Helical Ince-Gaussian laser beams as superpositions of Hermite-Gaussian beams

Area of Science:

• Physics
• Optics
• Mathematical Physics

Background:

• Helical Ince-Gaussian (hIG) modes are a class of optical beams.
• Understanding their properties is crucial for applications in optical communications and microscopy.
• The ellipticity parameter (ε) significantly influences beam characteristics.

Purpose of the Study:

• To theoretically and numerically analyze the ellipticity dependence of orbital angular momentum (OAM) in hIG modes.
• To derive explicit analytical relationships for the OAM of hIG modes (p=2,3,4,5) as a function of ellipticity (ε).

Main Methods:

• Expansion of hIG modes in terms of Hermite-Gaussian modes.
• Theoretical derivation of analytical relationships.
• Numerical analysis to validate theoretical findings.

Main Results:

• Explicit analytical relationships were derived for the ε-dependence of OAM in hIG modes.
• The orbital angular momentum (OAM) of hIG modes was shown to be an even function of the ellipticity parameter (ε).
• The OAM does not exhibit monotonic behavior as ε varies across its range.

Conclusions:

• The study provides a comprehensive understanding of OAM behavior in hIG modes concerning ellipticity.
• The findings are significant for manipulating and controlling OAM in optical systems.
• The non-monotonic and even nature of OAM dependence on ellipticity offers new possibilities for optical beam design.