Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.     

Nature of electric and magnetic dipoles gleaned from the Poynting theorem and the Lorentz force law of classical electrodynamics

Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, ρ_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S = μ_o^− 1E × B and S = E × H. Here E is the electric field, H is the magnetic field, B is the magnetic induction, and μ_o is the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is intimately tied to the nature of magnetic dipoles and the way in which these dipoles exchange energy with the electromagnetic field. In addition, the manifest nature of both electric and magnetic dipoles in their interactions with the electromagnetic field has consequences for the Lorentz law of force. If the conventional identification of magnetic dipoles with Amperian current loops is extended beyond Maxwell's macroscopic equations to the domain where energy, force, torque, momentum, and angular momentum are active participants, it will be shown that “hidden energy” and “hidden momentum” become inescapable consequences of such identification with Amperian current loops. Hidden energy and hidden momentum can be avoided, however, if we adopt S = E × H as the true Poynting vector, and also accept a generalized version of the Lorentz force law. We conclude that the identification of magnetic dipoles with Amperian current loops, while certainly acceptable within the confines of Maxwell's macroscopic equations, is inadequate and leads to complications when considering energy, force, torque, momentum, and angular momentum in electromagnetic systems that involve the interaction of fields and matter.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

Performance of a slow positron beam using a hybrid lens design

The University of Hong Kong positron beam employs conventional magnetic field transport to the target, but has a special hybrid lens design around the positron moderator that allows the beam to be focused to millimeter spot sizes at the target. The good focusing capabilities of the beam are made possible by extracting work-function positrons from the moderator in a magnetic field free region using a conventional Soa lens thus minimizing beam canonical angular momentum. An Einzel lens is used to focus the positrons into the magnetic funnel at the end of transportation magnetic field while at the same time bringing up the beam energy to the intermediate value of 7.5 keV. The beam is E × B filtered at this intermediate energy. The final beam energy is obtained by floating the Soa-Einzel system, E × B filter and flight tube, and accelerating the positrons just before the target. External beam steering saddle coils fine tune the position, and the magnetic field around the target chamber is adjusted so as to keep one of the beam foci always on the target. The system is fully computer controlled. Variable energy-Doppler broadened annihilation radiation (VEDBAR) data for a GaN sample are shown which demonstrate the performance of the positron beam system.     

Nonlinear optical absorption and fluorescence of phosphine-substituted bithiophenes in the violet-blue spectral region

The nonlinear optical absorptions of two 5,5′-bis(diphenylphosphino)-2,2′-bithiophene derivatives, Ph₂(X)P(C₄H₂S)₂P(X)Ph₂ (X = O, 1; S, 2), have been investigated by direct transmission measurement with both picosecond and nanosecond laser pulses from 420 nm to 480 nm. Saturated dichloromethane solutions of 1 and 2 exhibit strong nonlinear optical absorptions in this violet-blue spectral region with that of 2 being stronger at all wavelengths. In the picosecond regime, at 420 nm, the transmittance rapidly falls to 50% when the incident fluence is 0.22 J/cm² for 1 and 0.11 J/cm² for 2. Two-photon absorption appears to be the primary mechanism for this nonlinear absorption. The two-photon absorption coefficients β for 1 (2.1 cm/GW) and 2 (4.4 cm/GM) were obtained by fitting the measurement of transmittance as the function of incident beam intensity at 420 nm. These β values are comparable with some of the best results obtained for organic materials in the green, red and infrared spectral region. Both compounds also show fluorescence with an emission peak at 390 nm for 1 and 400 nm for 2. The fluorescence of 1 is considerably stronger than is that of 2. The combination of the wide band gap and strong fluorescence emission of 1 makes it a promising candidate as a host material for blue organic light emitting diodes.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Effect of C and SiC additions into in situ or mechanically alloyed MgB2 deformed in Ti sheath

Effect of 3.4 wt.% C and 5 wt.% SiC doping into the standard in situ (IN) process and mechanically alloyed (MA) MgB₂ was studied. Powders of IN and MA process were carried out in air and in argon filled glove box, respectively. Wire samples were prepared by two-axial rolling deformation of IN and MA powders inside the Ti tube. Titanium as sheath material allows to use higher sintering temperatures, we used 700 °C and 800 °C for 30 min in Argon. Critical current densities (J_c) were measured at variable temperatures 4.2 K, 10 K, 15 K and 20 K in the external magnetic fields ranging to 15 T. Critical temperatures, upper critical fields and irreversibility fields of IN and MA with SiC and C additions are compared and discussed. The highest transport properties were observed for wires with MA SiC doped MgB₂ in the whole scale of temperatures 4.2–20 K. Upper critical field was rapidly enhanced in the case of carbon doped MA samples at 4.2 K. MA samples have shown decreased J_c values for higher temperatures (15 K, 20 K), in some case even worse than for the not doped reference IN sample. Carbon substitution and grain connectivity of analyzed samples are compared and discussed. Presented results show that for 20 K applications some new ways (additions) have to be found for increasing the J_c substantially.     

Sensitized luminescence of Eu and Tb macrocyclic complexes bearing benzophenone antennae

Sensitized luminescence behavior of lanthanide (Ln=Eu³⁺, Tb³⁺) macrocyclic cyclen (1,4,7,10-tetraazacyclododecane) complexes bearing one or four benzophenone (BP) moieties as antenna (LnL1 and LnL4) has been studied in water. Despite higher molar extinction coefficient of EuL4 owing to four antennae, it shows only one-thirtieth the luminescence intensity of EuL1. Energy level of triplet excited-state of BP antenna (E_T) is only a few kJ mol⁻¹ higher than that of ⁵D₂ excited-state of Eu³⁺, thus promoting a back energy transfer (BET) from ⁵D₂ of Eu³⁺ to ground-state BP antennae. On EuL4 bearing four antennae, BET occurs more rapidly than that on EuL1, thus exhibiting much weaker luminescence. For Tb complexes, the energy gap between E_T of BP antenna and ⁵D₄ excited state of Tb³⁺ is large enough (>13 kJ mol⁻¹), such that practically no BET occurs. The luminescence intensity of TbL4 is, however, lower (two-third) than that of TbL1. Time-resolved luminescence measurement reveals that hydration number of Tb³⁺ within TbL4 is twice that within TbL1. This is because the structural distortion of ligands on TbL4, caused by an intramolecular dipole-dipole interaction among the BP antennae, allows coordination of higher number of H₂O molecules to Tb³⁺, thus leading to a strong Tb luminescence quenching via O-H oscillators.     

Synthesis and luminescent properties of two Schiff-base boron complexes

Schiff bases N,N′-o-phenylenebis (salicylideneimine) (H₂L¹), N,N′-p-phenylenebis (salicylideneimine) (H₂L²) and their corresponding boron complexes (BF₂)₂L¹, (BF₂)₂L² were synthesized, respectively. The two boron complexes have been characterized by ¹H NMR, mass spectrometry and elemental analysis, while the luminescent properties of them were investigated with UV-VIS spectroscopy and photoluminescence spectroscopy. Then the three-layer devices [ITO/NPB (60 nm)/(BF₂)₂L¹ (50 nm)/Alq3 (20 nm)/LiF (1 nm)/Al (200 nm)] (device I) and [ITO/NPB (60 nm)/(BF₂)₂L² (50 nm)/Alq3 (20 nm)/LiF (1 nm)/Al (200 nm)] (device II) were fabricated by vacuum deposition. These two devices both exhibited blue green emission at 500 nm, but showed different luminances and efficiencies.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Photophysical characteristics of 4,4′-bis(N-carbazolyl)tolan derivatives and their application in organic light emitting diodes

4,4′-bis(N-carbazolyl)tolan (BCT) and 4,4′-bis[N-(3,6-di-t-butyl)carbazolyl]tolan (BCT-t-Bu) were synthesized as π-expanded analogs of 4,4′-bis(N-carbazolyl)biphenyl. Their photophysical characteristics both in solution and films were thoroughly investigated. Interestingly, the phosphorescence spectrum of BCT was significantly medium-dependent, and the emission maximum was red-shifted by 131 nm from 489 nm in solution at 77 K to 620 nm in a deposited film at 5 K, suggesting the presence of strong intermolecular interactions in the film. BCT and BCT-t-Bu were found to be useful as host materials for fluorescence-based organic light emitting diodes (OLEDs). However, their low triplet energy levels in films negated their potential to act as hosts in phosphorescence-based OLEDs.     

Photoconductivity of thin organic films

Thin organic films were deposited on silicon oxide surfaces with golden interdigitated electrodes (interelectrode gap was 2 μm), and the film resistivities were measured in dark and under white light illumination. The compounds selected for the measurements include molecules widely used in solar cell applications, such as polythiophene (PHT), fullerene (C₆₀), pyrelene tetracarboxylic diimide (PTCDI) and copper phthalocyanine (CuPc), as well as molecules potentially interesting for photovoltaic applications, e.g. porphyrin-fullerene dyads. The films were deposited using thermal evaporation (e.g. for C₆₀ and CuPc films), spin coating for PHT, and Langmuir-Schaeffer for the layer-by-layer deposition of porphyrin-fullerene dyads. The most conducting materials in the series are films of PHT and CuPc with resistivities 1.2 × 10³ Ω m and 3 × 10⁴ Ω m, respectively. Under light illumination resistivity of all films decreases, with the strongest light effect observed for PTCDI, for which resistivity decreases by 100 times, from 3.2 × 10⁸ Ω m in dark to 3.1 × 10⁶ Ω m under the light.     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

Indium-induced superstructures formed on Si(1 1 0) surfaces

Si(1 1 0) surfaces covered with small amounts of In deposit and then annealed at high temperature were investigated by RHEED, and two kinds of superstructures with A = 3a and B = −a + 4b, and A = 3a − 2b and B = −2a + 4b as primitive translational vectors are reported to form on the surfaces.     

Photoluminescent properties of heteroleptic cyclometalated platinum(II) complexes bearing 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dionate as an ancillary ligand

A new series of heteroleptic cyclometalated platinum(II) complexes Pt-1a-f was synthesized, employing 2-arylpyridine (or 1-arylisoquinoline) (HC^∧N-1) and 1,3-bis(3,4-dibutoxyphenyl)propane-1,3-dione (HO^∧O-1) for cyclometalation and as ancillary ligands, respectively, and photoluminescent properties were investigated. Focusing on red-shifted phosphorescence, C^∧N ligands containing π-extended aromatics and electron-rich heterocycles were examined. All obtained complexes exhibited photoluminescence at ambient temperature, and the emission maxima ranged from green (λ_PL=518 nm) to far red (λ_PL=708 nm). The large Stokes shifts of more than 100 nm and sub-microsecond or microsecond emission lifetimes revealed that these complexes are phosphorescent emissive. The quantum yield of Pt-1 ranged from 0.02 to 0.59 at ambient temperature and decreased as the emission maximum was red-shifted. In comparison with the reference platinum(II) complexes, Pt-2 bearing an aliphatic ancillary ligand, such as 2,2,6,6-tetramethylheptane-3,5-dionate (O^∧O-2), the ligand O^∧O-1 did not significantly affect the photoluminescence emission maxima, indicating that the energy gap between the singlet ground state and the triplet level was predominantly dependent on the C^∧N ligand.     

Synthesis, characterization and optical limiting effect of nickel complexes of multi-sulfur 1,2-dithiolene

Three nickel complexes with a new multi-sulfur 1,2-dithiolene ligand, (n-Bu₄N)[Ni(cddt)₂] 1, (Ph₄P)[Ni(cddt)₂] 2 and [Ni(cddt)₂] 3 (cddt=4a, 6, 7, 7a-5H-cyclopenta[b]-1,4-dithiin-2,3-dithiolate), have been synthesized and characterized by electrochemical measurements, IR, EPR and UV-Vis-NIR spectroscopies. The crystal structure of complex 2 is determined. Their optical nonlinearities are measured by the Z-scan technique with an 8 ns pulsed laser at 532 nm and all exhibit NLO absorptive abilities. Complexes 1 and 2 both exhibit effective self-defocusing performance (n₂=−5.81×10⁻¹⁰ esu for 1 and −4.51×10⁻¹⁰ esu for 2). The optical limiting (OL) effects were observed with nanosecond and picosecond laser pulses. The OL capability of complex 3 is superior to C₆₀ at the same experimental condition in ns measurements.     

Intermolecular photoinduced electron-transfer processes between C60 and aniline derivatives in benzonitrile

The quenching behavior of the triplets of C₆₀ by various aniline derivatives (1a-d and 2a-e) was investigated by means of laser flash photolysis in benzonitrile at 293 K. Electron transfer process was proposed to be the main mechanism because of the direct detection of radical ions of aniline derivatives and C₆₀ in time-resolved transient absorption spectra. The quenching rate constants (k_q) of by different substrates determined at 740 nm approach or reach the diffusion-controlled limit. DFT method was employed to calculate the unknown oxidation potentials of substrates in solution. With these E_ox values, free energy changes (ΔG) were obtained through Rehm-Weller equation. Dependence of observed quenching rate constants on the free energy changes further indicates the photoinduced reactions between ³C₆₀^* and substrates proceed through an electron transfer mechanism. Obtained k_q values for the aniline derivatives are impacted obviously by ground-state configurations and the kinds substituents quantified by Hammett σ constant. Good correlation between log k_q and σ values conforms to the empirical Hammett equation. A more negative ρ value (−3.356) was gained for anilines (2a-e) than that of N,N-dimethylanilines (1a-d) (−1.382), which suggests a more susceptible reactivity for the former substrates. Charge density distribution of reaction center “N” originated from quantum calculation supports this suggestion. In addition, a relationship between quenching rate constants and solvent viscosity was gained from C₆₀/dimethyl-p-toluidine system in altered mixtures of acetonitrile and toluene.     

Measuring small compartments with relatively weak gradients by angular double-pulsed-field-gradient NMR

NMR diffusion–diffraction patterns observed in compartments in which restricted diffusion occurs are a useful tool for direct extraction of compartment sizes. Such diffusion–diffraction patterns may be observed when the signal intensity E_(q,?) is plotted against the wave-vector q (when q = (2π)^− 1γδG). However, the smaller the compartment sizes are, the higher are the q-values needed to observe such diffractions. Moreover, these q-values should be achieved using short gradient pulses requiring extremely strong gradient systems. The angular double-pulsed-field gradient (d-PFG) NMR methodology has been proposed as a tool to extract compartment sizes using relatively low q-values. In this study, we have used single-PFG (s-PFG) NMR and angular d-PFG NMR to characterize the size of microcapillaries of about 2 ± 1 μm in diameter. We found that these microcapillaries are characterized by relatively strong background gradients that completely masked the effects of the microscopic anisotropy (μA) of the sample, resulting in a completely unexpected E(φ) profile in the angular d-PFG NMR experiments. We also show that bipolar angular d-PFG NMR experiments can largely suppress the effect of these background gradients resulting in the expected E(φ) profile from which the compartment dimensions could be obtained with relatively weak gradient pulses. These results demonstrate that the above methodology provides a quick, reliable, non-invasive means for estimating small pore sizes with relatively weak gradients in the presence of large magnetic susceptibility.     

Spectroscopic and thermodynamic features of conical bubble luminescence

The influence on luminescence from conical bubble collapse (CBL) with varying Ar gas content while perturbing the liquid 1,2-Propanediol (PD) has been investigated. The temporal, spatial, and spectral features were analysed with regards to the dynamics of collapse and liquid degradation. Sulphuric acid and sodium chloride were added to disturb the liquid. The following three cases were studied: PD/Ar, (I), (PD + H₂SO₄)/Ar, (II), and (PD + H₂SO₄ + NaCl)/Ar, (III). The intensities of those cases decrease as III > II > I. Temporally, single and multiple light emissions were found to occur. The pulse shape exhibited a large variety of profiles with a main maximum and up to two local maxima around the main maximum. These local maxima resembled those generated by laser cavitation. Spatially, no radial symmetry was detected in the light emissions. Spectrally, the Swan, CH and CN lines were observed at low volumes of gas and driving pressure. The OH radical and OH-Ar bands, as well as the Na and K lines, consistently appeared superimposed on an underlying continuum that almost disappeared in (III). The Na line was observed with two satellite diffuse bands representing Na-Ar complexes in (I) and (II), whereas in (III), only the line of sodium could be seen. Weak and diffuse emission lines from the Ar atom in the near-IR region were observed in (I) and (II).The proposed mechanism of bright CBL was based on the energy transfer from electron-excited homolytic cleavage products to the chromophore molecules generated during the collapse-rebound time line (∼8200 K and ∼1 ms of collapse time from model), which had accumulated inside the liquid and remained on the walls of cavity during the repetition of the collapse. A general mechanism for the bright CBL is broached.     

Prepare high efficiency Mn-doped Zn2SiO4 green phosphors in air using nano-particles

In this study, nano-scale precursors of ZnO, SiO₂, and MnO₂ powders were used to prepare mixtures with the compositions of 2ZnO+SiO₂+X mol% MnO₂ (X=MnO₂/2ZnO, abbreviated as Zn₂SiO₄-X-MnO₂), where 2≤X≤5. The mixed Zn₂SiO₄-X-MnO₂ mixtures were calcined from 900 to 1300 °C in air in order to synthesize Zn₂SiO₄:Mn²⁺ green phosphors. The X-ray diffraction patterns of Zn₂SiO₄-X-MnO₂ particles indicated that ZnO was present in the 900 °C-calcined Zn₂SiO₄-X-MnO₂ phosphors, but not in particles calcined at temperatures of 1000 °C and higher. However, the unapparent secondary phase of ZnMnO₃ was found in the 1200 and 1300 °C-calcined Zn₂SiO₄-5-MnO₂ compositions. The luminescent characteristics of Zn₂SiO₄-X-Mn²⁺ phosphors were compared with that of a commercial product (Nichia Corp., Japan). The photoluminescence (PL) intensity of 1200 °C-calcined Zn₂SiO₄-4-MnO₂ phosphors was higher and the decay times of all synthesized Zn₂SiO₄-X-MnO₂ phosphors were longer than those of the commercial product.