The validity of a new asymptotic method for propagating waves in two-dimensional, smoothly varying inhomogeneous media is compared with that of other standard methods. Simple geometric validity conditions are derived along with expressions for the maximum wavelength at which the modulus of the complex-valued field error can be expected to be no more than approximately a few percent, and then 20%, of the local peak field amplitude. It is shown that the limiting error in the Maslov method is generated by the process of switching between representations. The new method is predicted to be accurate to within a few percent for wavelengths that are one to two orders of magnitude larger than the corresponding cutoff for the Maslov method. This ratio exceeds two orders of magnitude for accuracy of approximately 20%. These predictions are confirmed by numerical investigation of a simple example.

© 1998 Optical Society of America

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