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We investigate the temperature dependence of the lasing characteristics (lasing peak energy spontaneous emission factor β, and lasing threshold) of an irregular-shaped-ZnO-microparticle laser. The shift of the lasing peak energy with temperature is very small in the range of 120–300 K, thus, indicating that the peak is determined mainly by the resonance energy position of a given cavity mode, and not by the gain spectral peak. On the other hand, β and lasing threshold are strongly dependent on temperature; β reaches a maximum at a particular temperature, whereas the lasing threshold exhibits a minimum. In comparison with the theoretical calculations, it is found that β and lasing threshold are optimum at the temperature at which the spontaneous emission spectral peak is in resonance with the peak of the cavity mode.
© 2015 Optical Society of America
1. Introduction
ZnO is a promising material that can be used in light-emitting devices operating in the UV–blue region [1] because of its direct wide-bandgap (~3.37 eV) nature and large exciton binding energy (∼60 meV) [2]. The robustness, higher refractive index, and ease of crystal growth in the case of ZnO has led to the development of several types of ZnO-based lasers with ZnO acting as both the amplification medium and optical cavity. One such device is the micrometer-sized laser (microlaser) consisting of a ZnO nanowire [3] and another is a microlaser comprising a spherical microparticle [4, 5]. In these types of laser, optical positive feedback is achieved via well-defined optical cavity modes such as the Fabry–Pérot and whispering gallery modes. Thus, the lasing mode can be controlled through precise tuning of the size and morphology of the laser structure.
Another type of ZnO-based laser is the random laser, which usually consists of an assembly of ZnO particles with sizes of several hundreds of nanometers [6]. Because lasing oscillations in the random laser are caused by random multiple scatterings of light between the particles, precise tuning of the size and morphology of the structures is not required. However, due to the randomness of the scattering itself, mode control is essentially difficult to achieve and, as a result, a large number of lasing modes unexpectedly appear. Because its optical confinement is insufficient and unstable, the random laser also exhibits a strong background luminescence and large fluctuation in the lasing emission intensity. Note that a few lasing peaks have been observed in usual random lasers under a specific excitation condition, i.e., a limited excitation area that results in the decreased cavity mode number [7].
Recently, we developed a new type of ZnO microlaser, i.e., an irregular-shaped-microparticle laser [8]. In this type of laser, the lasing oscillation arises from random multiple scatterings of light within the microparticle. The lasing mechanism is similar to that of the random laser, but its lasing emission properties are quite different from those of the random laser. In fact, the microparticle laser exhibits single or a few lasing peaks, extremely low spontaneous emission background, and stable lasing emission intensity without requiring precise tuning of size and morphology. These unique properties are concluded to be due to the optical confinement of a laser cavity mode inside the irregular-shaped particle.
In general, the lasing characteristics such as the lasing threshold and lasing peak position are dependent on the gain properties of the amplification media and resonance properties of the cavity modes. In a previous work [9], we investigated the lasing characteristics of a ZnO random laser by systematically varying the temperature, and we observed that the characteristics are determined only by the temperature variation of the ZnO gain spectra. On the other hand, in the case of the irregular-shaped-microparticle laser, the resonance properties of the optically confined cavity modes are expected to strongly affect the temperature dependence of the lasing characteristics.
In this work, we investigate the temperature dependence of the lasing characteristics of an irregular-shaped-microparticle ZnO laser to clarify the role of cavity resonance and gain properties. The lasing peak energies are found to be almost independent of the temperature, and with decreasing temperature, one lasing peak abruptly disappears, and simultaneously, a new lasing peak appears in the higher-energy region. Furthermore, the lasing threshold exhibits a minimum at a particular temperature. We discuss in detail the mechanism of these unique temperature dependences by comparing the experimental results with theoretical calculations based on the standard laser theory.
2. Experimental
Commercially available ZnO microparticles procured HakusuiTech Co. Ltd were used in our study. Figure 1(a) shows the scanning electron microscope (SEM) image of a representative ZnO microparticle. The irregular-shaped microparticle has a diameter of ~2 μm. To examine the lasing properties of a single microparticle, a sample with a small number of scattered ZnO microparticles was prepared, similar to the procedure followed in our previous work [8]. The particles were dispersed in methanol, the resulting methanol solution was dropped onto a silicon substrate, and the substrate was rotated at 5000 rpm on a spin coater for 40 s. As a result, each ZnO microparticle exhibited clear separation (∼50 μm) from the other microparticles, as shown in Fig. 4(a) of [8]. To measure the lasing characteristics of a single ZnO microparticle, we set the excitation laser spot size (∼14 μm) to be smaller than the microparticle separation. The sample was pumped using a light pulse of 355 nm from a Q-switched laser with a pulse duration of 300 ps. The excitation laser was incident normal to the sample surface. Emission spectra were detected from the same direction as the incident beam via a single monochromator equipped with a charge-coupled device (CCD, Princeton Instruments, PIXIS:100B). All measurements were performed in a closed-cycle refrigerator cryostat (IWATANI CRT 105PL) at temperatures ranging between T = 120 and 300 K.
Fig. 1 (a) Scanning electron microscope (SEM) image of an irregular-shaped ZnO microparticle. (b) Temperature dependence of internal photoluminescence (PL) quantum efficiency. The inset shows the temperature dependence of the PL peak energy (left axis) and PL bandwidth (Γ, right axis).
3. Results and discussion
Firstly, in order to evaluate the intrinsic gain and loss properties of our ZnO microparticle, we measured its temperature-dependent photoluminescence (PL) properties. Figure 1(b) shows the internal PL quantum efficiency as a function of the temperature T. The quantum efficiencies were estimated from the integrated PL intensity with the reported extraction efficiency (~10%) for ZnO powder [10]. With decrease in T, the quantum efficiency gradually increased. This result indicates that the intrinsic losses of ZnO, such as those due to intraband and interband electronic absorption, decrease with decreasing T. In the inset of Fig. 1(b), the PL peak energy and PL bandwidth Γ (corresponding to the full width at half maximum of the PL peak) are plotted as a function of T. The PL peak energy shifts toward the higher-energy side due to the temperature-induced energy bandgap shift. This indicates that the gain spectra shift to higher energies with decrease in T. Further, Γ clearly decreases with decreasing T. Because Γ reflects the degree of thermal broadening and the resultant damping effect due to exciton–phonon coupling [11], the width of the gain spectral region becomes narrower and the phonon coupling loss decreases with decreasing T. The temperature-dependent gain spectra characterized by these PL properties are discussed later.
Figure 2(a) shows the lasing spectra of a ZnO microparticle measured at various values of T with a fixed excitation power density (P = 22 MW/cm2). At high temperatures (T = 270–220 K), only a single lasing peak (A) at ∼388 nm is observed, and its peak wavelength slightly shifts toward the shorter-wavelength side. With further decrease in T, a new lasing peak appears at ∼380.5 nm and the previously observed peak A disappears. At T = 160 K, this peak at ~380.5 nm also disappears, and one more lasing peak newly appears at ~378 nm. Furthermore, each lasing intensity exhibits a maximum at a particular T, e.g., T = 250 K for A. Essentially the same behavior is observed for the temperature dependence of the lasing spectra of a second ZnO microparticle, as shown in Fig. 2(b). For example, in the range of T = 300–250 K, the lasing emission at ∼391 nm is dominant, while at lower T values (220–140 K), a peak (B) at ∼381 nm is observed. The maximum of peak intensity for B is observed at 190 K.
Fig. 2 (a), (b) Lasing emission spectra of two different ZnO microparticles at various temperatures. The excitation power density was fixed at 22 MW/cm2 in both cases.
In our previous work [8], it was shown that the lasing oscillation in an irregular-shaped microparticle is due to multiple scattering within the microparticle. The observation of a single lasing emission also indicated that an optically confined cavity mode is formed in the microparticle. Thus, the temperature dependence of the lasing spectra shown in Figs. 2(a) and 2(b) suggests that a cavity mode can survive only in a specific T range, and in another T range, another cavity mode appears with the corresponding exhibition of a new lasing peak.
A possible reason for the observed switching between different lasing cavity modes is attributed to the temperature-induced shift in the gain (spontaneous emission) peak. The gain peak position is dependent on T while the resonance peak position of the cavity mode is nearly independent of T. If the two resonances of two cavity modes are clearly separated in terms of energy, one cavity mode ceases to lase and the second starts to lase when the gain peak shifts away from the resonance of the former one and approaches that of latter one with change in T. In other words, the available gain of a cavity mode has a maximum at a particular temperature where the gain peak coincides with the resonance of the corresponding cavity mode, and subsequently when the gain becomes smaller than its loss counterpart with change in T, lasing oscillation stops. This conjecture is supported by the experimental fact that the lasing intensity of each lasing peak is maximum at a particular T [see Figs. 2(a) and 2(b)].
To further investigate the temperature dependence of the lasing characteristics for each cavity mode in detail, we measured the excitation power (P) dependence of the lasing emission at different temperatures. Figures 3(a) and 3(b) show the lasing peak intensity as a function of P for peaks A and B, respectively. The corresponding lasing spectra at T = 240 K (A) and 190 K (B) are shown in each inset. From the figures, we observed that the lasing threshold behaviors depend on T. Furthermore, the sharpness of their thresholds is dependent on T (e.g., for peak B, the threshold at 190 K is shaper than that at 160 K). This difference in the sharpness originates from the temperature dependence of the spontaneous emission factor β [12].
As per the standard laser theory for a single-cavity-mode laser [13], the lasing dynamics can be expressed using the differential rate equations,
where np, Nu, and Nl represent the cavity photon number and the populations of the upper and lower levels for a given gain material, respectively. Further, γcav, γ, and Rp represent the cavity decay rate, total decay rate (i.e., the sum of radiative and nonradiative decay rates) at the upper level, and excitation rate, respectively. Parameter K represents the coupling constant between the cavity mode and the gain material, and it is expressed as K = βγr, where β and γr denote the spontaneous emission factor and radiative decay rate, respectively. The lasing light input-output curve can be reproduced by the steady-state solution (np versus Rp) of the above equations upon assuming Nl ∼ 0 [14]. The solid curves in Figs. 3(a) and 3(b) indicate the calculated results obtained using the steady-state solution, where β and γcav are treated as the fitting parameters, and the experimentally obtained internal quantum efficiency (ϕ = γr/γ) shown in Fig. 1(b). The calculated curves well reproduce the experimental ones.Fig. 3 Lasing intensity of peaks (a) A and (b) B as a function of the excitation power density at various temperatures. Insets of (a) and (b) show the corresponding lasing spectra at T = 240 and 190 K, respectively. Threshold (left axis) and β (right axis) values as a function of T for lasing peaks (c) A and (d) B. The solid curves in Figs. 2(c) and 2(d) represent the calculated results of β
The lasing threshold, at which the slope of the input-output curve changes is expressed as with
being given by the solution of Rp in Eq. (2) assuming np → 0 and at dNu/dt = 0 (the steady-state condition) [15]. In Figs. 3(c) and 3(d), the fit-obtained lasing threshold and spontaneous emission factor β are plotted as a function of T. The lasing threshold reaches a minimum at T ∼ 230 and 190 K for peaks A and B, respectively. The mechanism underlying such optimum behavior in the threshold versus T plots is discussed later.Interestingly, the spontaneous emission factor β exhibits an almost contrasting behavior as a function of T with respect to that of the lasing threshold, i.e., β exhibits a maximum at a particular T (240 K for peak A and 220 K for peak B). Because β essentially represents the fraction of spontaneous emission of the gain materials coupled with the optical cavity mode [16], its higher value means lower loss of the spontaneous emission energy. In this context, we remark that there are several theoretical analyses of the temperature dependence of β for various types of lasers [17, 18]. Further, a similar contrasting dependence between β and lasing threshold has been predicted from theoretical simulations [17, 19].
Parameter β can be calculated by means of the following equation [16]:
where λ and Vcav represent the optical wavelength and optical cavity volume, respectively. Further, wsp and Esp represent the width and peak energy of the spontaneous emission spectrum, respectively, and wcav and Ecav denote the spectral width and peak of the cavity mode, respectively. Here, we note that Eq. (4) can be used only when wcavity ≪ wsp.We calculated the temperature dependence of β (T) using Eq. (4) with the introduction of the experimentally obtained parameters, i.e., PL width and peak energy [Γ(T) and EPL(T) shown in the inset of Fig. 1(b)] being regarded as wsp(T) and Esp(T), respectively. Further, wcav and Ecav were also assumed to be independent of T, and we used the experimental values of the lasing width (1.5 meV) and its peak energy (3.195 and 3.258eV for peaks A and B, respectively) in our calculations. Parameter Vcav was considered as a temperature-independent fitting parameter and a slight energy offset value σ was taken into consideration for Esp(T) [i.e., Esp(T) = EPL(T)+σ ] because of its large experimental uncertainly in the estimation of the PL peak energy. The solid curves in Figs. 3(c) and 3(d) show the calculated β (T) results. From the figures, we note that the calculated curves agree with the experimental data.
From Eq. (4), we can easily infer β (T) exhibits a maximum at the resonance condition [Esp(T) = Ecav(T)], and that the coupling between the cavity mode and spontaneous emission of the gain material is optimum. From Eq. (3), the temperature-dependent lasing threshold of a cavity mode is expected to decrease when the resonance condition is approached. Thus, the contrasting temperature-dependence behaviors of β and the lasing threshold shown in Fig. 3 indicate that the lasing threshold of the present ZnO microparticle laser reflects variation in β (T), i.e., the degree of coupling between spontaneous emission and the cavity mode.
Next, we examine the temperature dependent gain properties of the ZnO microparticle laser. We theoretically calculate the gain spectra of ZnO using the same procedure as that described in our previous work [9]. The excited carrier density (n)- and temperature-dependent gain spectrum g(ω,n,T) at a frequency ω is given by the following equation:
where χ and c represent the complex susceptibility and speed of light in vacuum, respectively. In the calculation of χ, we used the temperature-dependent bandgap energy and damping factor obtained from the measured PL spectra in Fig. 1(b). The detailed procedure and other material parameters used in the calculation are described in our previous work [9]. Examples of the calculated g at 300, 220, and 120 K are shown in Figs. 4(a)–4(c) [solid curves, left axis], respectively. The excited carrier densities are n = 5.60, 5.45, and 2.90 ×1025m−3 for 300, 220, and 120 K, respectively.Fig. 4 Histograms of the lasing peak energy for various ZnO microparticles at T = (a) 300, (b) 220, and (c) 120 K (left axis). The solid curves indicate the theoretically calculated gain spectra (g; left axis). (d) Plot of lasing peak energy versus T for two different ZnO microparticles (solid and open symbols), with their corresponding spectra shown in Figs. 2(a) and 2(b), respectively. The counter plot represents the calculated gain as functions of energy and temperature. In the color scale, the white to black region represents gradation from high (6μm−1) to low gain (3μm−1) values.
In the case of the random laser, it has been previously shown that the bulk gain spectra correspond to the histograms of the lasing peak energies [9]. Because the ZnO microparticles used in this study have various sizes and shapes, their gain spectra should exhibit a relation with the lasing peak histograms. To confirm the validity of our calculated gain spectra, we constructed histograms of the lasing emission peak energies for a large number of ZnO microparticles measured at different values of T. We confirmed that our calculated g spectra agree well with the histograms [Figs. 4(a)–4(c)].
The counter plot in Fig. 4(d) shows the calculated gain spectra for T = 120–300 K. The lasing peak energies of each cavity mode for the two ZnO microparticles [in Figs. 2(a) and 2(b)] are also plotted in Fig. 4(d). With increase in T, the gain spectra shift to higher energies, whereas each lasing peak does not exhibit any strong T dependence. A lasing mode in the lower-energy side shifts to the higher-energy side as the gain spectra shift to high-energy side. This fact clearly indicates that the gain peak shift induces switching of the lasing mode. Moreover, the lasing peaks appear in the relatively higher gain region of g = 3–6 μm−1.
Finally, we discuss the differences of the temperature dependence of the lasing characteristics between the usual random laser and our present irregular-shaped microparticle laser. In the ZnO nanopowder random laser, the temperature dependence of the lasing characteristics is determined only by the gain properties, and thus, the lasing peak energy clearly follows the temperature shift of the gain spectra, and the lasing threshold monotonically decreases with decreasing T values due to increase in its g value. In contrast to the random laser, in our present irregular-shaped-ZnO-microparticle laser, the lasing peak appears at the resonance energy of the cavity mode in the higher-gain region, and further, the lasing threshold is dependent on β (T), i.e., the degree of coupling between the spontaneous emission (gain) and the cavity mode. Although these two different lasers have a similar feedback mechanism (i.e., random multiple scattering), the temperature dependences of the lasing characteristics are quite different between them.
The above differences arise from the number of cavity modes in the gain spectral region. In the usual random laser, there are many cavity modes in the gain spectral region. Therefore, upon shifting the gain spectra by changing T, the cavity modes in resonance at the gain spectral peak lase, and consequently, their lasing threshold is characterized by the gain value. On the other hand, in our microparticle laser, the number of cavity modes in the gain spectral region is nearly one due to the optical confinement effect. Thus, only a specifically selected cavity mode exhibits lasing oscillation, and as a result, the gain coupling to this specific cavity is crucial to the lasing threshold value.
4. Conclusions
We investigated the temperature dependence of the lasing characteristics of an irregular-shaped-ZnO-microparticle laser fabricated in this study. The peak energy for each lasing mode was almost independent of the temperature in the range of 120–300 K. With decrease in temperature, a new mode appears in the higher-energy region, accompanied by the disappearance of the old lasing mode. These phenomena are caused by the gain spectral shift that occurs with decreasing temperature. From our analysis of the excitation power density versus lasing emission intensity curves, we estimated the spontaneous emission factor β and lasing threshold for each lasing mode at various temperatures. Parameter β exhibited a maximum at a particular temperature. We showed that the theoretically calculated β can reproduce the experimental one and that this parameter has a maximum at the temperature at which the spontaneous emission (gain) peak coincides with the spectral peak of the cavity mode. The lasing threshold contrastingly reached a minimum at a particular temperature, indicating that the temperature dependence of the lasing threshold is mainly determined by the variation in β, i.e., the degree of coupling between the spontaneous emission and cavity mode. Our irregular-shaped-ZnO-microparticle laser exhibits a relatively high β value (∼0.3) although we did not optimize its morphology, which forms a requirement for the conventional semiconductor lasers [20]. Thus, our microparticle laser is a good candidate for future low-cost and high-efficiency microlaser systems.
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