## Using rays better. II. Ray families to match prescribed wave fields

JOSA A, Vol. 18, Issue 5, pp. 1146-1159 (2001)

http://dx.doi.org/10.1364/JOSAA.18.001146

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### Abstract

A key step in any ray-based method for propagating waves is the choice of a family of rays to be associated with the initial wave field. We develop some basic prescriptions for constructing initial ray families to match two particular types of waves. Various Gaussian and Bessel beams are separately given special treatment because of their general interest. These ideas are directly useful for a newly developed method for ray-based wave modeling. The new method expresses the wave as a superposition of ray contributions that is independent of the width of the field element associated with each ray. This insensitivity is investigated here even when the elemental width varies from ray to ray. The results increase the applicability of the new wave-modeling scheme.

© 2001 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(080.2710) Geometric optics : Inhomogeneous optical media

(080.2720) Geometric optics : Mathematical methods (general)

(350.7420) Other areas of optics : Waves

**History**

Original Manuscript: September 13, 2000

Revised Manuscript: December 14, 2000

Manuscript Accepted: December 14, 2000

Published: May 1, 2001

**Citation**

M. A. Alonso and G. W. Forbes, "Using rays better. II. Ray families to match prescribed wave fields," J. Opt. Soc. Am. A **18**, 1146-1159 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-5-1146

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### References

- G. W. Forbes, M. A. Alonso, “Using rays better. I. Theory for smoothly varying media,” J. Opt. Soc. Am. A 18, 1132–1145 (2001). [CrossRef]
- See, for example, the review presented in Section 5 of Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam1999), Vol. XXXIX, pp. 1–62.
- M. A. Alonso, G. W. Forbes, “Phase space distributions for high-frequency fields,” J. Opt. Soc. Am. A 17, 2288–2300 (2000). [CrossRef]
- N. G. de Bruijn, Asymptotic Methods in Analysis (Dover, New York, 1981), Chap. 5.
- N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986), Chap. 7.
- To see this, one must take into account Eq. (I-2.4).
- G. W. Forbes, M. A. Alonso, “Using rays better. III. Error estimates and illustrative applications in smooth media,” J. Opt. Soc. Am. A18 (to be published).
- Point sources are useful in this context because they corre-spond to Green’s functions. The propagator corresponds to the z0 derivative of the Green’s function and is used when considering plane-to-plane imaging. See, for example, M. A. Alonso, G. W. Forbes, “Semigeometrical estimation of Green’s functions and wave propagators in optics,” J. Opt. Soc. Am. A 14, 1076–1086 (1997). [CrossRef]
- This result also follows from using the saddle-point method in Eq. (1.1) with γ(ξ, z).
- As stated in Ref. 3, examples of these fields are the modes of z independent guiding smooth media.
- The arbitrary constant of integration in L is set to zero in Eq. (5.6), since it gives only a global phase that can be absorbed by c. The same is done in subsequent examples.
- Notice that we must now use the version of this method for integrals over two variables. See Ref. 4.
- R. L. Gordon, G. W. Forbes, “Optimal resolution with extreme depth of focus,” Opt. Commun. 150, 277–286 (1998). [CrossRef]

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