From Maxwell to paraxial wave optics (English)

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In: Physical Review A   ;  11 ,  4  ;  1365-1370  ;  1975
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In this paper we are concerned with the propagation of a light beam through an inhomogeneous, isotropic medium with a possibly nonlinear index of refraction. The customary paraxial approximations of neglecting grad div E and seeking a plane-polarized solution are shown to be incompatible with the exact Maxwell equations. By starting from Maxwell's equations, and scaling transverse and longitudinal distances by the beam waist w 0 and diffraction length l , respectively, an expansion procedure in powers of w 0 l is developed. The exact equations obeyed by the zeroth-order fields are not Maxwell's equations but the customary paraxial approximation to Maxwell's equations. Equations for the first-, second-, and third-order fields are developed. The first-order field is found to be a longitudinal field. It is solved for explicitly in terms of the zeroth-order field which is transverse. Thus a precise knowledge of the meaning and accuracy of paraxial wave optics is obtained.

Table of contents – Volume 11, Issue 4

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1125
Hyperfine-structure investigation of highly excited D 2 levels in Rb 87 and Cs 133 using a cw tunable dye laser in a two-step excitation scheme
Svanberg, S. / Tsekeris, P. | 1975
1138
Analytic potential with adjusted parameters for diatomic molecules
Hajj, Fuad Y. | 1975
1144
L 2 discretizations of the continuum: Radial kinetic energy and Coulomb Hamiltonian
Yamani, Hashim A. / Reinhardt, William P. | 1975
1157
Atomic Bethe-Goldstone calculations of term splittings, ionization potentials, and electron affinities. III. Al, Si, P, S, Cl, and Ar using orbital excitations
Moser, C. M. / Nesbet, R. K. | 1975
1162
Nuclear hexadecapole antishielding factors
Sen, K. D. / Narasimhan, P. T. | 1975
1168
Some applications of excited-state-excited-state transition densities
Yeager, D. L. / Nascimento, M. A. C. / McKoy, V. | 1975
1175
Collision quenching of the metastable 2 S state of muonic hydrogen and the muonic helium ion
Mueller, R. O. / Hughes, V. W. / Rosenthal, H. / Wu, C. S. | 1975
1187
Energy transfer in noble-gas mixtures: Penning ionization in He/Xe
Shuker, R. / Szöke, A. / Zamir, E. / Binur, Y. | 1975
1193
Electron-impact ionization cross sections and bound-free generalized oscillator strengths for atomic systems
Robb, W. Derek / Rountree, Steven P. / Burnett, Tom | 1975
1200
Nonmetastable Penning ionization in He ( 3 P 1 ) -Ne, Ar, Kr, Xe collisions
Kubota, S. / Davies, C. / King, T. A. | 1975
1205
Binding effects in high-energy scattering applied to K -shell ionization
Binstock, J. / Reading, J. F. | 1975
1214
Electron excitation cross sections of N 2 + B Σ u + 2 , N i, and N ii states and their temperature dependence
Lewis, J. W. L. / Price, L. L. / Powell, H. M. | 1975
1223
Electron impact excitation of Hg +
Crandall, D. H. / Phaneuf, R. A. / Dunn, Gordon H. | 1975
1233
K -shell ionization cross sections in asymmetric heavy-ion-atom collisions
Brandt, Werner / Laubert, Roman | 1975
1239
Ionization in low-keV-energy Ar+Ar collisions
Eriksen, F. J. / Fernandez, S. M. / Bray, A. B. / Pollack, E. | 1975
1245
Collisions between rare-gas atoms at low keV energies. I. Symmetric systems
Brenot, J. C. / Dhuicq, D. / Gauyacq, J. P. / Pommier, J. / Sidis, V. / Barat, M. / Pollack, E. | 1975
1267
Anisotropy of characteristic K -shell x rays from heavy-ion—atom collisions
Pedersen, E. Horsdal / Czuchlewski, Stephen J. / Brown, Matt D. / Ellsworth, Louis D. / Macdonald, James R. | 1975
1271
Spin conservation during chemi-ionization and surface-electron ejection by He ( 2 S 3 )
Keliher, P. J. / Dunning, F. B. / O'Neill, M. R. / Rundel, R. D. / Walters, G. K. | 1975
1279
Intense polarized electron beams from chemi-ionization reactions with optically pumped He ( 2 S 3 )
Keliher, P. J. / Gleason, R. E. / Walters, G. K. | 1975
1286
Comparison of calculational methods for straggling in thin absorbers
Bichsel, Hans / Saxon, Roberta P. | 1975
1297
Molecular scattering: Convergence of close-coupling expansions in the presence of many open channels
Garrett, W. R. | 1975
1303
Electron emission from proton-hydrocarbon-molecule collisions at 0.3-2.0 MeV
Wilson, W. E. / Toburen, L. H. | 1975
1309
Vibrational excitation in N 2 O via the 2.3-eV shape resonance
Azria, R. / Wong, S. F. / Schulz, G. J. | 1975
1314
Resonant electron-molecule scattering: The impulse approximation in N 2 O
Dubé, L. / Herzenberg, A. | 1975
1326
High-energy behavior of the vibrational excitation cross section σ 01 for H + - H 2
Azziz, N. / Herrero, F. A. / Mendez-Plácido, R. | 1975
1334
Theoretical low-energy scattering cross sections for He ( 2 S 1 ) + He ( 1 S 1 ) He ( 2 P 1 ) + He ( 1 S 1 )
Shipsey, E. J. / Browne, J. C. / Olson, R. E. | 1975
1340
Ab initio cross sections for excitation of the 2 p state of hydrogen by electron impact at intermediate energies
Brandt, Maynard A. / Truhlar, Donald G. | 1975
1347
Energy lost to ionization by 254-eV Ge 73 atoms stopping in Ge
Jones, K. W. / Kraner, H. W. | 1975
1354
Perturbative solution to the single-mode model of superradiance
Narducci, L. M. / Bluemel, V. | 1975
1358
Stimulated and spontaneous radiative frequency shifts of a two-level system
Hioe, F. T. / Eberly, J. H. | 1975
1365
From Maxwell to paraxial wave optics
Lax, Melvin / Louisell, William H. / McKnight, William B. | 1975
1371
Fluctuations on the approach to equilibrium: The Gordon local-equilibrium conjecture
Abbott, R. J. / Wilson, R. S. | 1975
1375
Self-focusing, absorption, and stimulated Rayleigh-wing scattering
Smith, Durand M. / Wiggins, T. A. | 1975
1380
Quantum-beat phenomena described by quantum electrodynamics and neoclassical theory
Chow, Weng W. / Scully, Marlan O. / Stoner Jr., John O. | 1975
1389
Quantum electrodynamic and semiclassical interference effects in spontaneous radiation
Herman, R. M. / Grotch, H. / Kornblith, R. / Eberly, J. H. | 1975
1397
Brownian motion of a quantum oscillator
Carusotto, Salvatore | 1975
1407
Relaxation of a driven harmonic oscillator
Carusotto, Salvatore | 1975
1414
Analytic critical scattering intensity with a nonscaling correlation function
Alexanian, Moorad / Medina-Noyola, Magdaleno | 1975
1417
New computational method in the theory of spinodal decomposition
Langer, J. S. / Bar-on, M. / Miller, Harold D. | 1975
1430
Molecular dynamical studies of rough-sphere fluids
Subramanian, G. / Davis, H. T. | 1975
1440
Quasielastic light scattering from nematic p -methoxybenzylidene- p - n -butylaniline (MBBA)
Fellner, Hans / Franklin, Wilbur / Christensen, Stanley | 1975
1446
Power dissipated by a harmonically bound Brownian particle in an ac field: A regeneralization of the Rayleigh problem
Harris, S. | 1975
1450
Collective motions in classical liquids. IV. Liquid rubidium
Bansal, Ravinder / Pathak, K. N. | 1975
1454
Effects of an attractive- δ -potential impurity center on Bose-Einstein condensation
Rosa Jr., S. Goulart / Hipólito, O. / Lobo, R. | 1975
1462
Noniterative calculation of the radial-distribution function in a high-density classical electron gas. II. Correlation and perturbation corrections
Mo, K. C. / Hooper Jr., C. F. | 1975
1468
Symmetric ion-atom collisions at medium energies: Noncharacteristic radiation
Laubert, R. / Haselton, H. H. / Mowat, J. R. / Peterson, R. S. / Sellin, I. A. | 1975
1472
Eikonal approximation applied to many-electron atoms
Williamson Jr., W. / Foster, G. | 1975
1475
Electron impact autoionization in heavy alkali metals
Nygaard, Kaare J. | 1975
1479
Two-electron S and P term values with smooth Z dependence
Accad, Y. / Pekeris, C. L. / Schiff, B. | 1975
1482
Comments on the departure from the Z 2 dependence in ionization by heavy projectiles
Hopkins, Forrest / Brenn, Rudiger / Whittemore, Anthony R. / Cue, Nelson / Dutkiewicz, Vince | 1975
1485
Comment on "Coherent and incoherent scattering laws of liquid argon"
Dasannacharya, B. A. | 1975