2D Complex Point Source Radiation Problem I. Complex Distances and Complex Angles

E. GAGO-RIBAS; M.j. González MORALES

Makale detayları

2D Complex Point Source Radiation Problem I. Complex Distances and Complex Angles

Yazarlar:

E. GAGO-RIBAS | M.j. González MORALES

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Electrical Engineering and Computer Science 2002 Vol.10 Issue 2, pp.317-344

Belge Tipi:

Makale

Yayın Tarihi:

1/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000744334

Sıklık:

İki Aylık

eISSN:

1303-6203

pISSN:

1300-0632

Özet:

 

A methodology based on the complex spaces analysis, which  allows to generalize the study of wave radiation and scattering  problems is presented in this paper.  From the analytic continuation  of functions defined in the real domain (real propagation or  scattering spaces) into the complex space (space of complex  coordinates), general non homogeneous phase field solutions are  obtained for a particular wave problem.  From these general solutions,  other common solutions obtained under different approximations will  arise.  This procedure allows to obtain a complete classification of  the solutions for the wave problem under analysis, and also to study  both the ranges of validity of the different approximations, and the  behavior of any particular solution, leading to a more general  representation of the problem.  In the present paper, the basis for  this methodology will be presented in detail, and will be applied to  the general complex beams wave propagation problem arising from the  analytic continuation from homogeneous cylindrical waves and the  corresponding free-space wave equation.  As a direct consequence, new  magnitudes arise from this formulation.  Complex distances, complex  angles and other complex magnitudes related to these are the essential  ones.  All of them are carefully analyzed in this first paper, mapping  their meaning into the real propagation space, and emphasizing the  interpretation of the results.  All these magnitudes will play a  fundamental role not only in the analysis of the radiation problem  associated to a particular wave problem, but also in the later  analysis of scattering problems involving non homogeneous general wave  solutions (i.e. scattering problems under complex beams incidence).   In this sense, the complex mappings presented in this paper will  constitute the fundamental step to: (i) understand the general problem  which involves all the particular solutions; (ii) characterize the  behavior and ranges of validity of these particular solutions; (iii)  understand the meaning of the complex magnitudes, such as complex  distances and angles, and the information they can carry out into the  real space in later practical problems such as scattering problems,  and (iv) extend this methodology to represent other types of wave  problems, such as those involving evanescent plane waves, surface  waves, etc.

 

A methodology based on the complex spaces analysis, which  allows to generalize the study of wave radiation and scattering  problems is presented in this paper.  From the analytic continuation  of functions defined in the real domain (real propagation or  scattering spaces) into the complex space (space of complex  coordinates), general non homogeneous phase field solutions are  obtained for a particular wave problem.  From these general solutions,  other common solutions obtained under different approximations will  arise.  This procedure allows to obtain a complete classification of  the solutions for the wave problem under analysis, and also to study  both the ranges of validity of the different approximations, and the  behavior of any particular solution, leading to a more general  representation of the problem.  In the present paper, the basis for  this methodology will be presented in detail, and will be applied to  the general complex beams wave propagation problem arising from the  analytic continuation from homogeneous cylindrical waves and the  corresponding free-space wave equation.  As a direct consequence, new  magnitudes arise from this formulation.  Complex distances, complex  angles and other complex magnitudes related to these are the essential  ones.  All of them are carefully analyzed in this first paper, mapping  their meaning into the real propagation space, and emphasizing the  interpretation of the results.  All these magnitudes will play a  fundamental role not only in the analysis of the radiation problem  associated to a particular wave problem, but also in the later  analysis of scattering problems involving non homogeneous general wave  solutions (i.e. scattering problems under complex beams incidence).   In this sense, the complex mappings presented in this paper will  constitute the fundamental step to: (i) understand the general problem  which involves all the particular solutions; (ii) characterize the  behavior and ranges of validity of these particular solutions; (iii)  understand the meaning of the complex magnitudes, such as complex  distances and angles, and the information they can carry out into the  real space in later practical problems such as scattering problems,  and (iv) extend this methodology to represent other types of wave  problems, such as those involving evanescent plane waves, surface  waves, etc.

Makale detayları

2D Complex Point Source Radiation Problem I. Complex Distances and Complex Angles

Yazarlar: E. GAGO-RIBAS | M.j. González MORALES

Yayıncı: TUBITAK

Dergi: Turkish Journal of Electrical Engineering and Computer Science 2002 Vol.10 Issue 2, pp.317-344

Belge Tipi: Makale

Yayın Tarihi: 1/2002

Belge Dili: Türkçe

Document ID (Org No.): 2000744334

Sıklık: İki Aylık

eISSN: 1303-6203

pISSN: 1300-0632

Sayı

Yazarlar:

E. GAGO-RIBAS | M.j. González MORALES

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Electrical Engineering and Computer Science 2002 Vol.10 Issue 2, pp.317-344

Belge Tipi:

Makale

Yayın Tarihi:

1/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000744334

Sıklık:

İki Aylık

eISSN:

1303-6203

pISSN:

1300-0632