Comparison of non-Hermitian three-dimensional quantization line shape in ion-doped microcrystals

In this paper, we studied the relationship between non-Hermitian quantization and line shape in ion-doped microcrystals. We depict the Eu³⁺: BiPO₄ exhibited a broad line shape in contrast to Eu³⁺: NaYF₄, and Dy³⁺: BiPO₄. The line shape is controlled through angle quantization (constructive and destructive quantization) and phonon detuning effects. The Eu³⁺: BiPO₄ and Eu³⁺: NaYF₄ exhibits less sensitivity to line shape as compared to Dy³⁺: BiPO₄. The more sensitivity of Dy³⁺: BiPO₄ is supported by the presence of multiple levels, which disrupt the transition from destructive (out of phase de-phase rate Г) to constructive (in phase dressing Rabi frequency G) three-dimensional quantization. The line shape evolution from out of phase to in phase could be tuned by changing time gate position (the ratio of G and Г regulated largely) and time gate width (the ratio of G and Г regulated on a small scale). We observed that the line shape ratio in Dy³⁺: BiPO₄ is significantly smallest (13.63 %) as compared to Eu³⁺: NaYF₄ (61.29 %) and Eu³⁺: BiPO₄ (85.18 %). Furthermore, the angle quantization affects the line shape evolution of fluorescence and Autler-Townes. However, spontaneous four-wave mixing line shape evolution can not be controlled by the angle quantization. Such results hold significant potential for applications in long band stop filter.