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35. P. D. Einziger and S. Raz, “Beam-series representation and the parabolic ap-
proximation: The frequency domain,” J. Opt. Soc. Am. A 5: 1883–1892 (1998).
36. J. M. Arnold, “Rays, beams and diffraction in a discrete phase space: Wilson
bases,” Opt. Express 10: 716–727 (2002).
37. B. Z. Steinberg, E. Heyman, and L. B. Felsen, “Phase-space beam summation
for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8: 41–59
(1991).
38. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. 20: 594–598 (1946).
39. G. W. Forbes and M. A. Alonso, “Using rays better. I. Theory for smoothly
varying media,” J. Opt. Soc. Am. A 18: 1132–1145 (2001).
40. 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).
41. M. A. Alonso and G. W. Forbes, “Using rays better. III. Error estimates and
illustrative applications in smooth media,” J. Opt. Soc. Am. A 18: 1357–1370
(2001).
42. G. W. Forbes, “Using rays better. IV. Theory for refraction and reflection,” J. Opt.
Soc. Am. A 18: 2557–2564 (2001).
43. M. A. Alonso and G. W. Forbes, “Stable aggregates of flexible elements give a
stronger link between rays and waves,” Opt. Express 10: 728–739 (2002).
44. E. J. Heller, “Frozen Gaussians: A very simple semiclassical approximation,”
J. Chem. Phys. 75: 2923–2931 (1981).
45. M. F. Herman and E. Kluk, “A semiclassical justification for the use of non-
spreading wavepackets in dynamics calculations,” J. Chem. Phys. 91: 27–35
(1984).
46. W. P. Schleich, Quantum Optics in Phase Space, Wiley, Berlin, 2001, p. 324.
47. M. A. Alonso and G. W. Forbes, “New approach to semiclassical analysis in
mechanics,” J. Math. Phys. 40: 1699–1718 (1999).
48. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-
Hill, New York, 1965.
49. See, e.g., Ref. 1, pp. 883–891.