Gaussian-beam-propagation theory for nonlinear optics involving an analytical treatment of orbital-angular-momentum transfer

Abstract

We present a general, Gaussian spatial mode propagation formalism for describing the generation of higher order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical angular momentum transfer interactions, and show how one can optimize the interaction to reduce the undesired modes. Past theoretical treatments of this problem have often been phenomenological, at best. Here we present an exact solution for the single-pass no-cavity regime, in which the the nonlinear interaction is not overly strong. We apply our theory to two experiments, with very good agreement, and give examples of several more configurations, easily tested in the laboratory.

Spiral bandwidth of four-wave mixing in Rb vapour

“…As the pump OAM increases ( ≥ 4) we observe the 420 nm light in an incoherent superposition of an increasing number of OAM modes, as predicted in Ref. [33], indicating that the 5.2 µm and 420 nm two-photon state becomes OAM entangled. We obtain the experimental spiral bandwidth and entanglement entropy via the full and p-mode decomposition of the generated blue light for a range of pump .…”

“…Due to the large wavelength difference of the two generated fields, the OAM distribution between them is pump-mode dependent. A simple theoretical model 15,33 , which we adapted to include a full and p description of all four fields, describes our system well, but could be improved by including propagation effects and a more accurate generated field waist prediction. For small pump OAM ( ≤ 3), our results are consistent with all OAM being transferred to the 420 nm light.…”

“…Overlap integral. The generated field and p mode decomposition for a particular pair of pump modes can be predicted by considering the FWM field overlap within the Rb cell 15,33 . The probability amplitude to generate a particular pair of 5.2 µm and 420 nm modes, when pumping with LG 780 p 780 and LG 776 p 776 , can be found by evaluating the integral: LG IR p IR dθdrdz, (9) where the mode waists are given by Eq.…”

Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince–Gaussian and Hermite–Laguerre–Gaussian modes

“…As distinctive structured light fields with phase singularities, optical vortices carrying orbital angular momentum (OAM) have hatched plenty of modern scientific applications in optical tweezers [1][2][3], optical communications [4,5], quantum entanglement [6][7][8] and nonlinear optics [9][10][11]. Besides the classical Laguerre-Gaussian (LG) beams carrying integer OAM with a single phase singularity, the multi-singularity vortex beams carrying fractional OAM were also reported [12][13][14][15][16][17].…”

Mode-selective image upconversion through turbulence

“…Nonlinear optics (NLO) underpins optical parametric oscillation [1,2], parametric downconversion [3,4], harmonic generation [5,6], sum-frequency generation [7,8], four wave mixing [9,10], etc., with wide applications in optical communications [11,12], biomedical engineering [13], metrology [14], and quantum information [15]. For optical signal processing and detection, NLO techniques can offer significant advantages over their linearoptics counterparts [5,16,17], as demonstrated repeatedly in temporal mode-selective frequency conversion [18][19][20][21][22][23][24], lossless photon shaping [25], spiral phase contrast imaging of the edges [26], and field-of-view enhancement [8,27]. To capitalize on the rich spatial features of light, frequency upconversion has been utilized for mode-selective detection of spatially orthogonal signals in few-mode waveguides [7,28], and more recently in nonlinear crystals to selectively convert overlapping Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes [29,30].…”