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We demonstrate optically pumped continuous-wave photonic band-edge microlasers on a two-dimensional photonic crystal slab. Lasing was observed at a photonic band-edge, where the group velocity was significantly small near the K point of the band structure having a triangular lattice. Lasing was achieved by using a quantum dot gain material, which resulted in a significant decrease in the laser threshold, compared with photonic band-edge lasers using quantum well gain material. Extremely low laser thresholds of ~80 nW at 6 K was achieved. Lasing was observed in a defect-free photonic crystal as small as ~7 μm square.
©2009 Optical Society of America
1. Introduction
With recent advances in nanofabrication technology, two-dimensional photonic crystal (PhC) lasers have attracted considerable attention. In particular, PhC nanocavity lasers have been investigated due to their small mode volumes, which are of the order of cubic wavelength, high quality factors (Qs), and ultra-low thresholds. In the last decade, many groups have studied and reported lasing action under various operating conditions [1–5]. Another type of the two-dimensional PhC laser is a Ph band-edge laser whose intrinsic feedback mechanism is based on that of Bloch waves near the Ph band edge. In such a defect-free laser, Bragg reflections caused by grating reduce the group velocity of photons to zero along defined directions of crystallographic symmetry.
There have been several reports on the fabrication of Ph band-edge lasers using organic [6–8] and semiconductor [9–14] gain materials. The strength of the distributed feedback depends on the degree of modulation of the active area of the device. Efficient distributed feedback can be obtained by performing periodic modulation of the entire structure of the active material. The feedback mechanism of structures having high refractive index contrast, such as material-air combination, which results in small-area lasing, is the most efficient. Recently, Lee et al. successfully observed lasing in air-bridged PhC structures at 80 K by performing optical pulsed pumping and at room temperature using quantum wells (QWs) as gain materials [15, 16]. Their report at cryogenic temperature was also a challenge to a smaller laser threshold and smaller area using strong feedback with high refractive index contrast, which resulted in a very low threshold pump power of 35 μW at 80 K in ~20 μm square PhC patterns.
Thus far, QWs have been used as the gain materials of semiconductor-based Ph band-edge lasers. In a laser system with a relatively low cavity loss, the laser threshold obtained using quantum dots (QDs) as the gain material is lower than that obtained using QWs. Therefore, we used QDs as the gain material to realize a Ph band-edge laser having an extremely low laser threshold.
In this letter, we report the fabrication of a two-dimensional Ph band-edge laser having extremely low threshold pump powers of 80 nW at 6 K. Lasing was achieving using continuous-wave (CW) pumping when InAs self-assembled QDs were used as the gain material. Quantitative analyses and comparison of the thresholds of QD-based and QW-based lasers indicated that the low transparent carrier density of QDs mainly contributed to a significant decrease in the laser threshold by about three orders of magnitude.
2. Fabrication of Ph band-edge lasers and experimental setup
2.1 Crystal growth and structure
Self-assembled QDs were grown by molecular beam epitaxy on an undoped (100)-oriented GaAs substrate. First, a 300-nm-thick GaAs buffer layer was deposited on the substrate at 580 °C. Then, a 700-nm-thick Al0.7Ga0.3As sacrificial layer was grown at 570 °C. Finally, a 165-nm-thick GaAs slab layer along with a single self-assembled InAs QD layer was grown at the center of the substrate at 580 °C. The photoluminescence (PL) peak of the QD ensemble was observed at 920 nm at 6 K. The nominal areal QD density was ~1 × 1010 cm-2. A detailed description of the crystal growth condition can be found in ref. 17.
2.2 Fabrication of Ph crystal nanostructures
PhC microstructures were fabricated by electron beam lithography, inductively coupled plasma reactive ion etching, and a wet etching process using a hydrofluoric acid solution, which formed 165-nm-thick air-bridge structures by removing the sacrificial layer. We fabricated a sample with a period of the lattice a between 225 nm and 240 nm and radius of the air hole r ~0.3 a. Triangular lattice air holes were patterned using an electron beam lithography system and an inductively coupled plasma reactive ion etching process. Finally, the AlGaAs sacrificial layer was removed to form the air bridge structures. This series of processes were used to fabricate a semiconductor based air-bridged PhC slab with an air-hole array, which produces an in-plane photonic bandgap. A detailed description of this fabrication method can be found in our previous paper [5]. The size of this micro Ph band-edge laser is ~7 μm square.
Fig. 1. Scanning electron micrograph of a two-dimensional Ph band-edge laser with InAs QD gain material. Efficient distributed feedback at a photonic band-edge causes lasing in this defect-free PhC microstructure.
2.3 Experimental setup
The measurements were performed at 6 K using a micro-photoluminescence (μ-PL) setup. A CW laser diode operated at 785 nm was used an excitation source. An excitation beam was focused on the surface of the sample using a microscope objective lens (50x, numerical aperture = 0.42) in the normal direction, and positioned on the PhC using piezoelectric nanopositioners. The theoretical diameter of an excitation spot formed on the surface of the sample was calculated to be ~2.3 μm, which was smaller than that of the PhC pattern. The PL was collected by the same microscope objective lens as that used for focusing the excitation beam.
Fig. 2. (a) Band structure of the TE-like mode of a two-dimensional PhC with r/a = 0.30 and d/a = 0.67. (b) Magnetic field distribution normal to the slab of the band-edge mode at a/λ ~ 0.255 and the K point calculated using the FDTD method. (c) Spatial Fourier spectrum of the in-plane electric field of the band-edge mode. The circular and hexagonal white broken lines denote the air light line and the first Brillouin zone, respectively.
3. Experimental results and discussions
3.1 The band-edge mode used for lasing
Figure 2(a) shows the band structure of the transverse electric (TE)-like mode of a PhC structure with structural parameters of r/a = 0.30 and d/a = 0.67, where d is the thickness of the air-bridge structure. In this study, the band-edge mode on the K point at the frequency a/λ ~ 0.255 was investigated. At the photonic band-edge, the interaction between the photons and the materials increased due to a significant reduction in the group velocity. We also calculated the magnetic field distribution normal to the slab Hz for a band-edge mode at a/λ ~ 0.255 on the K point by a finite-difference time-domain (FDTD) method. The magnetic field distribution was calculated for the same structure, as shown in Fig. 1, used in the experiments with perfectly matched layers in all dimensions. An amplitude profile of the band-edge mode is formed over the PhC area, as shown in Fig. 2(b). In the figure, the black circle denotes an air-hole edge, and the area outside the circle denotes the GaAs layer. Figure 2(c) shows the corresponding spatial Fourier spectrum of an in-plane electric field. The circular and hexagonal white broken lines denote the air light line and the first Brillouin zone, respectively. The band-edge mode shows intensity peaks at the K points, which are the vertexes of the hexagon, in the Brillouin zone due to two-dimensional Bragg diffraction. In Fig. 2(c), all the non-zero intensity points lie outside the air light line. Therefore, most of the emitted photons travel in the slab. Our experimental setup detects photons emitted in the normal direction, and the detection area on the k-space plane is within a circle whose area is smaller than that of the air light line. During FDTD simulation, the radiation intensity is almost zero within the detection area of the experimental setup; however, sample edges and some extraneous matters scatter and diffract photons traveling in the in-plane into the detection area.
3.2 Ph band-edge lasers with QD gain
Figure 3(a) shows the PL spectra of the PhCs with the values of a ranging from 225 nm to 240 nm measured at an excitation power of 1 μW at 6 K. The spectra were vertically shifted by an arbitrary amount. The relatively broad PL peak observed between 860 nm and 940 nm originates from the optically pumped QD ensembles. Several sharp peaks were observed for each PhC, and the wavelengths were in good agreement with the calculated frequencies for the Ph band-edge modes at the K point. Among the wavelengths of the observed peaks, the shortest wavelength corresponds to that of the band-edge mode. Figure 3(b) shows the experimental and calculated band-edges mode wavelengths for the lasers with different lattice constants. The experimental data are in good agreement with the simulation results. The FDTD simulation also predicted the presence of a few resonant peaks around a frequency of 0.26. These peaks are originated from other Bloch modes near the band edge. The Fabry-Perot effect may also causes the oscillation in the PL spectra due to the finite device size. Several experimentally observed sharp resonant peaks in the long wavelength side of the band-edge mode can be assigned to the abovementioned peaks. Some of these peaks also exhibited lasing characteristics. In QD-based lasers, more than one mode can easily oscillate since the gain medium is basically independent if the wavelengths are different, while in QW-based lasers, the oscillation of the modes is restricted by competitive gain consumption.
Fig. 3. (a) Photoluminescence spectrum of PhC patterns with different periods of lattice at CW pumping of 1 μW and measured at 6 K. (b) Experimental and simulated band-edge mode wavelengths for the lasers with different lattice constants.
Figure 4(a) shows the lasing spectrum of the band-edge mode of the PhC at 919.3 nm and an excitation power of 1 μW with a = 240 nm. The PL spectrum was recorded by another detection system with a higher resolution of ~20 pm to focus the sharp lasing mode. The full width at half maximum (FWHM) of the band-edge mode was ~77 pm at a pump power of 80 nW; this corresponds to a quality factor of ~12,000. Figure 4(b) shows the light-in versus light-out (L-L) plot of the band-edge mode on a log-log scale. The horizontal axes in both Figs. 4(b) and 4(c) represent the irradiated pump power, which is measured on the surface of the sample. The plot shows a super-linear increase in the output power around the threshold (yellow-colored region) caused by a centered photon emission in the band-edge mode induced by a stimulated emission process. Figure 4(b) shows a gentle s-shaped L-L plot. Such a smooth transition from the thermal to stimulated emission region is typically observed in high-β lasers in which spontaneous emission efficiently couples to the lasing mode [4, 18]. Figure 4(c) shows the dependence of linewidth on the pump power. Linewidth narrowing was observed below the laser threshold due to a reduction in the absorption of the gain material. Around the laser threshold, the linewidth was constant (yellow-colored region); however, it gradually decreased when the excitation power was increased above the laser threshold (pink-colored region). In microcavity lasers, the linewidth is constant around the laser threshold [19], and the experimental data in Figs. 4(b) and 4(c) show these characteristics distinctly. In Figure 4(b), the point of inflection at ~80 nW can be defined as the laser threshold, and this value agrees well with the conventional value of the laser threshold, which is obtained by extrapolating the linear line above the laser threshold to zero output power on a linear-linear scale plot.
Fig. 4. (a) Lasing spectrum of the optically pumped QD-based Ph band-edge laser at CW pumping of 1 μW and measured at 6 K. (b) Light-in versus light-out plot of the band-edge mode at 919.3 nm plotted on a log-log scale. The green broken lines denote a linear increase of an eye guide. The threshold pump power was ~80 nW, which was measured on the surface the sample. (c) Dependence of the linewidth on the pump power of the investigated band-edge mode. The linewidth shows typical lasing characteristic, which is observed in a microcavity laser.
Here, we compare the Ph band-edge laser with the PhC nanocavity laser. These lasers differ from each other in terms of feedback mechanism and modal volume. The Ph band-edge laser has a broad amplitude distribution as shown in Fig. 2(b), while the PhC nanocavity laser has a localized mode, which is formed by confining photons in very small volume. Therefore, the number of QDs interacting with the lasing mode is much larger than that of QDs interacting with a nanocavity mode. However, the strength of the feedback of the band-edge laser is generally lower than that of the nanocavity laser. Therefore, the threshold of the band-edge laser is usually higher than that of the nanocavity laser. We have reported a PhC nanocavity laser, which has Q = 24,000 and mode volume of 0.02 μm3 [20]. In fact, the laser has a threshold of 8 nW, which is lower than the demonstrated Ph band-edge laser. However, for a large gain area, the Ph band-edge laser has a higher output power than the nanocavity laser. In-plane relative spatial position insensitivity of a pump beam spot is also an advantage. The Ph band-edge laser has a periodic structure. Therefore, the influence of spatial fluctuation of the pump spot is much smaller in the Ph band-edge laser as compared to that in the nanocavity laser, which has a position-sensitive characteristic.
As indicated in Figs. 2(a), 2(b), and 2(c), the Ph band-edge laser emits photons mainly in the in-plane direction, because it oscillates near the K point. Therefore, such a Ph band-edge laser is a better on-chip micro coherent light source than a vertical emission laser is. In order to fabricate an on-chip photonic circuit in the future, the active material area should be grown only for the lasing area using a selective area growth technique to avoid ineffective waveguide loss due to absorption. The Ph band-edge laser of the same structure can be used as a vertical emission laser by designing it to oscillate at the Γ point; the demonstrated Ph band-edge laser oscillated at the K point.
3.3 Ph band-edge laser with QW gain
It is well known that the pump power required to saturate the QD gain material is much lower than that required to saturate the QW gain material. Therefore, the threshold pump power can be reduced by using the QD gain material in a relatively low-loss feedback system. To demonstrate the advantage of using QDs to lower the pump threshold value, we fabricated a Ph band-edge laser with InGaAs QW as the gain material. The QW-based sample has nearly the same design parameters as the investigated QD-based sample except for the active material, lattice constant, and radius. The structural parameters of the QW-based laser, which showed the resonance at the PL peak of the QW at 901 nm, were a = 225 nm and r/a ~ 0.28. The lattice constant and radius of the air-hole are different from those of the QD-based laser, but these slight differences in the parameters do not change the physics much in the system. The active material is a 3-nm-thick single InGaAs QW, which exhibits a PL peak at 901 nm at 6 K. The sample was fabricated using the same fabrication process as that used to fabricate the QD-based sample; this ensured that both the sample had the same optical qualities.
Fig. 5. (a) Lasing spectrum of the optically pumped QW-based Ph band-edge laser at quasi-CW (1 kHz, duty cycle: 1%) pumping of 1 mW and measured at 6 K. (b) Light-in versus light out plot of the QW-based band-edge mode at 901 nm plotted on the log-log scale. The threshold peak pump power is ~350 μW. (c) Dependence of the linewidth on the pump power of the band-edge mode. The linewidth reached a spectral resolution limit of ~20 pm of the detection system, which was sufficiently above the laser threshold.
Figures 5(a)–(c) show the lasing characteristics of the QW-based Ph band-edge laser with a = 225 nm measured at 6 K. In the experiment, stable lasing was observed at 500 μW during complete CW pumping. However, above 1 mW, the PhC structure suffered thermal damage, and the output power gradually decreased. Then, the optical measurements for the QW-based sample were performed during quasi-CW pumping with a duty cycle of 1% and at a repetition frequency of 1 kHz, to ensure reliable measurements. In this pumping condition, the pumping duration is 10 μs, which can be regarded as quasi-CW, not pulsed pumping, because the timescale of the main dynamics, which is an electron-hole recombination time, is ~ 1 ns.
Figure 5(a) shows the lasing spectrum with a peak pump power of 1 mW. The spectrum shows a single peak under the lasing condition; however it showed a few peaks at other wavelengths below the laser threshold. In the QD-based laser studied in the above subsections, since the gain material was inhomogeneous, other modes could reach the lasing condition. On the other hand, in the QW-based laser, due to the homogeneity of the gain material, only one mode could reach the lasing condition.
Figure 5(b) shows the L-L plot on the log-log scale. The horizontal axes in Figs. 5(b) and 5(c) represent the peak pump power. The L-L plot shows a distinct transition from the spontaneous to lasing region. This is partially attributed to the fact that a stronger absorption is observed in the QW-based laser than in the QD-based laser. The estimated threshold peak pump power is ~350 μW. From this result, it can be inferred that the threshold of the QD-based Ph band-edge laser (80 nW) is lower by more than three orders of magnitude than that of the QW-based laser. The reasons for this difference in laser thresholds are discussed in the next subsection.
Figure 5(c) shows the dependence of the linewidth on the pump power. The linewidth decreased and reached the spectral resolution limit of the detection system of ~20 pm with an increase in the pump power. The significant narrowing of the linewidth around the phase transition is attributed to saturation of the strong absorption in the QW-based laser. This strong absorption also resulted in an abrupt change in the lasing behavior of the QW-based laser, as shown in Fig. 5(b), while the lasing behavior of the QD-based laser did not change significantly. The plateau behavior in the linewidth, which was observed for a QD-based laser, was not observed for the QW-based laser. At present, it is difficult to reasonably explain the difference in lasing behaviors between QW- and QD-based lasers; this difference is yet to be investigated.
3.4 Quantitative discussion of the laser thresholds
In the above subsections, significantly different values of the laser threshold were obtained for the QD- (~100 nW) and QW-based (~300 μW) Ph band-edge lasers. In this section, we investigate the reasons for the significantly different threshold values, by performing order estimation.
There are some factors such as absorption of pump beam, material gain, spontaneous emission coupling factor, and cavity loss that have an effect on the value of the threshold pump power. The structures of the QD- and QW-based lasers are almost the same except for their gain materials. Therefore, they should exhibit the same cavity losses. The difference in the gain materials may result in a difference in the spontaneous emission coupling factors; however, this difference will not be large. The number of photogenerated carriers at a certain pump power is nearly the same for both the lasers, because most of the carriers are generated in the GaAs slab layer. Then, the material gain factor is expected to be the dominating factor among abovementioned factors. Other factors also affect the laser threshold, for example, the internal quantum efficiency; however, they are expected to have a much smaller influence as compared to the influence of the material gain on the laser threshold. Therefore, we focus on comparing the material gains of QD- and QW-based lasers.
In a cavity system with small loss, a gain material with a low transparent carrier density results in a low laser threshold. Here, we compare the transparent carrier densities of the investigated QD- and QW-based lasers in order to discuss the drastic improvement in the threshold value. In a simplified form, the material gain of the ground state of the QD ensemble is given by [21]
where
In this equation, P( ħωσ E) is the energy broadening function, which generally assumes a Gaussian distribution with a spectral width σ E. M is the bulk matrix element, n; the refractive index, and V0; the volume of a QD. For simplicity, we assume that the injected electrons and holes are identical; therefore, fv = 1 − fc and fc − fv = 2fc − 1. In addition, we assume that all the QDs are identical and they do not couple. In this case, the total number of excitons Nex is 2fcN QD, where NQD is the number of QDs. These excitons are equally distributed among the QDs. Then, the material gain is expressed as
The material gain g increases linearly from CgP with the carrier density, and it saturates at +CgP when the ground states of all the QDs are filled with two electrons and holes (N ex = 2N QD) each. At the condition N ex = N QD, the gain material is transparent. In our case, areal QD density is ~1 × 1010 cm-2. Then, the transparent sheet carrier density can be roughly estimated to be ~1 × 1010 cm-2, and the transparent carrier density N tr to be ~1 × 1015 cm-3. The transparent carrier density of the QW-based Ph band-edge laser is expected to be ~1018 cm-3, which is the typical value of a conventional GaAs-based QW semiconductor laser. Therefore, the transparent carrier density of the QD-based laser is lower by approximately three orders of magnitude than that of the QW-based laser.
In our experiment, the laser threshold of the QD-based laser (80 nW) was lower by ~4,400 times than that of the QW-based laser (350 μW). This value is roughly in the same order as that of the order estimation performed on the transparent carrier density. However, this value differs by several times. The difference is attributed to the complex effect of other factors. Therefore, we can conclude that the significant reduction in the threshold of the QD-based laser is attributed to the inherent low transparent carrier density of the QD-based gain material. In addition to the well-known low temperature dependent threshold feature [22], the observed low threshold characteristics show one of the attractive aspects of QD-based light sources.
Both QW- and QD-based Ph band-edge lasers will complementary construct future nanophotonic systems by utilizing each advantage. A QD-based Ph band-edge laser, which has a low threshold, will be suitable for ultralow power consumption devices. On the other hand, a QW-based laser, which has much higher saturation output power, will be suitable for higher power device applications.
4. Summary
The fabrication of optically pumped CW Ph band-edge micro lasers with an extremely low laser threshold of 80 nW at 6 K was demonstrated. Lasing was achieved at a Ph band-edge near the K point using an InAs/GaAs QD gain material. The laser threshold of the QD gain material was lower by about three orders of magnitude than that of the QW-based material, due to low transparent carrier density of the QD gain material. The strong distributed feedback due to a high semiconductor-air refractive index contrast enabled lasing in a small area of ~ 7 μm square.
Acknowledgments
The authors would like to thank S. Ishida and Dr. K. Watanabe for their technical support. This work was supported by the Special Coordination Funds for Promoting Science and Technology and by Grant-in-Aid for Young Scientists (B), KAKENHI 20760030, and the Ministry of Education, Culture, Sports Science and Technology, Japan.
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