An approximate method of sideband intensity calculation in magic angle spinning NMR

A theory of sideband intensity is derived by expanding into a Taylor series the free induction decay observed under magic angle spinning (MAS). According to this procedure, the free induction decay signal is completely represented by a basis of irreducible tensors from rank zero to rank infinity. After averaging over all orientations, only the zero-order irreducible tensors contribute to the sideband intensities. Symmetry properties of the sidebands can be seen clearly in this expansion and an approximate formula up to ninth order is obtained by truncating the series. Sideband intensities can be calculated rapidly with this formula. The results agree satisfactorily with the exact sideband intensities obtained by numerical simulation if the ratio of the anisotropy to the spinning speed, ω₀δ/ω_r, is smaller than 3. The relationship of the sideband intensities with the moments of a MAS spectrum shows that the proposed method is an alternative to moment analysis when the spinning speed is not very slow. Anisotropic information about the chemical shift anisotropy interaction therefore can be extracted efficiently from experimental spectra by this approximate method.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

Hexagonal optical structures in photorefractive crystals with a feedback mirror

A nonlinear theory is presented for the formation of hexagonal optical structures in a photorefractive medium equipped with a feedback mirror. Oppositely directed beams in photorefractive crystals are unstable against the excitation of sideband waves. It is shown here that as this instability evolves to its nonlinear stage, the three-wave interaction between weak sideband beams does not stabilize it, but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors form angles that are multiples of π/3. As a result, sideband beams at these angles are found to be correlated. A range of parameters is found in which four-wave interactions saturate the explosive instability, which explains the appearance of stable hexagons in the experiment. Outside this region, nonlinearities of higher order saturate the explosive instability, and the process of hexagon generation must be studied numerically. Matrix elements are obtained for the three-and four-wave interactions as functions of the distance to the feedback mirror, and an equation for the time evolution of the sideband wave amplitudes is derived that describes the hexagon generation. A comparison is made with experimental results for the photorefractive crystals KNbO₃ and BaTiO₃. Zh. éksp. Teor. Fiz. 113, 1122–1146 (March 1998)     

The transmission performance of the single sideband optical millimeter-wave with BPSK signal in the duplex radio-over-fiber link

This paper has investigated the transmission performance of the single sideband (SSB) optical millimeter (mm)-wave with signal carried by the sideband in BPSK format in duplex radio-over-fiber (RoF) system theoretically and numerically. The SSB optical mm-wave signal is generated by a LiNbO₃ Mach–Zehnder modulator and there exists an optimal modulation index to generate the SSB optical mm-wave with a maximal RF photocurrent. The SSB optical mm-wave is much suitable for the duplex ROF link with the uplink lightwave recovered from the downlink because the optical carrier carries no signal. In such a duplex RoF link, although there are the spurs on the optical carrier, they have little influence on the downlink and the uplink signal even if the modulation index is large.     

Heterodyne mixing at 70 GHz with superconductor-insulator-superconductor tunnel junctions

A laboratory heterodyne receiver working at 70 GHz was built up using superconductor-insulator-superconductor tunnel junction as mixing element. Single sideband conversion loss L_C as low as 1.92±0.23 and mixer noise temperature T_M of less than 100 K have been achieved while local oscillator pump power is 4·10^–8W.     

The sub-bandgap energy loss satellites in the RIXS spectra of beryllium compounds

Resonant X-ray inelastic scattering spectra have been measured in BeO, phenakite (Be₂SiO₄) and chrysoberyl (BeAl₂O₄) with the excitation energy near the beryllium K edge.The RIXS spectra excited in the vicinity of the Be 1s core resonance show two principal features: the scattering on a valence excitation (which at higher excitation energies verges into the characteristic K_α emission), and a remarkably strong energy loss sideband to the elastic scattering peak. The energy loss shoulder appears to result from lattice relaxation in the absorption site. The comparison of the RIXS spectra of phenakite, chrysoberyl and BeO shows that the strength of the low energy sideband differs greatly; it is strongest in BeO and weakest in phenakite. The Si 2p RIXS spectra of phenakite also display a similar strong sub-bandgap energy loss tail.To gain further insight to this process, transitions in a system with a single vibrational mode have been modelled. The phonon relaxation has been simulated empirically by “smearing” the photoabsortion-populated vibrational levels with lower levels. This simple model is able to qualitatively explain this wide energy loss shoulder.     

Experimental determination of exponential parameters for multiphonon residual absorption in a ZBLAN: Er3+ fibre

Determination of exponential parameters for both Stokes and anti-Stokes sidebands by excitation of a ZBLAN: Er³⁺ fibre and bulk samples gives values of 9.4×10^-3 cm and 14.1×10^-3 cm, respectively. Observed values are larger than equivalent parameters usually found for nonradiative transitions. As examples, the measured parameters are used to determine the multiphonon sideband absorption between the ⁴I_11/2 and the ⁴I_13/2 electronic transitions of Er³⁺ and also between ¹G₄ and ³F₄ of Pr³⁺. Available energy ranges for sideband pumping of distributed amplifiers are given as well as the minimum multiphonon background losses intrinsic to the rare-earth plus pure glass base combination.     

FTIR-spectra of solid O2, N2 and CO

FTIR measurements of thin films of N₂, O₂ and CO at about 20 K contain a line due to the allowed or induced fundamental transition and a broad structure shifted to higher frequencies. This phonon sideband is explainable by coupling of lattice vibrations to the molecular fundamental vibration, and mirrors the weighted one phonon density-of-states. This IR-derived density-of-states can be compared with those from other experimental studies (neutron scattering, Raman) and from theoretical models.     

EPR in the impurity-doped two-dimensional ferromagnetic system K2CucZn1−cF4

EPR measurements of the half-field sideband as well as of the main line are reported in the impure two-dimensional ferromagnetic system K₂Cu_cZn_1?cF₄. A drastic change of the decay rate of spin correlation near the percolation limit and direct evidence for a correlation between these two lines have been observed.     

Dynamics of F2 centers in LiF: One phonon sideband and Raman scattering

The vibrational structure of the F₂⁺ emission in LiF was investigated, together with the resonant Raman scattering from the first excited electronic state. The one phonon sideband of the emission and the resonant Raman spectrum were found to be very similar, as expected for transitions involving non degenerate electronic states.     

Energy level diagram, wavefunctions, and probabilities of optical transitions in KCuF3

Using modern concepts of the crystal field in ion-covalent compounds, we calculate the energy level diagram, wavefunctions, and probabilities of optical transitions in the orbital ordering phase of KCuF₃. On this basis, we discuss the possible mechanisms by which an optical absorption sideband structure forms, accompanied by the creation of magnons.     

Frequency-shifting submillimeter single-sideband receiver

A single sideband (SSB) receiver has been developed and implemented for use with a submillimeter sideband generator. While the sideband generator emits both an upper and lower sideband, and even some unshifted laser radiation, the receiver responds to only one sideband. The operator of the system can choose which sideband to receive. Rejection of the undesired signal is accomplished through selective frequency shifting coupled with the use of a commercially available single-sideband microwave mixer.     

光的单边带传输的性能研究

对一种光单边带传输系统用MATLAB进行了仿真,结果表明：在完全消光条件下,10Gb/s单边带信号在常规单模光纤传输可达140 km, 而双边带仅为70 km;消光比对双边带传输和单边带传输的影响是不一样的. 双边带传输消光比为10 dB就够了, 单边带传输消光比要在20 dB以上,只有消光比大于20 dB时单边带传输相对于双边带传输的优越性才逐渐呈现出来.     

Calibration of STUD+ Parameters to Achieve Optimally Efficient Broadband Adiabatic Decoupling in a Single Transient

To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field,RF_max, the length of the sech/tanh pulse,T_p, the extent of the frequency sweep,bwdth,and the coupling constant,J_o. Less critical parameters, the effective (or actual) decoupled bandwidth,bw_eff, and the sech/tanh truncation factor, β, which become more important asbwdthis decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for¹³C decoupling, covering the range of one-bond¹³C¹H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the productJ_oT_p. The ratiobwdth/(RF_max)²can be viewed as a characteristic time scale, τ_c, affecting sideband levels, with τ_c≈T_pgiving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships betweenbwdthand less critical parameters,bw_effand β, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile for a single sech/tanh pulse. Residual splitting of the centerband, normally associated with incomplete or inefficient decoupling, is not seen in sech/tanh decoupling and therefore cannot be used as a measure of adiabatic decoupling efficiency. The calibrated experimental performance levels achieved in this study are within 20% of theoretical performance levels derived previously for ideal sech/tanh decoupling at high power, indicating a small scope for further improvement at practical RF power levels. The optimization procedures employed here will be generally applicable to any good combination of adiabatic inversion pulse and phase cycle.     

Strong Squeezing of Duffing Oscillator in a Highly Dissipative Optomechanical Cavity System

In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ⁽²⁾ nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter-rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved-sideband regime.     

Heterodyne spectroscopy for astrophysical applications using tunable laser sidebands at 10 microns

A heterodyne system was assembled from a microwave tunable sideband laser, a blackbody source, a gas cell, a CdHgTe photomixer and a filterbank. A measurement of line profiles of CH₃F is presented and compared with absorption measurements. System sensitivity is sufficient for high resolution measurement of fine structure lines from astronomical objects, though falling short by a factor of 12, when compared with the most sensitive astronomical heterodyne spectrometers. The usefulness of such a system for astrophysical applications is discussed.     

Dispersion Robustness of Millimeter Waves Generated by Up-Conversion Strategies

Abstract

The performance degradation caused by transmission along dispersive single-mode fibers of optically generated millimeter-wave signals using up-conversion is theoretically assessed and validated by numerical simulation. Up-conversion techniques based on optical double sideband, optical single sideband, and optical carrier suppression are considered. The generation of 60 GHz by frequency tripling using the optical single sideband is shown to be particularly tolerant to the fiber dispersion. The practical imbalance of Mach-Zehnder modulators is taken into account for optical carrier suppression modulation, where the finite extinction ratio is found to increase tolerance to fiber dispersion.     

Generation and detection of very high frequency acoustic phonons in diamond

Generation and detection of very high frequency acoustic phonons in diamond is reported. We generate phonons at a frequency of 28 THz by defect-induced one-phonon absorption of CO₂ laser radiation and observe, after pulsed excitation, phonon decay products in the frequency range from 1 THz to 7 THz. For detection vibronic sideband spectroscopy is used. We find strongly frequency dependent lifetimes for frequencies above 4 THz which we attribute to spontaneous phonon decay.Dedicated to K. Dransfeld on occasion of his 60th birthday     

On the theory of lasing at vibronic transitions in impurity crystals

Some aspects of lasing at vibronic transitions in impurity crystals are theoretically studied. The threshold conditions for a vibronic laser are shown to be dependent on the strength of the interaction of optical centers with a local vibration, which forms the vibronic spectrum, and the crystal lattice temperature. The theory can easily be generalized to the spectrum containing a structureless phonon sideband and well agrees with the experimental temperature dependence of the output power of a Mg₂SiO₄:Cr⁴⁺ forsterite laser.     

Study of ~t and ~b at LHC

In supersymmetric models a gluino can decay intotb _x ^~ ₁ ^+- through a stop or a sbottom. The decay chain produces an edge structure in the m_tb distribution. Monte Carlo simulation studies show that the end-point and the edge height would be measured at the CERN LHC by using a sideband subtraction technique. The stop and sbottom masses as well as their decay branching ratios are constrained by the measurement. We study interpretations of the measurement.