Pump induced lasing suppression in Yb:Er-doped microlasers

A pump source is one of the essential prerequisites in order to achieve lasing, and, in most cases, a stronger pump leads to higher laser power at the output. However, this behavior may be suppressed if two pump beams are used. In this work, it is shown that lasing around the 1600 nm band can be suppressed completely if two pumps, at wavelengths of 980 nm and 1550 nm, are applied simultaneously to a Yb:Er-doped microlaser, whereas it can be revived by switching one of them off. This phenomenon can be explained by assuming that the existence of one pump (980 nm) changes the role of the other pump (1550 nm); more specifically, the 1550 nm pump starts to consume the population inversion instead of increasing it when the 980 nm pump power exceeds a certain value. As a result, the two pump fields lead to a closed-loop transition within the gain medium (i.e., erbium ions). This study unveils an interplay similar with coherence effects between different pump pathways, which provides a reference for designing the laser pump and may have applications in lasing control.


Introduction
The presence of a pump can be considered to be one of the most fundamental elements to achieve lasing in a system. In solid state lasers, the function of the pump is to invert the population by transferring ions from ground states to metastable states via intermediate states with the assistance of a quick decay channel. For many gain media, there are several intermediate states from which ions can decay to the same metastable state [1]. This implies that the laser can be pumped at several wavelength bands separately or co-operatively. For instance, erbium ions have two frequently-used pump bands to produce emission in the 1.55 µm region, i.e., 980 nm and 1450-1480 nm, corresponding to transitions from the ground-state manifold 4 I 15/2 to the 4 I 11/2 and 4 I 13/2 manifolds, respectively [2]. Since the absorption cross-section is high at 980 nm and the absorption band is wide at 1450 nm, it is quite natural to combine the two pumps in order to gain higher laser power output in the C-band [3][4][5]. Aside from providing gain in the C-band, the Er 3+ ions pumped by 1530-1550 nm light may also be used as a gain medium for L-band lasing [6][7][8].
In this work, we experimentally observe that, unlike the 980 nm and 1480 nm co-pumping case, L-band lasing can be enhanced or completely suppressed when two pumps at 980 nm and 1550 nm are simultaneously applied to a Yb:Er co-doped laser. This counter-intuitive phenomenon indicates that it is incorrect to simply sum up the effects induced by the two pumps, since they may actually have opposing effects and lead to a reduction in the lasing output. According to our experimental results and theoretical model, we reveal that the lasing suppression phenomenon originates from the emergence of a closed transition cycle for the gain medium formed by the two pumps. Therefore, this phenomenon should not be limited exclusively to Yb:Er lasers or even solid state lasers -it may well exist in other laser systems that are co-pumped at different wavelengths. One would thus expect this phenomenon to have striking consequences for laser pumping or control.

Experimental Method
Here, we will consider a variety of lasers with different gain media and ion concentrations. For convenience, we use silica microsphere lasers with whispering gallery (WGM) cavity modes. In the last decades, lasers based on WGMs have attracted significant attention for both fundamental research and applications [9][10][11][12][13][14][15][16][17][18][19]. We make full use of the advantages of WGM lasers, such as ease off fabrication and low cost. The diameters of our microspheres are about 150 µm and they are fabricated in a standard way by focusing a CO 2 laser beam directly onto a piece of commercial fiber (Thorlabs, SMF 28). Initially, a section of fiber is mounted vertically and tapered by heating via the CO 2 laser while a small weight pulls it downwards. The fiber is next cut using the CO 2 laser beam and the tapered part acts as the stem of the microsphere. This thin section of fiber is dipped for a few seconds into a sol-gel precursor solution in which erbium and ytterbium ions have been dissolved. The sol-gel precursor fabrication method has been discussed in detail elsewhere [15,20]. The sphere is then formed at the sol-gel coated section via a reflow process using the CO 2 laser. During the reflow process, the residual sol-gel solvent is removed and the ions are embedded into the silica matrix due to the high temperature. This fabrication method means that the precise concentration of the erbium and ytterbium ions cannot be obtained; however, their ratio and maximum concentrations can be determined by the sol-gel precursor. Hence, concentrations stated in the following are actually the maximum possible values.
To pump the microsphere laser and couple laser emissions out from it, a tapered optical fiber with a diameter of 1-2 µm is used in a contact coupling configuration. We use three broadband, multiple-mode lasers, with 5-10 nm linewidths and wavelengths centered at 980 nm, 1440nm, and 1550 nm, as pump sources. Though the frequency of the pump lasers cannot be tuned, some light can couple into the microsphere with a few percent of the light being absorbed by the cavity modes. For co-pumping of the microsphere by two lasers simultaneously, we combine the two beams using wavelength-division multiplexing (WDM) before coupling them into the tapered fiber. To avoid possible damage, only 50% of the laser output is sent into an optical spectrum analyzer (OSA) for measurement, the resolution of which is set to 0.5 nm.

Experimental Results
First, we characterized the Yb:Er laser while it was pumped by the 980 nm laser and the 1550 nm laser separately. The concentrations of the trivalent erbium and ytterbium ions in the surface layer of the microspheres were 5 × 10 19 /cm 3 and 2 × 10 20 /cm 3 , respectively. The WGM laser demonstrated multiple-mode output at the L-band (around 1600 nm, see Fig.1). It was also observed random mode hopping; therefore, the spectra were sampled stochastically. For both pump wavelengths, the number of lasing modes and the total output power increased with pump power. It was also noted, see Fig. 1(b), that some lasing peaks had a tendency to shift towards shorter wavelengths, i.e., towards 1580 nm, when the power of the 980 nm pump reached 13.6 mW. However, the shortest wavelengths are still longer than 1580 nm. This phenomenon can be attributed to the complex energy level structure of Er 3+ as discussed elsewhere [21,22]. Figure 2 shows the output of the Yb:Er co-doped WGM laser pumped simultaneously by the 1550 nm laser and 980 nm laser. The concentrations of the two samples are the same as in the above. Figure 2(a) shows the total power of the WGM laser output, calculated from the measured spectra on the OSA. For each plot, the power of the 1550 nm pump is fixed while the 980 nm pump launched into the coupling fiber is increased from 0 to 76.7 mW. From plots I to VIII, the power of the 1550 nm laser is also increased. For clarity, the following discussion is based on one sample (A) only, since sample A and B are fabricated by using the same method and have similar sizes. As shown in plots I and II of Fig. 2(a), when the power of the 1550 nm laser is low, the total power of the WGM laser output increases with the 980 nm pump. When the power of the 1550 nm pump increases to a certain level (6.8mW), the total power of the laser output start to decrease after a slight increase, as shown in plots III to V; however, it can revive after reaching zero. As seen in plots VI,VII and VIII of Fig. 2(a), when the power of the 1550 nm pump is high, the total power of the WGM laser may be completely suppressed after slight augmentation of the 980 nm pump. Figure 2 For comparison, we did similar experiments for microspheres doped purely with Er 3+ ions, see Fig. 3 . The concentration of Er 3+ was kept at 5 × 10 19 /cm 3 . As in Fig. 2, we increased the power of the 980 nm pump for each plot. From Plot I to Plot VIII, the power of the 1550 nm pump was also increased gradually. In qualitative contrast to the observations for the co-doped WGM laser, we clearly see that the total output power keeps increasing as a function of the 980 nm power, no matter the power of the 1550 nm pump. Figure 3(b) depicts a series of output spectra, corresponding to the blue data (open circles) in plot V.
To further inspect the effect of the pump wavelength on WGM lasing, we conducted another group of experiments. The microsphere samples are the same two as used for Fig. 2, but we use a 1440 nm pump instead of the 1550 one, and the results are given in Fig. 4. From plot I to plot VIII, we increased the 1440 nm pump power from 0 to 97.7 mW for sample A and from 0 to 63.3 mW for sample B. When the 1440 nm pump power is low (plot I-plot III) the output power of  the WGM laser increases with respect to the 980 nm pump. When the 1440 nm pump power is increased to 62.8 mW (plot VI-plot VIII), the total output power of the laser initially increases and gradually reaches a maximum value, though with some fluctuations. In particular, sample A exhibits considerable power fluctuations. Since the pump laser we used supports multiple-mode emission, and considering mode hopping, it is impossible to conclude whether the lasing is suppressed or enhanced by the 980 nm pump.

Theoretical Model and Discussion
To better understand the experimental results, we consider the energy levels of the Er 3+ and Yb 3+ ions, see Fig.5. It is well-known [23] that the 1600 nm lasing emission is generated by the transition from the 4 I 13/2 to 4 I 15/2 energy level in Er 3+ . Due to Stark splitting effects [2], the energy levels of rare earth ions in an SiO 2 matrix are in fact energy manifolds consisting of many sublevels, and, as a result, the transitions corresponding to pumping by 1440 nm and 1550 nm, as well as the 1600 nm emission, occur between the same two manifolds, i.e., 4 I 13/2 and 4 I 15/2 . Though the energy level structures of rare earth ions are very complicated, some phenomenological parameters, such as absorption and emission cross-sections, can be introduced to encompass the main physical properties. For example, with the assumption that 1550 nm light has a higher absorption to emission cross-section ratio than 1600 nm light, we can illustrate why the former can be used as a pump to produce the latter. In the Yb:Er co-doped laser, the 980 nm pump can excite both Er 3+ and Yb 3+ [24, 25], corresponding to the transitions from their ground states to the levels 4 I 11/2 and 2 F 5/2 , respectively, see Fig. 5(a). Compared to Er 3+ , Yb 3+ can absorb the 980 nm pump more efficiently and energy can be transferred to the erbium ions in the ground-state manifold. In principle, Er 3+ can also transfer energy back to Yb 3+ ; however, the probability of this happening is negligible due to the short lifetime (less than 1 µs [26]) of the Er 3+ intermediate state, 4 I 13/2 [27, 28]. In our system, the concentration of Yb 3+ is higher than that of Er 3+ , therefore, the effective absorption and emission cross-sections for the Yb 3+ -sensitized Er 3+ ions at the 980 nm band are significantly increased. For simplicity and clarity, in the following we will ignore the complicated Yb:Er energy exchange dynamics and simply treat the co-doped medium as a three-level atom, with an energy level structure similar to that of Er 3+ . The differences we consider are only the absorption and emission cross-sections at the 980 nm band. In our model, we assume that the former is an order of magnitude larger than the latter.
As a proof-of-principle, we assume that the cavity is pumped by two single mode lasers, one at 980 nm and the other at either 1440 nm or 1550 nm. For the waveguide-coupled WGM cavity, where the subscripts p 1 , p 2 and L denote the 980 nm pump, the 1440 or 1550 nm pump, and the 1600 nm lasing, respectively; a is the amplitude of the intracavity field, κ 0 and κ ex are the decay ratios caused by intrinsic losses and fiber coupling loss, respectively; a in designates the input field in the fiber and |a in | 2 is the input power. For simplicity, we also assume that each input field is resonant with its corresponding cavity modes. ξ is the input noise to the laser mode originating from spontaneous emission; g p 1 , g p 2 and g L denote the gain coefficients for the 980 nm pump, the 1440/1550 nm pump, and the 1600 nm lasing, respectively, and are determined from where c denotes the speed of light in vacuum, n stands for the effective refractive index, σ a and σ e describe the absorption and emission cross-sections of Er 3+ , N 1 , N 2 and N 3 are the density of Er 3+ in the states 4 I 15/2 , 4 I 13/2 , and 4 I 11/2 , respectively. The dynamical behavior of this three-level system is described by the following laser rate equations where τ 32 and τ 21 denote the decay time for spontaneous emission from 4 I 11/2 to 4 I 13/2 and from 4 I 13/2 to the ground level, 4 I 15/2 , respectively. C p 1 , p 2 , L = λ p 1 , p 2 , L /2πRA p 1 , p 2 , L n p 1 , p 2 , L h, where A is the effective mode area for the probe and pump modes, R is the radius of the microsphere and h is Planck's constant. Eqs. (1)-(8) can be solved numerically. Here, we only consider the steady-state case. The values of the parameters we use in this model are as follows [29]: the density of Er 3+ is 2 × 10 19 /cm 3 , R = 75 µm, A p 1 , p 2 , L = 5 × 10 −8 cm 2 , λ p 1 = 980 nm, λ p 2 = 1440/1550 nm, λ L = 1600 nm, n p 1 , p 2 , L = 1.35, τ 21 = 6 ms, τ 32 = 1 µs, σ a p 1 = 3.3 × 10 −21 cm 2 , σ e p 1 = 2 × 10 −21 cm 2 , σ a L = 3.3 × 10 −22 cm 2 , and σ e L = 1 × 10 −21 cm 2 . For the 1440 nm pump, σ a p 2 = 2 × 10 −22 cm 2 and σ e p 2 = 5 × 10 −23 cm 2 , whereas for the 1550 nm pump, σ a p 2 = 2.5 × 10 −21 cm 2 and σ e p 2 = 3×10 −21 cm 2 . For the Yb:Er co-doped laser, we use σ a p 1 = 3.3×10 −20 cm 2 and σ e p 1 = 2×10 −20 cm 2 , as mentioned previously. Figure 6(a)-(c) presents the theoretical estimates for the output power of the 1600 nm laser, corresponding to the experiments shown in Figs. 2, 3 and 4, respectively. From Fig. 6(a), the 1600 nm laser output increases with the 980 nm pump when the power of the 1550 nm pump is low; however, the lasing output may decrease or even be completely suppressed as the 980 nm pump is increased when the 1550 nm pump is strong (red solid line and black dotted line). This behavior is similar to our experimental observations. It should be noted that our model cannot explain the right ascending parts in plots IV and V of Fig. 2(a). This phenomenon may originate from our simplification of the energy manifold to an energy level considering that the lasing has a blue shift tendency; in fact, the dynamics of the transitions between different energy sublevels of one manifold is not reflected in the absorption and emission cross-sections, thus a more complete model is needed to explain the phenomenon.
In order to further understand the lasing suppression phenomenon, we depict some parameters of the Yb:Er co-doped laser evolving with respect to the 980 pump in Fig. 6(d)-(f), corresponding to the black dotted line in Fig. 6(a). Figures 6(d) and (e) illustrate the normalized intracavity power and gain coefficient for the pump and laser modes, respectively, whereas Fig. 6(f) depicts the population percentage of erbium ions in different levels. The emergence of lasing suppression can be intuitively explained as follows. When the 980 nm pump power is low, the gain provided for the 1600 nm lasing mode is mainly due to the 1550 nm pump (see Fig. 5(a) and (b)), thus the 1550 nm gain coefficient is negative, as shown in Fig. 6(e). The 980 nm pump excites the Er 3+ ions to the 4 I 11/2 state, resulting in a reduction of the ground state population. Therefore, the output laser power increases with the 980 nm pump initially. As more and more ions are transferred to the 4 I 11/2 level (Fig. 5(c)), the gain coefficient of the 1550 nm pump increases until, eventually, it is positive; hence, the intracavity power of the 1550 nm pump keeps increasing, thereby decreasing the population in the metastable state, 4 I 13/2 , back to the ground state through stimulated emission. In other words, the 1550 nm pump field within the cavity opens a loss-path for the gain provided by the 980 nm pump. There is a competition between the 1550 nm field and the 1600 nm field [30]. Strictly speaking, the 1550 nm light should not be termed a pump in this situation since its role has changed.
For the pure Er 3+ laser case, the absorption cross-section of 980 nm is much smaller than for the co-doped case and it is comparable with that for the 1550 nm pump. Therefore, this situation is akin to the Yb:Er co-doped laser pumped by by a low power 980 nm source. In principle, lasing suppression should be observable as long as the 980 nm pump power is sufficiently high. However, in our experiments, this effect is limited by the maximum ouptut power available from our 980 nm laser (i.e., 76.5 mW). In contrast, for the 980 nm and 1440 nm pumped Er:Yb co-doped laser, no such lasing suppression mechanism exists, since the ratio of the emission to absorption cross-sections is much lower than that for 1600 nm. The main function of the 1440 nm light is to transfer the Er 3+ ions from the ground state to the metastable state rather than inducing stimulated emission. While we did not perform a set of experiments using a 1480 nm pump, we expect that the results would be similar to those for the 1440 nm pump. The 980 nm and 1480 nm co-pumping scheme has been already widely explored in Er 3+ doped amplifiers [3,5,31].

Summary
In this work, we investigated the output behavior of a Yb:Er co-doped microsphere laser when it was pumped with two light sources at different wavebands. We show that the two pumps may contribute both constructively and destructively to the lasing generation depending on their powers and wavelengths, and the lasing can be completely suppressed when both of the pumps are strong. The observations are qualitatively explained by our simple theoretical model, which reveals that these phenomena originate from the diversity of energy levels in the gain medium. Aside from its use for Yb:Er co-doped lasers, these phenomena should exist in lasers with many other gain media. Considering most earlier studies are based on a single pump, there may be many as of yet unrevealed phenomena in lasers that involve two or more pumps. In particular, it may be worth exploring whether such effects emerge when studying quantum behaviors of single-atom lasers [32,33]. Moreover, the phenomenon of pump-induced lasing suppression may lead to new methods for controlling lasing and may add new insights into laser operation.

ACKNOWLEDGMENTS
This work was supported by the Okinawa Institute of Science and Technology Graduate University.