Recently, the up-conversion (UC) luminescence of luminescent material doped with rare-earth ions, which converts the low-frequency stimulation into high-frequency emission via two-photon or multi-photon absorption process, has attracted considerable attention because of its unique optical properties, such as narrow emission spectrum, intense luminescence intensity, high conversion efficiency, good optical stability, and long luminescence lifetime, and has been widely used in various related fields, such as light-emitting diodes,^[1,2] fiber optic communication,^[3,4] laser sources,^[5,6] color display,^[7,8] medical imaging,^[9,10] biological labels,^[11,12] etc. If the UC luminescence can be controlled, such as in enhancement, suppression or multi-color tuning, its relevant applications can be greatly extended. By now, several schemes have been proposed to experimentally realize the UC luminescence enhancement, suppression, and tuning. For example, a common method is to adjust the material property by varying its dopant-host combination,^[13–15] nanoparticle size,^[16,17] and dopant concentration^[18,19] in the synthesis process, and the other common method is to control the laser parameter by varying the excitation wavelength,^[20] power density,^[21] pulse duration,^[22] spectral phase^[23,24] or polarization.^[25,26] In addition, applying an electric or magnetic field has also been proved to be an available method to control the UC luminescence.^[27,28]

Because of the surface effect, volume effect, quantum size effect, and macroscopic quantum tunnel effect, the nanocrystal material shows different performances in magnetic, optic, electric, and chemical properties compared with normal bulk material.^[29,30] The nanocrystal material doped with rare-earth ions combines the unique optical properties of both nanocrystals and rare-earth ions, and therefore is shown to be a promising alternative to luminescent materials, such as NaGdF₄-based nanocrystals for biological fluorescence imaging,^[31] NaYbF₄:Tm³⁺/Ho³⁺/Er³⁺ and NaYF₄:Yb³⁺ used as biological markers.^[32] In the present work, we experimentally and theoretically show that the UC luminescence in Er³⁺-doped NaYF₄ nanocrystals dispersed in the silicate glass can be controlled by varying the femtosecond laser polarization. Our experimental results show that the UC luminescence intensity can be reduced when the laser polarization is changed from linear through elliptical to circular, but the control efficiency will be affected by the laser repetition rate, and the lower repetition rate will yield the higher control efficiency. Our theoretical studies indicate that the polarization modulation depends on the near-resonant two-photon absorption but is independent of the on-resonant two-photon absorption, energy transfer up-conversion, and excited state absorption. In addition, a two-color femtosecond laser field is proposed to improve the polarization control efficiency of UC luminescence by keeping the near-resonant two-photon absorption process but excluding the other excitation processes.

Our experimental arrangement is shown in Fig. 1, where a Ti-sapphire mode-locked regenerative amplifier (Spectra-Physics, Spitfire) with a pulse duration of about 50 fs, central wavelength of 800 nm, and repetition rate of 1 kHz and a mode-locked Ti-sapphire laser oscillator (Spectra-Physics, Tsunami) with a pulse duration of about 35 fs, central wavelength of 800 nm, and repetition rate of 80 MHz are used as the excitation sources, and two removable mirrors are utilized to switch the two laser sources. A quarter wave plate (Thorlabs, AQWP05M-980, 690–1120 nm) is used to vary the laser polarization from linear through elliptical to circular. The polarization-modulated femtosecond laser pulse is focused into the experimental sample with a lens of 50-mm focal length, and the laser intensities at the focus area are estimated to be 4× 10¹³ W/cm² for the 1-kHz laser amplifier and about 2×10¹¹ W/cm² for the 80-MHz laser oscillator respectively. All luminescence signals emitted from the sample are collected perpendicularly by a telescope system and recorded by a spectrometer with charge-coupled device (CCD).

Fig. 1.

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	Fig. 1. Schematic diagram of experimental arrangement for polarization control of UC luminescence in Er3+-doped NaYF4 nanocrystals. Here, M1 and M3 are removable mirrors, which are used to switch the 1-kHz femtosecond laser amplifier and 80-MHz femtosecond laser oscillator.

In our experiment, the glass ceramic containing Er³⁺-doped NaYF₄ nanocrystals is used as our study example, which is synthesized via modification from melt-quenching to subsequent heat treatment. The precursor sample is prepared with the molar ratio of 40SiO₂-25Al₂O₃-18Na₂CO₃-10YF₃-7NaF-1ErF₃. The original material is mixed and melted in a covered platinum crucible at a temperature of 1450 °C for 45 min in the ambient atmosphere and then cast into a brass mold followed by annealing at a temperature of 450 °C for 10 h. The synthesized glass is heated to a temperature of 600 °C in steps of 10 K/min, kept at this temperature for 2 h, and then cooled to room temperature to form the glass ceramic through crystallization. The glass ceramic sample is cut and polished for optical measurement in our experiment. X-ray diffraction (XRD) analysis is performed to identify the crystallization phase with a power diffractometer (Bruker D8 Advance) operated at 40 kV and 40 mA, and the measured result is shown in Fig. 2, where Cu Kα is used as a radiation source, and 2θ is scanned in a range of 20°–90° in steps of 0.01°. Multiple sharp peaks are observed in the XRD curve, which can be attributed to cubic α -NaYF₄ crystalline phase, indicating the crystallization of α -NaYF₄ during thermal treatment.

Fig. 2.

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	Fig. 2. XRD curve of glass ceramic containing Er3+-doped NaYF4 nanocrystals. Here, those peaks from α-NaYF4 are indexed.

Transmission electron microscopy (TEM) images of the sample are provided in Fig. 3(a), which show that nanocrystals with an average size of 20 nm–30 nm disperse densely in the glass matrix. Besides, the high-resolution TEM (HRTEM) of an individual α-NaYF₄ in Fig. 3(b) displays the lattice fringe with a distance of 0.3 nm.

Fig. 3.

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	Fig. 3. The TEM (a) and HRTEM (b) images of the glass ceramic containing Er3+:NaYF4 nanocrystals.

The UV-VIS-NIR absorption spectrum of Er³⁺-doped NaYF₄ nanocrystals is shown in Fig. 4(a). As can be seen, six main absorption peaks appear around the wavelengths of 377, 407, 487, 545, 651, and 799 nm, which can be attributed to the absorptions of these excited states ⁴G_11/2, ²H_9/2, ⁴F_7/2, ⁴S_3/2, ⁴F_9/2, and ⁴I_9/2. The measured UC luminescence spectrum in the visible light region is shown in Fig. 4(b). One can see that five luminescence signals are observed around the wavelengths of 408, 475, 527, 547, and 656 nm, which can be attributed to the state transitions from the five excited states ²H_9/2, ⁴F_7/2, ²H_11/2, ⁴S_3/2, and ⁴F_9/2 to the ground state ⁴I_15/2, respectively. It is easy to observe that the green and red UC luminescence signals dominate the visible light spectrum, and therefore our goal in this work is to control the green and red UC luminescence by varying the femtosecond laser polarization.

Fig. 4.

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	Fig. 4. The UV-VIS-IR absorption (a) of the glass ceramic containing Er3+:NaYF4 nanocrystals and UC luminescence spectrum (b) of the sample excited by 800-nm femtosecond laser with a repetition rate of 1 kHz.

Figure 5(a) shows the green (546 nm) (green triangles) and red (656 nm) (red circles) UC luminescence intensities each as a function of quarter wave plate angle excited by the 1-kHz laser amplifier. The quarter wave plate angle has no effect on the intensity of the laser past the λ/4 plate, which is confirmed experimentally. As can be seen, both the green and red UC luminescence intensities can be controlled by the laser polarization modulation, which decreases when the laser polarization changes from linear through elliptical to circular. But their control efficiencies are different, which are, respectively, 13% and 6%, and the green UC luminescence obtains the higher control efficiency. Here, the control efficiency is defined as η = 1 − I^min/I^max, where I^max and I^min represent the maximum and minimum luminescence intensities (in units of a.u., i.e., atomic unit), respectively. However, when the excitation source is switched to the 80-MHz laser oscillator, as shown in Fig. 5(b), both the green and red UC luminescence intensities almost remain constant, that is to say, the green and red luminescence are independent of the laser polarization. Obviously, the laser repetition rate will affect the polarization control efficiency of UC luminescence intensity, and a higher repetition rate will yield a lower control efficiency. Therefore, to obtain the effective polarization control of the green and red UC luminescence in the Er³⁺-doped NaYF₄ nanocrystals, it is critical to utilize the low laser repetition rate, such as 1 kHz.

Fig. 5.

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	Fig. 5. Variations of experimental green (546 nm) (green triangles) and red (656 nm) (red circles) up-conversion luminescence intensities with λ/4 wave plate angle with using a 1-kHz laser amplifier (a) and an 80-MHz laser oscillator (b), together with the theoretical simulations (solid lines).

According to the absorption and luminescence spectra of Er³⁺-doped NaYF₄ nanocrystals in Fig. 4, we present the excitation and detection scheme in our experiment as shown in Fig. 6. The population in the ground state ⁴I_15/2 is pumped to the excited state ²H_9/2 through a resonance-mediated two-photon absorption (TPA) process, which contains on- and near-resonant two-photon absorption. The on-resonant two-photon absorption means that the population in the ground state ⁴I_15/2 is pumped to the intermediate state ⁴I_9/2 by absorbing one photon and then is further pumped to the excited state ²H_9/2 by absorbing another photon, whereas the near-resonant two-photon absorption means that the population in the ground state ⁴I_15/2 is directly pumped to the excited state ²H_9/2 by simultaneously absorbing two photons without passing through the intermediate state ⁴I_9/2. The population in the excited state ²H_9/2 can spontaneously decay to the ground state ⁴I_15/2 through these lower excited states ²H_11/2, ⁴S_3/2, and ⁴F_9/2, and emits the green and red up-conversion luminescence. The population in the intermediate state ⁴I_9/2 by single photon absorption (SPA) process can also relax to the two lower excited states ⁴I_11/2 and ⁴I_13/2, and then is further pumped to the higher excited states ⁴F_7/2 and ⁴F_9/2 by energy transfer up-conversion (ETU) process due to the higher dopant concentration. Generally, the excited state lifetime of rare-earth ions is relatively long in the range of microseconds. If the time separation between the laser pulses is shorter than the excited state lifetime, the populations in the excited states ⁴I_9/2, ⁴I_11/2, and ⁴I_13/2 can be further pumped to these higher excited states ²H_9/2, ⁴F_3/2, and ⁴S_3/2 by absorbing the photons from subsequent laser pulses (see Fig. 6(b)), which is called excited state absorption (ESA) process, and also emits green and red UC luminescences.

Fig. 6.

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	Fig. 6. Energy levels of Er3+ ions and possible pathways of green and red UC luminescences generated by a 1-kHz laser amplifier (a) and an 80-MHz laser oscillator (b).

As can be seen in Fig. 6, the green or red UC luminescence produced by the on-resonant TPA, ETU, and ESA processes depends on the population in the intermediate state ⁴I_9/2, and thus their intensities cannot be controlled by varying the laser polarization since the absorption in the intermediate state ⁴I_9/2 is a single photon process, which is independent of the laser polarization. Consequently, the polarization modulations of green and red UC luminescence should result from the near-resonant TPA process. Thus, the experimental observation in Fig. 5 can be well explained. In the case of the low repetition rate of 1 kHz, corresponding to the laser pulse separation of 1 ms, only one laser pulse arrives within the lifetime of the excited state since the excited state lifetime is far smaller than the laser pulse separation (see Fig. 6(a)). Compared with the green UC luminescence, the red UC luminescence generation additionally contains the ETU2 process, which will suppress the polarization control efficiency of red UC luminescence, and therefore the polarization control efficiency of red UC luminescence is lower than that of green UC luminescence (see Fig. 5(a)). However, for the case of the high repetition rate of 80 MHz, corresponding to the laser pulse separation of 12.5 ns, multiple laser pulses arrive within the lifetime of the excited state because the excited state lifetime is far longer than the laser pulse separation (see Fig. 6(b)). The green and red UC luminescence contain the contribution of the ESA process, and thus their polarization control efficiencies will be greatly suppressed since the ESA process is independent of the laser polarization (see Fig. 5(b)).

As discussed above, the polarization modulations of green and red UC luminescence come from the contribution of the near-resonant TPA process. In order to demonstrate the effect of the femtosecond laser polarization on the near-resonant TPA process, we theoretically simulate the resonance-mediated TPA in the Er³⁺ ions by a time-dependent perturbation theory.^[33] Usually, the multi-photon absorption in a quantum system with a broad absorption line can be simplified into the sum of all individual transitions. Based on the theoretical model of the atom system with narrow absorption line limit,^[34,35] the resonance-mediated two-photon transition probability S⁽¹⁺¹⁾ in the Er³⁺ ions can be approximated as

When a linearly polarized laser field is modulated by the quarter wave plate, its polarization status will be changed. Mathematically, the polarization-modulated laser field can be defined by the function of

Since the polarization modulations of green and red UC luminescence result from the near-resonant TPA process, it is necessary to increase the weight of the near-resonant TPA component in the whole excitation process in order to improve the polarization control efficiency. One simple way is to keep the near-resonant TPA process and exclude other excitation processes. In this experiment, the on-resonant TPA, ESA and ETU processes are correlated with the absorption in the intermediate state ⁴I_9/2, and thus a two-color laser field may be a well-established tool to eliminate these excitation processes but keep the near-resonant TPA process. In the two-color excitation process, both laser fields should be far from the resonant absorption of intermediate state ⁴I_9/2, but the sum of their frequencies should be equal to the transition frequency of excited state ²H_9/2. By such a two-color laser field excitation, the green and red UC luminescence may be suppressed, but their polarization control efficiencies should be improved, and the polarization modulation should not be affected by the laser repetition rate.

In this study, we experimentally and theoretically demonstrate that the femtosecond laser polarization can control the UC luminescence in Er³⁺-doped NaYF₄ nanocrystals dispersed in the silicate glass. It is shown that the circular polarization will suppress the UC luminescence, but the polarization control is affected by the laser repetition rate, and a higher repetition rate leads to a lower control efficiency. It is also shown that the UC luminescences come from the TPA, ETU, and ESA processes, but the polarization modulation only results from the near-resonant TPA process. Furthermore, the two-color femtosecond laser field is shown to be a feasible method to keep the near-resonant TPA process and exclude other excitation processes, and consequently can improve the polarization control efficiency. The study presents a clear physical process for the polarization control of UC luminescence in Er³⁺-doped NaYF₄ nanocrystals, which is very useful for further understanding and controlling the UC luminescences in various luminescent materials. The laser polarization modulation provides a very simple method to control various nonlinear optical processes, and therefore these theoretical and experimental results can be used as the study basis in related fields.