Summing Pauli asymptotic series to solve the wedge problem.

The use of the asymptotic treatment for the wedge diffraction problem established long ago by Pauli [Phys. Rev.54, 924 (1938)] is here revisited and proposed in the character of a powerful computational tool for accurately retrieving the total electromagnetic field even in the near zone. After proving its factorial divergent character, the Pauli series is summed through the Weniger transformation, a nonlinear resummation scheme particularly efficient in the case of factorial divergence. Numerical results are carried out to show the accuracy and effectiveness of the proposed approach.

[1]  Paolo Ribeca,et al.  From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions , 2007, 0707.1596.

[2]  E. Heyman,et al.  Phase Space Gaussian Beam Summation Analysis of Half Plane Diffraction , 2007, IEEE Transactions on Antennas and Propagation.

[3]  R. Borghi.  Evaluation of diffraction catastrophes by using Weniger transformation. , 2007, Optics letters.

[4]  Riccardo Borghi,et al.  Complete far-field asymptotic series for free fields. , 2006, Optics letters.

[5]  Y. Umul.  Modified theory of the physical-optics approach to the impedance wedge problem. , 2006, Optics Letters.

[6]  M. Berry.  Universal oscillations of high derivatives , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Y. Umul.  Modified theory of physical optics approach to wedge diffraction problems. , 2005, Optics express.

[8]  M. Santarsiero,et al.  Summing Lax series for nonparaxial beam propagation. , 2003, Optics letters.

[9]  J. Hannay,et al.  Exact scattering theory for any straight reflectors in two dimensions , 2003, physics/0303093.

[10]  J. Zamastil,et al.  New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field , 2003 .

[11]  G. Scarpetta,et al.  Casimir Effect for a Perfectly Conducting Wedge in Terms of Local Zeta Function , 2002, hep-th/0202089.

[12]  M. Vesnik.  Analytical solution for electromagnetic diffraction on 2-D perfectly conducting scatterers of arbitrary shape , 2001 .

[13]  Álvarez,et al.  Calculation of the Aharonov-Bohm wave function. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[14]  H. Bruus,et al.  Edge diffraction, trace formulae and the cardioid billiard , 1995, chao-dyn/9509005.

[15]  Schmit,et al.  Diffractive orbits in quantum billiards. , 1995, Physical Review Letters.

[16]  E. J. Weniger.  Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series , 1989, math/0306302.

[17]  F. Gori.  Diffraction from a half-plane. A new derivation of the Sommerfeld solution☆ , 1983 .

[18]  P. Clemmow.  SOME EXTENSIONS TO THE METHOD OF INTEGRATION BY STEEPEST DESCENTS , 1950 .

[19]  W. Pauli.  On Asymptotic Series for Functions in the Theory of Diffraction of Light , 1938 .