Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section

Carter, William H.

doi:10.1364/josa.62.001195

Cited by 171 publications

(70 citation statements)

References 4 publications

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“…Several authors have addressed the analysis of the longitudinal component of the focused light beams. Carter showed that a focused light beam has a longitudinal component [19]. Lax, Louisell and McKnight showed a way to calculate the longitudinal component under the paraxial approximation using a perturbation analysis [20].…”

Section: Introductionmentioning

confidence: 99%

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Gillen¹,

Seck²,

Guha³

2010

Opt. Express

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Abstract:Vector diffraction theory is applied to the case of focused TEM 00 Gaussian beams passing through a spatially limiting aperture in order to investigate the propagation of these clipped focused-Gaussian beams. Beam distributions at different axial distances show that a traditional M 2 propagation model cannot be used for the propagation of clipped focus-Gaussian beams. Using Luneberg's vector diffraction theory and Fresnel approximations, an analytical model for the on-axis transverse and longitudinal electric fields and intensity distributions is presented including predictions of the maximum obtainable intensity. In addition, an analytical expression is provided for the longitudinal component of the electric field of a TEM 00 mode unperturbed Gaussian beam. Experimental results are also presented and compared to the model's predictions.

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Section: Introductionmentioning

confidence: 99%

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Gillen¹,

Seck²,

Guha³

2010

Opt. Express

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“…(17) and (18) can be performed by utilizing the method of stationary phase [19,20]. In this paper, the utilization of this method indicates that, the integrals in Eqs.…”

Section: Analytical Expressions For the Far-field Te And Tm Termsmentioning

confidence: 99%

“…(17) and Eq. (18) can be applicable to both the paraxial and non-paraxial cases [19,20], in the far-field region. Therefore, the analytical form of Eq.…”

Section: Energy Flux Distributions Of the Pfg Beam In The Far Fieldmentioning

confidence: 99%

“…It has been proved that, for an arbitrary polarized electromagnetic beam, which can be expressed in terms of vectorial angular spectrum, is approximately composed of the transversal electric (TE) term and the transversal magnetic (TM) term [6][7][8]. Many investigations have been carried out dealing with vectorial structural characteristics of various laser beams in the far field [9][10][11][12][13][14][15][16][17][18], by means of the method of stationary phase [19,20]. Based on these studies, a question may arise: what impact would a π flip phase have on the TE term, TM term and the whole beam in the far field?…”

Section: Introductionmentioning

confidence: 99%

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Vectorial Structure of a Phase-Flipped Gauss Beam in the Far Field

Li¹,

Chen²,

Xu³

et al. 2010

PIER B

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Abstract-Based on the vectorial angular spectrum representation and the method of stationary phase, internal vectorial structures of a phase-flipped Gauss (PFG) beam diffracting in the far field are derived in analytical forms. The energy flux for the TE term, TM term and the whole beam are derived and depicted by numerical examples. Influences of the f parameter on the whole energy flux distributions are analyzed. Discrepancies of the whole energy flux distributions between the paraxial and non-paraxial cases are shown in detailed manners. Furthermore, influences of the f parameter on discrepancies between two cases are also studied.

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“…(19) is close to one, which leads to the incoherent scattering cross section as the same as that for an incident plane wave. Because the condition mentioned above normally occurs in practice, a taped plane wave (paraxial gaussian beam) is used commonly instead of a plane wave in the rough surface scattering numerical calculations fro many researchers [14][15][16].…”

Section: The Coherent and Incoherent Scattered Intensity And Section mentioning

confidence: 99%

Investigation on the Scattering Characteristics of Gaussian Beam From Two Dimensional Dielectric Rough Surfaces Based on the Kirchhoff Approximation

Wang¹,

Wu²,

Li³

2008

PIER B

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Abstract-The scattering characteristic of paraxial gaussian beam from two dimensional dielectric rough surfaces is studied in this paper. The modification of the Kirchhoff approximation theory for rough surface scattering by an incident gaussian beam instead of a plane wave are developed based on conventional Kirchhoff scattering theory and plane wave spectrum expansion method. The coherent and incoherent scattered intensity and cross section of two dimensional dielectric rough surfaces is derived in detail. As a application, under incidence wave length λ = 1.06 µm, we calculate the coherent and incoherent scattered intensity and cross section of Gaussian beam scattering from plating aluminium dielectric rough surfaces change with the scattering zenith angles in different rough surface correlation length, rough surface height root mean square and other conditions. In the same scattering conditions, we compare the coherent and incoherent scattered section between the gaussian beam and plane wave to prove that our methods and programming cods is correct. The numerical results are shown 224 Wang, Wu, and Li that the incident gaussian beam size is much larger compared with the surface height correlation length, the normalized scattering cross section is the same as for an incident plane wave. The ratio between the beam size and the surface height correlation length play an important role in the scattering characteristic of the gaussian beam from two dimensional dielectric rough surfaces. The ratio is bigger, the coherent and scattered intensity and section is more remarkable and on the contrary the incoherent scattered intensity and section is relatively smaller.

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Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section

Cited by 171 publications

References 4 publications

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Vectorial Structure of a Phase-Flipped Gauss Beam in the Far Field

Investigation on the Scattering Characteristics of Gaussian Beam From Two Dimensional Dielectric Rough Surfaces Based on the Kirchhoff Approximation

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