Beyond Conservation of Orbital Angular Momentum in Stimulated Parametric Down-Conversion

Stimulated parametric down-conversion is a nonlinear optical process in which the orbital angular momentum of light is conserved under most practical conditions. However, there are instances in which the topological charge is not compatible with the remaining modal structure of the stimulated idler beam. As a result, the stimulated down-converted light diffracts and gives rise to Laguerre-Gaussian-like beams with nonzero radial indices. We present a theoretical and experimental analysis demonstrating this fundamental aspect of nonlinear processes with light beams possessing orbital angular momentum.

Figure 1

Illustration of the generation of radial modes and the conservation of angular momentum in StimPDC. BBO, $\beta$-barium borate. Box: examples of idler field generated for different combinations of pump and seed beams, and their decomposition into Laguerre-Gaussian modes ${\mathrm{LG}}_{q\ell }$. Int., intensity. The far-field patterns are computed for a propagation distance of $5z_R$, and all scale bars correspond to $1000{\lambda }_i$ (where ${\lambda }_i$ is the wavelength of the idler field).

Figure 2

Experimental setup. The pump and seed beams are collimated using telescopes, prepared as optical vortices using spatial light modulators (SLMs), and overlapped on a nonlinear crystal. The down-converted field (idler) is imaged in the near and far field with a telescope and a CCD camera.

Figure 3

Experimental and simulated idler-beam profiles at a fixed plane in the far field, for different combinations of topological charges of the pump and seed beams. The azimuthally averaged profiles are displayed instead of the images, given the cylindrical symmetry of the transverse intensity distribution. Each profile is individually normalized by its maximum intensity value.

Figure 4

Experimental and simulated idler-beam profiles as a function of the propagation distance (starting from the crystal plane), for different combinations of topological charges of the pump and seed beams. The azimuthally averaged profiles show the buildup of the far-field intensity distribution.