D. 188. Sheppard CJR, Saghafi S (1996) Flattened light beams, Opt. Commun. 132, 144-152
A model for flattened beams defined by a non-integer parameter
D. 206. Sheppard CJR, Saghafi S (1998) Beam modes beyond the paraxial approximation: a scalar treatment, Physical Review A., 57, 2971-2979
Proposal of a non-paraxial Gaussian beam that is valid for all space
D. 210. Saghafi S and Sheppard CJR (1998) The beam propagation factor for higher order Gaussian beams, Opt. Comm. 153, 207-210
D. 212. Saghafi S and Sheppard CJR (1998) Near and far field of elegant Hermite- and Laguerre-Gaussian modes, J. Mod. Opt. 45, 1999-2010
E.71. Sheppard CJR and Saghafi S (1998) Gaussian beams beyond the paraxial approximation, ICO Topical Meeting on Optics for Information Infrastructure, Tianjin, China , Aug. 3-6, in: Proc. OII '98, Optics for Information Infrastructure, GG Mu, ed. J. Optoelectronics Laser (JOEL) 9, Suppl. pp. 42-44
E.72. Sheppard CJR, Saghafi S (1998) High Aperture Gaussian beams, III Reunion Iberoamericana de Optica y VI Encuentro Latinoamericano de Optica, Lasers y sus Applicaciones, Cartagena, Colombia,28 Sept.- 2 Oct., pp. 17-18, plenary, Proc. SPIE 3572, 57-61 (1999)
D. 217. Sheppard CJR (1999) Focal distributions and Hertz potentials, Opt. Comm. 160, 191-194
D. 219. Sheppard CJR and Saghafi S (1999) Electromagnetic beam modes beyond the paraxial approximation, J. Opt. Soc. Am. A. 16, 1381-1386
D. 228. Sheppard CJR and Saghafi S (1999) Electric and magnetic dipole beam modes beyond the paraxial approximation, Optik 110, 487-491
D. 229. Sheppard CJR, Saghafi S (1999) Transverse electric and magnetic beam modes beyond the paraxial approximation, Opt. Lett. 24, 1543-1545
D. 232. Sheppard CJR (2000) Polarization of almost plane waves, J. Opt. Soc. Am. A 17, 335-341
D. 233. Sheppard CJR and Larkin KG (2000) Focal shift, optical transfer function, and phase-space representations, J. Opt. Soc. Am. A 17, 772-779
D. 243. Sheppard CJR (2001) High aperture beams, J. Opt. Soc. Amer. A 18, 1579-1587 (invited review paper)
D. 244. Sheppard CJR, Larkin KG (2001) Comment on "The uncertainty principle applied to estimate focal spot dimensions [Opt. Commun. 173 (2000) 51], Opt. Commun., 189, 1-2
D. 248. Saghafi S, Sheppard CJR, Piper J (2001) Characterising elegant and standard Hermite-Gaussian beam modes, Opt. Commun., 191, 173-179
D. 256. Sheppard CJR (2002) Comment on 'TM,TE and 'TEM' beam modes: exact solutions and their problems,' J. Opt. A: Pure and Applied, 4, 217-218
D. 13. Sheppard CJR, Wilson T (1978) Gaussian-beam theory of lenses with annular aperture, IEE J. Microwaves, Optics and Acoustics 2, 105-112.
Proposal of Bessel-Gauss beams
“The radial distribution of amplitude for a d ring is given by a zero-order Bessel function in any plane (in the region of validity) perpendicular to the optic axis. That this is so is not surprising because such a wave is the circularly-symmetric mode of free space. We are aquainted with modes of this form in circular waveguides, and we can consider free space as the limiting case of a waveguide of very large diameter. Such an overmoded waveguide has an infinity of circularly symmetric modes,that is the scale of the Bessel functions can be chosen at will. A wave with zero-order Bessel function radial distribution propagates without change.”
D. 18. Sheppard CJR (1978) Electromagnetic field in the focal region of wide- angular annular lens and mirror systems, IEE J. Microwaves, Optics and Acoustics 2, 163-166.
Derivation of vectorial non-paraxial Bessel beam
Reproduced in SPIE Milestone Series MS-168, Selected reprints on Electromagnetic fields in focal regions, JJ Stamnes, ed. ISBN 0-8194-4117-1, pp, 305-308
D. 158. Gu M, Sheppard CJR (1994) Analysis of confocal microscopy under ultrashort light-pulse illumination - comments, J. Opt. Soc. Amer. A 11, 2742-2743
D. 165. Gu Min, Sheppard CJR (1994) 3-D image formation in confocal microscopy under ultra-short laser-pulse illumination, J. Mod. Opt.. 42,747-762
E.47. Gu M, Sheppard CJR (1995) Fundamental improvement in axial resolution of confocal microscopy under ultra-short pulse illumination, Conference on three-dimensional microscopy: image acquisition and processing II, San Jose, February 1995, Proc. SPIE 2549, 254-260
D. 167. Gu Min, Tannous T, Sheppard CJR (1995) Three-dimensional confocal fluorescence imaging under ultra-short pulse illumination, Opt. Commun. 117, 406-412
D. 189. Sheppard CJR, Gan XS (1997) Free-space propagation of femtosecond light pulses, Optics Commun., 133 1-6
Isodiffracting pulses as output from laser resonator.
C. 27. Gu M, Tannous T, Sheppard CJR (1999) Axial resolution in confocal imaging under ultrashort pulsed beam illumination, in Focus on Multidimensional Microscopy, Vol. 1, PC Cheng, PP Hwang,JL Wu, G Wang, H Kim, eds., World Scientific. ISBN 981 02 3991 2
D. 253. Sheppard CJR (2001) Bessel pulse beams and focus wave modes, J. Opt. Soc. Am.A 18, 2594-2600
Selected for November 2002 issue (Photonics) of Virtual Journal of Ultrafast Science, American Physical Society, http://www.vjultrafast.org
D. 259. Sheppard CJR (2002) Generalized Bessel pulse beams, J. Opt. Soc. Am. A 19, 2218-2222
D. 211. Sheppard CJR and Larkin KG (1998) Similarity theorems for fractional Fourier transforms and fractional Hankel transforms, Optics Comm. 154, 173-178
D. 213. Sheppard CJR (1998) Free-space diffraction and the fractional Fourier transform, J.Mod. Opt. 45, 2097-2104
D. 250. Sheppard CJR, Larkin KG (2001) The three-dimensional transfer function and phase space mappings, Optik, 112, 189-192
D. 251. Sheppard CJR, Larkin KG (2001) The Wigner function for highly-convergent three-dimensional wavefields, Opt. Lett. 26, 968-970
D. 252. Sheppard CJR, Larkin KG (2001) Wigner function for non-paraxial wavefields, J. Opt. Soc. Am. A 18, 2486-2490
E. 83. Sheppard CJR, Larkin KG (2001) Wigner function and ambiguity function for non-paraxial three-dimensional wavefields, Optical Processing and Computing: A Tribute to Adolf Lohmann, Orlando, 17 April, SPIE Invitational Conference, Proc. SPIE 4392, 99-103
C.37. Sheppard CJR, Larkin KG (2002) Wigner function and ambiguity function for non-paraxial three-dimensional wavefields, in Optical Processing and Computing: A Tribute to Adolf Lohmann, ed. HJ Caulfield, SPIE Press, Bellingham, ISBN 0-8194-4498-7, pp 37-56
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