1. Introduction

Since dimensional photonic crystals (PCs) developed for years, many efforts have been concentrated on their optical properties, especially the photonic band gap [1–3]. Mainly due to Bragg diffraction, periodical structures in submicron range lead to photon localization in the forbidden region. Recently, various applications of PCs have been carried out as a reflector [4,5], a sensor [6], or to enhance luminescence [7,8] and Raman spectroscopy [9]. In addition, PCs were often used to induce lasing emission that luminescent materials embedded inside PCs can be excited to interact with them, as well as pumping in a resonance cavity [10,11]. So far, low threshold lasing has been demonstrated with the combination of opal/inverse opal PCs and several active materials. Examples are fluorescent dye molecules or semiconductors embedded in 1-D, 2-D, and 3-D PCs, in which the photonic stop band can range from ultraviolet (UV) to near infrared (NIR) [12–16].

Despite lasing emissions have been developed with various materials in PCs, some obstacles still need to be overcome. In general, dye is accompanied with a broader band emission than the width of the photonic stop band [12], resulting in incomplete photon suppression inside PCs. Moreover, luminescence of dye is easily quenched especially under high power excitation. Meanwhile, for a large area of semiconductor PCs, the developed opal or inverse structures have the disadvantage of generating defect-free emission during the fabrication process [17]. To achieve high lasing efficiency and complete photon suppression, strong and stable luminescent active materials embedded in PCs are necessary. Recently, Er³⁺ doped-fiber has been used as a resonance cavity to perform lasing modes [18]. With strong, stable, and narrow multiple emissions of intra-4f transition in near infrared range, it offers a very practical opportunity for the application in optical communication. Similarly, Tb³⁺, one kind of rare earth ions with emission bands from UV to visible range, also has the same advantages [19]. In one of our published reports, Tb ions encapsulated in monodispersed silica nanoparticles (Tb(OH)₃/SiO₂ core/shell nanosphere) have been successfully synthesized [20]. After self-assembling in a closed pack structure, the periodicity of these nanospheres exhibits a pronounced photonic stop band. In addition to preventing coalescence and controlling size, the SiO₂ shell is very useful in manipulating interparticle interaction and in biological targeting research. By taking the advantages of the well-defined PCs developed in our previous work [20], here we demonstrate laser action of ⁵D₃→⁷F₆ transition of Tb ions based on the assistance of the formation of optical stop band in PCs. Our results provide an excellent alternative for creating reliable solid state emitters, laser materials, as well as biological markers.

2. Experiment

Tb(OH)₃/SiO₂ core/shell nanospheres were synthesized by a one-pot method and deposited on a quartz or silicon (100) substrate by a slow evaporation method. Details were described in our previous report [20]. The particle size of the nanospheres ranged from 125 nm to 300 nm was examined by transmission electron microscopy (TEM) and scanning electron microscopy (SEM, JEOL JSM-6500). After the nanospheres were assembled to several cm² in area as PCs, the samples were excited at room temperature by a Q-switched Nd: YAG laser (266 nm, 3–5 ns pulse). The diameter of the laser beam focused on the sample is about 0.5 mm.

3. Results and discussions

 

Fig. 1. (a) Top and (b) Cross sectional scanning electron microscope image of assembled Tb(OH)₃/SiO₂ nanospheres (d=230 nm). (c) The size distribution of Tb(OH)₃/SiO₂ nanospheres.

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The SEM image of assembled Tb(OH)₃/SiO₂ core/shell nanospheres (d=230 nm) exhibits highly monodispersed and a fcc close-packed lattice structure as shown in Fig. 1(a). More than 30 layers were accumulated on silicon or quartz substrate, forming 3-D PCs, as shown in Fig. 1(b). The size distribution of the Tb(OH)₃/SiO₂ nanosphere is shown in Fig. (c). We can see that most nanospheres have a diameter of 230 ± 10 nm. Owing to the Bragg diffraction from (111) crystal plane, the reflectance spectrum shows a peak at 490 nm with a linewidth of 200 nm as shown in Fig. 2(a). To confirm the fact that the peak at 490 nm really arises from the formation stop band due to the inherent nature of photonic crystals, we have performed the band structure calculation based on PWE (plane wave expansion) method as shown in Fig. 2(b). The experiment result is indeed consistent with the band structure calculation. By varying the nanospheres size, we can shift the stop band position from 330 nm to 650 nm, as shown in Fig. 2(b). The variation of the stop band versus particle size shows a linear relationship as predicted by the theory of Bragg diffraction [21]. The slightly nonlinear behavior may be due to the variation of refractive index of silica in UV range, disorder, and the resulting changed filling fraction [22]. Moreover, when the diameter of the nanospheres decreases and is comparable to that of the core material (10 nm), influence of Tb ions on effective refractive index needs to be considered.

 

Fig. 2. (a) Reflectance spectrum of the sample as shown in Fig. 1(a). (b) Band structure calculation of the photonic crystal with 230 nm Tb(OH)₃/SiO₂ nanospheres. (c) First Bragg stop band of assembled Tb(OH)₃/SiO₂ PCs versus Tb(OH)₃/SiO₂ particle size. The straight line represents the prediction according to the Bragg diffraction. Full widths at half maximum of the stop bands are labeled as error bars.

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For single or random dispersed Tb(OH)₃/SiO₂ core/shell nanoparticles, the luminescence spectrum reveals multiple emissions from 380 nm to 625 nm [23] as shown in Fig. 3(a). Among these emissions, most strong emission occurs at the transition from ⁵D₄ to ⁷F₅ bands. As the nanospheres were assembled showing a periodic nanostructure, relative emission intensities of ⁵D₃ to ⁷F₆, ⁵D₃ to ⁷F₅, and ⁵D₃ to ⁷F₄ transitions with respect to other transitions change due to the inhibited propagating wave in photonic crystals. As shown in Fig. 3 (b), the emission bands of 497 nm were largely suppressed when the nanospheres with a diameter of 230 nm were assembled as photonic crystals. This behavior can be easily understood due to the formation of the stop band from 400 nm to 600 nm as shown in Fig. 2(a), and therefore the emission is confined inside the PCs and unable to escape away.

 

Fig. 3. Cathodoluminescence spectra of (a) Tb(OH)₃/SiO₂ nanoparticle powder and (b) assembled Tb(OH)₃/SiO₂ nanoparticles with a diameter of 230 nm taken at electron acceleration voltage of 10 kV and current of 5×10^-9 A.

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To show lasing or optical resonance effect in PCs, the samples with a diameter of 230 nm (with stop band at around 500 nm) was chosen to demonstrate the influence on the excited luminescence spectrum. Figure 4(a) shows the emission spectra of Tb(OH)₃/SiO₂ PCs with a diameter of 230 nm with different excitation energies. Below 74 µJ/pulse, the emission spectra at around 400 nm showed a broader emission peak. A sharp peak appears as the pumping energy is increased. The plot of emission intensity versus excitation current is shown in Fig. 4(b). After the pumping energy reached 74 µJ/pulse, the emission near 400 nm occurred as a protrusion, which is near the stop band edge. The narrow width of the emission and the threshold nature clearly prove the lasing emission behavior. Most emission in the stop band was suppressed due to the low photonic density of state (DOS). In contrast, high photonic density of states near the band edge can enhance the emission rate. Laser emission can be achieved with the relative low group velocity and high photonic density of states (DOS) near the band edge of the stop band in PCs.

Quite interestingly, it is found that the lasing peaks exhibit an equal space of about 4 nm as shown in Fig. 4(c). This intriguing behavior can be interpreted well based on the Fébry-Pérot resonance. According to the Fébry-Pérot resonance,²⁵ the resonance length l can be estimated by

where n is the refractive index of PCs, λ₁ and λ₂ are wavelengths of multimodes. Our experimental result can be well interpreted when the resonance length l is set equal to two times of the thickness of PCs as shown in Fig. 1(b). Therefore, the obtained lasing behavior is attributed to the slow light, high photonic density of states, and the Fébry-Pérot resonance.

 

Fig. 4. (a) Photoluminescence (PL) spectra of Tb(OH)₃/SiO₂ PCs with d=230 nm. (b) Output PL emission intensity as a function of pumping energy. (c) Lasing emission spectrum with the excitation energy of 85 µJ.

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4. Conclusion

In summary, the stop band of Tb(OH)₃/SiO₂ PCs for different particle sizes was observed in a wide range, from UV to red. Utilizing this tuning band property, the cavity of different periodicities can be used to assist lasing emissions for multiple transitions of Tb ions. Due to the large density of states near the stop band edge in PCs lasing emissions can be easily obtained. In view of the strong, stable, and narrow emission bands of Tb ions as well as several advantages of SiO₂ monodispersed nanoparticles, the work shown here should be very useful for the development of optoelectronic devices in practical applications.