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Cherenkov Radiation Versus X-shaped Localized Waves: Reply
No full textOur aim in this paper is a reply to Seshadri's comments [J. Opt. Soc. Am. A 29, 2532 (2012)] on a previous article of ours, titled "Cherenkov radiation versus X-shaped localized waves" [J. Opt. Soc. Am. A 27, 928 (2010)], as well as to his more extended criticism of the extended special relativity theory, called by him nonrestricted relativity, and in particular of the extended Maxwell equations. © 2012 Optical Society of America.291225362541Seshadri, S.R., Cherenkov radiation versus X-shaped localized waves: Comment (2012) J. Opt. Soc. Am. A, 29, pp. 2532-2535Zamboni-Rached, M., Recami, E., Besieris, I.M., Cherenkov radiation versus X-shaped localized waves (2010) J. Opt. Soc. Am. A, 27, pp. 928-934Walker, S.C., Kuperman, W.A., Cherenkov-Vavilov formulation of X waves (2007) Phys. Rev. Lett., 99, p. 244802Hernández-Figueroa, H.E., Zamboni-Rached, M., Recami, E., (2008) Localized Waves, Theory and Applications, , WileyLu, J.-Y., Greenleaf, J.F., Experimental verification of nondiffracting X-waves (1992) IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 39, pp. 441-446Saari, P., Reivelt, K., Evidence of X-shaped propagation invariant localized light waves (1997) Phys. Rev. Lett., 79, pp. 4135-4138Recami, E., Zamboni-Rached, M., Dartora, C.A., Localized X-shaped field generated by a superluminal charge (2004) Phys. Rev. e, 69, p. 027602. , and references thereinRecami, E., Zamboni-Rached, M., Localized waves: A review (2009) Adv. Imaging Electron Phys., 156, pp. 235-355Sommerfeld, A., Überlichtgeschwindigkeitsteilchen (1904) Proc. K. Ned. Akad. Wet., 8, pp. 346-367Sommerfeld, A., Zur electronentheorie (3 Tiele) (1905) Nach. Kgl. Ges. Wiss. Göttingen, Math. Naturwiss. Klasse 99-130, pp. 363-439. , 1904, 201-236Fröman, P.O., Historical background of the tachyon concept (1994) Arch. Hist. Exact Sci., 48, pp. 373-380Bilaniuk, O.-M., Deshpande, V.K., Sudarshan, E.C.G., Meta' relativity (1962) Am. J. Phys., 30, pp. 718-723Bilaniuk, O.-M., Sudarshan, E.C.G., Particles beyond the light barrier (1969) Phys. Today, 22, pp. 331-339Recami, E., Classical theory of tachyons (1986) Riv. Nuovo Cimento, 9 (6), pp. 1-178Mignani, R., Recami, E., Crossing relations derived from (extended) relativity (1975) Int. J. Theor. Phys., 12, pp. 299-320Pavšič, M., Recami, E., Charge conjugation and internal space-time symmetries (1982) Lett. Nuovo Cimento, 34, pp. 357-362Recami, E., Tachyon mechanics and causality: A systematic thorough analysis of the tachyon causal paradoxes (1987) Found. Phys., 17, pp. 239-296Barut, A.O., MacCarrone, G.D., Recami, E., On the shape of tachyons (1982) Nuovo Cimento A, 71, pp. 509-533Mignani, R., Recami, E., Tachyons do not emit Cherenkov radiation in vacuum (1973) Lett. Nuovo Cimento, 7, pp. 388-390Utkin, A.B., Droplet-shaped waves: Causal finite-support analogs of X-shaped waves (2012) J. Opt. Soc. Am. A, 29, pp. 457-462Morse, P.M., (1985) Theoretical Acoustics, , Princeton UniversityArias, E., Bessa, C.H.G., Svaiter, N.F., An analog fluid model for some tachyonic effects in Field Theory (2011) Mod. Phys. Lett. A 26, pp. 2335-2344. , and references thereinRecami, E., The Tolman antitelephone paradox: Its solution by tachyon mechanics 1985, reprinted in Electron (2009) J. Theor. Phys. (EJTP), 6, pp. 1-8Recami, E., Superluminal motions? A bird's-eye view of the experimental status-of-The-Art (2001) Found. Phys., 31, pp. 1119-1135Recami, E., Superluminal Waves and Objects: An Up-dated Overview of the Relevant Experiments, , arXiv :0804.1502 [physics]Recami, E., Rodrigues, W.A., A model theory for tachyons in two dimensions (1985) Gravitational Radiation and Relativity, 3, pp. 151-203. , J. Weber and T. M. Karade, eds., of Proceedings of the Sir Arthur Eddington Centenary Symposium World ScientificBarut, A.O., Chandola, H.C., Localized' tachyonic wavelet solutions to the wave equation (1993) Phys. Lett. A, 180, pp. 5-8Recami, E., Mignani, R., Magnetic monopoles and tachyons in special relativity (1976) Phys. Lett. B, 62, pp. 41-4
Finite Aperture Realization Of The Diffraction-attenuation Resistant Beams In Absorbing Media
No full textIn this work, by making numerical simulations of the Rayleigh-Sommerfeld diffraction integral, we show the finite aperture realization of the recently discovered diffraction-attenuation resistant beams in absorbing media. © 2007 IEEE.761764M. Zamboni-Rached, Diffraction-Attenuation Resistant Beams in Absorbing Media, Optics Express, 14, pp. 1804-1809 (2006). (Also available as e-print arXiv:physics/0506067 v2 15 Jun 2005)Recami, E., Zamboni-Rached, M., Nóbrega, K.Z., Dartora, C.A., Hernández-Figueroa, H.E., On the localized superluminal solutions to the Maxwell equations (2003) IEEE Journal of Selected Topics in Quantum Electronics, 9, pp. 59-73. , and refs. therein. For a review, seeZamboni-Rached, M., Recami, E., Hernández- Figueroa, H.E., New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies (2002) European Physical Journal D, 21, pp. 217-228. , See, e.gSushilov, N.V., Tavakkoli, J., Cobbold, R.S.C., Propagation of limited-liffraction X-waves in dissipative media (2002) IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49, pp. 675-68
Structure of the non-diffracting waves, and some interesting applications
No full textThis work is Chapter 2 of the Book. -- Since the early works on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially, the theory was developed taking into account only free space; however, in recent years, it has been extended for more complex media exhibiting effects such as dispersion, nonlinearity, anisotropy and losses. Such extensions have been carried out along with the development of efficient methods for obtaining nondiffracting beams and pulses in the subluminal, luminal and superluminal regimes. This Chapter (only partly a review) addresses some theoretical methods related to nondiffracting solutions of the linear wave equation in unbounded homogeneous media, as well as to some interesting applications of such waves. In section II we analyze the general structure of the Localized Waves, develop the so called Generalized Bidirectional Decomposition, and use it to obtain several luminal and superluminal (especially X-shaped) nondiffracting solutions of the wave equation. In section III we develop a space-time focusing method by a continuous superposition of X-Shaped pulses of different velocities. Section IV addresses the properties of chirped optical X-Shaped pulses propagating in material media without boundaries. Finally, in Section V, we show how a suitable superposition of Bessel beams can be used to obtain stationary localized wave fields, with a static envelope and a high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval of the propagation axis
Localized Waves: A scientific and historical introduction
No full textIn the first part of this paper we present general and formal (simple) introductions to the ordinary gaussian waves and to the Bessel waves, by explicitly separating the cases of the beams from the cases of the pulses; and, finally, an analogous introduction is presented for the Localized Waves (LW), pulses or beams. Always we stress the very different characteristics of the gaussian with respect to the Bessel waves and to the LWs, showing the numerous and important properties of the latter w.r.t. the former ones: Properties that may find application in all fields in which an essential role is played by a wave-equation (like electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). h In the second part of this paper (namely, in its Appendix) we recall at first how, in the seventies and eighties, the geometrical methods of Special Relativity (SR) predicted
---in the sense below specified--- the existence of the most interesting LWs, i.e., of the X-shaped pulses. At last, in connection with the circumstance that the X-shaped waves are
endowed with Superluminal group-velocities (as carefully discussed in the first part of this article), we briefly mention the various experimental sectors of physics in which Superluminal motions seem to appear: In particular, a bird's-eye view is presented of the experiments till now performed with evanescent waves (and/or tunneling photons), and with the ``localized Superluminal
solutions" to the wave equations
Production Of Dynamic Frozen Waves: Controlling Shape, Location (and Speed) Of Diffractionresistant Beams
No full textIn recent times, we experimentally realized quite an efficient modeling of the shape of diffraction-resistant optical beams, thus generating for the first time the so-called frozen waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen within a prefixed space interval of the propagation axis. In this Letter, we extend our theory of FWs, which led to beams endowed with a static envelope, through a dynamic modeling of the FWs whose shape is now allowed to evolve in time in a predetermined way. Further, we experimentally create such dynamic FWs (DFWs) in optics via a computational holographic technique and a spatial light modulator. Experimental results are presented here for two cases of DFWs, one of zeroth order and the other of higher order, the latter being the most interesting exhibiting a cylindrical surface of light whose geometry changes in space and time. © 2015 Optical Society of America.402458345837Zamboni-Rached, M., (2004) Opt. Express, 12, p. 4001Zamboni-Rached, M., Recami, E., Hernández-Figueroa, H.E., (2005) J. Opt. Soc. Am. A, 22, p. 2465Zamboni-Rached, M., (2006) Opt. Express, 14, p. 1804Durnin, J., Miceli, T.J., Eberly, J.H., (1987) Phys. Rev. Lett., 58, p. 1499Saari, P., Reivelt, K., (1997) Phys. Rev. Lett., 79, p. 4135Recami, E., (2003) IEEE J. Sel. Top. Quantum Electron., 9, p. 59Zamboni-Rached, M., Ambrosio, L.A., Hernández Figueroa, H.E., (2010) Appl. Opt., 49, p. 5861Vieira, T.A., Gesualdi, M.R.R., Zamboni-Rached, M., (2012) Opt. Lett., 37, p. 2034Vieira, T.A., Zamboni-Rached, M., Gesualdi, M.R.R., (2014) Opt. Commun., 315, p. 374Prego-Borges, L.J., Zamboni-Rached, M., Hernández-Figueroa, H.E., Recami, E., (2013) IEEE Trans. Ultrason. Ferroel. Freq. Control, 60, p. 2414Hernández-Figueroa, H.E., Zamboni-Rached, M., Recami, E., (2008) Localized Waves, p. 386. , WileyHernández-Figueroa, H.E., Recami, E., Zamboni-Rached, M., (2014) Non-diffracting Waves, p. 507. , WileyVasara, A., Turunen, J., Friberg, A., (1989) J. Opt. Soc. Am. A, 6, p. 1748Arrizón, V., (2003) Opt. Lett., 28, p. 2521Recami, E., Zamboni-Rached, M., Nóbrega, K.Z., Dartora, C.A., Hernández-Figueroa, H.E., (2013) Method and Apparatus for Producing Stationary (intense) Wavefields of Arbitrary Shape, , U. S. patent, August, 1
Soliton-like Solutions To The Ordinary Schrödinger Equation Within Standard Quantum Mechanics
Full text linkIn recent times attention has been paid to the fact that (linear) wave equations admit of "soliton-like" solutions, known as localized waves or non-diffracting waves, which propagate without distortion in one direction. Such localized solutions (existing also for K-G or Dirac equations) are a priori suitable, more than gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, localized solutions exist even for the ordinary (linear) Schrödinger equation within standard quantum mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions (even if localized and "decaying") are not square-integrable, as well as plane or spherical waves: we show therefore how to obtain finite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. © 2012 American Institute of Physics.535Bateman, H., Courant, R., Hilbert, D., Stratton, J.A., (1941) Electromagnetic Theory, 2, p. 356. , (Cambridge University Press, Cambridge)(Wiley, New York), (McGraw-Hill, New York)Rached, M.Z., Recami, E., Figueroa, H.E., Rached, M.Z., Recami, E., Figueroa, H.E., Recami, E., Rached, M.Z., Localized waves: a review (2009) Adv. Imaging Electron Phys., 156, pp. 235-355. , 10.1140/epjd/e2002-00198-7, H. E. H. Figueroa, M. Z. Rached, E. Recami, 10.1016/S1076-5670(08)01404-3, See, e.g. e-print arXiv:physics/0109062;, references therein;, edited by and (Wiley, New York)Rached, M.Z., Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures (2006) J. Opt. Soc. Am. A, 23, pp. 2166-2176. , 10.1364/JOSAA.23.002166, See, e.g.references thereinLu, J., Greenleaf, J.F., Nondiffracting X-waves: exact solutions to free-space scalar wave equation, and their finite aperture realizations (1992) IEEE Trans. Ultrason. Ferroelectricity Freq. Control, 39, pp. 19-31. , 10.1109/58.166806Donnelly, R., Ziolkowski, R.W., Designing localized waves (1993) Proc. R. Soc., London A, 440, pp. 541-565. , 10.1098/rspa.1993.0033, Cf., e.g.references thereinBarut, A.O., Maccarrone, G.D., Recami, E., Recami, E., Recami, E., Zamboni-Rached, M., Dartora, C.A., Recami, E., Superluminal waves and objects: an up-dated overview of the relevant experiments (1995) Phys. Lett. A, 209 (6), p. 227. , 10.1007/BF02770989, 10.1007/BF02724327, 10.1103/PhysRevE.69.027602, 10.1016/0375-9601(95)00735-3, references therein;cf. also e-print arXiv:0804.1502Recami, E., Lu, J., Greenleaf, J.F., Recami, E., Limited diffraction solutions to Maxwell (and Schrödinger) equations (1998) Physica A, 252, pp. 586-610. , 10.1016/S0378-4371(97)00686-9, references therein;cf. also e-print arXiv:physics/9610012Recami, E., Rached, M.Z., Figueroa, H.E.H., Rached, M.Z., Recami, E., Figueroa, H.E.H., Structure of the nondiffracting waves and some interesting applications (2008) Localized Waves, pp. 43-77. , H. E. H. Figueroa, M. Z. Rached, E. Recami, H. E. H. Figueroa, M. Z. Rached, E. Recami, e-print arXiv:0708.1655;, edited by and (Wiley, New York), Chap. 1, e-print arXiv:0708.1209;, edited by and (Wiley, New York), Chap. 2Ziolkowski, W., Besieris, I.M., Shaarawi, A.M., Aperture realizations of exact solutions to homogeneous wave-equations (1993) J. Opt. Soc. Am. A, 10, p. 75. , 10.1364/JOSAA.10.000075, See, e.g., SectionsLu, J., Greenleaf, J.F., Saari, P., Reivelt, K., Bowlan, P., Valtna-Lukner, H., Lohmus, M., Trebino, R., Measuring the spatiotemporal field of ultrashort Bessel-X pulses (2009) Opt. Lett., 34, pp. 2276-2278. , 10.1109/58.143178, 10.1103/PhysRevLett.79.4135, 10.1364/OL.34.002276, see alsoRached, M.Z., Recami, E., Rached, M.Z., Recami, E., Sheppard, C.J.R., Longhi, S., Salo, J., Greenleaf, J.F., Comparison of sidelobes of limited diffraction beams and localized waves (1995) Acoust. Imaging, 21 (1), pp. 145-152. , 10.1103/PhysRevA.77.033824, 10.1364/JOSAA.19.002218, 10.1364/OL.29.000147, 10.1121/1.1350398, 10.1007/978-1-4615-1943-0, e-print arXiv:0709.2372 cf. also thomamperRached, M.Z., Recami, E., Figueroa, H.E.H., Rached, M.Z., Recami, E., Figueroa, H.E.H., Rached, M.Z., Stationary optical wave fields with arbitrary longitudinal shape, by superposing equal-frequency Bessel beams: frozen waves (2004) Opt. Express, 12, pp. 4001-4006. , 10.1364/JOSAA.22.002465, 10.1364/OPEX.12.004001, e-print arXiv:physics/0502105Shaarawi, A.M., Besieris, I.M., Ziolkowski, R.W., Shaarawi, A.M., Besieris, I.M., Ziolkowski, R.W., Shaarawi, A.M., Ziolkowski, R.W., (1994) Phys. Lett. A, 188, pp. 218-224. , 10.1063/1.528995, 10.1016/0920-5632(89)90450-7, 10.1016/0375-9601(94)90442-1, especially SectionBarut, A.O., Barut, A.O., Ignatovich, V.K., Barut, A.O., Grant, A., Barut, A.O., Bracken, A.J., Hillion, P., Quantum theory of single events: localized de Broglie-wavelets, Schrödinger waves and classical trajectories (1992) Phys. Lett. A, 172, p. 1. , 10.1016/0375-9601(90)90369-Y, 10.1016/0375-9601(92)90120-B, 10.1007/BF00717580, 10.1007/BF00769701, 10.1007/BF01889713, L. de Broglie, 10.1016/0375-9601(92)90179-P, cf. also , in , edited by (Kluwer, Dordrecht)Conti, C., Trillo, S., Conti, C., Generalition and nonlinear dynamics of X-waves of the Schrödinger equation (2004) Phys. Rev. E, 70, p. 046613. , 10.1103/PhysRevLett.92.120404, 10.1103/PhysRevE.70.046613, Cf., e.gFor some work in connection with the ordinary Schrödinger equation, see for instance, besides Ref. 7, also Ref. 14Christodoulides, D.N., Efremedis, N.K., Di Trapani, P., Malomed, B.A., Bessel X-waves in two- and three-dimensional bidispersive optical systems (2004) Opt. Lett., 29, pp. 1446-1448. , 10.1364/OL.29.001446Small, E., Katz, O., Esshel, Y., Silderberg, Y., Oron, D., Faccio, D., Averchi, A., Trillo, S., Spontaneously generated X-shaped light bullets (2003) Phys. Rev. Lett., 91, p. 093904. , 10.1364/OE.17.018659, 10.1364/OE.15.013077, 10.1103/PhysRevLett.91.093904Berry, M.V., Balas, N.L., Kalnius, E.G., Miller, W., Lie theory and separation of variables (1974) J. Math. Phys., 15, pp. 1728-1737. , 10.1119/1.11855, 10.1063/1.1666533, see alsoBesieris, I.M., Shaarawi, A.M., Ziolkowski, R.W., Nondispersive accelerating wave packets (1994) Am. J. Phys., 62, pp. 519-521. , 10.1119/1.17510Chong, A., Renninger, W.H., Christodoulides, D.N., Wise, F.W., Christodoulides, D.M., Bandres, M.A., Gutiérrez-Vega, J.C., Airy-Gauss beams and theirtransformation by paraxial optical systems (2007) Opt. Express, 15, pp. 16789-16728. , 10.1038/nphoton.2009.264, 10.1038/nphoton.2008.211, 10.1364/OE.15.016719Martin, T., Landauer, R., Chiao, R.Y., Kwiat, P.G., Steinberg, A.M., Ranfagni, A., Mugnai, D., Steinberg, A.M., (1995) Phys. Rev. A, 52, p. 32. , 10.1103/PhysRevA.45.2611, 10.1016/0921-4526(91)90724-S, 10.1063/1.104544, 10.1103/PhysRevA.52.32, See, e.g. references therein;see alsoRached, M.Z., Nóbrega, K.Z., Recami, E., Figueroa, H.E.H., Rached, M.Z., Nóbrega, K.Z., Recami, E., Fontana, F., Superluminal localized solutions to Maxwell equations propagating along a waveguide: the finite-energy case (2003) Phys. Rev. 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Rep., 398, pp. 133-178. , 10.1016/j.physrep.2004.06.001, and references thereinMcLeod, J.H., McLeod, J.H., Durnin, J., Miceli, J.J., Eberly, J.H., Sheppard, C.J.R., Wilson, T., Sheppard, C.J.R., Gaussian-beam theory of lenses with annular aperture (1978) IEE J. Microwaves, Opt. Acoust., 2, pp. 163-166. , 10.1364/JOSA.44.000592, 10.1364/JOSA.50.000166, 10.1103/PhysRevLett.58.1499, 10.1049/ij-moa.1978.0023, 10.1049/ij-moa.1978.0035, see alsoFor pulses, however, the generation technique must deviate from optics', since in the Schrödinger equation case the phase of the Bessel beams produced through an annular slit would depend on the energyMackinnon, L., A nondispersive de Broglie wave packet (1978) Found. Phys., 8, p. 157. , 10.1007/BF00715205Gradshteyn, I.S., Ryzhik, I.M., (1965) Integrals, Series and Products, , 4th ed. 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Localized Waves: A Historical And Scientific Introduction
No full textIn the first part of this introductory chapter, we present general and formal (simple) introductions to the ordinary Gaussian waves and to the Bessel waves, by explicitly separating the cases of the beams from the cases of the pulses; and, finally, an analogous introduction is presented for the localized waves (LW), pulses or beams. Always we stress the very different characteristics of the Gaussian with respect to the Bessel waves and to the LWs, showing the numerous and important properties of the latter w.r.t. the former ones: Properties that may find application in all fields in which an essential role is played by a wave-equation (like electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). In the second part of this chapter (namely, in its Appendix), we recall at first how, in the seventies and eighties, the geometrical methods of special relativity (SR) predicted-in the sense below specified-the existence of the most interesting LWs, i.e., of the X-shaped pulses. At last, in connection with the circumstance that the X-shapedwaves are endowed with superluminal group-velocities (as carefully discussed in the first part of this chapter), we mention briefly the various experimental sectors of physics in which superluminal motions seem to appear: In particular, a bird's-eye view is presented of the experiments till nowperformed with evanescentwaves (and/or tunneling photons), and with the "localized superluminal solutions" to the wave equations. © 2008 John Wiley & Sons, Inc.141Recami, E., Classical tachyons and possible applications (1986) Rivista Nuovo Cimento, 9 (6), pp. 1-178. , issue 6, and refs. thereinRecami, E., Mignani, R., Magnetic monopoles and tachyons in special relativity (1976) Phys. Lett., 62 B, pp. 41-43Petrillo, V., Refaldi, L., (2003) Phys. Rev., 67 A, p. 012110Petrillo, V., Refaldi, L., (2000) Opt. 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Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures
Full text linkStarting from some general and plausible assumptions based on geometrical optics and on a common feature of the truncated Bessel beams, a heuristic derivation is presented of very simple analytical expressions capable of describing the longitudinal (on-axis) evolution of axially symmetric nondiffracting pulses truncated by finite apertures. The analytical formulation is applied to several situations involving subluminal, luminal, or super-luminal localized pulses, and the results are compared with those obtained by numerical simulations of the Rayleigh-Sommerfeld diffraction integrals. The results are in excellent agreement. The present approach can be rather useful, because it yields, in general, closed-form expressions, avoiding the need for time-consuming numerical simulations, and also because such expressions provide a powerful tool for exploring several important properties of the truncated localized pulses, such as their depth of fields, the longitudinal pulse behavior, and the decaying rates. (c) 2006 Optical Society of America.2392166217
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