Expansion of a plane wave into Gaussian beams

Červený, Vlastislav; Vaněk, J.

doi:10.1007/bf01582305

Cited by 53 publications

(31 citation statements)

References 5 publications

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“…On the other hand, we define the effective illumination region (EIR b ) as that surface that is illuminated by the beam wave incidence and restricted by the 2kW as shown in Figure 2-b. According to (9) and as shown in Figure 2, EIR p > EIR b , which results in increase in the surface current generated and that leads to the relation: σ 0 > σ b , as we are going to see in the numerical results. Also, from Figure 2, we expect that the target configuration including δ and ka together with kW are going to affect the EIR generally.…”

Section: Numerical Resultsmentioning

confidence: 88%

“…This can not be available easily especially for plane waves wide sufficiently at the fronts of large size targets in the far field. In an attempt to generate plane wave, an expansion of plane wave into Gaussian beam waves was derived [9]. Gaussian beams play a key role in different fields of physics; let us mention applications in lasers, electromagnetic waves, etc.…”

Section: Introductionmentioning

confidence: 99%

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On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

El-Ocla¹

2006

PIER

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Abstract-In this paper a study is presented to handle the behavior of radar cross section (RCS) of partially convex targets of large sizes up to five wavelengths in free space. The nature of incident wave is an important factor in the remote sensing and radar detection applications. To investigate the effects of incident wave nature on the RCS, scattering problems of plane and beam wave incidences are considered. Targets are taking large sizes to be bigger enough than the beam width with putting into consideration a horizontal incident wave polarization (E-wave incidence). The effects of the target configuration together with the beam width on the laser RCS compared to the case with the plane wave incidence are numerically analyzed. Therefore, we will be able to have some sort of control on radar detection using beam wave incidence.

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Section: Numerical Resultsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

El-Ocla¹

2006

PIER

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“…Considering this point, many authors proposed the Gaussian beam approach; see [5,3,21] for examples. The Gaussian beam approach also resorts to the ray tracing system: the beam center is exactly a single ray.…”

Section: Gaussian Beamsmentioning

confidence: 99%

“…The asymptotic solution ceases to be valid at caustics where the rays intersect and the amplitudes blow up. Many remedies have been proposed to overcome this difficulty, among which is the Gaussian beam (summation) approach; see [5,3,21] for examples. In a way similar to the GO approach, the Gaussian beam approach also resorts to the concept of ray tracing: the central curve of each Gaussian beam is exactly a specific ray.…”

Section: Introductionmentioning

confidence: 99%

Gaussian beam approach for the boundary value problem of high frequency Helmholtz equation

Zheng

2010

Communications in Mathematical Sciences

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Abstract. We propose an asymptotic numerical method called the Gaussian beam approach for the boundary value problem of high frequency Helmholtz equation. The basic idea is to approximate the traveling waves with a summation of Gaussian beams by the least squares algorithm. Gaussian beams are asymptotic solutions of linear wave equations in the high frequency regime. We deduce the ODE systems satisfied by the Gaussian beams up to third order. The key ingredient of the proposed method is the construction of a finite-dimensional beam space which has a good approximating property. If the exact solutions of boundary value problems contain some strongly evanescent wave modes, the Gaussian beam approach might fail. To remedy this problem, we resort to the domain decomposition technique to separate the domain of definition into a boundary layer region and its complementary interior region. The former is handled by a domain-based discretization method, and the latter by the Gaussian beam approach. Schwarz iterations should then be performed based on suitable transmission boundary conditions at the interface of two regions. Numerical tests demonstrate that the proposed method is very promising.

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“…This cannot be available easily especially for plane waves sufficiently wide at the incidence fronts of large size targets in the far field. In an attempt to generate plane wave, an expansion of plane wave into Gaussian beam waves was derived [10]. Gaussian beams play a key role in different fields of physics; let us mention applications in lasers, electromagnetic waves, etc.…”

Section: Introductionmentioning

confidence: 99%

Backscattering From Partially Convex Targets in Free Space With H-Beam Wave Incidence

El-Ocla¹

2007

PIER

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Abstract-In [9], scattering problems of plane and beam wave incidences were presented. In that study, it was found that the target configuration together with beam width have a major effect on the laser RCS (LRCS). This conclusion was proved for horizontal incident wave polarization (E-polarization) in free space. The polarization of incident waves is one of the key parameters in the scattering problems and in particular in the resonance region where the target has a comparable size with the wave length. In this work, we extend our study and investigate the impact of vertical incident wave polarization (H-polarization) on the LRCS of large size targets and compare it with RCS of targets with plane wave incidence.

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Expansion of a plane wave into Gaussian beams

Cited by 53 publications

References 5 publications

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

Gaussian beam approach for the boundary value problem of high frequency Helmholtz equation

Backscattering From Partially Convex Targets in Free Space With H-Beam Wave Incidence

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