1. Introduction

Er³⁺-doped LiNbO₃ (LN) crystal is a promising substrate material for integrated optics as it combines excellent electro-optic, acousto-optic and nonlinear optical properties of LN with Er³⁺ laser property. Such an effective combination, together with the possibility of fabricating a waveguide of low loss, enables the broadband amplification and lasing at 1.5 µm. Over the past years, a family of Ti (or vapor ZnO)-diffused Er:LN waveguide lasers (amplifiers) and integrated devices have been demonstrated [1–4 ]. However, the photorefractive effect not only affects the performance of these devices, but also limits both the pumping and operating wavelengths. Although doping with >4.9 mol% MgO can effectively suppress the effect [5], heavy MgO doping leads to the difficulty in growing high quality single-crystal when bulk codoped with rare earth ions, and the decrease in diffusivity and solid solubility when rare-earth ions are incorporated by diffusion-doping method. It has been reported that a near-stoichiometric (NS) LN crystal needs less amount of MgO (>0.8 mol%) to prevent the photorefractive effect [6]. In addition, the NS crystal also exhibits some other advantages such as lower coercive field, larger electro-optic and nonlinear effects. Thus, an NS Er:LN crystal codoped with moderate MgO concentration would be a promising substrate material.

It is crucial to have the knowledge of Er³⁺ absorption and emission cross sections. People have reported the knowledge of bulk material [4, 7, 8 ] and waveguide [9, 10 ]. However, previous study focused on the congruent material while a systematic study of composition effect on the cross section could not be found yet. Present work focuses on the study.

2. Experimental description

Singly Er³⁺-doped and Er³⁺/Mg²⁺-codoped congruent LN crystals used in present study were grown by Czochralski method. Tables 1 and 2 summarize the samples and the dopant concentration, determined by neutron activation analysis with an error of ± 5%. The NS crystals were obtained by carrying out Li-rich vapor transport equilibration (1100 °C/100 h) on the as-grown congruent plates. The Li compositions in these NS crystals were determined from either the measured optical absorption edge (OAE) [11, 12 ] or the linewidth of 153 cm⁻¹ phonon [13]. The obtained Li/Nb ratios are summarized in Tables 1 and 2 . The data labeled by the superscript a/b represents the Li/Nb ratio in the congruent/NS crystals. It has been proved that Er³⁺ ions occupy the Li sites in the LN lattice [14], and this is also the case for the Mg²⁺ dopant when its concentration is below the threshold (C_th) [15]. This means that the Er³⁺ or Mg²⁺ doping causes different extents of decrease in the Li/Nb ratio. One can see from Tables 1 and 2 that the Li/Nb ratios in the NS crystals are definitely higher than those of the as-grown ones, and are closer to the stoichiometry. For reader’s convenience, the Li/Nb ratios in the ideal stoichiometric Er³⁺/Mg²⁺-codoped crystals are also given in Table 2.

Table 1. Dopant concentration, Li/Nb ratio and σ, π, unpolarized emission (σ_e) and absorption (σ_a) cross section values ( × 10⁻²⁰ cm²) of 551, 864, 980 1530 and 2700 nm transitions of only Er ³⁺-doped congruent and NS LNs.

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Table 2. Dopant concentration, Li/Nb ratio and σ, π, unpolarized emission (σ_e) and absorption (σ_a) cross section values ( × 10⁻²⁰ cm²) of 551, 864, 980 1530 and 2700 nm transitions of Er ³⁺/M g ²⁺-codoped congruent and NS LNs.

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All visible, near- and mid-infrared emission spectra were measured by a Horiba Jobin-Yvon Fluorolog-3 double-grating-excitation spectrofluorometer. A 450 W continuous xenon lamp was used as the source to excite all visible, near- and mid-infrared emissions. A rectangular excitation-probe configuration was used. A σ-polarized excitation beam was incident onto the sample along the direction perpendicular to the surface of each Y-cut plate.

The polarized or unpolarized fluorescence was collected along the direction perpendicular to the excitation beam. The spectra of the 0.53, 0.55, 1.5 and 2.7 μm emissions were recorded under the σ-polarized 980 nm (~20 mW) excitation. A couple of 1200 grooves/mm gratings blazed at the wavelength of 750 nm were used to disperse the excitation light. The visible, near- and mid-infrared fluorescence was dispersed by a 1200, 600 and 300 grooves/mm grating, respectively. The 0.86 and 0.98 μm spectra were measured under the σ-polarized 527 nm (~10 mW) excitation and another couple of 1200 grooves/mm gratings blazed at 330 nm were used to disperse the excitation light and the 600 grooves/mm grating to disperse the fluorescence. Both the π- and σ-polarized spectra were recoded for all visible and near-infrared emissions and the recording conditions under the two polarizations were identical for each sample. Due to lack of a polarizer, unpolarized mid-infrared spectrum was recorded. For better detection of relatively weak mid-infrared emission, the excitation light was modulated at a frequency of 140 Hz and a standard lock-in amplifier was used.

3. Results and discussion

The polarization-resolved emission cross section is given by [8]

The absorption and emission cross sections are related by the McCumber relation:

Comparison reveals that both spectral shape and polarization dependence show little effects of Mg²⁺-codoping and crystal composition effect. Instead, the cross section value shows definite Er³⁺ doping, crystal composition and Mg²⁺-codoping effects. Next, we exemplify the typical 1530 nm electronic transition to demonstrate these effects.

First, we discuss the Er³⁺ doping effect. Figure 1 shows the σ-polarized Er³⁺ 1530 nm emission (a) and absorption (b) cross section peaks of five congruent LNs with different Er³⁺ concentrations of 0.3, 0.9, 1.4, 2.3 and 2.7 mol%. We note that the cross section decreases with increased Er³⁺ concentration. To more clearly show the dependence, the peaking cross section is plotted against the Er³⁺ concentration in Fig. 2 . As the Er³⁺ concentration goes from 0.3 to 2.7 mol%, the decrease is as much as 12%, which is beyond the error (6%).

 

Fig. 1 σ-polarized 1530 nm emission (a) and absorption (b) cross section peaks of congruent LNs doped with different Er³⁺ concentrations.

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Fig. 2 σ-polarized 1530 nm emission (a) and absorption (b) cross section versus Er³⁺ doping level. Red/green balls: Er³⁺- only doped congruent/NS LNs; blue/magenta asterisks: Er³⁺/Mg²⁺-codoped congruent/NS LNs.

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Second, attention is paid to the Mg²⁺ codoping effect. Figure 3 shows a comparison of σ-polarized Er³⁺ 1530 nm cross section peaks of three Er³⁺/Mg²⁺-codoped congruent LNs doped with similar Er³⁺ concentrations (1.16-1.26 mol%) but different Mg²⁺ concentrations 1.2, 2.4 and 4.8 mol%. For comparison, the peaks of the Er³⁺ (1.4 mol%)-only doped LN are also shown. It appears that Mg²⁺ codoping causes the cross section increase by ~10%. To more clearly show the Mg²⁺-codoping effect, the peaking cross section is plotted against the Er³⁺ concentration in Fig. 2, together with the results of other samples. The Mg²⁺ codoping effect appears to be true when we compare the blue asterisk and red ball plots.

 

Fig. 3 σ-polarized 1530 nm emission (a) and absorption (b) cross sections of congruent LNs with similar Er³⁺ but different Mg²⁺ concentrations.

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Third, we turn to discuss the composition effect. Figure 4 shows σ-polarized Er³⁺ 1530 nm cross section peaks of five NS LNs doped with different Er³⁺ concentrations of 0.3, 0.9, 1.4, 2.3 and 2.7 mol%. The peaking cross section is plotted against the Er³⁺ concentration in Fig. 2, together with the results of other NS samples (the green ball plot is for the Er³⁺-only doped NS LNs and magenta asterisk curve is for the Er³⁺/Mg²⁺-codoped NS LNs). The cross section increases from a congruent to an NS crystal, whether the crystal is Er³⁺-only doped orEr³⁺/Mg²⁺-codoped. As the composition is close to the stoichiometry, the cross section increases by 20% and no longer changes with the concentration of either Er³⁺ or Mg²⁺(due to this reason, the 1530 nm peaks of the Er/Mg-codoped NS LNs are not shown for save space).

 

Fig. 4 σ-polarized 1530 nm emission (a) and absorption (b) cross section peaks of NS LNs doped with different Er³⁺ concentrations.

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Similar Er³⁺-doping, Mg²⁺-codoping and composition effects are also observed for other transitions ²H_11/2↔⁴I_15/2 + ⁴S_3/2↔⁴I_15/2, ⁴S_3/2↔⁴I_13/2 (~0.86 μm), ⁴I_11/2↔⁴I_15/2 and ⁴I_11/2↔⁴I_13/2. We no longer repeat the discussion. For convenience, the cross section values of some typical peaks of these transitions are given in Tables 1 and 2 . Because the transition with the lower polarization shows the features similar to that with the higher polarization, here we give only the cross section values of each transition with the higher polarization.

In words, Er³⁺ doping causes the cross section decrease by 12% while Mg²⁺ codoping causes the cross section increase by 10%. As the composition is increased from congruent point to stoichiometry, the cross section increases by 20%. These effects are related to their respective effects on Er³⁺ site distributions. Site selective spectroscopy study on Er:LN has shown that rare-earth doping, Mg²⁺ codoping and composition alteration all cause redistribution of non-equivalent energetic Er³⁺ sites [16]. The site redistribution associated with an increase in Er³⁺ concentration is similar to that associated with an increase in Li deficiency. Increasing Er³⁺ concentration tends to increase Li-deficiency and decrease crystal composition. Increasing composition not only reduces cluster site concentration but also increases the absorption upon the light [16], implying that the cross section of Er³⁺ transition is larger for the isolated sites while smaller for the clustered sites. Regarding the congruent crystals under study, it is reasonable that the cross section decreases with a rise in Er³⁺ concentration as high Er³⁺ concentration increases successively the concentration of clustered Er³⁺ sites, the probability of cooperative upconversion, which depends on the concentration of clustered site, and the quenching effect on the fluorescent intensity, which is associated with the upconversion effect. For the NS crystals, the composition increase induces the increase of optical absorption and hence the increase of cross section. As composition is close to the stoichiometry, the defects in crystal are almost completely removed, and the defect-related site redistribution no longer changes noticeably from one NS crystal to another, regardless of Mg²⁺ codoping. Thus, the cross section in the NS composition case tends to a constant and does not change noticeably with the dopant concentration. The Mg²⁺ codoping effect can be explained similarly. According to the defect model for MgO-doped LN [15], doping with an Mg²⁺ concentration below the threshold C_th leads to the composition increase. It is thus comprehensible that, for the Er³⁺/Mg²⁺-codoped crystals studied, in which the Mg²⁺ concentration is lower than C_th, the Mg²⁺ codoping leads to slight cross section increase. For samples 2, 3 and 4 in Table 2, which are heavily doped with Mg²⁺, one should observe the cross section decrease because doping with an Mg²⁺ concentration above C_th causes the defect concentration increase [15]. However, as shown in Fig. 2, the cross section does not reveal such feature because of the lower Er³⁺ concentration and its small Mg²⁺ doping effect.

Finally, it is worthy to note that the effects of Er³⁺ doping, Mg²⁺ doping and crystal composition match with their effects on the width of spectral line. One can see from Figs. 1, 3 and 4 that the spectral line broadens as more Er³⁺ ions are doped while narrows as the Mg²⁺ ions are codoped or the crystal composition is increased. The spectral line broadening/narrowing matches with the cross section decrease/increase.

4. Conclusion

We have demonstrated crystal composition effect on Er³⁺ cross section of singly Er³⁺-doped and Er³⁺/Mg²⁺-codoped LNs. Increasing doped Er³⁺ concentration tends to decrease the cross section, while codoping with Mg²⁺ or increasing crystal composition tends to increase the cross section. As the composition is close to the stoichiometry, the cross section tends to a constant. These effects are mainly related to the Er³⁺ site redistribution induced by doping or composition alteration.