Abstract-The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(1x 2 ) provided the discontinuity coincides with a mesh point or lies midway between two mesh points. Furthermore, the formula allows a general position of the interface, when used with the beam-propagation method (BPM). To demonstrate the effectiveness of the formula, asymmetric step-index waveguides are analyzed using the imaginary-distance BPM.

Abstract-To improve a wide-angle beam propagation method using a finite-difference technique, the generalized Douglas scheme for variable coefficients is applied to a multistep method. A truncation error of ~( A z ) " is achieved in the transverse direction. The effectiveness of the present method is demonstrated in the analysis of a tilted step-index slab waveguide.

Abstract-Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r = 1 + O(1x). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method.Index Terms-Finite-difference methods, optical beam propagation, optical waveguides.

A fluorescence thermometer using the temperature dependence of the phase shift of fluorescence response was developed using a ruby phosphor sheet. The ruby phosphor sheet was compounded of ruby powder and silicone resin. The fluorescence lifetime from the ruby phosphor sheet was measured with a phase shift measurement technique. The phase shift of the fluorescence response from the ruby phosphor sheet decreased linearly with temperature from 270to350K. The ruby phosphor sheet is found to be powerful tool for temperature measurement, and can be used for noncontact temperature measurement.

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