Topological charge algebra of optical vortices in nonlinear interactions

Abstract

We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams.

Orbital angular momentum mixing in type II second harmonic generation

“…In appendix A, the calculation of the corresponding overlap integral is detailed and two selection rules are derived. The first one leads to the expected OAM conservation, already discussed in previous works [40,41,43,48,49]. The second one is less obvious and predicts that higher radial orders are generated in the second harmonic field when opposite helicities are combined in the nonlinear process.…”

Generation of coupled orbital angular momentum modes from an optical vortex parametric laser source

“…Such helical structures are expected to offer new research avenues, for example, chiral selective imaging systems (e.g., atomic force microscopes [47]), optoelectro-mechanical systems, and plasmon-enhanced chiral metamaterials. Frequency extension of the optical vortex via nonlinear optical interactions [48], such as second harmonic generation [49][50][51][52][53][54][55], sum frequency generation [56,57], optical parametric generation [58][59][60], and stimulated Raman scattering [61] provides not only wavelength versatile optical vortex sources that match their wavelengths with the absorption bands of individual materials for such applications but also a variety of new fundamental physical insights. In particular, an optical parametric oscillator (OPO) provides an efficient method to achieve widely tunable optical vortex sources in the near-and mid-infrared regions, and it also inspires a question concerning the OAM conservation law, that is, how the OAM of a pump beam is divided between the signal (higher energy photon) and idler (lower energy photon) outputs [62].…”

Detection of mixed OAM states via vortex breakup

“…Because nonlinear process amplify small perturbations (noise) [24,25], these extra components play a large role for OVs in different nonlinear processes such as second harmonic generation [26], Raman generation with femtosecond OVs [27,28,29], or white light generation [30]. As a result, the nonlinearly generated beams may become so distorted that they represent a mixed state [31] containing comparable amounts of different OAM values. This mixed state may be coherent -when components do interfere with each other [32] or incoherent -when components do not interact with each other.…”