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Chinese Physics B

Simulating the resonance-mediated (1 + 2)-three-photon absorption enhancement in Pr3+ ions by a rectangle phase modulation

Wenjing Cheng, Yuan Li, Hongzhen Qiao, Meng Wang, Shaoshuo Ma, Fangjie Shu, Chuanqi Xie, Guo Liang

Published Feb 10, 2022• 0 citations
Publisher

Abstract

Enhancing the upconversion luminescence of rare earth ions is crucial for their applications in the laser sources, fiber optic communications, color displays, biolabeling, and biomedical sensors. In this paper, we theoretically study the resonance-mediated (1 + 2)-three-photon absorption in Pr3+ ions by a rectangle phase modulation. The results show that the resonance-mediated (1 + 2)-three-photon absorption can be effectively enhanced by properly designing the depth and width of the rectangle phase modulation, which can be attributed to the constructive interference between on-resonant and near-resonant three-photon excitation pathways. Further, the enhancement efficiency of resonance-mediated (1 + 2)-three-photon absorption can be affected by the pulse width (or spectral bandwidth) of femtosecond laser field, final state transition frequency, and absorption bandwidths. This research can provide a clear physical picture for understanding and controlling the multi-photon absorption in rare-earth ions, and also can provide theoretical guidance for improving the up-conversion luminescence.

DOI
10.1088/1674-1056/ac5398

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Enhancing the upconversion luminescence of rare earth ions is crucial for their applications in the laser sources, fiber optic communications, color displays, biolabeling, and biomedical sensors. In this paper, we theoretically study the resonance-mediated (1 + 2)-three-photon absorption in Pr3+ ions by a rectangle phase modulation. The results show that the resonance-mediated (1 + 2)-three-photon absorption can be effectively enhanced by properly designing the depth and width of the rectangle phase modulation, which can be attributed to the constructive interference between on-resonant and near-resonant three-photon excitation pathways. Further, the enhancement efficiency of resonance-mediated (1 + 2)-three-photon absorption can be affected by the pulse width (or spectral bandwidth) of femtosecond laser field, final state transition frequency, and absorption bandwidths. This research can provide a clear physical picture for understanding and controlling the multi-photon absorption in rare-earth ions, and also can provide theoretical guidance for improving the up-conversion luminescence.
We extend the third perturbation theory to study the polarization control behavior of the intermediate state absorption in Nd 3+ ions. The results show that coherent interference can occur between the single-photon and three-photon excitation pathways, and depends on the central frequency of the femtosecond laser field. Moreover, single-photon and three-photon absorptions have different polarization control efficiencies, and the relative weight of three-photon absorption in the whole excitation processes can increase with increasing the laser intensity. Therefore, the enhancement or suppression of the intermediate state absorption can be realized and manipulated by properly designing the intensity and central frequency of the polarization modulated femtosecond laser field. This research can not only enrich theoretical research methods for the up-conversion luminescence manipulation of rare-earth ions, but also can provide a clear physical picture for understanding and controlling multi-photon absorption in a multiple energy level system .
We theoretically and experimentally demonstrate the quantum coherent control of the resonance-mediated two-photon absorption in rare-earth ions by the phase-shaped femtosecond laser pulse. Our theoretical results show that the resonance-mediated two-photon absorption can be effectively controlled, but the control efficiency depends on the laser repetition rate in real experiment due to the long lifetime and the short decoherence time of the excited state, and the larger laser repetition rate yields the lower control efficiency. These theoretical results are experimentally confirmed in glass sample doped with Er3+ by utilizing the femtosecond lasers with low repetition rate of 1 kHz and high repetition rate of 80 MHz.
We study in detail coherent phase control of femtosecond resonance-mediated (2+1)(2+1)(2+1) three-photon absorption and its dependence on the spectral bandwidth of the excitation pulse. The regime is the weak-field regime of third perturbative order. The corresponding interference mechanism involves a group of three-photon excitation pathways that are on resonance with the intermediate state and a group of three-photon excitation pathways that are near resonant with it. The model system of the study is atomic sodium (Na), for which experimental and numerical-theoretical results are obtained. Prominent among the results is our finding that with simple proper pulse shaping an increase in the excitation bandwidth leads to a corresponding increase in the enhancement of the three-photon absorption over the absorption induced by the (unshaped) transform-limited pulse. For example, here, a 40 nm bandwidth leads to an order-of-magnitude enhancement over the transform-limited absorption.
Abstract Controlling the up-conversion luminescence of rare-earth ions in real-time, in a dynamical and reversible manner, is very important for their application in laser sources, fiber-optic communications, light-emitting diodes, color displays and biological systems. In previous studies, the up-conversion luminescence control mainly focused on the weak femtosecond laser field. Here, we further extend this control behavior from weak to intermediate femtosecond laser fields. In this work, we experimentally and theoretically demonstrate that the up-conversion luminescence in Dy 3+ ion doped glass can be artificially controlled by a π phase step modulation, but the up-conversion luminescence control behavior will be affected by the femtosecond laser intensity, and the up-conversion luminescence is suppressed by lower laser intensity while enhanced by higher laser intensity. We establish a new theoretical model (i.e. the fourth-order perturbation theory) to explain the physical control mechanism by considering the two- and four-photon absorption processes, and the theoretical results show that the relative weight of four-photon absorption in the whole excitation process will increase with the increase in laser intensity, and the interference between two- and four-photon absorptions results in up-conversion luminescence control modulation under different laser intensities. These theoretical and experimental works can provide a new method to control and understand up-conversion luminescence in rare-earth ions, and also may open a new opportunity to the related application areas of rare-earth ions.
Femtosecond coherent phase control of resonance mediated (2+1)(2+1)(2+1) three-photon absorption is studied both theoretically and experimentally. The regime is perturbative of third order. The photoexcitation coherently combines elements of both nonresonant and resonance-mediated multiphoton transitions. By proper simple pulse shaping the three-photon absorption in Na is effectively controlled experimentally, enhanced up to $\ensuremath{\sim}300%$ of the absorption induced by the transform-limited pulse. It is achieved by phase manipulating intra- and intergroup interferences involving two groups of three-photon excitation pathways: (i) on resonance and (ii) near resonance with the intermediate resonance state accessed by nonresonant two-photon transition.
We theoretically and experimentally demonstrate the up-conversion fluorescence control via resonance-mediated two-photon absorption in rare-earth ions by varying both the laser polarization and phase. We show that both the laser polarization and phase can control the up-conversion fluorescence, and the up-conversion fluorescence intensity is decreased when the laser polarization changes from linear through elliptical to circular. We also show that the laser polarization will affect the control efficiency of the up-conversion fluorescence by varying the laser phase, and the circular polarization will reduce the control efficiency. Furthermore, we suggest that the control efficiency by varying the laser polarization and the effect of the laser polarization on the control efficiency by varying the laser phase can be artificially manipulated by controlling the laser spectral bandwidth. This optical control method opens a new opportunity to control the up-conversion fluorescence of rare-earth ions, which may have significant impact on the related applications of rare-earth ions.