Using rays better. III. Error estimates and illustrative applications in smooth media

Area of Science:

• Optics
• Wave Propagation
• Computational Physics

Background:

• Accurate computation of optical wave fields is crucial for understanding light-matter interactions.
• Existing ray-based methods often face limitations in accuracy and applicability.
• Analytic solutions provide benchmarks for validating new computational techniques.

Purpose of the Study:

• To develop and demonstrate a new, accurate ray-based method for approximating optical wave fields.
• To compare the accuracy of the new method against exact solutions in simplified scenarios.
• To introduce a robust error estimation and correction strategy for ray-based field approximations.

Main Methods:

• Demonstration of a novel ray-based approximation technique for optical wave fields.
• Utilizing free space and gradient-index waveguide propagation as test cases with known analytic solutions.
• Development and application of a simple root-mean-square (RMS) error estimation.
• Testing corrections to the basic ray-based field estimate.

Main Results:

• The new ray-based method provides accurate approximations to optical wave fields.
• Comparison with analytic solutions confirms the efficacy of the developed method.
• A simple RMS error estimate was successfully developed and applied.
• Corrections were tested and shown to improve the accuracy of the field estimates.

Conclusions:

• The demonstrated ray-based method offers a viable approach for computing optical wave fields.
• Maximal accuracy requires careful selection of rays, considering both the initial wave field and the propagation medium.
• The developed error estimation and correction techniques enhance the reliability of ray-based approximations.