Phase structure transfer is demonstrated through a FWM process in the 5S1/2 → 5P3/2 → 5D5/2 ladder configuration of 87Rb which is excitable with 780 nm and 776 nm laser light. This leads to the cascade decay 5D5/2 → 6P3/2 → 5S1/2 generating light in 5.2 µm and 420 nm respectively. The second decay yields a collimated blue light (CBL) that is easy to detect. We are carrying out two studies about angular momentum within this frequency conversion scheme. The first is one is focused on the heritage of the orbital angular momentum (OAM) arrays using the helical Mathieu beams; whereas the second was the first demonstration of elliptical angular momentum transfer in a FWM process. To do the later experiments we employed even and odd Mathieu modes.
Both experiments share the same experimental setup, adding a Michelson interferometer for the recognition of optical vortex with OAM.
(P1) Pumping beam of 780nm, (PBS) Polarizing beam splitter, (IF) Interference filter, (BF) Blue Filter, (T1, T2) Telescopes, (BS)beam splitter, (M1, M2) Mirror.
The images show experimental results obtained from the FWM for the even Mathieu beams of forth order in both wavelengths of 776nm (P2, in red) and 420nm (CBL, in blue). Specifically, the top line exhibits the corresponding intensity distribution space associated to its structure (or space of configuration), while the bottom line illustrates the intensity spectrum distribution space (or Fourier space).
The way to analyse the structure of the transferred modes is based on the measurement of the ellipticity parameter which is characteristic to Mathieu modes. This is done through quantitative measurements in the configuration and Fourier spaces obtained from images taken with CMOS camera (and a lens for the Fourier space). The quantitative analysis of the Mathieu modes that participate in the FWM process confirm that the blue Mathieu modes (even and odd) do inherit the ellipticity and transverse linear momentum of their infrared analogues. Thus the full modes are transferred throughout the FWM process.
It was possible to identify the multiple optical vortices in the CBL with the help of the interferometer. This was done by interfering the blue decay beam with itself.
Image (a) corresponds to a pumping beam with the structure of a helical Mathieu beam with order m = 4 and ellipticity q = 21.78; (b) is an image of the corresponding CBL fully inheriting its structure.