Analytical results for a Bessel function times Legendre polynomials class integrals

Neves, Antonio Alvaro Ranha; Padilha, Lázaro A.; Fontes, Adriana; Rodríguez, E.; Cruz, C. H. Brito; Barbosa, L. C.; César, Carlos L.

doi:10.1088/0305-4470/39/18/l06

Cited by 58 publications

(35 citation statements)

References 4 publications

(5 reference statements)

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“…(29) or the sum of these two residues times k − is exactly zero. Therefore, we consider only the remaining case K ≥ 0, where only two poles k 1− and k 2+ have positive imaginary parts.…”

Section: Appendixmentioning

confidence: 99%

Nonadiabatic tunneling in circularly polarized laser fields. II. Derivation of formulas

Barth

Smirnova

2013

Phys. Rev. A

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We provide detailed analysis of strong field ionization of degenerate valence p orbitals by circularly polarized fields. Our analytical approach is conceptually equivalent to the Perelomov, Popov, and Terent'ev (PPT) theory and is virtually exact for short range potentials. After benchmarking our results against the PPT theory for s orbitals, we obtain the results for p orbitals. We also show that, as long as the dipole approximation is valid, both the PPT method and our results are gauge invariant, in contrast with widely used strong field approximation (SFA). Our main result, which has already been briefly outlined in [I. Barth and O. Smirnova, Phys. Rev. A 84, 063415 (2011)], is that strong field ionization preferentially removes electrons counter-rotating to the circularly polarized laser field. The result is illustrated using the example of Kr atom. Strong, up to one order of magnitude, sensitivity of strong field ionization to the sense of electron rotation in the initial state is one of the key signatures of non-adiabatic regime of strong field ionization.

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Section: Appendixmentioning

confidence: 99%

Nonadiabatic tunneling in circularly polarized laser fields. II. Derivation of formulas

Barth

Smirnova

2013

Phys. Rev. A

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“…To facilitate the implementation of integral operation over h analytically, an exact solution to the integral on the hybrid product including the associated Legendre, Bessel, and exponential functions in spherical coordinates was verified rigorously by Neves et al 18 as follows: …”

Section: Multipole Expansion Of Helicoidal Bessel Beamsmentioning

confidence: 99%

Multipole expansion of acoustical Bessel beams with arbitrary order and location

Gong

Marston

2017

The Journal of the Acoustical Society of America

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An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

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“…This integral resembles a formerly reported one [56], the solution of which is Now, we are interested in taking the limit α → 0 of the above integral. Because of the properties of the Bessel function and associated Legendre functions, we obtain, for q = +1 and q = −1, 5) thereby eliminating the radial-dependency term, j p (kr)/kr, from the BSCs.…”

Section: Appendix a Shape-coefficient Integrals Of The Beammentioning

confidence: 63%

Photonic nanojets in optical tweezers

Neves

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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Photonic nanojets have been brought into attention ten years ago for potential application in ultramicroscopy, because of its sub-wavelength resolution that can enhance detection and interaction with matter. For these novel applications under development, the optical trapping of a sphere acts as an ideal framework to employ photonic nanojets. In the present study, we generated nanojets by using a highly focused incident beam, in contrast to traditional plane waves. The method inherits the advantage of optical trapping, especially for intracellular applications, with the microsphere in equilibrium on the beam propagation axis and positioned arbitrarily in space. Moreover, owing to optical scattering forces, when the sphere is in equilibrium, its center shifts with respect to the focal point of the incident beam. However, when the system is in stable equilibrium with a configuration involving optical tweezers, photonic nanojets cannot be formed. To overcome this issue, we employed double optical tweezers in an unorthodox configuration involving two collinear and co-propagating beams, the precise positioning of which would turn on/off the photonic nanojets, thereby improving the applicability of photonic nanojets.

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Analytical results for a Bessel function times Legendre polynomials class integrals

Cited by 58 publications

References 4 publications

Nonadiabatic tunneling in circularly polarized laser fields. II. Derivation of formulas

Nonadiabatic tunneling in circularly polarized laser fields. II. Derivation of formulas

Multipole expansion of acoustical Bessel beams with arbitrary order and location

Photonic nanojets in optical tweezers

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