Green function theory of biquadratic heisenberg ferromagnet

The Heisenberg ferromagnet with the biquadratic exchange interaction is studied. The low temperature expansion of magnetization, the Curie temperature and the susceptibility at high temperatures are obtained.     

A coupled-mode theory analysis of intermixing in semiconductor distributed Bragg reflectors

On the basis of the coupled-mode theory, we have been able to successfully model and analyse the effect of intermixing on important optical properties of semiconductor distributed Bragg reflectors (DBRs). An expression for the coupling coefficient $\kappa $ κ as a function of diffusion length $L_D$ L D for intermixed DBRs has been derived. The derived expression for the intermixed DBRs allows the reflectivity, stop-band width, and penetration depth, to be calculated analytically. A 25 period GaAs/AlAS DBR centred at 980 nm was used to validate and test the model. It has been shown that the obtained results agree with those reported earlier using the transfer matrix method. As so, the presented model may provide a simple yet versatile rapid technique for the analysis of intermixed DBRs composed of any material system in which the diffusion process is Fickian and its corresponding refractive index is known.     

On the theory of magnetocaloric effect in cooperative paramagnets

The theory developed in [1] is used as a basis for analyzing the magnetocaloric effect observed experimentally in cooperative paramagnets [2, 3]. Even though the degenerate ground state of such magnetic systems is strongly correlated, the final formulas describing the magnetocaloric effect are found to be very similar to those for a normal paramagnet. The order of magnitude of the effect is discussed, and theoretical results are compared with experimental data.     

Complex coupled-mode theory for tapered optical waveguides

A coupled-mode formulation based on complex local modes is developed for tapered and longitudinally varying optical waveguides. Different from the conventional coupled-mode theory that requires integration over the entire spectrum of radiation modes, the new formulation treats the radiation fields via discrete complex modes similarly to the guided modes. Accuracy, convergence, and scope of validity for the solutions of the complex coupled-mode equations are investigated in detail for a typical single-mode waveguide taper. It is demonstrated that the complex coupled-mode theory has overcome the difficulties of the conventional theory in simulation of radiation field effects while preserving the simplicity and intuitiveness of this popular method.     

Mean field theory of a quantum heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.     

统一非对称光波导横向耦合模理论分析

光波导横向耦合模理论包含正交耦合模理论和非正交耦合模理论两大类, 为了追求形式上的完美, 两类理论没有统一的解析解, 并且都没有对非匹配耦合系统中耦合功率的非对称性进行深入研究. 本文一方面由Helmholtz方程出发推导出了一种新型的非正交耦合模方程, 并对两类理论中的耦合模方程进行了统一处理和求解, 得到了一种统一的解析解; 另一方面根据所得到的统一的解析解对非匹配耦合系统中耦合功率的非对称性进行了详细研究, 计算结果表明非匹配耦合系统中的最大互耦合功率和最小自耦合功率均可用统一的解析解进行近似计算. 关键词： 光波导 耦合模理论 耦合器 最大耦合功率     

Green's function theory of biquadratic exchange in a heisenberg ferromagnet

In this paper the effect of biquadratic exchange on Curie temperature has been discussed on the basis of double-time temperature-dependent Green-function formalism with the utilization of Callen decoupling scheme. Calculation has been done for a spin-1 bcc Heisenberg ferromagnet by the method of Flax and Raich and it has been observed that the variation of Curie temperature with the biquadratic exchange parameter α obeys a law prescribed by the previous authors.     

Analysis of groove NRD waveguide bend using the coupled-mode theory

In this paper, the propagation characteristics of the dominant mode in GNRD guide bend are analysed employing the coupled-mode theory. The curves of bending loss vs. The groove depth or width, radius of curvature and frequency are given, which caused by the mode conversion of the operatingLSM ₁₁ ^x mode to the parasiticLSE ₁₁ ^x mode. It is found that the groove depth has a great influence upon the bending loss than the other parameters. According to the theoretical results, appropriate sizes of groove and radius of curvature should be chosen in designing a GNRD bend structure.     

Analysis and engineering of coupled cavity waveguides based on coupled-mode theory

The analytical expression for the transmission spectra of coupled cavity waveguides （CCWs） in photonic crystals （PCs） is derived based on the coupled-mode theory （CMT）. Parameters in the analytical expression can be extracted by simple numerical simulations. We reveal that it is the phase shift between the two adjacent PC defects that uniquely determines the flatness of the impurity bands of CCWs. In addition, it is found that the phase shift also greatly affects the bandwidth of CCWs. Thus, the engineering of the impurity bands of CCWs can be realized through the adjustment of the phase shift. Based on the theoretical results, an interesting phenomenon in which a CCW acts as a single PC defect and its impurity band possesses a Lorentz lineshape is predicted. Very good agreement between the analytical results and the numerical simulations based on transfer matrix method has been achieved.     

A mean-field,effective medium theory of random magnetic alloys. II. The random heisenberg model

A classical Heisen berg model is analysed. The interaction is of the RKKY type and only between sites randomly occupied by magnetic atoms. The possible phases are described at various temperatures and concentration of magnetic atoms. The procedure is realistic and not the ‘exactly’ solvable kind studied by earlier workers.     

Frustrated heisenberg magnets: A nonperturbative approach

Frustrated magnets are a notorious example of where usual perturbative methods fail. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of frustrated Heisenberg magnets everywhere between d = 2 and d = 4. We recover all known perturbative results in a single framework and find the transition to be weakly of first order in d = 3. We compute effective exponents that are in good agreement with numerical and experimental data.     

Local-field fluctuations in paramagnets

Equations are derived for the local-field fluctuations in a paramagnet. A comparison is made with the second moment and with the Lorentz local field.     

Transport coefficients in Heisenberg paramagnets

The Heisenberg model is discussed in the paramagnetic region, using the method of moments in the spectral representation of spin correlation functions. We discuss the validity of Green's function decoupling approximations and derive expressions for the spin diffusion and thermal conductivity of a simple cubic lattice and linear chain. The results of the calculations are in qualitative agreement with previous work.     

Nonlinear coupled-mode equations

Nonlinear coupled-mode equations governing the modal coupling of a two-mode coupled system (such as twin core couplers) are integrable; power swapping in such a system follows a periodical manner and can be expressed analytically. When three or more modes (for systems such as multiple-core couplers) are involved, the nonlinear coupled-mode equations are no longer integrable and chaotic power swapping is expected. A numerical approach is required, in general, to solve such nonlinear coupled systems involving the coupling of three or more modes. We find, however, that for certain structural configurations, such as triple-core couplers with the cores arranged in the shape of an isosceles triangle, the nonlinear coupled-mode equations for multiple-core couplers can be solved analytically under a resonant condition. The analytical solution indicates that power swapping among, for example, the three cores placed in the shape of an isosceles triangle can be aperiodic at high power, although power may flow from core to core periodically at low power.     

A general dispersion relation for spin-phonon excitations in paramagnets

The advantage of using standard basis operators in evaluating the semi-invariants occurring in the diagrammatic theory of spin-phonon modes is discussed. The dispersion relation of the coupled-mode excitations is derived for paramagnetic ions of arbitrary spin having a general static spin hamiltonian.     

Dynamics of paramagnets at zero temperature

A macroscopic theory of low-frequency excitations in nearly unstable exchange spin systems with the singlet ground state is developed. Examples of dynamics near the pressure-and magnetic-field-instability points are considered. The development of the theory for the case of the instability of the system with respect to the appearance of magnetization is complicated.     

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d₁, diameters of outer core holes d₂ and hole to hole pitch Λ on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.     

A two-way marching coupled-mode method for range-dependent propagation

##正##An efficient,accurate,and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide.This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation.In addition,by combining a forward marching and a backward marching,this method provides accurate solutions for range-dependent propagation problems,especially those characterized by large bottom slope angle and/or high impedance contrast between water and the bottom.Furthermore,this two-way solution also provides high efficiency,which is achieved by applying the single-scatter approximation.Numerical examples are also provided to demonstrate the efficiency,accuracy, and stability of this method.