General eigenvalue equations for optical planar waveguides witharbitrarily graded-index profiles

Accurate eigenvalue equations for planar waveguides with arbitrarily graded-index profile are derived and expressed in closed forms. A combination of the modified Airy functions and the Wenzel-Kramers-Brillouin (WKB) solutions are employed as field solutions, which turn out to represent almost exact field profiles. The use of new trial solutions enables us to calculate phase shifts at turning points very precisely, allowing us almost exact eigenvalues. It is demonstrated that the results obtained by the proposed method are in excellent agreement with those by the finite element method, achieving significant improvement over the conventional WKB method     

Iterative solution of the eigenvalue problem for a dielectricwaveguide

The authors present a numerical approach to the simulation of dielectric waveguides that is free of spurious modes and is based on the solution of an eigenvalue problem for the two transverse components of the magnetic field. They introduce a new discretization which has several computational advantages. In particular, by careful design of the discretization procedure, the authors obtain systems of equations for the two components which are equivalent in the sense that a rotation over 900 corresponds to a suitable permutation of indices. The eigenvalue problem is solved iteratively by using an adapted version of the Chebyshev-Arnoldi algorithm. This approach takes full advantage of the sparsity of the matrix and circumvents the large memory requirements and the large computational complexity associated with dense methods. This allows the authors to employ meshes that are sufficiently fine to resolve higher modes without large discretization errors     

Robust finite-element solution of lossy and unbounded electromagnetic eigenvalue problems

An efficient algorithm is presented for the finite-element solution of electromagnetic eigenvalue problems associated with lossy and unbounded structures. The algorithm is based on the E/spl I.oarr/ - B/spl I.oarr/ formulation of the finite-element approximation of the electromagnetic equations. The special relationship between the vector bases used for the expansion of the electric field vector E/spl I.oarr/ and the magnetic flux density vector B/spl I.oarr/ is used to reduce the computational complexity of the proposed formulation. The occurrence of spurious DC modes is avoided through the careful selection of divergence-free initial vectors in the Lanczos-Arnoldi-based iterative schemes used by the proposed algorithm. The resultant algorithm is only marginally more expensive than standard finite-element-based algorithms used for electromagnetic eigenvalue problems involving lossless structures. Numerical experiments from the application of the proposed algorithm to the eigenvalue analysis of both lossless and lossy cavities are used to demonstrate its accuracy, computational efficiency, and robustness.     

Sparse matrix eigenvalue solver for finite element solution of dielectric waveguides

A method is presented to find a selected set of eigenvalues and the respective eigenvectors of the generalised eigenvalue problem Ax= lambda Bx for large, sparse, real or complex, nonHermitian matrices. Although the method is clearly applicable to other problems, results are given of application to the vectorial finite element analysis of dielectric waveguides.<>     

Efficient numerical solution of unbounded field problems

An efficient numerical method for solving certain unbounded field problems is presented. The method uses both the differential and integral formulations of the field problem and combines the particular advantages of each. The results obtained from an application of the method to a 2-dimensional exterior Laplacian problem are compared with those obtained by other methods.     

Time-domain solution of field-excited multiconductor transmissionline equations

Analytical solution of lossless field-excited multiconductor transmission lines is presented. The equivalent circuit of a multiconductor transmission line with distributed sources is reduced to a simple lumped parameter circuit with independent voltage sources at both the ends of the transmission line. The transient source waveforms are analytically estimated for exponential time dependence of the external field, as EMP, ESD, and lightning. The method is suitable for a direct implementation in computer-aided circuit analysis codes and enables a very fast analysis for any load condition. Some numerical results are presented for single conductor and multiconductor lines excited by all EMP plane-wave field     

Constrained maximum likelihood solution of linear equations

The total least squares (TLS) is used to solve a set of inconsistent linear equations Ax≈y when there are errors not only in the observations y but in the modeling matrix A as well. The TLS seeks the least squares perturbation of both y and A that leads to a consistent set of equations. When y and A have a defined structure, we usually want the perturbations to also have this structure. Unfortunately, standard TLS does not generally preserve the perturbation structure, so other methods are required. We examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations, given an a priori perturbation probability density function. While our approach is applicable to both Gaussian and non-Gaussian distributions, we show in the uncorrelated Gaussian case that our method is equivalent to several existing methods. Our approach is therefore more general and can be applied to a wider variety of signal processing problems     

Eigenfunctions and the solution of sensitivity equations

An elegant expression for the evaluation of the sensitivity of response of a linear time-invariant multivariable system is obtained. It is of interest that the expression does not involve any of the sensitivity coefficients of the eigenfunctions.     

Finite-element solution of integrated optical waveguides

A vectorH-field finite-element method has been used for the solution of optical waveguide problems. The permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless. To extend the domain of the field representation, infinite elements have been introduced. To eliminate spurious solutions and to improve eigenvectors, a penalty function method has been introduced. To show the validity and usefulness of this formulation, computed results are illustrated for step channel waveguide, diffused channel waveguide, anisotropic channel waveguide, and channel waveguide directional couplers.     

Efficient optical camera tracking in virtual sets

Optical tracking systems have become particularly popular in virtual studios applications tending to substitute electromechanical ones. However, optical systems are reported to be inferior in terms of accuracy in camera motion estimation. Moreover, marker-based approaches often cause problems in image/video compositing and impose undesirable constraints on camera movement, present work introduces a novel methodology for the construction of a two-tone blue screen, which allows the localization of camera in three-dimensional (3-D) space on the basis of the captured sequence. At the same time, a novel algorithm is presented for the extraction of camera's 3-D motion parameters based on 3-D-to-two-dimensional (2-D) line correspondences. Simulated experiments have been included to illustrate the performance of the proposed system.     

Efficient optical amplifier using a low-concentration erbium-dopedfiber

A gain coefficient of 3.8 dB/mW was achieved for an erbium-doped fiber amplifier pumped by a 1.48 μm laser diode. The main reasons for the improvement are high NA (0.23) and low concentration (43 p.p.m.). Pump-to-signal energy conversion efficiency was 18% at 3 dB gain compression. A decrease in saturation power with increasing erbium concentration was also demonstrated. In high-concentration fiber, fluorescence at 0.98 μm due to cooperative upconversion was detected. These results indicate that several kilometers of distributed fiber amplifier with high gain and high output saturation power could be possible, because the absorption coefficient at 1.48 μm is still two orders higher than the background loss in the 43 p.p.m. fiber     

Efficient TM-pass multilayer planar optical waveguide polariser

A novel TM-pass polariser using the form birefringence of a stratified periodic medium is proposed. The mode-filter properties of a planar waveguiding structure with form birefringent buffer layer on a lossy substrate are investigated numerically. A structure with TM/sub 0/-mode attenuation of less than 3 dB/cm at lambda /sub 0/=633 nm and TE-mode losses exceeding 300 dB/cm has been demonstrated experimentally.<>     

Efficient dc-free RLL codes for optical recording

We report on new dc-free runlength-limited codes (DCRLL) intended for the next generation of DVD. The efficiency of the newly developed DCRLL schemes is extremely close to the theoretical maximum, and as a result, significant density gains can be obtained with respect to prior art coding schemes. With a newly developed DCRLL (d=2) code we can achieve a 9% higher overall rate than that of DVD's EFMPlus.     

Efficient pump wavelengths of erbium-doped fibre optical amplifier

By choosing pump wavelengths at which excited state absorption does not occur, efficient high gain operation of erbium-doped fibre amplifiers is possible. Practical pump wavelengths of 532 nm and 980 nm are identified as optimal, giving gains as high as 1.35 dB/mW and 2.2 dB/mW of pump at the two wavelengths, respectively.<>     

Efficient coupling of optical fiber to silicon photodiode

A technique to couple an optical fiber to a silicon p-n junction diode photodetector is described. Spin on glass is used to create an alignment sheath to receive the tapered end of an optical fiber, to stabilize the structure, and to eliminate the air gap between the fiber and the photodetector. By using an antireflective film, differential responsivity of 0.58 A/W at a wavelength of 810 nm has been measured. Dark leakage current is less than 10 nA/cm²     

Efficient scheduling of transmissions in optical broadcast networks

All-optical networks (AONs) with a broadcast-star based physical topology offer the possibility of transmission scheduling to resolve channel and receiver conflicts. This paper considers the problem of scheduling packet transmissions in a wavelength-division multiplexed (WDM) optical network with tunable transmitters and fixed-tuned receivers. The scheduling problem is complicated by tuning latency, a limited number of channels, and arbitrary traffic demands. We first analyze scheduling all-to-all packet transmissions and obtain a new lower bound for the schedule length. The lower bound is achieved by an algorithm proposed by Pieris and Sasaki (1994). We then extend the analysis to the case of arbitrary traffic demands and obtain lower bounds for the schedule length. Two constructions for scheduling algorithms are provided through list scheduling and multigraphs. The upper bounds so obtained not only provide performance guarantees with arbitrary demands, but also nearly meet the lower bound in simulations     

无畸变传输线方程的解析解

对均匀传输线方程作拉氏变换，得出线上电压电流的复频域解，在无畸变的条件下，根据拉氏变换表和拉氏变换的有关性质，得出了线上电压电流在阶跃激励下的时域解，通过计算实例验证了该算法的有效性。