1. Introduction

Light sources account for a major part of the total energy consumed by optical communication or photonic processing. If we pursue large-scale photonic integrated circuits to realize chip-scale dense optical interconnect or photonic network-on-chip architecture, it is crucially important to reduce the energy consumption of light sources. Since the number of photons needed to transmit optical information by coherent light is rather small, the final energy consumption should be limited by the lasing threshold. This suggests that a thresholdless laser would be an ideal light source for chip-scale photonic integrated circuits when there is no need for a large number of photons. In fact, it is well known that high-$\text{β}$ (spontaneous emission coupling factor) micro-lasers would exhibit thresholdless lasing and are expected to be ultimately efficient devices [1, 2] because they generate an output light with a high quantum efficiency even at a very low input power. These lasers are generally demonstrated using quantum dots (QDs) with a photonic crystal (PhC) cavity [3–5] or a plasmonic cavity [6]. However, as described later, the emitted power is very weak and the applications are very limited. Therefore, if such lasers based on multiple-quantum-well-structures (MQW) with a large output power can be realized, they would have the potential for such future applications as efficient on-chip light emitters with ultralow energy consumption [7, 8].

However, the conditions for realizing thresholdless lasers are severe. First, the cavity should have a large Q factor and a small mode volume (V) to increase the Purcell factor. If the Purcell enhancement is sufficiently large for us to neglect other emission leakage such as emissions from higher order modes and the emission from off-resonant condition, β can be unity. Second, the non-radiative recombination rate of the active material should be low. Even if β becomes unity, if the non-radiative recombination rate is high, a kink structure can appear in the light-in vs light-out (L-L) curve. Third, emission from outside the cavity resonance should be suppressed by the photonic bandgap (PBG) effect (the Kleppner effect [9]) because the emission leakage from the off-resonant condition does not contribute to lasing oscillation. Therefore, a single mode cavity (or large mode separation between a fundamental mode and higher order modes) should be designed to improve the PBG effect. Most high- β lasers using QDs satisfy the first condition. This is because the emission width of a QD spectrum is comparable to that of the cavity spectrum, and it is easy to achieve a large Purcell factor. On the other hand, an MQW laser exhibits large homogeneous broadening, so the emission leakage from outside the cavity resonance and from other cavity modes is not negligible. To realize high- β MQW lasers, the second and third condition should also be satisfied, which is the main reason for thresholdless operation being more difficult with MQW lasers. As we show later, the key point is to employ a deep PBG to suppress unwanted emission from an MQW.

When measuring high- β lasers, it is not easy to determine lasing oscillation, because the lasing threshold becomes ambiguous as β increases. Even if the L-L curve is very smooth, other parameters (emission lifetime, linewidth and ${\text{g}}^{\text{2}}\text{(0)}$) will have changed after a lasing transition. These values should constitute strong evidence for a lasing transition. However, in previous experiments, there were no systematic investigations that include both lifetime and photon correlation measurements.

Until now, thresholdless operation or smooth lasing transition has been demonstrated for plasmonic coaxial lasers with MQWs and QDs with PhCs. With a plasmonic cavity [6], the mode volume is generally 1-2 orders of magnitude smaller than that of a PhC cavity. Therefore, even low Q plasmonic cavities can achieve large Purcell enhancement. The authors [6] employed the L-L curve property and the full width at half maximum (FWHM) to estimate the lasing transition, although the output power was severely limited due to a large absorption loss and a small gain volume. However, it is difficult to distinguish between lasing behavior and the nonlinear response of a gain material when β is close to unity. Therefore, photon correlation measurements and lifetime measurements are clearly needed. The operation of a high- β laser has also been observed with some PhC lasers based on QDs [3–5]. QDs have very narrow emission peaks and are localized in a small area, so they can couple to a cavity mode very efficiently and realize a high- β laser if they are in the center of the cavity and their spectra are in the cavity resonance condition. These kinds of devices are promising as single photon sources, but fabrication remains difficult and they are unsuitable for applications requiring a large output power. A 1D nanobeam geometry based on an MQW [10] also achieved high- β lasers. A 1D nanobeam PhC cavity can obtain a high Q, and so can also achieve large Purcell enhancement and increase β. However, these structures still suffer from high carrier loss, high non-radiative recombination, and insufficient PBG. A previous report [10] showed no clear systematic evidence for a lasing transition.

In this study, we realized 2D PhC nanolasers with MQWs embedded within a high Q nanocavity [11]. They have a relatively large gain volume in which the carriers are strongly confined by heterostructure barriers. We confirmed that non-radiative recombination is negligibly small (at most 6 ns) in our devices [12]. Although our previous nanolasers [11] were based on modulated modegap nanocavities, in this study we employed L3 nanocavities whose resonance is located in the middle of their wide PBG (Fig. 1). To achieve a high- β, we need to suppress the wideband emission (other than the cavity mode) from the MQW by employing the Kleppner effect. However, the mode separation between the fundamental mode and high order modes in modulated modegap nanocavities is generally small. As we show later by numerical simulation, the L3 nanocavities significantly improve β, which is well suited for our purpose. As described above, our devices can solve many of the problems related to high- β lasers based on MQWs, and we believe that they are promising as high-quantum-efficiency coherent light sources with ultralow energy consumption.

 

Fig. 1 (a) Schematic of L3 photonic crystal (PhC) cavity structure. An active region is embedded inside L3 PhC cavity. (b) Schematic diagram of energy decay from calculation region. (c) Schematic of calculation condition. (d) Calculation result for magnetic field by FDTD method.

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To investigate high- β nanolasers appropriately, we paid particular attention to unambiguously demonstrating lasing oscillation for our high- β nanolasers because the lasing was not distinct in most previously reported thresholdless-like lasers. To accomplish this, we conducted a series of systematic studies including L-L curve analysis, emission linewidth analysis, lifetime measurements and photon correlation measurements. In this paper, first, we show that our buried MQW 2D PhC cavities with Q values of a few thousand can achieve a high- β by using the FDTD method if the cavities have only one mode in the emission spectra of the MQW. Here we investigated the dependence of β on excitation position and detuning. Next, we estimated a smooth lasing transition using our L3 cavity. To confirm whether our devices lase or not, we measured the emission lifetime and the photon correlation. Finally, we measured the detuning dependence of β using several different lattice constant cavities. Here, we can obtain the clear detuning dependence of β experimentally. When the cavity resonance is at the center of the wide MQW spectrum, β can be 0.9. This result was well explained by our FDTD simulation.

2. Numerical simulation

First, we estimated the theoretical β values for our device. We simulated light emission from three types of buried MQW PhC L3 cavities with the finite-difference time-domain (FDTD) method. The InP slab thickness, air hole radius, and lattice constant were 240, 100, and 435 nm, respectively. The embedded InGaAsP MQW was $\text{1}\text{.3}\times \text{0}\text{.35}\times \text{0}\text{.15}{\text{μm}}^{\text{3}}$. The resonance wavelength was 1540 nm and the Q value was 7500, 2200, or 150. The experimental Q value of an L3 cavity is typically a few thousand, so a Q of 2200 approximates a realistic condition. In this calculation, we excited a magnetic field that was perpendicular to the slab and created an electric field in the lateral direction. Here, we regarded this electric field as the emission of an MQW, because the electric field of emission from heavy-holes exciton lies in the MQW plane. In a previously reported calculation [13], the authors employed several dipole sources with different polarizations and excited them simultaneously. However, our excitation method includes all polarization in the lateral direction, and so it simplifies this process. The field excitation time is 1.25 ps and the pulse shape in the time domain is Gaussian. We found that this excitation pulse width in the time domain corresponds to 12 nm from an MQW spectrum obtained by Fourier transformation. We regarded this width as the homogeneous broadening of the MQW spectrum and neglected inhomogeneous broadening. Here we defined β as

Figure 1(b) is a schematic diagram of the energy dissipation process from our calculation region. While the light source is excited, the energy dissipation in the system is increased. Then the energy dissipation decreases rapidly because light leaks from the low Q cavity or light is not coupled with the cavity. Finally, energy is dissipated from the high Q cavity and this represents${\displaystyle \int P_{\text{cav}}}\cdot dS$. To simplify the calculation, we approximate β for a specific place (node) as${\displaystyle {\int }_{t_{\text{ex}}}^{\infty }{\displaystyle \int P_{\text{cav}}}}\cdot dSdt/{\displaystyle {\int }_{\text{0}}^{\infty }{\displaystyle \int P}}\cdot dSdt$, where $t_{ex}$ is half the excitation time. This approximation is reasonable when the emission decay time from the cavity exceeds the excitation time. Figure 1(c) shows the calculation condition. The red boxes are the integration area ($S$) of the Poynting vector and the black boxes are perfectly matched layers. The total calculation area is $\text{14}\text{μm}\times \text{9}\text{μm}\times \text{4}\text{μm}$ and one grid is 30 nm. Figure 1 (d) shows the magnetic field of an FDTD result for our sample. Using Eq. (2), we calculated β by changing the excitation position every 30 nm on the x- and z-axes.

Figure 2(a) and 2(b) show an enlarged PhC diagram and the steady state of electric field, respectively. In this calculation, the emitter is affected by the electric field of the cavity mode profile (sum of the x-axis electric field and the z-axis electric field). Therefore, β should be changed depending on the excitation position. Figure 2 (b) shows the dependence of β on the excitation position on x- and z-axes. The blue squares, red triangles and black circles represent Q values of 7400, 2200 and 150, respectively. This result reveals that β is increased when an emitter is the anti-node of the electric field. On the other hand, β decreases when the emitter is a node of electric field. This effect can be explained by Purcell enhancement. This tendency is clear when Q is low, because β is saturated when Q is high.

 

Fig. 2 (a) Enlarged image of L3 photonic crystal and electric field by FDTD method. The slab thickness, air hole radius, and lattice constant are 240, 100, and 435 nm, respectively. (b) Dependence of β on excitation position for x and z-axes. (c) Dependence of β on detuning between cavity mode and emission spectrum. (d) Dependence of β on FWHM of MQW for L3 and width modulation cavity.

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Next we calculated the dependence of β on the detuning frequency between the cavity mode and the emitter wavelength (Fig. 2(c)). Although we detuned the cavity frequency by changing the lattice constant in our experiment, here we changed the excitation wavelength. To include the spatial mismatch factor, β was spatially averaged by using the all β values in a MQW region. Here a weighting function for carrier distribution was not considered, because carrier is uniformly excited (our MQW is much smaller than pumping beam region) and a carrier diffusion effect can be neglect in a buried MQW. The polarization mismatch has already been included because the excitation source has all the polarizations in the lateral direction as mentioned above. Here we determined as 1/2 from the spectral averaging factor [12, 14]. From this calculation, we found that β can be close to unity when the cavity mode is in the on-resonant condition even if Q is a few thousand. Moreover, β could exceed 0.5 even though the detuning is larger than the FWHM of the MQW spectra. This indicates that our devices can strongly suppress the MQW emission around the cavity mode as a result of the Kleppner effect, and this effectively prevents any spectra mismatch.

In Fig. 2(d), we also compare β for an L3 cavity (Q ~7400) and a width-modulation cavity [11] (Q ~11000) for MQWs with different FWHMs. The simulation result shows that L3 has a larger β than the width-modulation cavity. There is a large leakage path due to the continuum mode and little cavity mode separation between the first and second modes, and so in principle the β of a width-modulation cavity cannot be increased. This is a structural merit of the L3 cavity. This figure also shows that β can still be large (>0.1), even if the MQW has a broad FWHM. This implies that our device can work as a high- β device at high temperature. On the other hand, β can easily be unity when the FWHM of the MQW is narrow. This explains why QD devices achieve high- β. In these calculations, we found that our devices are extremely efficient and have a large tolerance for a high- β when Q exceeds a few thousand.

3. Experiment

Generally, it is difficult to estimate the lasing transition of a high- β laser from an L-L curve because it is unclear. When β is completely unity and the nonradiative recombination is sufficiently small, the L-L curve changes smoothly and there is no clear lasing transition. Therefore, to amass convincing evidence of lasing for high- β devices, we have performed emission lifetime and photon correlation measurements in parallel. We excited our samples with an 80-MHz mode-locked titanium sapphire laser (λ = 810 nm) from the top of the sample and measured the emission spectrum with a conventional spectrometer and an InGaAs detector array (see Fig. 3). For time resolved and photon counting measurements, we used a superconducting single-photon detector (SSPD) and a time-correlated single photon counting (TSCPC) module. This detector has a 10% quantum efficiency and a 32 ps time jitter. Our 240 nm-thick InP PhCs have L3 cavities. The lattice constants of the PhC range from 380 to 424 nm every nano meter. Three InGaAsP/InGaAs quantum wells are embedded inside each PhC cavity with the regrowth method [11]. The gain medium has a 12 nm spectrum at 4 K. Because one lattice constant change corresponds to a 4 nm cavity resonance shift (4 nm/lattice), the cavity resonance range (over 100 nm) in our samples covers the emitter spectrum width.

 

Fig. 3 (a) Schematic of measurement setup. (b) SEM image of L3 cavity.

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Figure 4 (a) shows the L-L curve in an almost a resonant condition at 4 K. The cavity resonant wavelength is 1428 nm and the detuning from the center of the gain spectrum is 2 nm. The L-L curve in Fig. 4(a) does not exhibit any clear lasing threshold. Figure 4(b) shows that there appears to be a lasing transition at the FWHM and a wavelength shift when the excitation power is in the blue area in the figure. Generally, a cold cavity Q is determined at the lower pump power edge of the lasing transition. In this case, we regard it as being around 200 nW (actual pump power) and the determined Q as being 2400. Here, there is a slight change in the L-L curve, but this result is too small to determine whether or not lasing oscillation has occurred. This implies that our device has a high- β. The other cavity parameter also shifts at the lasing threshold, however, unlike conventional low- β lasers, the shift is not great.

 

Fig. 4 (a) Light-in versus light-out (L-L) curve for 2 nm detuning sample. (b) Lifetime, cavity wavelength shift and full width at half maximum for excitation power. (c) Photon correlation measurement for different pump powers. Red dotted line represents${\text{g}}^{\text{(2)}}\text{(0)}=\text{1}$. (d) L-L curve for 15 nm detuning sample. (f) Lifetime, cavity wavelength shift and full width at half maximum of excitation power. (g) Photon correlation measurement for different pump powers.

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Next, we measured the emission lifetime to investigate the lasing transition. Generally, the stimulated emission process makes carriers recombine fast and thus the emission in the lasing condition is normally much faster than the spontaneous emission. Therefore, if we can demonstrate the accelerated emission, we can regard it as an indication of lasing [15, 16]. As shown in Fig. 4(b), we observed a distinct decrease in the emission lifetime when the pump power was increased. When the pump power was weak, the lifetime was 0.26 ns. This lifetime is shorter than the typical 0.75 ns lifetime of a buried MQW at 4K without a cavity [12] because of Purcell enhancement. As the excitation power was increased, the lifetime became shorter until 0.033 ns. This is close to the measurement limit of our SSPD. In our sample, there was no carrier diffusion and non-radiative recombination was negligible because the carrier was well confined by the buried hetero structure. Therefore, the dependence of the reduced emission lifetime on pump power strongly indicates stimulated emission.

Figure 4(c) shows the result of a photon correlation measurement performed using a Hanbury-Brown and Twiss setup. This is also a strong method for determining whether or not lasing oscillation occurs [17–19]. When the pump power is below the lasing threshold, the light emitted from a cavity behaves like thermal light (chaos light) and bunching (${\text{g}}^{\text{(2)}}\text{(0)}$ > 1) should be observed in the ${\text{g}}^{\text{(2)}}\text{(t)}$ curve. Once lasing oscillation occurs, the emitted light exhibits coherence (Poisson distribution of photons), so the bunching in the ${\text{g}}^{\text{(2)}}\text{(t)}$ curve can no longer be observed. In this experiment, we clearly observed this transit from chaotic light below the lasing threshold to coherent light above the lasing threshold. We observed bunching when the pump power was around 500 nW and ${\text{g}}^{\text{(2)}}\text{(0)}$ = 1.22. On the other hand, when the excitation power exceeded $\text{1}\text{μW}$, ${\text{g}}^{\text{(2)}}\text{(0)}$ was unity and bunching was not evident. This shows that the emission from the cavity changed from chaotic to coherent light. This behavior is clear evidence of a lasing transition. Unfortunately, we could not measure clear bunching under a very low pumping condition because the emission intensity was not strong enough for us to measure the bunching and the coherence time was short due to the broad cavity width. This result is common to other experiments [3, 20]. In addition, a high-β laser generally reduced the maximum ${\text{g}}^{\text{(2)}}\text{(0)}$ and could not be 2 practically [20, 21]. Therefore, ${\text{g}}^{\text{(2)}}\text{(0)}$= 1.22 is a reasonable value at around the lasing transition. Although we cannot determine the exact location of the lasing threshold for high-β lasers, from the results we concluded that our device exhibits a lasing transition in the blue area in Fig. 4(a).

To compare the nature of this operation for high and low β values, we performed the same systematic measurement under a large detuning condition as shown Figs. 4 (d)-4(g). The detuning value from the center of the gain spectrum is 15 nm (the cavity resonant wavelength is 1415 nm) and under this condition it is expected that β will be 10 times lower as we calculated before. Therefore, we can easily detect clear lasing behavior. Figure 4(d) shows the typical lasing behavior of an L-L curve, which has a clear kink. There are also large changes in the FWHM wavelength shift and lifetime. The emission lifetime is clearly faster with a high pump power than with a low pump power, so it is a stimulated emission. Here we also measured large bunching (${\text{g}}^{\text{(2)}}\text{(0)}$= 1.6) near the lasing threshold in Fig. 4(g). This value is larger than with small detuning. Generally, the intensity of the spontaneous emission fluctuates around the threshold in low β lasers, so it is easier to measure bunching in the ${\text{g}}^{\text{(2)}}\text{(t)}$ curve at around the threshold than with high- β lasers [20]. Comparing these results, we found that there is certainly a smooth lasing transition at 4K and detuning and the gain band spectra affect β.

Finally, we investigated β as a function of detuning by measuring the L-L curve obtained for several different devices and compared this with the FDTD simulation. We estimated β by fitting it to L-L curves using the laser rate equation. For high- β devices, β is difficult to estimate by fitting the rate equation, so systematic tuning-detuning measurements are an efficient way to estimate β. This is the first time such a systematic measurement has been performed. To change the detuning, we shifted the lattice constant of the PhCs. We show the results we obtained for our samples in Figs. 5 (a)-5(c) (cavity resonant wavelength: 1428, 1423, and 1415 nm). Here the cavity resonant wavelength of 1428 nm is sample with largest detuning (15 nm). We also include the emission lifetime in this figure because the information is strong evidence for a lasing transition. To estimate β, the L-L curve was fitted by a rate equation that assumed a two-level system and a linear gain/absorption model [1, 2]. We assumed the transparency carrier density$N_{\text{0}}={\text{10}}^{\text{-18}}{\text{cm}}^{\text{-3}}$, active-medium volume sand nonradiative recombination${\tau }_{\text{nr}}=\text{6}\text{ns}$. We could not measure the nonradiative recombination directly but we employed the measured emission lifetime of 6 ns in an off resonant condition as the nonradiative recombination lifetime. This can be suppressed by the PBG effect up to the nonradiative recombination limit. Therefore we used this value as the upper limit of nonradiative recombination [12]. Figure 5(a) shows the L-L curve and lifetime for the same sample as in Fig. 4(a). From this result, we found by fitting that β was 0.9. This value is extremely large for a MQW PhC system with low nonradiative recombination. Under this condition, as described above, the lasing transition is very smooth in the L-L curve due to a large Purcell factor and a strong PBG effect. Next, we measured a sample where we tuned the cavity resonance by shifting the lattice constant in Figs. 5(b) and (c). In Fig. 5(c), there is a very clear kink in the L-L curve and β was clearly reduced to 0.015 when the detuning was 15 nm. We also compared these L-L curves on a linear scale in Fig. 5(d). This shows that the output power becomes large when β is high. This in turn indicates that the device works as a laser, and that the laser performance improved when the detuning was small. These results agree well with the simulation, as shown in Fig. 5(e). Although there is a small mismatch between the measurement and the simulation, the discrepancy was within the error range. In addition, we found that our sample exhibited a 2.5-fold Purcell enhancement and a 5.3-fold Kleppner suppression when we compared the lifetimes under each conditions. This result also implies that our devices have small nonradiative recombination. Note that a high- β generally does not necessarily mean thresholdless operation with finite non-radiative recombination, the high- β value of our device is directly related to the thresholdless-like operation because of the very small non-radiative contribution.

 

Fig. 5 (a) Light-in versus light-out curve, fitting curve and lifetime for three different samples. (a) 1428 nm of cavity resonance. (b) 1423 nm of cavity resonance. (c) 1415 nm of cavity resonance. (d) Comparison of these devices on linear scale. (e) Summary of experimental β value for our several devices and β simulated by FDTD (Q ~2200).

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4. Conclusion

We realized high- β buried MQW PhC nanocavities, and our results agree well with simulations. Although MQW lasers generally suffer from a wide gain bandwidth, we have unambiguously demonstrated high- β lasing with a smoothed transition by means of L-L curve analysis, emission linewidth analysis, and photon correlation measurements. Because our 2D buried MQW PhC can achieve a strong PBG effect and carrier confinement, our devices demonstrated high- β lasing with a smoothed transition. This implies that our lasers are close to achieving the theoretically predicted thresholdless lasing. We believe that this highly efficient buried MQW PhC can lead to a device with lower energy consumption and could be applied to a photonic network on a chip.