Molecular modulation and the coherent transfer of optical orbital angular momentum in femtosecond radiation.

We investigate the nonlinear parametric interaction of optical radiation in various transverse modes in a Raman-active medium. Our pioneering work has allowed us to take a next step in molecular modulation by including optical orbital angular momentum. We have verified the orbital angular momentum algebra (OAM-algebra) derived by [Strohaber et al., Opt. Lett. 37, 3411 (2012)] to hold for higher-order Laguerre Gaussian modes. This same algebra was also found to describe the coherent transfer of OAM when Ince-Gaussian modes were used. New theoretical considerations extend the OAM-algebra to even and odd Laguerre Gaussian, and Hermite Gaussian modes. The results of this novel research are relevant to the spatiotemporal synthesis of custom sub-femtosecond pulse.