Second-Harmonic Generation from a Thin Cylindrical Layer: II. Analysis of Solution

Kapshaǐ, V. N.; Shamyna, A. A.

doi:10.1134/s0030400x19060134

Cited by 5 publications

(16 citation statements)

References 8 publications

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“…Here and elsewhere, m, m 1 , m 2 are arbitrary integer numbers. Similar properties have been found earlier in the analysis of second-harmonic generation and sum-frequency generation in surface layers of spherical and cylindrical dielectric particles [2][3][4][5]. They remain valid at any values of generation parameters (∀χ…”

Section: Properties Of the Spatial Distribution Of Double-frequency R...supporting

confidence: 84%

“…4, c with σ = −0.5, one can see that the polarizations of radiation generated in the same direction at σ = 0.5 and σ = −0.5 are opposite, while the amplitude remains constant. These features persisted in second-harmonic generation in the surface layer of spherical [3] and cylindrical [2] dielectric particles.…”

Section: Analysis Of Directivity Patternsmentioning

confidence: 88%

“…Let us direct Cartesian axes in such a way that the wave vector of an incident electromagnetic wave lies in plane OXZ, the spheroidal particle axis is aligned with axis OZ, and the geometric particle center is at the origin of coordinates. The diagrams of the problem being solved is similar in this case to the diagram of second-harmonic generation in the surface layer of a cylindrical particle [1], and formulae for the explicit form of vectors similar to the ones found in [2] may be used: k (ω) = k ω sin θ in e x + k ω cos θ in e z , k (2ω) = k 2ω e r , e (ω) = cos θ in (− cos ϕ in + iσ sin ϕ in )…”

Section: Explicit Form Of Vectorsmentioning

confidence: 91%

“…The notation used in plotting the patterns is similar to the one from [2][3][4][5]. It is assumed in all directivity patterns that a particle is located at the origin of coordinates.…”

Section: Directivity Patterns Notationmentioning

confidence: 99%

“…It was noted in [2][3][4][5]7,8] that the size of a dielectric particle has a considerable effect on the distribution of second-harmonic radiation in the far-field region. A similar dependence is typical of generation in the surface layer of spheroidal particles.…”

Section: Analysis Of Directivity Patternsmentioning

confidence: 99%

See 4 more Smart Citations

Second-harmonic generation in the surface layer of a dielectric spheroidal particle: II. Analysis of the solution

Shamyna

Kapshaǐ

Talkachov

2022

Optics and Spectroscopy

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The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed. Keywords: second-harmonic generation, spheroidal dielectric particle, symmetry of the spatial distribution of radiation, conditions for the absence of generation, conditions for the generation of linearly polarized radiation.

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Section: Properties Of the Spatial Distribution Of Double-frequency R...supporting

confidence: 84%

Section: Analysis Of Directivity Patternsmentioning

confidence: 88%

Section: Explicit Form Of Vectorsmentioning

confidence: 91%

“…The notation used in plotting the patterns is similar to the one from [2][3][4][5]. It is assumed in all directivity patterns that a particle is located at the origin of coordinates.…”

Section: Directivity Patterns Notationmentioning

confidence: 99%