The scattering matrix method for quantum waveguides

A scattering matrix method for investigating the electron transport in quantum waveguides is presented. By dividing the structure into a number of transverse slices, the global scattering matrix is obtained by the composition of the individual scattering matrices associated with each interface. Complicated geometries and inhomogeneous external potentials are included in the formulation. It is shown that the proposed scattering matrix method possesses many advantages over the traditional mode-matching and transfer matrix methods, especially in treating the electron wave propagation in complicated geometries. Justification for the method is provided by the unitarity of the calculated scattering matrix, and the consistency of the results with those obtained by the recursive Green's function method.

A transfer matrix approach to conductance in quantum waveguides

A transfer matrix approach is presented for the study of electron conduction in an arbitrarily shaped cavity structure embedded in a quantum wire. Using the boundary conditions for wave functions, the transfer matrix at an interface with a discontinuous potential boundary is obtained for the first time. The total transfer matrix is calculated by multiplication of the transfer matrix for each segment of the structure as well as numerical integration of coupled second-order differential equations. The proposed method is applied to the evaluation of the conductance and the electron probability density in several typical cavity structures. The effect of the geometrical features on the electron transmission is discussed in detail. In the numerical calculations, the method is found to be more efficient than most of the other methods in the literature and the results are found to be in excellent agreement with those obtained by the recursive Green's function method.

Optical Factors Determined by the T-matrix Method in Turbidity Measurement of Absolute Coagulation Rate Constants

Turbidity measurement for the absolute coagulation rate constant of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor to derive the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed in the aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion about the physical insight of using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the calculated data of the optical factor by the T-matrix method for a range of particle radii and incident light wavelengths are listed.

Simple ABCD matrix method for evaluating optical coupling system of laser diode to single-mode fiber with a lensed-tip

In this paper, we present a simple technique to determine the coupling efficiency between a laser diode and a lensed-tip based on the ABCD transformation matrix method. We have compared our analysis technique to that of previous work and have found that the presented method is reliable in predicting the coupling efficiency of lensed-tip and has the advantage of simplicity of coupling efficiency calculation even by a pocket calculator. The results can be useful for designing coupling optics. (c) 2005 Elsevier GmbH. All rights reserved.

Fast calculation technique for scattering in T-matrix method

In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al. (c) 2008 Elsevier B.V. All rights reserved.

反射型磁光多层膜隔离器的频率响应及宽容性研究

通过传输矩阵法分析了材料介电常数的变化对于单缺陷结构的磁光多层膜隔离器性能的响，并提出了一种多缺陷结构的磁光多层膜结构．同单缺陷结构相比，多缺陷结构的旋转角的频谱响应带宽有很大增加，对于材料介电常数变化的宽容性得到了一个数量级的提高．同时这种多缺陷的结构对于膜层厚度的变化和入射角度也有很好的宽容性．

Mode Characteristics for Square Resonators With a Metal Confinement Layer

Microsquare resonators laterally confined by SiO2/Au/air multilayer structure are investigated by light ray method with reflection phase-shift of the multiple layers and two-dimensional (2-D) finite-difference time-domain (FDTD) technique. The reflectivity and phase shift of the mode light ray on the sides of the square resonator with the semiconductor/SiO2/Au/air multilayer structure are calculated for TE and TM modes by transfer matrix method. Based on the reflection phase shift and the reflectivity, the mode wavelength and factor are calculated by the resonant condition and the mirror loss, which are in agreement well with that obtained by the FDTD simulation. We find that the mode factor increases greatly with the increase of the SiO2 layer thickness, especially as d < 0.3 mu m. For the square resonator with side length 2 mu m and refractive index 3.2, anticrossing mode couplings are found for confined TE modes at wavelength about 1.6 mu m at d = 0.11 mu m, and confined TM modes at d = 0.71 mu m, respectively.

Optical response of high-level bandgap in one-dimensional photonic crystal applying in-plane integration

A new broadband filter, based on the high level bandgap in 1-D photonic crystals (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si is designed by the plane wave expansion method (PWEM) and the transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-level bandgaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and the PC device. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Optical response of high-order band gap photonic crystal applying in-plane in one-dimensional integration

A new broadband filter, based on the high-order band gap in one-dimensional photonic crystal (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si, has been designed by the plane wave expansion method (PWEM) and transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device. (c) 2007 Elsevier B.V. All rights reserved.

One-dimensional quantum waveguide theory of Rashba electrons

The ballistic spin transport in one-dimensional waveguides with the Rashba effect is studied. Due to the Rashba effect, there are two electron states with different wave vectors for the same energy. The wave functions of two Rashba electron states are derived, and it is found that their phase depend on the direction of the circuit and the spin directions of two states are perpendicular to the circuit, with the +pi/2 and -pi/2 angles, respectively. The boundary conditions of the wave functions and their derivatives at the intersection of circuits are given, which can be used to investigate the waveguide transport properties of Rashba spin electron in circuits of any shape and structure. The eigenstates of the closed circular and square loops are studied by using the transfer matrix method. The transfer matrix M(E) of a circular arc is obtained by dividing the circular arc into N segments and multiplying the transfer matrix of each straight segment. The energies of eigenstates in the closed loop are obtained by solving the equation det[M(E)-I]=0. For the circular ring, the eigenenergies obtained with this method are in agreement with those obtained by solving the Schrodinger equation. For the square loop, the analytic formula of the eigenenergies is obtained first The transport properties of the AB ring and AB square loop and double square loop are studied using the boundary conditions and the transfer matrix method In the case of no magnetic field, the zero points of the reflection coefficients are just the energies of eigenstates in closed loops. In the case of magnetic field, the transmission and reflection coefficients all oscillate with the magnetic field; the oscillating period is Phi(m)=hc/e, independent of the shape of the loop, and Phi(m) is the magnetic flux through the loop. For the double loop the oscillating period is Phi(m)=hc/2e, in agreement with the experimental result. At last, we compared our method with Koga's experiment. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3253752]

Birefringence of UV-written channel waveguides

The combination of the effective index method and the transfer matrix method is adopted to calculate the indices of quasi-TE and quasi-TM modes in a UV-written channel waveguide, and the difference between the indices is used to characterize its birefringence. The dimensions, the ratio of width to thickness, the original index of the core layer, the index of the cladding, and the index profile are all taken into account. The simulation results indicate that the birefringence decreases with increasing dimensions, ratio of width to thickness, and indices of the cladding; on the contrary, increases of the original index of the core layer and of the vertical index gradient intensified the birefringence. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

1.55 mu m GaInNAs resonant-cavity-enhanced photodetector grown on GaAs

We report the design, growth, fabrication, and characterization of a GaAs-based resonant-cavity-enhanced (RCE) GaInNAs photodetector operating at 1.55 mu m. The structure of the device was designed using a transfer-matrix method (TMM). By optimizing the molecular-beam epitaxy growth conditions, six GaInNAs quantum wells were used as the absorption layers. Twenty-five (25)- and 9-pair GaAs/AlAs-distributed Bragg reflectors were grown as the bottom and top mirrors. At 1.55 mu m, a quantum efficiency of 33% with a full width at half maximum of 10 nm was obtained. The dark current density was 3x10(-7) A/cm(2) at a bias of 0 V and 4.3x10(-5) A/cm(2) at a reverse bias of 5 V. The primary time response measurement shows that the device has a rise time of less than 800 ps. (c) 2005 American Institute of Physics.

Tunable ultra-narrow band-gap of anomalous dispersion photonic crystals

We use the transfer-matrix method to research the band structures in one-dimensional photonic crystals composed of anomalous dispersion material ( saturated atomic cesium vapor). Our calculations show that that type of photonic crystal possesses an ultra-narrow photonic band gap and this band gap is tunable when altering the electron population in the atomic ground state of the anomalous dispersion material by the optical pumping method. Copyright (C) EPLA, 2007.

Peculiar photocurrent response due to Gamma-X coupling in a GaAs/AlAs heterostructure

Peculiar current jumps and hysteresis in current-voltage curves are reported in an illuminated heterostructure consisting basically of a thick AlAs layer and a narrow GaAs quantum well. These novel features come from the photon-assisted transfer of electron-hole pairs and the resultant charge polarization in the structure, mainly caused by the resonant Gamma-X coupling at the heterointerfaces. Using the transfer-matrix method, the simulated current density-voltage curve reproduces the main features of the experimental observations in the case where the influence of resonant Gamma-X coupling at the heterointerfaces is included, further confirming the physical mechanism involved. The structure presented here may be used as a new type of photonic memory cell and also as an optically controlled switch.

Accurate mode analysis of ultraviolet-written channel waveguides

The transfer matrix method combined with the effective index method is adopted to model the silica-based channel waveguide patterned by UV writing. The effective indexes of the graded index channel waveguides with different dimension are calculated. The maximal error of the effective index is less than 3 x 10(-5). By this method, the number of the guided mode and the dimension range to guide certain modes can be obtained easily. Finally, the dimension range to guide a single mode is presented. (c) 2005 Society of Photo-Optical Instrumentation Engineers.