Analytic solution of flat-top Gaussian and Laguerre–Gaussian laser field components

Cerjan, Alexander; Cerjan, C.

doi:10.1364/ol.35.003465

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…For the trivial case with p ¼ l ¼ 0, f ≤ 0:2 allows for accuracy greater than 10 −2 . This result is in agreement with previously published results [12,20], noting the difference in the definition of the beam waist from these previous results,…”

Section: Error Integral Analysissupporting

confidence: 94%

“…This last expression represents a significantly cleaner result for Laguerre-Gaussian beams using the angular spectrum method than has previously been presented [17,20]. Note that the field component appears as an expansion in powers of the natural order parameter f .…”

Section: Angular Spectrum Methodssupporting

confidence: 52%

“…each of which converges absolutely for fixed n. It is clear from the form of these integrals that the large b behavior is controlled by the Gaussian exponential term, especially because 1=f 2 is large. For certain ranges of f with fixed values of l and p, the second integral may be neglected as has been previously demonstrated [11,12,20]. A thorough discussion of when this is possible is presented in a section below, but for now we will proceed assuming that we are within the acceptable parameter space.…”

Section: Angular Spectrum Methodsmentioning

confidence: 99%

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Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation

Cerjan

2011

J. Opt. Soc. Am. A

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We derive a full field solution for Laguerre-Gaussian beams consistent with the Helmholtz equation using the angular spectrum method. Field components are presented as an order expansion in the ratio of the wavelength to the beam waist, f=λ/(2πw₀), which is typically small. The result is then generalized to a beam of arbitrary polarization. This result is then used to reproduce the signature angular momentum properties of Laguerre-Gaussian beams in the paraxial limit. The subsequent higher-order term is similarly obtained, which does not display a clear separation of orbital and spin angular momentum components.

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Section: Error Integral Analysissupporting

confidence: 94%

Section: Angular Spectrum Methodssupporting

confidence: 52%

Section: Angular Spectrum Methodsmentioning

confidence: 99%

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Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation

Cerjan

2011

J. Opt. Soc. Am. A

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“…With the fixed values of n and m, the second integral can be neglected for the certain range of f , which has been demonstrated in Refs. [35][36][37][38]. When n = m = 0, the omission of the second integral is allowed for the case of f ≤ 0.2.…”

Section: Orbital Angular Momentum Density Of An Elegant Lagurre-gaussmentioning

confidence: 99%

Orbital Angular Momentum Density of an Elegant Laguerre-Gaussian Beam

Zhou¹,

Ru²

2013

PIER

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Abstract-Based on the method of the vectorial angular spectrum, an analytical expression of the electric field of an elegant LaguerreGaussian beam in free space is derived beyond the paraxial approximation, and the corresponding magnetic field is obtained by taking the curl of the electric field. By using the expressions for the electromagnetic fields, the expression of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is derived, which is applicable to both the near and far fields. The effects of the three beam parameters on the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam are studied. The distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is also compared with that of the standard Laguerre-Gaussian beam. The result shows that the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is more simple and centralized than that of the standard Laguerre-Gaussian beam.

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“…The integral in the above equation normally is difficult to evaluate analytically [2,20]. To obtain an analytic solution to the optical field, a widely used approximation is to extend the upper limit of integration from 1 to ∞ [2,[20][21][22][23][24][25],…”

mentioning

confidence: 99%

Highly nonparaxial propagation and optical power exchange in uniaxial crystals: Analytical and numerical study

Wang

et al. 2015

EPL

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We present an analytical solution to the nonparaxial propagation of a Gaussian beam, which is based on the asymptotic expansion of a highly oscillatory integral. The advantage of this method is its application to a highly nonparaxial beam and large transverse radius regime, which are hard to reach by previous approximations. The validity of this analytical expansion is fully investigated, by benchmarking it against the accurate numerical solutions. We extend this method to deduce the analytical expression for a nonparaxial optical field in uniaxial crystals, from which we reveal the vortex generation in each component of the optical field and discuss their evolution dynamics. Moreover, we study the optical power exchange between two circular components of a nonparaxial field. We find that the powers carried by both components undergo a saturation and become equal as the propagating distance increases.

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Analytic solution of flat-top Gaussian and Laguerre–Gaussian laser field components

Cited by 6 publications

References 11 publications

Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation

Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation

Orbital Angular Momentum Density of an Elegant Laguerre-Gaussian Beam

Highly nonparaxial propagation and optical power exchange in uniaxial crystals: Analytical and numerical study

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