Optimal spectral phase control of femtosecond laser-induced up-conversion luminescence in Sm³⁺:NaYF₄ glass

Abstract

The spectral phase of the femtosecond laser field is an important parameter that affects the up-conversion (UC) luminescence efficiency of dopant lanthanide ions. In this work, we report an experimental study on controlling the UC luminescence efficiency in Sm³⁺:NaYF₄ glass by 800-nm femtosecond laser pulse shaping using spectral phase modulation. The optimal phase control strategy efficiently enhances or suppresses the UC luminescence intensity. Based on the laser-power dependence of the UC luminescence intensity and its comparison with the luminescence spectrum under direct 266-nm femtosecond laser irradiation, we propose herein an excitation model combining non-resonant two-photon absorption with resonance-mediated three-photon absorption to explain the experimental observations.

Graphical abstract

Keywords

up-conversion luminescence / rare earth ions / quantum control / femtosecond laser / spectral phase

Manipulating the up-conversion (UC) luminescence of lanthanide ion-doped luminescent materials has attracted considerable attention owing to its significant and wide applications. Over the years, a number of schemes have been developed to enhance or control the UC luminescence efficiency of doped lanthanide ions. These goals are often achieved by changing the properties of the luminescent materials, such as varying the lanthanide dopant [1, 2], dopant concentration [3, 4, 5], and nanoparticle size [6, 7], preparing a core–shell structure [8-10], and even synthesizing a “native” layer via the high-temperature air annealing process [11]. Another option is modulating the environment around the sample using various means, such as applying an electric or magnetic field [12, 13] or varying the sample temperature [14]. Further, controlling the laser parameters of the excitation source, such as varying the excitation wavelength [15], pulse duration [16], repetition rate [17], or spectral phase [18, 19], is also an efficient way.

Near-infrared lasers have been widely used as the excitation source for UC luminescence generation from doped lanthanide ions because of their important advantages, such as deep tissue penetration, small background spontaneous fluorescence, and reduced risk of light bleaching and damage. Under near-infrared laser excitation, Sm³⁺ ion-doped luminescent materials can emit strong UC luminescence signals in the visible region [20], which have important applications in phosphors [21, 22], laser materials [23], sensors [24] and other optoelectronic devices [25]. Near-infrared femtosecond lasers, which have high peak power and wide spectral bandwidth, are particularly excellent light sources for UC luminescence excitation via non-resonance or resonance-mediated multi-photon absorptions. Spectral phase modulation can be used for femtosecond pulse shaping, which can induce constructive or destructive interference of the multi-photon excitation pathways. In this way, the UC luminescence efficiency can be adjusted.

The co-doping strategy (using dopants such as Yb³⁺/Er³⁺, Yb³⁺/Ho³⁺, or Yb³⁺/Tm³⁺) achieves higher UC luminescence efficiency than the single-doping strategy (using ions such as Er³⁺, Ho³⁺, or Tm³⁺). Nevertheless, we focus on exploring the physical excitation mechanism of single-doped Sm³⁺ irradiated with an 800-nm femtosecond laser pulse. As one of the most widely used substrates, NaYF₄ is selected owing to its low phonon energy [26]. There is no intermediate energy level that is corresponding to the single-photon absorption of the 800-nm femtosecond laser for the doping Sm³⁺ ion, Therefore, the most probable absorption from the ground state ⁶H_5/2 to the excited state ⁶P_3/2 is a non-resonant two-photon process. According to previous studies [27, 28], the absorption probability of a non-resonant two-photon process is maximized under transform-limited laser pulses, and spectral phase modulation of the excitation pulse suppresses rather than enhances the absorption probability. However, we have experimentally observed UC luminescence enhancement under spectral phase modulation. These observations cannot be explained by the conventional excitation model of non-resonant two-photon absorption. Therefore, we propose a new excitation model that combines non-resonant two-photon absorption with resonance-mediated three-photon absorption and support it with experimental proofs. This study can further our understanding of the excitation mechanism of dopant Sm³⁺ ions and will make positive contributions to the related applications of co- or multi-doping strategies.

Figure 1 shows a schematic of the experimental arrangement. A Ti–Sapphire mode-locked regenerative amplifier outputs femtosecond laser pulses with a central wavelength of 800 nm, an approximate pulse duration of 50 fs, and a repetition rate of 1 kHz. The output femtosecond laser pulse is steered into a programmable 4f-configuration zero-dispersion pulse shaper, which comprises a pair of diffraction gratings (1200 lines/mm), a pair of concave mirrors (focal length 200 mm), and a one-dimensional liquid-crystal spatial light modulator (SLM) of 640 pixels. Then, the shaped femtosecond laser pulse is guided through a variable attenuator and a beam splitter and finally focused on the measured sample through a lens with 50-mm focal length. Here, the femtosecond laser intensity irradiating the sample is varied using the attenuator and the beam splitter reflects a small portion of the laser intensity onto a dynamometer, which monitors the femtosecond laser intensity incident on the sample. The fluorescence signals from the sample are measured by a fiber spectrometer with a charge-coupled device in the direction perpendicular to the laser propagation. A PC is used to record the luminescence spectrum and updates the SLM control voltage.

The experimental sample was Sm³⁺:NaYF₄ glass comprising 39.5% SiO₂, 25% Al₂O₃, 18% Na₂CO₃, 10% YF₃, 7% NaF, and 0.5% Sm (mol%). First, the mixed raw materials are melted into a liquid at 1350°C for approximately 45 min in a platinum crucible at atmospheric pressure. The melted liquid is injected into a metal mold and annealed for 10 h at 450°C. Finally, the obtained glass is properly cut and polished prior to measurement.

Figure 2(a) shows the UV–VIS–NIR absorption spectrum of the Sm³⁺:NaYF₄ glass sample. In addition to the strong absorption band in the UV region, an obvious absorption peak appears at approximately 402 nm corresponding to the transition from the ground state ⁶H_5/2 to the excited state ⁶P_3/2; this is more clearly shown in the inset. Note that no absorption peak appears around 800 nm because there are no corresponding energy levels. Under 800-nm femtosecond laser excitation, the UC luminescence signals in the visible region can be clearly observed [see Fig. 2(b)]. The four distinct emission bands are centered around 563, 599, 647, and 710 nm. Generally, these luminescence peaks are assigned to the state transitions of ⁴G_5/2→⁶H_5/2, ⁴G_5/2→⁶H_7/2, ⁴G_5/2→⁶H_9/2, and ⁴G_5/2→⁶H_11/2, respectively [29].

The femtosecond laser has a wide spectral bandwidth and can induce many excitation pathways in the UC luminescence generation of rare earth ions. However, the spectral phase distribution of the laser pulse can determine the constructive or destructive interference of these excitation pathways and affect the UC luminescence efficiency. In this work, we use an optimal phase control strategy based on a generic algorithm (GA) to manipulate the UC luminescence intensity. The GA-based adaptive program has been described previously [30]. In our experiment, the luminescence intensity at 599 nm is used as the feedback signal for optimization, and the femtosecond laser intensity is set to approximately 1.6×10¹³ W/cm². As shown in Fig. 3(a), the luminescence intensity can be either efficiently enhanced (red line) to approximately 1.4 times that of the transform-limited laser pulse (black line) or greatly suppressed (blue line) to approximately 5% of its value via phase optimization. The phase masks of the femtosecond laser spectrum under enhancement and suppression are shown in Figs. 3(b) and (c), respectively. The spectral phase distribution of the laser pulse was strongly modulated, particularly in the case of luminescence suppression.

The energy level structures of rare earth ions doped in solid substrates are rather complicated. Detailed knowledge of the doping rare earth ions is usually difficult to obtain; therefore, the real experimental situation might be far from the theoretical ideal. Many other factors will make unknown contributions to the experimental results, such as the asymmetry of the femtosecond pulse in the time and frequency domains, mismatch between the central laser frequency and ion resonant frequency, and different phases introduced to various spectral components by the optical elements (e.g., lenses). The GA-based adaptive optimization control adopted herein incorporates all of these influencing factors without any prior knowledge. Depending on the real conditions of the system under study, various phase distributions can be tailored to control and, in particular, suppress the UC luminescence intensity. From the phase masks, direct observation of the excitation mechanisms for luminescence enhancement or suppression is difficult. Consequently, more auxiliary experiments and theoretical analysis are needed.

For the femtosecond laser-induced multi-photon absorption process, the relationship between the luminescence intensity I and pump laser intensity P can be described as I\propto P^n, where n is the number of absorbed photons. Figure 4 is a log–log plot showing the laser-intensity dependence of the luminescence intensity at 599 nm. The luminescence intensity increases (initially slow and subsequently fast) with increasing laser intensity within the explored laser intensity range. The experimental data for the low and high laser intensities were linearly fitted with slopes of 1.8 and 2.3, respectively. This experimental observation indicates that two-photon absorption dominates the whole excitation process at low laser intensities but three-photon absorption process might play a role at high laser intensities. To verify the existence of three-photon absorption excitation, we measured the down-conversion (DC) luminescence spectrum of the glass sample under 266-nm femtosecond laser excitation. The experimental result is given in Fig. 2(b) (cyan line). Here, the 266-nm laser is obtained via the third-harmonic generation of an 800-nm laser pulse. As expected, the spectral shape is very similar to that obtained under 800-nm femtosecond laser excitation and the four characteristic luminescence peaks can be clearly observed.

Based on the above studies and the energy level structure of Sm³⁺ [31], we propose the following excitation model to account for the observed luminescence variation under phase-modulated 800-nm femtosecond laser irradiation (see Fig. 5). The population in the ground state ⁶H_5/2 is first pumped to the excited state ⁶P_3/2 through the simultaneous absorption of two photons. Then, the population in the excited state ⁶P_3/2 can decay to the excited state ⁴G_5/2 via phonon-assisted relaxation, emitting various fluorescence signals in the visible spectrum [32]. This excitation process, labeled channel 172 in Fig. 5, is a non-resonant two-photon absorption process. Moreover, the population in the excited state ⁶P_3/2 can be further pumped to the higher excited state ²H_9/2 through the absorption of a third photon. Similarly, the population in the higher excited state ²H_9/2 can decay to the lower excited state ⁴G_5/2 and the same fluorescence signals are emitted. This excitation process is a resonance-mediated (2+1) three-photon absorption and labeled as channel 173. In addition, the population in the ground state ⁶H_5/2 can be directly excited to the higher excited state ²H_9/2 by simultaneously absorbing three photons without via the intermediate state ⁶P_3/2; this is called direct non-resonant three-photon absorption. As we know, compared with the resonance-mediated (2+1) three-photon absorption, direct non-resonant three-photon absorption has significantly lower transition probability. Previous studies have confirmed that the transition probability of a non-resonant three-photon excitation can only be suppressed by spectral phase modulation [28]; however, the transition probability of the resonance-mediated (2+1) three-photon absorption can be either enhanced or suppressed, depending on the spectral phase distribution [33]. Based on the aforementioned analysis, we expect that the resonance-mediated (2+1) three-photon absorption should play a much considerably more important role than the direct non-resonant three-photon absorption for the UC luminescence excitation in our case.

In the excitation model shown in Fig. 5, the total transition probability P^{(T)} of Sm³⁺ ions under 800-nm femtosecond laser excitation is given by

\begin{array}{}\text{(1)}& P^{(T)}=P^{(2)}+P^{(2+1)}\mathrm{,}\end{array}

where P^{(2)} and P^{(2+1)} are the transition probabilities of non-resonant two-photon absorption and resonance-mediated (2+1) three-photon absorption, respectively. For convenience of description, the symbols of |g\rangle, |i\rangle, and |f\rangle are used to represent the ground state ⁶H_5/2, intermediate excited state ⁶P_3/2, and final excited state ²H_9/2, respectively. Here, the transition probability P^{(2)} can be calculated as follows:

\begin{array}{}\text{(2)}& P^{(2)}={\displaystyle {\int }_{-\infty }^{\infty }}g({\omega }_i)|a_i^{(2)}{|}^2\text{d}{\omega }_i\mathrm{,}\end{array}

with

\begin{array}{}\text{(3)}& a_i^{(2)}=-\frac{1}{\text{i}{\hslash }^2}{\mu }_{ig}^2{A}^{(2)}({\omega }_i)\mathrm{,}\end{array}

\begin{array}{}\text{(4)}& A^{(2)}(\text{Ω})={\displaystyle {\int }_{-\infty }^{\infty }}E(\omega )E(\text{Ω}-\omega )\text{d}\omega \mathrm{.}\end{array}

Here, a_i^{(2)} represents the transition amplitude from state |g\rangle to state |i\rangle via non-resonant two-photon absorption, {\mu }_{ig}^2 is the effective non-resonant two-photon dipole coupling from state |i\rangle to state |g\rangle, g({\omega }_i) is the absorption line-shape function of state |i\rangle, {\omega }_i is the corresponding transition frequency, and E(\omega )=E_0(\omega )\exp [\text{i}\text{Φ}(\omega )], where E_0(\omega ) and \text{Φ}(\omega ) are the spectral amplitude and phase, respectively. The transition probability P^{(2+1)} can be obtained as follows:

\begin{array}{}\text{(5)}& P^{(2+1)}={\displaystyle {\int }_{-\infty }^{\infty }}g({\omega }_f)|a_f^{(2+1)}{|}^2\text{d}{\omega }_f\mathrm{,}\end{array}

with

\begin{array}{}\text{(6)}& \begin{array}{ll}{a}_f^{(2+1)}\text{}=\hfill & \frac{1}{\sqrt{2\pi }{\hslash }^3}{\mu }_{fi}{\mu }_{ig}^2[\text{i}\pi \text{}{\displaystyle {\int }_{-\infty }^{\infty }}\text{}g({\omega }_i)A^{(2)}({\omega }_i)E({\omega }_f\text{}-\text{}{\omega }_i)\text{d}{\omega }_i\hfill \\ \hfill & +\wp {\displaystyle {\int }_{-\infty }^{\infty }}{A}^{(2)}({\omega }_i-\text{Δ})E({\omega }_f-{\omega }_i+\text{Δ})\text{d}\text{Δ}/\text{Δ}]\mathrm{.}\hfill \end{array}\end{array}

Here, a_f^{(2+1)} represents the transition amplitude from states |g\rangle to |f\rangle via resonance-mediated (2+1) three-photon absorption, {\mu }_{fi} is the dipole matrix element from state |f\rangle to state |i\rangle, g({\omega }_f) is the absorption line-shape function of the state |f\rangle, and {\omega }_f is the corresponding transition frequency. The first term within bracket in Eq. (6), called the on-resonance term, represents the contributions of all three-photon excitation pathways from the states |g\rangle to |f\rangle that are in resonance with state |i\rangle. The second term within brackets in Eq. (6), called the near-resonance term, represents the contributions of all the complementary three-photon excitation pathways in near resonance with state |i\rangle, where Δ is the frequency detuning. The on-resonance pathways (i.e., \text{Δ}=0) are excluded from the near-resonance term by the Cauchy’s principal-value operator \wp.

As shown in Eqs. (2)–(4), for non-resonant two-photon absorption, the transition probability P^{(2)} can be suppressed but not enhanced by modulating the laser spectral phase. As shown in Eqs. (5) and (6) for the resonance-mediated (2+1) three-photon absorption, the on-resonance term within brackets in Eq. (6) cannot be enhanced. The near-resonance term within brackets in Eq. (6) integrates over both positive (\text{Δ}>0) and negative () components; therefore, destructive interference is induced by the transform-limited femtosecond laser pulse. A feasible way to enhance the near-resonance contribution is to induce constructive interference instead of destructive interference via spectral phase modulation.

In summary, we have experimentally studied the control of the UC luminescence intensity in the Sm³⁺-ion-doped NaYF₄ glass by phase shaping the 800-nm femtosecond excitation laser. The UC luminescence intensity was enhanced or suppressed by adaptively optimizing the spectral phases of the femtosecond laser field. After measuring the laser-power dependence of the UC luminescence intensity and comparing it with the luminescence spectrum of 266-nm femtosecond laser excitation, we proposed an excitation model by combining non-resonant two-photon absorption and resonance-mediated (2+1) three-photon absorption; this was done to account for the experimental observations under phase shaping. Our work provides new insights into the excitation mechanism of dopant Sm³⁺ ions under femtosecond laser irradiation and is potentially valuable for developing related applications.

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