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Journal of Nonlinear Optical Physics & Materials

Coherent transfer of optical vortices via three-wave mixing in an Er3+-doped YAG crystal

Tong Zhang, Kai-Kai Zhang, Xuan-Xue Luo, Shubo Cheng, Tao Shui, Xu Deng, Wen-Xing Yang

Published Jul 3, 2026• 0 citations
Publisher

Abstract

In this paper, we investigate the effect of Er[Formula: see text]ion concentration on the transfer of orbital angular momentum (OAM) in an Er[Formula: see text]-doped yttrium aluminum garnet (YAG) crystal with a three-level ladder-type configuration, mediated by the optical nonlinear process of three-wave mixing (TWM). The OAM information from the incident vortex probe field can be transferred to the generated mixing field through the optical nonlinear process. Due to the change of electric dipole moment and spontaneous emission decay induced by Er[Formula: see text]ion concentration, the OAM transfer depends sensitively on the ion concentration. Furthermore, under different Er[Formula: see text] ion concentrations, the intensity and detuning of the control field have different effects on the conversion efficiency of OAM. More importantly, the conversion efficiency of OAM can be significantly enhanced by choosing suitable values of the control intensity and detuning at [Formula: see text] Er[Formula: see text]ion concentration. Finally, we explore the effect of Er[Formula: see text]ion concentration on the spatial distribution of the probe absorption. Moreover, the spatial absorption of the probe field is shown to evolve with propagation distance within the medium. It is obvious that the spatial pattern of the probe absorption can be effectively controlled via adjusting the detuning of the probe field. Therefore, our scheme enables efficient OAM transfer via second-order nonlinear three-wave mixing in an Er[Formula: see text]-doped YAG crystal by selecting suitable Er[Formula: see text] ion concentration, and may find potential applications in nonlinear quantum optics.

DOI
10.1142/s0218863526500372

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In this paper, we investigate the effect of Er[Formula: see text]ion concentration on the transfer of orbital angular momentum (OAM) in an Er[Formula: see text]-doped yttrium aluminum garnet (YAG) crystal with a three-level ladder-type configuration, mediated by the optical nonlinear process of three-wave mixing (TWM). The OAM information from the incident vortex probe field can be transferred to the generated mixing field through the optical nonlinear process. Due to the change of electric dipole moment and spontaneous emission decay induced by Er[Formula: see text]ion concentration, the OAM transfer depends sensitively on the ion concentration. Furthermore, under different Er[Formula: see text] ion concentrations, the intensity and detuning of the control field have different effects on the conversion efficiency of OAM. More importantly, the conversion efficiency of OAM can be significantly enhanced by choosing suitable values of the control intensity and detuning at [Formula: see text] Er[Formula: see text]ion concentration. Finally, we explore the effect of Er[Formula: see text]ion concentration on the spatial distribution of the probe absorption. Moreover, the spatial absorption of the probe field is shown to evolve with propagation distance within the medium. It is obvious that the spatial pattern of the probe absorption can be effectively controlled via adjusting the detuning of the probe field. Therefore, our scheme enables efficient OAM transfer via second-order nonlinear three-wave mixing in an Er[Formula: see text]-doped YAG crystal by selecting suitable Er[Formula: see text] ion concentration, and may find potential applications in nonlinear quantum optics.
We theoretically investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er YAG three-level system. Using the density-matrix formalism and coupled Maxwell-Bloch equations, we derive analytical expressions for the probe and generated beams that explicitly incorporate Er ion concentration. We show that an incident vortex-carrying probe beam transfers its OAM to a generated signal beam through a concentration-dependent sum-frequency nonlinear process, with complete phase and topological-charge preservation. By analyzing conversion efficiency, spatial phase, and intensity distributions, we identify an optimal Er concentration (3 percent) that maximizes vortex-transfer efficiency. Furthermore, the absorption and dispersion spectra of the probe and generated beams reveal the mechanism underpinning the vortex transfer and demonstrate tunable transitions between fast and slow regimes. These results establish Er YAG as a viable solid-state platform for the coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering for applications in high-dimensional quantum communication, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.
We investigate the effect of doped E r 3 + ion concentration on an electromagnetically induced grating in an E r 3 + -doped yttrium aluminum garnet (YAG) crystal. Due to the change of electric dipole moment and spontaneous emission decay induced by E r 3 + ion concentration, the Fraunhofer diffraction of the solid-state grating is sensitively dependent upon E r 3 + ion concentration. The three-level E r 3 + ion system with a closed loop leads to probe gain appearing in some concentrations of the E r 3 + ion, which significantly improves the first-order diffraction efficiency of the solid-state grating. Furthermore, it is demonstrated that the relative phase, signal detuning, and grating thickness have different effects on the first-order diffraction efficiency of the solid-state grating under different concentrations of the E r 3 + ion. Therefore, our scheme may provide a basis for selecting a suitable concentration to realize high-efficiency optical switching and routing in future integrated systems.
We investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er³⁺: YAG three-level system. Using the density-matrix formalism and coupled Maxwell-Bloch equations, we derive analytical expressions for the probe and generated beams that explicitly incorporate Er³⁺-ion concentration. We show that an incident vortex-carrying probe beam transfers its OAM to a generated signal beam through a concentration-dependent sum-frequency nonlinear process, with complete phase and topological-charge preservation. By analyzing conversion efficiency, spatial phase, and intensity distributions, we identify an optimal Er³⁺ concentration (3%) that maximizes vortex-transfer efficiency. Furthermore, the absorption and dispersion spectra of the probe and generated beams reveal the mechanism underpinning the vortex transfer and indicate the potential for concentration-selectable transitions between fast and slow propagation regimes. These results establish Er³⁺: YAG as a viable solid-state platform for coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering, with potential relevance to classical and quantum OAM-based communication protocols, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.
The effect of Er[Formula: see text] ion concentration and incoherent pumping field on the Fraunhofer diffraction pattern of the transmitted light beam in Er[Formula: see text]: YAG crystal is discussed. It is shown that under different concentration of Er[Formula: see text] ion in crystal, the energy of the probe light can transfer to the higher orders of the grating. Also, it is shown that the switching from electromagnetically induced grating to electromagnetically induced phase gratin or vice versa can be obtained by different concentration of Er[Formula: see text] ion and incoherent pumping rate in crystal. Moreover, we have found that by replacing the probe light by optical vortex light, the asymmetric diffraction pattern can be obtained by tuning the optical vorticity of optical vortex light. In this case, the asymmetric diffraction pattern can also be controlled at different ion concentration.
We investigate the effect of doped Er 3+ ion concentration on the Goos–Hänchen (GH) shift of a reflected beam in a Kretschmann–Raether structure, where an Er 3+ -doped yttrium aluminum garnet crystal is employed as the substrate. Due to the difference in the electric dipole moment and spontaneous emission decay induced by Er 3+ ion concentration, the reflected GH shift is sensitively dependent upon Er 3+ ion concentration. Furthermore, it is demonstrated that the intensity and detuning of the control field have different effects on the magnitude, sign, and position of the GH shift under different concentrations of Er 3+ ion. Therefore, our scheme may provide a basis for selecting suitable concentrations to realize high-performance optical devices in future integrated systems.
A scheme for high-efficiency transfer of optical vortices is proposed by an inelastic two-wave mixing (ITWM) process in an inverted-Y four-level atomic medium, which is originally prepared in a coherent superposition of two ground states. The orbital angular momentum (OAM) information in the incident vortex probe field can be transferred to the generated signal field through the ITWM process. Choosing reasonable experimentally realizable parameters, we find that the presence of the off-resonance control field can greatly improve the conversion efficiency of optical vortices, rather than in the absence of a control field. This is caused by the broken of the destructive interference between two one-photon excitation pathways. Furthermore, we also extend our model to an inelastic multi-wave mixing process and demonstrate that the transfer efficiency between multiple optical vortices strongly depends on the superposition of the ground states. Finally, we explore the composite vortex beam generated by collinear superposition of the incident vortex probe and signal fields. It is obvious that the intensity and phase profiles of the composite vortex can be effectively controlled via adjusting the intensity of the control field. Potential applications of our scheme may exist in OAM-based optical communications and optical information processing.