Cascade Raman sideband generation and orbital angular momentum relations for paraxial beam modes.

Area of Science:

• Nonlinear optics
• Quantum optics
• Laser physics

Background:

• Understanding the behavior of optical radiation in various transverse modes is crucial for advanced light manipulation.
• Orbital angular momentum (OAM) algebra provides a framework for describing the properties of light beams carrying OAM.
• Raman-active media enable nonlinear interactions for generating new optical frequencies and properties.

Purpose of the Study:

• To investigate the nonlinear parametric interaction of optical radiation in diverse transverse modes within a Raman-active medium.
• To experimentally and theoretically verify the established orbital angular momentum algebra (OAM-algebra) for high-order Laguerre-Gaussian modes.
• To extend the OAM-algebra to encompass Ince-Gaussian, even/odd Laguerre-Gaussian, and Hermite-Gaussian beam modes.

Main Methods:

• Experimental investigation of nonlinear parametric interactions in a Raman-active medium.
• Theoretical verification of OAM-algebra for high-order Laguerre-Gaussian modes (ℓ>1).
• Application of a change of basis for theoretical extension of OAM-algebra to other beam types.

Main Results:

• The orbital angular momentum algebra (OAM-algebra) was successfully verified for high-order Laguerre-Gaussian modes.
• The OAM-algebra was found to accurately describe the coherent transfer of OAM for Ince-Gaussian modes.
• New theoretical insights extended the OAM-algebra to include even/odd Laguerre-Gaussian and Hermite-Gaussian beam modes.

Conclusions:

• The OAM-algebra is a robust framework applicable to a wider range of optical beam modes beyond initial formulations.
• This work provides detailed insights into the spatiotemporal synthesis of custom broadband pulses via Raman sideband generation.
• The findings facilitate the development of novel techniques for controlling and generating tailored optical radiation.