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Helical Ince-Gaussian modes as superpositions of Hermite-Gaussian modes
E.G. Abramochkin 1, V.V. Kotlyar 2,3

1 Lebedev Physical Institute,
Novo-Sadovaya Str. 221, Samara, 443011, Russia;
2 Image Processing Systems Institute, NRC "Kurchatov Institute",
Molodogvardeyskaya Str. 151, Samara, 443001, Russia;
3 Samara National Research University,
Moskovskoye Shosse 34, Samara, 443086, Russia

 PDF, 2153 kB

DOI: 10.18287/2412-6179-CO-1647

Pages: 867-875.

Full text of article: Russian language.

Abstract:
We theoretically and numerically investigate helical Ince-Gaussian modes, hIGp,q(x, y, ε). Explicit analytical expressions are derived that describe dependence of the orbital angular momentum of the helical Ince-Gaussian modes at p=2, 3, 4, 5 on the ellipticity parameter ε. For this purpose, the earlier obtained expansions of Ince-Gaussian modes in terms of Hermite-Gaussian modes are used. We demonstrate that in general the orbital angular momentum is an even function of ε, which changes non-monotonically when ε varies from zero to infinity. At zero ε, the orbital angular momentum is equal to the index q of the Ince-Gaussian mode, whereas at ε=∞, the orbital angular momentum is [q(p–q+1)]1/2. Topological charge of the helical Ince-Gaussian mode depends on ε and is equal to the index q at ε=0 and to the index p at ε=∞.

Keywords:
mode beams, Ince-Gaussian modes, optical vortices, Hermmite-Gaussian beams, Laguerre-Gaussian beams, orbital angular momentum, topological charge.

Citation:
Abramochkin EG, Kotlyar VV. Helical Ince-Gaussian modes as superpositions of Hermite-Gaussian modes. Computer Optics 2025; 49(6): 867-875. DOI: 10.18287/2412-6179-CO-1647.

Acknowledgements:
This work was financially supported by the Russian Science Foundation (Project No. 22-12-00137, theory and numerical simulation). This work was also performed within the State assignment of NRC "Kurchatov Institute" (Introduction and Conclusion).

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