magnetic dipole mode of the silicon sphere in a narrow wavelength range. The effects of the silicon sphere size, distance between the two spheres, and excitation configuration on the optical responses of the dimers are studied. Our study reveals the coherent feature of the electric fields of magnetic dipole modes in dielectric nanostructures and the strong interactions of the coherent fields with other nanophotonic structures.     

All-dielectric left-handed metamaterial based on dielectric resonator: design, simulation and experiment

Dipoles with Lorentz-type resonant electromagnetic responses can realise negative effective parameters in their negative resonant region. The electric dipole and magnetic dipole can realise, respectively, negative permittivity and negative permeability, so both the field distribution forms of electric and magnetic dipoles are fundamentals in designing left-handed metamaterial. Based on this principle, this paper studies the field distribution in high-permittivity dielectric materials. The field distributions at different resonant modes are analysed based on the dielectric resonator theory. The origination and influence factors of the electric and magnetic dipoles are confirmed. Numerical simulations indicate that by combining dielectric cubes with different sizes, the electric resonance frequency and magnetic resonance frequency can be superposed. Finally, experiments are carried out to verify the feasibility of all-dielectric left-handed metamaterial composed by this means.