1. Introduction

High-intensity ultra-short-pulse laser, which can generate some extreme physical conditions in aspects of temperature, pressure, electric/magnetic field, energy density and so on [1], is one of the most powerful research tools in many major scientific subjects, including fast ignition (FI) for laser fusion, generation of high brightness X-ray, laboratory astrophysics, advanced accelerator techniques, exploration of the effects between strong light and materials, etc.

In general, the ultra-short-pulse laser is developed mainly in two directions, one is broad-spectrum ultra-short-pulse, and another is large energy and high peak power. Both are interrelated. Some negative factors such as gain-narrowing of spectrum, nonlinear optical phenomena and optical damage are restricting the development of large-energy, high-power and narrow-pulse laser. For the most popular used Ti: sapphire, although it has deeply promoted the commercialization of femto-second laser and atto-second pulse output, it cannot produce ultra-short-pulse laser with large energy due to small crystal size, narrow bandwidth and short fluorescence lifetime. Novel laser medium with large size and high performance such as broad spectrum is required [2, 3].

Glass is an attractive host because that depending on the composition, the glasses can be highly transparent from UV to IR and the solubility of the rare earth ions is higher compared to that in crystals. Furthermore, glass is easy to be shaped and processed, especially to be formed in large size. Presently, high-power Nd³⁺-doped glass laser drivers are being used to generate large-energy short-pulse laser in some world-famous facilities such as OMEGA in United States and “SHEN-GUANG” in China.

In the traditional silicate and phosphate laser glasses, emission bandwidths of Nd³⁺ are about 25nm [4], and a laser pulse with a duration of 50fs can be produced under the diffraction limit condition. However, more short duration can hardly be obtained because of the negative effects of spectral gain narrowing and dispersion. For enhancing the spectral width of Nd³⁺-doped glass, some approaches are performed. One direct method is to form a glass by mixing both silicate and phosphate components. But since the discrepancy of emission peaks in Nd³⁺-doped silicate and phosphate laser glasses is about 10nm, the broadening of transmission bandwidth is limited [3].

Another method is to choose wide-bandwidth laser glass as gain medium. Due to the low phonon energy, good fluorescence spectra and long lifetimes, the heavy metal oxide glasses (such as tantalum silicate glasses [5], Bi₂O₃-PbO-Ga₂O₃ [6], phospho-tellurite [7]), heavy metal fluoride glasses [8], oxyfluoride glass [9] and fluorophosphate glass [10] have been paid close extensive attention.

In this paper, a novel Nd³⁺-doped lead fluorosilicate glass (NPS glass) prepared by a two-step melting process was reported. The fluorescence bandwidth obtained in this glass is more than 40nm and the decay lifetime of Nd³⁺ for the ⁴F_3/2 level is up to 586±20µsec.

2. Experimental procedure

The NPS glass composition studied in this work was (in mol %): 67SiO₂-10PbO-2PbF₂-12K₂O-8Na₂O-0.76Nd₂O₃-0.24As₂O₃. The high-purity (ࣙ99.99%) raw materials were added in the form of SiO₂, Pb₃O₄, PbF₂, KNO₃, NaNO₃, Nd₂O₃ and As₂O₃ powders. The contents of the most common transition metal ions are less than 5ppm and that of the physically or chemically absorbed water is less than 0.1wt%. A mixture of required amounts (typically 1.9kg) of raw materials was carefully grinded, thoroughly mixed and pre-melted in a quartz crucible at 1250 °C. At this temperature, the first melting can be carried out quickly with low-level fluoride evaporation. After melted into vitreous state, the mixture was manually transferred into a Φ95mm×100 mm high-purity platinum metal crucible with lid, then refined at 1420 °C to remove bubbles and homogenized at 1380 °C by platinum stirrer for 3h separately. The molten glass was removed out at 1360 °C and cast into a copper mold to form plates, which had been heated to 350 °C beforehand. Finally the glass was annealed in a custom-designed annealing oven to reduce residual stress. It was kept for 24h at 470 °C just above the glass transition temperature, T _g, firstly and then cooled to room temperature at a rate of about 10 °C/h.

The glass was cut and polished for optical and spectroscopic measurements. These samples have fine performances such as stria-free, the parallelism with 1 minutes of arc, the surface flatness with <λ/4 at 633nm in the 90% area of central aperture, surface quality with 40-20 scratch-dig.

All optical and spectroscopic measurements were carried out at room temperature. The refractive indices were measured using a WYV V-Prism Refractometer from Shanghai Precision & Scientific Instrument Co., Ltd with accuracy of ±5×10^-5. Refractive index dispersion curve was fitted with the Sellmeier formula using the values of refractive indices at six wavelengths including 435.8, 486.1, 546.1, 589.3, 656.3 and 706.5nm. The absorption spectrum in the range of 400–1000nm was recorded with a Lamda 950 UV/VIS/NIR spectrophotometer from Perkin-Elmer. The resolution was set to 1nm and the precision for the various measured quantities is as follows: wavelength (±0.08nm) and optical transmission (±0.1%). The luminescent spectrum was determined using a spectrophotometer (JobinYvon Triax320, France), with an 808nm laser diode (LD) (Coherent, U.S.A) as the excitation source, and the power is 400mw. The fluorescence decay rates were measured by changing the excitation source to pulsed output, with the pulse-width and period are 20μs and 5000μs, respectively. The signals were detected by an InGaAs photodetector (J22TE2-66C-R05M-1.7, Judson) in the range of 800–1650nm wavelength. The temporal decay of the fluorescence signal was recorded by a storage digital oscilloscope (Tektronix TDS3012B, U.S.A). Errors in the fluorescence and lifetime measurements are estimated to be ±0. 1nm, ±20µs, respectively.

To perform the laser oscillation, a resonator was applied with the parameter R₁=100%, R₂=90%, respectively. An 808nm semiconductor laser array with the pulse duration of 200 µs at a repetition rate of 1 Hz was used as the pumping. The laser output energy is measured by Rj-7620 with RjP-735 Pyroelectric Probe from Laser Probe Inc. with a calibration uncertainty of ±5%. The laser spectrum is carried out by HR2000+ High-resolution Spectrometer from Ocean Optics Inc. with an optical resolution of 0.05nm.

3. Results and discussion

3.1 Application of Judd-Ofelt theory

The fitted refractive index dispersion curve and the absorption spectrum of NPS glass are shown in Fig. 1. The refractive index decreases with the increase of light’s wavelength, which follows as typical dispersion curves of heavy metal fluoride glasses. The absorption bands of Nd³⁺ ions in NPS glass are parallel to those of commercial Nd³⁺-doped aluminum-phosphate laser glass LG-770 (Schott Glass Technologies, Inc.), except for lower absorption cross sections. Eight absorption bands centering at 431, 473, 531, 574, 684, 740, 807 and 881 nm are ascribed to 4I_9/2→²P_1/2+²D_5/2, ⁴I_9/2→² K _15/2+²G_9/2+⁴G_11/2+(²D,²F)_3/2, ⁴I9/₂→⁴G_9/2+²K_13/2 +⁴G_7/2, ⁴I_9/2→²G_7/2+⁴G_5/2+²H_11/2, ⁴I_9/2→⁴F_9/2, ⁴I_9/2→⁴S_3/2+⁴F_7/2, ⁴I_9/2→⁴F_5/2+²H_9/2 and ⁴I_9/2→ ⁴F_3/2 transitions, respectively.

The Judd-Ofelt theory was used to calculate the radiative rates of Nd³⁺ ions in the NPS glass. According to the Judd-Ofelt theory [11, 12], the experimental oscillator strength, f_meas, can be calculated by the following equation,

where m and e are the mass and charge of the electron respectively, c is the vacuum velocity of light, N ₀ is the number of rare-earth ions per unit volume in the glass, and the k(λ) is absorption coefficient at a given wavelength λ, which is given by

where l is the thickness of glass, I ₀ andIare the intensities of incident and emergent lights, respectively.

 

Fig. 1. Room temperature optical absorption spectra of Nd³⁺-doped NPS glass (size: 10mm×10mm×3mm) and commercial Nd³⁺-doped aluminum-phosphate laser glass LG-770. All transitions start from ⁴I_9/2 level to the indicated levels. The fitted refractive index dispersion curve of the NPS glass (red in color) is also shown.

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The theoretical oscillator strengths, f_cal, are given by electric dipole oscillator strength, f_cal^ed, magnetic-dipole oscillator strengths, f_cal^md, and electric-quadrupole, f_cal^eq, where the values of f_cal^md (~10^-9) and f_cal^eq (~10^-11) are much smaller in comparison to that of f_cal^ed (~10^-6), therefore can be neglected generally [11, 12]. Thus, the f_cal is expressed by the equation,

where J is the total angular momentum of the initial level, which for Nd³⁺ is 9/2, and (n ²+²)²/9 is the local field correction using the tight binding approximation. The reduced matrix elements of the unit tensor operators, <‖U^(t)‖>, are calculated in the intermediate-coupling approximation. They are found to be almost invariant to the environment and are given by Carnall et al. [13].

The oscillator strengths both experimentally and theoretically obtained are presented in Table 1. The three Judd-Ofelt intensity parameters, Ω_t(t=2, 4, 6) are therefore obtained by the least-square fitting of the theoretical oscillator strength values to the measured ones. The quality of the fitting can be expressed by the root-mean-square, δ _rms, which is calculated by the following formula,

where N_bands regards the number of transitions bands analyzed, N_p is 3 in this case, which is the number of Q_t parameters.

The spontaneous emission probability, A (J′→J″), for excited levels of rare earth ions from an initial state J′ to a final ground state J″ can be identified as

By using the Ω_t, values and the matrix elements <‖U ^(t)‖> for Nd³⁺ obtained from the literature [14] the probabilities for emission from ⁴ F _3/2 to the ⁴ I_J″(J″=9/2, 11/2, 13/2, 15/2) manifolds were calculated. These probabilities are listed in Table 2. The Ω_t values are used to calculate the radiative transition probabilities, branching ratios and radiative lifetimes.

Table 1. Measured and calculated oscillator strengths for NPS glass

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Table 2 . Calculated radiative transition rates A_J, luminescence branching ratios β and corresponding radiative lifetime τ_rad for Nd³⁺ in NPS glass

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The Nd³⁺ fluorescence bands are asymmetric, therefore an effective line-width, Δλ_eff, is defined by

where I _max is the maximum intensity at each fluorescence emission peak.

The radiative lifetime can be shown as

The branching ratio can be written as

Finally, the emission cross section, σ_emi, can be determined by the following relation

The calculated Judd-Ofelt intensity parameters and many important spectroscopic characteristics in this work and earlier reports [5, 6, 7, 8, 9, and 15] are summarized in Table 3.

Table 3 . Optical Properties of NPS glass

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It is currently accepted that the parameter Ω ₂ exhibits the dependence on the covalency between Nd³⁺ ions and ligand anions, and the Ω ₂ also reflects the asymmetry of the local environment at the Nd³⁺ ions site [10, 16]. In this way, the weaker the value of Ω ₂ is, the more centre-symmetrical of the ion site and ionic of its chemical bond with the ligands are. This indicates that Nd³⁺ ions in NPS glass present low covalence and asymmetry in bonding.

Emission intensity could be expressed in terms of the ratio Ω₄/Ω₆ because Ω₂ is not included to calculate branching ratios for the laser ⁴ F _3/2→⁴ I _11/2 transition of Nd³⁺ ions. The value of Ω₄/Ω₆ for the NPS glass is 0.86. This value is near the range of 0.9–1.1, which implies the good fluorescent performance [17].

As shown in Table 3, the value of the stimulated emission cross section for the ⁴F_3/2→⁴I_11/2 transition is 0.87×10^-20cm² at the peak emission wavelength. The relatively small cross section for the NPS glass arises in part from smaller intensity parameters Ω₆ and from the fluorescence bandwidth which is much broader than those of the similar systems illustrated in Table 3. In addition, containing of larger sized potassium in NPS glass composition is also blamed to induce small emission cross section [17].

3.2 Fluorescence spectra and Radiative properties

 

Fig. 2. (a) Room temperature emission spectrum of NPS glass under diode laser excitation at 808nm. (b) Nd³⁺ energy level diagram for Nd³⁺ doped NPS glass obtained from room temperature absorption and emission spectra. (c) Luminescence decay curve of ⁴F_3/2 level of Nd³⁺ ions in NPS glass. (The sample sizes: 5mm×5mm×1mm)

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Fluorescence spectrum of NPS glass under 808nm LD measured at room temperature is shown in Fig.2 (a). Three major emission bands were observed at 880, 1055 and 1325nm, corresponding to the ⁴F_3/2→⁴I_9/2, ⁴F_3/2→⁴I_11/2 and ⁴F_3/2→⁴I_13/2 transitions, respectively. Fig.2 (b) shows Nd³⁺ energy level diagram in Nd³⁺-doped NPS glass obtained from its absorption and emission spectra. Fig. 2(c) also shows the recorded luminescence decay curve of Nd³⁺ for the most characteristic peak of ⁴F_3/2 → ⁴I_11/2 transition. Analysis of the decay curve results in a long lifetime of 586±20µs. The value is much longer than those of other glass systems reported before (as summarized in Table 3). According to Equ.5 and 7, the radiative lifetime of rare-earth ions is strongly depending on the refractive index, J-O parameters Ω ₄ and Ω ₆. Compared to other host glasses labeled in Table 3 and Fig. 3, the NPS glass has relatively small refractive index, J-O parameters Ω ₄ and Ω ₆, therefore presents longer radiative lifetime.

Figure 3 shows the emission spectrum of NPS glass at room temperature. It can be seen that NPS glass has much broader effective line-width than Nd³⁺: Bi₂O₃-PbO-Ga₂O₃ [6], Phosphotellurite [7], and Phosphate (LG-770) [15] glass systems, except for tantalum silicate glasses (K-824) [5].

 

Fig. 3. Emission spectra for ⁴F_3/2→⁴I_11/2 level of Nd³⁺ ion in laser glasses at room temperature (The sample sizes: 5mm×5mm×1mm).

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The broad effective line-width of 1056nm emission in NPS glass derives from two possible factors. Firstly, in NPS glass, Pb²⁺ ion in the [PbO₄] tetragonal pyramid has a pair inert electron in outer shell, thus remains large polarizability [18]. Secondly, the amount of ionic bonds in NPS glasses is relatively high due to the substitution of F^- for O^2- in part. The asymmetry of [NdO₆] octahedron is therefore large. These two factors induce the Stark splitting of Nd³⁺ ion’s J″ manifolds and result in the inhomogeneous broadening of emission spectra. Relatively large value of Ω ₂ for NPS glass also proved the high-level asymmetry of [NdO₆] octahedron in NPS glass.

The peak wavelength of fluorescence spectra has a tight relation with the basic glass former network [17]. The NPS glass is adjudged to lead silicate system, and the fluorescence peak wavelength is therefore similar to those in the silicate glasses. The introduction of F can make a little blue-shift of fluorescence peak wavelength [9]. So, the emission linewidth of NPS glass is much broader than those of Nd³⁺-doped laser glasses reported in previous works and the fluorescence lifetime is also much longer. The peak emission cross section is small compared with that of most materials, but the emission lifetime and effective bandwidth is unique among Nd³⁺-doped materials, thereby permitting the efficient extraction of energy from an Nd3+-doped NPS glass amplifier [2, 4].

3.3 Laser output property

In the laser oscillation measurement, laser output was observed with increasing the input pump energy. The observed laser emission spectrum is displayed in Fig. 4(a), together with the measured threshold and slope efficiency curve. It can be seen that the laser peak was centered at the wavelength of 1062±0.05nm and the full width at half maximum of the laser spectrum above threshold was 0.6±0.05nm. While in Fig. 4 (b), along with the enhancement of pumping power, a sharp bend in that curve was observed indicating a threshold value of approximately 415±21mJ. The maximum laser output was 32mJ and the slope efficiency was determined to be 23.7±1.2%.

 

Fig. 4. (a) Laser oscillation at 1062 nm in the Nd³⁺-doped NPS glass. (b) Measured threshold and slope efficiency. (The sample sizes: 20mm×20mm×10mm)

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4. Conclusion

A novel Nd³⁺-doped lead fluorosilicate glass 67SiO₂-10PbO-2PbF₂-12K₂O-8Na₂O-0.76Nd₂O₃-0.24As₂O₃ (in mol %) was prepared by a two-step melting process. The optical properties were investigated by means of optical absorption, luminescence and lifetime measurements. The Judd-Ofelt parameters were calculated and the radiative rates, lifetimes and branching ratios were obtained. Laser output was achieved with a wavelength of 1062nm. The laser threshold was 415mJ and the slope efficiency was 23.7%. The broad emission bandwidth and long fluorescence lifetime make NPS-glass a good candidate for uses in ultra-short pulse generation and amplification.