Phase-Matching Controlled Orbital Angular Momentum Conversion in Periodically Poled Crystals

Nonlinear interactions between light waves can exchange energy, linear momentum, and angular momentum. The direction of energy flow between frequency components is usually determined by the conventional phase-matching condition related to the linear momentum. However, the transfer law of orbital angular momentum (OAM) during frequency conversion remains to be elucidated. Here, we demonstrate experimentally that OAM transfer depends strongly on the phase-matching condition defined by both linear and orbital angular momenta. Under different phase-matching configurations, the second-harmonic wave exhibits variable OAM spectral characteristics such as the presence of just a single value or of odd orders only. Our results pave the way toward unveiling the underlying mechanism of nonlinear conversion of OAM states.

Figure 1

(a) Schematic of a general SHG process in a periodically poled crystal (nonlinear grating). The arrows represent the directions of the spontaneous polarization. For $\theta =90°$ and $\alpha =0°$, this is the collinear SHG. (b) Phase-matching configurations for collinear SHG [18], nonlinear Bragg diffraction [19], and nonlinear Raman-Nath diffraction [20].

Figure 2

Intensity profiles and OAM spectra of SH waves from (a) third-, (b) fifth-, and (c) sixth-order nonlinear Bragg diffraction with the TC of the FW being $l=3$. The corresponding diffraction angles are 4.71°, 7.97°, and 9.86° respectively.

Figure 3

Intensity profiles and OAM spectra of SH waves with different phase mismatch $\mathrm{\Delta }{k}_y$. For comparison, nonlinear Bragg diffraction with $\mathrm{\Delta }{k}_y=0.0$ is shown in (c), and cases of nonlinear Raman-Nath diffraction are shown in (a), (b), (d), and (e). The TC of the FW is $l=3$.

Figure 4

Intensity profiles and OAM spectra of SH waves for (a) first- and (b) second-order Raman-Nath diffraction from a short-pitched PPKTP; the corresponding phase mismatches $\mathrm{\Delta }{k}_y$ are shown in each panel. The TC of the FW is $l=1$.