Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation

Landesman, Barbara Tehan; Barrett, Harrison H.

doi:10.1364/josaa.5.001610

Cited by 36 publications

(35 citation statements)

References 9 publications

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“…These phasors are expressed in terms of associated Legendre functions and spherical Hankel functions of complex arguments (Couture & Bélanger, 1981). Landesman and Barrett obtained the same solutions using the oblate spheroidal coordinates (Landesman & Barrett, 1988). Such phasors can be viewed as being generated with the complex point-source method, leading to nonphysically realizable beams.…”

Section: Higher-order Nonparaxial Gaussian Beamsmentioning

confidence: 93%

“…The phasor of the nonparaxial Gaussian beam obtained with the help of the complex sourcepoint method depends on the parameter a, which is the confocal parameter of the oblate spheroidal coordinates (Landesman & Barrett, 1988). In fact, it turns out that the oblate spheroidal coordinates (,,) ξ ηφ are the ones in which it is natural to express the phasor of the nonparaxial Gaussian beam.…”

Section: The Confocal Parametermentioning

confidence: 99%

See 1 more Smart Citation

Ultrashort, Strongly Focused Laser Pulses in Free Space

April¹

2010

Coherence and Ultrashort Pulse Laser Emission

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Section: Higher-order Nonparaxial Gaussian Beamsmentioning

confidence: 93%

Section: The Confocal Parametermentioning

confidence: 99%

Ultrashort, Strongly Focused Laser Pulses in Free Space

April¹

2010

Coherence and Ultrashort Pulse Laser Emission

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“…Higher-order corrections [11][12][13] have been also suggested, which may provide an approximate solution with minimal numerical errors if a set of parameters is carefully chosen. Nevertheless, the lack of an exact solution for the description of tightly focused beams without any approximation, provided the impetus to further extend a method based on the complex source point (CSP) formalism [14][15][16][17][18][19][20] (Note the misprint in Eq. (3) of [20]; as written, Eq.…”

Section: Introductionmentioning

confidence: 99%

“…The same method can be also applied using the CSP formalism (Eq. (22) in [16]) [14,15,18,19,[41][42][43], and the result remains an exact solution of the Helmholtz equation. The effect of having the description of a generalized solution in a complex coordinates system, which may appear at first glance a simple artifice, has a major physical meaning in the description of evanescent waves [44] and the production of finite directional beams [17].…”

Section: Introductionmentioning

confidence: 99%

Vector spherical quasi-Gaussian vortex beams

Mitri

2014

Phys. Rev. E

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Model equations for describing and efficiently computing the radiation profiles of tightly sphericallyfocused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w 0 , a diffraction convergence length known as the Rayleigh range z R , and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave-fields without the need of neither the higher-order corrections nor the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist. PACS number(s): 41.20.Jb, 42.25.Bs, 42.15.Dp, 42.25.Fx, 02.90.+p

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“…12 The oblate spheroidal beams presented here do not present any singularity whenever c = 0. Using the CSPM, 7,8,9,10 it is usually proposed that in the paraxial limit d can take the value of R 0 . From eq.…”

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confidence: 99%

Exact nonparaxial beams of the scalar Helmholtz equation

Rodríguez-Morales

Chávez-Cerda

2004

Opt. Lett.

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It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.

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Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation

Cited by 36 publications

References 9 publications

Ultrashort, Strongly Focused Laser Pulses in Free Space

Ultrashort, Strongly Focused Laser Pulses in Free Space

Vector spherical quasi-Gaussian vortex beams

Exact nonparaxial beams of the scalar Helmholtz equation

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