Rotation-controlled nonlinear orbital-angular-momentum filtering via slow-light four-wave mixing

Abstract

Abstract We propose a rotation-controlled nonlinear orbital-angular-momentum (OAM) filter based on photonic-band-gap-assisted four-wave mixing (PBG-FWM) in rubidium vapor. The model follows the field convention of PBG-FWM experiments: an OAM probe field $E_1$ is Bragg-reflected through the nonlinear polarization produced with two counterpropagating Gaussian coupling fields $E_3$ and $E_3'$, while the generated field is denoted by $E_F$. The coupling pair forms a standing-wave Rabi frequency $|G_{3s}|^2=|G_3|^2+|G_3'|^2+2G_3G_3'\cos(2k_3z)$, which creates the longitudinal PBG modulation and enters the resonant denominator of the third-order susceptibility. Rotation adds an OAM-dependent rotational Doppler shift to the probe and generated FWM modes. In a slow-light PBG-FWM medium this shift is converted into a longitudinal phase-matching perturbation, giving $\eta_m(\Omega)=\eta_0{\rm sinc}^2[\Delta k_{\rm rot}^{(m)}L/2]$ in the phase-matching-dominated limit. Rotation can also perturb $\chi^{(3)}$ through Doppler-shifted detunings, producing envelope and asymmetry corrections. The theory predicts OAM-dependent FWM quenching, the readable petal rotation, and a rotationally tunable OAM cutoff. The results provide a design route for rotation-sensitive structured-light processing in atomic nonlinear media.