1. Introduction

The subject of random lasers (RLs) is receiving large attention due to the unique properties of RLs and to their potential applications [1–16]. Generation of laserlike emission from strongly scattering media has been observed and studied in a large variety of systems such as dye solutions containing scattering particles, semiconductor powders, polymers, and nanoparticles doped with rare-earth (RE) ions.

There are two main classes of RLs: one in which passive scatterers are embedded in a gain medium (such as TiO₂ nanoparticles suspended in a colloid containing dye molecules [5]) and another class in which the scatterers are active (such as ZnO nanorods arrays [6]). The RL action may occur when there is an excitation threshold, due to the multiple scattering, above which the total optical gain is larger than the losses. Optical modes with a central frequency, narrow bandwidth, short lifetime and a complex spatial profile are defined by the scattering process [3].

The first RL based on a Nd³⁺ doped powder was reported in 1986 [2]. Crystalline particles with dimensions from 1 to 10 μm were excited by a dye laser operating in the orange-red region and RL emission was obtained at 1.06 μm. The experiment was made at 77 K and the laser threshold was ≈600 kW/cm². More recently Nd³⁺ nanocrystals have been investigated and the mechanisms of excitation and relaxation participating in the process were studied. A list of more than 30 materials doped with Nd³⁺ as well as many reports based on other RE ions are given in Ref. [2]. It was observed that the maximum efficiency is obtained for particles with dimensions between 1 and 100 μm. In the blue region RL was obtained for Nd³⁺ doped alumina nanoparticles for excitation by electron beams with energy varying from 2 to 10 KeV [9,10].

Most of the optically pumped RLs reported for RE doped systems are based on Stokes processes, i.e.: the RL wavelength is larger than the pumping wavelength. RL based on an anti-Stokes process involving RE ions was reported only for Tm³⁺-doped fluorozirconate glass powder containing micrometer size titanium dioxide particles excited with a laser operating at 1064 nm [11]. Frequency upconversion (UC) RL emission at 793 nm (450 nm) was observed with pump intensity threshold of 2.6 kW/cm² (6.3 kW/cm²).

In the present paper we report on the operation of a UC random laser emitting at 381 nm obtained from a Nd³⁺ - doped glass powder pumped by a pulsed dye laser operating at 575 nm, in resonance with the Nd³⁺ transition ⁴I_9/2 → ²G_7/2. The RL threshold was 30 kW/cm² and RL pulses of 29 ns were observed for pumping above the threshold.

A fluoroindate glass (FIG) was used because it is a very efficient upconverter [17–20]. Besides the large UC efficiency and its capability to incorporate large concentration of RE ions into the matrix, FIG has high resistance to moisture, good chemical and mechanical stability, and large transparency window from 0.2 to 8 μm. UC processes due to energy transfer involving pairs, triads, and quartets of RE ions in FIG were studied under appropriate conditions for various RE ions [17–20]. In particular we refer to a previous experiment with Nd³⁺ doped FIG samples pumped at 577 nm that showed strong UC emission in the violet – blue region [19] and experiments where samples excited in the green – orange region showed large optical gain at 382 and 414 nm [20]. The gain measured when pumping with a laser beam near resonance with the Nd³⁺ transition ⁴I_9/2 → ²G_7/2 was four orders of magnitude larger than when the sample was excited at 532 nm.

2. Experimental details

Glass samples with compositions (in mol %) (41-x)InF₃-20ZnF₂-20SrF₂-16BaF₂-2NaF-1GaF₃-xNdF₃ (x = 0.5, 1.0, and 3.0) were fabricated. Standard pro-analysis oxides and fluorides were used as starting materials for the glass synthesis and the classical ammonium bifluoride process was employed [17]. The fluoride powders were mixed together and heat treated at 700 °C for melting and then 800 °C for refining. The melt was poured and cooled into a preheated mold. Finning, casting, and annealing were carried out under dry argon atmosphere and samples with good optical quality were obtained. Afterwards a powder with grains having average size between 25 and 38 μm (measured using an electron microscope) was prepared by crushing the glass samples and passing the grains through calibrated sieves. Finally the amorphous powder was gently pressed to a volume of ≈8 mm³ using a sample-holder fabricated for the optical experiments.

The absorption spectra of the bulk samples were measured using a commercial spectrophotometer from the near-ultraviolet to the near-infrared. A dye laser using Rhodamine 590 dissolved in ethanol, pumped by the second harmonic of a pulsed Nd: YAG laser (532 nm, 8 ns, 5 Hz) was used as the excitation source. The dye laser beam was focused on the sample using a 20 cm focal length lens. The signal emitted by the sample was collected using a 5 cm focal length lens, along ≈45° direction with respect to the laser beam propagation direction. The luminescence spectrum was recorded through a 0.5 m monochromator followed by a photomultiplier coupled to a computer.

3. Results and discussion

Figure 1 shows the absorption spectrum of the bulk sample with x = 3.0. The features correspond to electronic transitions involving states in the 4f configuration, starting from the ground state (⁴I_9/2) of the Nd³⁺ ions to the excited states labeled in the figure. The other samples present similar spectrum. The positions of the Nd³⁺ bands are independent of the concentration but their amplitudes are proportional to the Nd³⁺ concentration. The large bandwidths are due to the inhomogeneous broadening caused by the different crystalline fields in the various sites occupied by the Nd³⁺ ions.

 

Fig. 1 Absorption spectrum of fluoroindate glass doped with Nd³⁺ ions. Sample length: 1.8 mm.

Download Full Size | PDF

Figure 2 shows the luminescence spectrum of the powder samples for excitation at 575 nm in resonance with the transition ⁴I_9/2 → ²G_7/2. Other luminescence transitions were observed in other wavelengths but they are not relevant for the present experiment (the complete UC spectrum for the bulk sample was published in Ref. [19]). The spectra for the other powder samples present the same emission lines. For small excitation intensity the violet and blue luminescence exhibited a quadratic dependence with the laser intensity indicating that two laser photons are necessary to generate each UC photon.

 

Fig. 2 Luminescence spectra in the wavelength range of interest. Excitation wavelength: 575 nm.

Download Full Size | PDF

The UC lines in the 365 to 435 range were also reported for bulk samples in [20]. Gain parameters were determined for both spectral lines using a broad band incoherent light source as the probe beam at the spectral region of interest (~360–440 nm) and a pump beam at 583 or 532 nm. The emission at 381 nm was attributed to transitions ⁴D_7/2 → ⁴I_13/2 and ⁴D_3/2 → ⁴I_11/2 while the emission at 412 nm was attributed to the transition ⁴D_3/2 → ⁴I_13/2. The measured gain for the line at 381 nm for Nd³⁺ concentrations (x = 0.5, 1.0, and 3.0) assumed values between 30% and 100% larger than for the 412 nm line.

In the present experiments with FIG powders, the RL behavior was identified only for the emission at 381 nm and therefore the intensity behavior of the emission at 412 nm will not be discussed.

Although the UC light was emitted along a large solid angle, the signal recorded was contained in a small solid angle centered in the 45° direction with respect to the propagation of the pump laser. The intensity emitted did not change much for small angular deviations with respect to the direction of observation.

Figure 3(a) shows the dependence of the intensity at 381 nm as a function of the incident laser intensity for the sample with x = 3.0. A fast signal with ≈29 ns duration is observed for pump intensities of 40 and 50 kW/cm² followed by a long tail that extends for microseconds. For pump intensity of 20 kW/cm² only the slow signal, with the decay and rise times given in Table 1 , is observed. Figure 3(b) shows the time evolution of the 381 nm signal for the three samples for pump intensity of 50 kW/cm². Figure 3(c) shows the UC lineshapes for pump at 575 nm and at 532 nm, with intensity of 50 kW/cm². The spectral change is attributed to the signal amplification of a particular class of ions in the inhomogeneously broadened line.

 

Fig. 3 (a) Intensity at 381 nm versus the input intensity at 575 nm (sample with x = 3.0). (b) Temporal evolution of the UC signal. Laser intensity: 50 kW/cm². (c) UC spectra for pumping at 575 nm (red line) and 532 nm (green line).

Download Full Size | PDF

Table 1. Decay and Rise Times of the 381 nm Signal for Pump Intensities Smaller Than 20 kW/cm², Obtained Through Fittings of the Function$f\left(t\right)\propto \left|e^{-t/t_1}-e^{-t/t_2}\right|$

View Table

To analyze the results we first consider that two possible UC pathways may contribute for the results. From the energy level scheme of the Nd³⁺ ions, shown in Fig. 4(a) , we observe that one possible pathway would start by one–photon absorption from the ground state to state ²G_7/2 followed by excited state absorption to states with energy of ≈34780 cm⁻¹.

 

Fig. 4 (a) Simplified energy level scheme of Nd³⁺ ions with indication of the radiative transitions (solid lines) and the relevant energy transfer process (dashed lines). (b) Pair states involved in the UC process.

Download Full Size | PDF

However this pathway is discarded because the UC intensity would vary linearly with the Nd³⁺ concentration. Hence, another UC pathway has to be considered because of the quadratic dependence of the 381 nm signal with the Nd³⁺ concentration and its dynamical behavior that presents a rise time slower than the laser pulse. We attribute the UC emission to energy transfer between excited Nd³⁺ ions. Accordingly, after resonant excitation of the Nd³⁺ ions to level ²G_7/2, pairs of coupled ions may exchange energy in such way that one ion is promoted to level ⁴D_7/2 while the other decays to level ⁴I_3/2. The cross–relaxation process (²G_7/2, ²G_7/2) → (⁴I_13/2, ⁴D_7/2) is resonant being efficient and fast. Finally the ions at level ⁴D_7/2 may decay radiatively to level ⁴I_13/2 or, by nonradiative decay, they reach level ⁴D_3/2 from where they decay to level ⁴I_11/2 emitting at 381 nm. The equations describing the dynamics of the anti-Stokes signal are written considering the pair states indicated in Fig. 4(b) in the first approximation, neglecting mixing of individual ions’ states due to the interaction potential. The population densities $N_2\left(t\right)$ and $N_3\left(t\right)$ of the pair states $|2〉$ and $|3〉$ satisfy the coupled equations

The rise time of the 318 nm signal is due to the cross-relaxation rate between two excited Nd³⁺ ions at level ²G_7/2 that is a function of the Nd³⁺ ions concentration, and the time to populate level ⁴D_3/2 by nonradiative decay from level ⁴D_7/2. According to the energy gap law [21] the nonradiative relaxation rate is inversely related to the energy gap between two electronic states. Considering the cutoff phonon energy of the FIG matrix (≈500 cm⁻¹), we estimate that the level ⁴D_7/2 has lifetime of ≈22 ns. Also using the energy gap law, we estimate ≈4 μs for the lifetime of level ⁴D_3/2. Then, considering the slow UC decay for low pump intensity, we concluded the emission at 381 nm is mainly due to transition ⁴D_3/2 → ⁴I_11/2. The contribution of transition ⁴D_7/2 → ⁴I_13/2 is negligible.

On the other hand, the 381 nm signal exhibits contributions of both transitions: ⁴D_7/2 → ⁴I_13/2 (fast UC signal) and ⁴D_3/2 →⁴I_11/2 (slow UC signal) when the excitation intensity is larger than 30 kW/cm². In this case the number of ions excited to level ⁴D_7/2 becomes large enough and the amplified spontaneous emission corresponding to transition ⁴D_7/2 → ⁴I_13/2 becomes relevant. Therefore, the dynamical behavior of the 381 nm signal is described by $f\left(t\right)=A_1{e}^{-t/t_1}+A_2{e}^{-t/t_2}-A_3{e}^{-t/t_3}$, where $A_2{e}^{-t/t_2}$ is due to the transition ⁴D_7/2 →⁴I_13/2. The fitting of $f\left(t\right)$ to the 381 nm signal for the sample with x = 3.0 is shown of Fig. 5(a) where $A_1$ = 0.9; $A_2$ = 19.9; $A_3$ = 57.9; $t_1$ = 2.1 μs; $t_2$ = 0.02 μs; and $t_3$ = 0.01 μs. The horizontal scale used in Fig. 5(a) allows observing clearly the signal rise time. The inset in Fig. 5(a) shows the fitting for longer times. Figure 5(b) shows the temporal profile of the fast signal component for the sample with x = 3.0, after subtraction of the slow signal component. The inset of the figure shows the signal time behavior at the pumping intensity 20 kW/cm². The amplitude of the ≈29 ns pulse is shown in Fig. 5(c) as a function of the pump intensity. The inset in Fig. 5(c) shows the log-log plot of the data. A RL threshold of ≈30 kW/cm² can be observed. Notice that by increasing the pump intensity from 20 kW/cm² to 55 kW/cm² we obtained a 70-fold increase in the emitted intensity at 381 nm.

 

Fig. 5 (a) Temporal behavior of the 318 nm signal for the sample with x = 3.0. Laser intensity: 50 kW/cm². The solid blue line represents a fitting of $f\left(t\right)$ with the parameters indicated in the text. (b) Temporal behavior of the RL signal (pump intensity: 50 kW/cm²). The inset shows the signal behavior for pump intensity of 20 kW/cm². (c) RL intensity as a function of the laser intensity. Sample: x = 3.0.

Download Full Size | PDF

In summary, the results presented demonstrate a UC random laser operating in the ultraviolet. The laser is based on the orange-to-ultraviolet conversion obtained in a Nd³⁺ doped fluoride glass powder. The contribution of an energy transfer mechanism for RL generation is reported here for the first time. Considering the large variety known of efficient UC processes involving rare-earth ions the present results show that there is good potential to operate RLs with basis in other UC schemes.