Biomedical subjects

Eng Leong Tan

Publications and source records attributed to Eng Leong Tan.

5 recordsLinked to original sources

PubMed2006

Enhanced R-matrix algorithms for multilayered diffraction gratings.

I present enhanced R-matrix algorithms for analysis of general multilayered diffraction gratings. The previous R-matrix algorithms are enhanced in three aspects: computational efficiency, numerical stability, and application of half R-matrix in addition to full and quarter R-matrix recursions. On the basis of the eigensolutions of rigorous coupled-wave analysis, the enhanced R-matrix algorithms deal with eigen-submatrices directly and bypass the auxiliary layer R matrix. Such exclusion of a layer matrix leads to improvements in efficiency and algorithm robustness particularly for zero or small layer thickness relative to wavelength. Application of the enhanced algorithms to grating diffraction is exploited especially for the half and quarter R-matrix recursions. Comparison of various R-matrix algorithms via a table of flop counts shows that the enhanced algorithms are more efficient apart from being well conditioned.

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PubMed2006

Hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media.

This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.

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PubMed2003

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids.

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.

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PubMed2002

A robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies.

This paper presents a robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies. The formulation is an alternative to that based on the transfer matrix method, which suffers from numerical instabilities when the frequency and/or thickness parameters become large. This numerical difficulty can be attributed to the mixture of exponentially growing and decaying terms during the transfer matrix calculations. To be more instructive, the numerical instability is delineated in terms of upward-bounded and downward-bounded waves within each layer. In accordance with such boundedness association, a recursive scheme not involving any growing terms is developed based on the scattering matrices to eliminate the instability. The resulting reflection matrix method is extremely concise and preserves the simplicity and convenience of the transfer matrix method. Using the reflection matrices, the generalized Green's functions that relate the particle velocity and the rate of electric potential change to the surface stress and charge are formulated succinctly. These Green's functions are useful for having incorporated the electrical properties of the vacuum above the surface. Numerical computations are exemplified to demonstrate the instabilities of the transfer matrix method and to justify the robustness of the reflection matrix formula.

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PubMed2002

Note on formulation of the enhanced scattering- (transmittance-) matrix approach.

The enhanced transmittance matrix approach developed by Moharam et al. [J. Opt. Soc. Am. A 12, 1077 (1995)] is reformulated in a concise and illuminating form in terms of scattering (reflection and transmission) matrices directly. Two equivalent recursive formulations, corresponding to their full- and partial-solution approaches, are presented and extended to allow simultaneous determination of both reflected and transmitted amplitudes. The relationships between these formulations and the S-matrix algorithm, together with their relative efficiencies and usefulness, are ascertained and compared by means of compact formulas featuring parallel algebraic structures. It is made evident that given the eigenmode solutions, the enhanced approach is the most direct and efficient way for deducing global scattering matrices.

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