⇦Chinese Physics Letters, 2017, Vol. 34, No. 2, Article code 024202 Static and Dynamic Analysis of Lasing Action from Single and Coupled Photonic Crystal Nanocavity Lasers * Peng-Chao Zhao(赵鹏超)1,2, Fan Qi(祁帆)1,2, Ai-Yi Qi(齐爱谊)1,2, Yu-Fei Wang(王宇飞)2, Wan-Hua Zheng(郑婉华)1,2** Affiliations 1State key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Beijing 100083 2Laboratory of Solid-state Optoelectronics Information Technology, Institute of Semiconductors, Beijing 100083 Received 12 October 2016 *Supported by the National Key Basic Research Special Fund/CNKBRSF of China under Grant Nos 2012CB933501, 2016YFA0301102, 2016YFB0401804 and 2016YFB0402203, the National Natural Science Foundation of China under Grant Nos 61535013, 61321063 and 61137003, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant Nos XDB24010100, XDB24010200, XDB24020100 and XDB24030100, and the One Hundred Person Project of the Chinese Academy of Sciences.
**Corresponding author. Email: whzheng@semi.ac.cn Citation Text: Zhao P C, Qi F, Qi A Y, Wang Y F and Zheng W H 2017 Chin. Phys. Lett. 34 024202 Abstract The single and coupled photonic crystal nanocavity lasers are fabricated in the InGaAsP material system and their static and dynamic features are compared. The coupled-cavity lasers show a larger lasing efficiency and generate an output power higher than the single-cavity lasers, results that are consistent with the theoretical results obtained by rate equations. In dynamic regime, the single-cavity lasers produce pulses as short as 113 ps, while the coupled-cavity lasers show a significantly longer lasing duration. These results indicate that the photonic crystal laser is a promising candidate for the light source in high-speed photonic integrated circuit. DOI:10.1088/0256-307X/34/2/024202 PACS:42.55.Tv, 42.65.Re, 42.55.Ah © 2017 Chinese Physics Society Article Text Two-dimensional photonic crystal (PhC) lasers hold great promise as single-mode light sources for low-threshold, high-speed applications in optical communications, optical interconnects and data storage.[1] A small mode volume and a high quality factor $Q$ in the PhC laser enable a controllable spontaneous emission (SpE) rate through the so-called Purcell effect.[2,3] This effect can improve the performance of a laser by increasing the spontaneous emission rate into the mode of interest while suppressing emission into all other modes, creating a large spontaneous emission coupling efficiency $\beta$.[4-6] The Purcell effect can also increase the direct modulation speed,[7] especially in nanocavity lasers where the relaxation oscillation can exceed the cutoff frequency.[8] In this Letter, we investigate the single-cavity and coupled-cavity PhC lasers in the InGaAsP material system. Their static and dynamic lasing actions are compared in both theory and experiment. The output power of the coupled-cavity PhC laser is nearly twenty times of magnitude higher than that of the single-cavity laser. We also find higher efficiency in the coupled-cavity PhC laser, which is explained by a rate equation model. To better understand the lasing dynamics of the PhC laser and to find out its potential modulation rate, we investigate the time-domain lasing characteristics of such single- and coupled-cavity PhC lasers. Under optical excitation, we obtain a lasing response as short as 114 ps for the single-cavity laser while the coupled-cavity laser has a longer response time of 208 ps. The structures studied here are fabricated in a 260-nm-thick In$_{0.81}$Ga$_{0.19}$As$_{0.42}$P$_{0.58}$ membrane with seven 9-nm-thick In$_{0.74}$Ga$_{0.26}$As$_{0.77}$P$_{0.23}$ quantum wells (QWs), separated by 15 nm barriers. The membrane rests on an InP substrate. The PhC structures are patterned using an electron-beam lithography system followed by a combination of wet and dry etching. To reduce nonradiative surface recombination of the large QWs area exposed in PhC patterning, the sample is passivated with (NH$_{4})_{2}$S.[9] The PhCs are in square lattice with a period of $a=500$ nm and hole radii ranging from 170 nm to 220 nm to change the resonance frequency of cavities. The coupled array consists of 25 cavities ($5\times5$) separated by two rows of air holes (Fig. 1(a)). It supports a coupled non-degenerate quadrupole mode (Fig. 1(b)), which is designed to overlap with the QWs gain. The structures are measured in a confocal microscope setup at room temperature.[10] The cavities were pumped by a pulsed laser at an 80 MHz repetition rate with a pulse duration of 60 ps and a central wavelength of 640 nm. The emission was measured with an optical spectrum analyzer for the static analysis and an InGaAs avalanche photodiode (APD, ID Quantique ID201) for the time-resolved analysis. Several single-cavity and coupled-cavity lasers with different $r/a$ were measured. The response of one laser (with $r/a\approx0.38$) is shown in the light-in/light-out (LL) curve in Fig. 2. The threshold of the single-cavity laser is $L_{\rm in}=10.5$ μW while the coupled-cavity laser is $L_{\rm in}=51$ μW. The maximum power achieved in the coupled-cavity laser is almost 20 times larger than that of the single-cavity laser, and the lasing efficiency of the coupled-cavity laser is about 5 times larger than that of the single-cavity laser.
cpl-34-2-024202-fig1.png
Fig. 1. (a) SEM picture of coupled-cavity PhC lasers. The inset shows the zoomed 5$\times$5 coupled PhC nanocavities. (b) Electric field intensity of the coupled quadrupole mode.
cpl-34-2-024202-fig2.png
Fig. 2. LL-curves of the single-cavity and the coupled-cavity PhC lasers. The break region in the $x$-axis is from 16 μW to 45 μW. The inset shows a magnified curve for the single-cavity PhC laser.
Single-mode lasing is observed from both single- and coupled-cavity lasers. The spectrum of the coupled-cavity laser pumped at 60 μW is shown in Fig. 3, with a peak locating at 1551 nm. The N.A. of the objective lens is 0.4, which is wide enough to collect the emission from any other possible modes. However, we observe only a single mode in the spectrum, even with large pump power. A slight linewidth broadening is observed above threshold, while the spectrum below the threshold is hard to measure due to the poor sensitivity of the spectrum analyzer. The following single-mode rate equations $$\begin{align} \frac{dN}{dt}=\,&\eta \frac{L_{\rm in}}{\hbar \omega _{\rm p} V_{\rm a}}-\frac{V_{\rm s}}{d_{\rm a}}N-BN^2\\ &-CN^3-{\it \Gamma}G(N)P,~~ \tag {1} \end{align} $$ $$\begin{align} \frac{dP}{dt}=\,&{\it \Gamma}G(N)P+\beta BN^2-\frac{P}{\tau _{\rm p}}~~ \tag {2} \end{align} $$ are used to analyze the static difference between the single-cavity laser and the coupled-cavity laser on our experimental conditions. Parameters for InGaAsP-InP QWs used in solving rate equations are listed in Table 1.
cpl-34-2-024202-fig3.png
Fig. 3. Spectrum of the coupled-cavity laser with a peak at 1551 nm. The PhC hole radius in this structure is about 192 nm. The inset on the left shows the QW photoluminescence from the unprocessed wafer. The inset on the right shows the zoomed-in portion of the spectrum fitted with a Gaussian (red dashed) curve of 0.91 nm linewidth.
Table 1. Typical parameters for InGaAsP-InP QWs.
Parameters Values
Surface recombination velocity $V_{\rm s}=10^{4}$ cm/s
Bimolecular recombination coefficient $B=1.6\times10^{-10}$ cm$^{3}$/s
Auger nonradiative recombination rate $C=5\times10^{-29}$ cm$^{6}$/s
Transparency carrier density $N_{\rm tr}=1.5\times10^{18}$ cm$^{-3}$
Mode group refractive index $n_{\rm eq}=4$
Spontaneous emission factor $\beta=0.1$
Gain coefficient $G_{0}=1500$ cm$^{-1}$
Absorption ration of pump in the QW region $\eta=0.26$
Confinement factor ${\it \Gamma}=0.1$
Propagation distance for surface recombination $d_{\rm a}=2\times10^{-5}$ cm
Pumping active volume $V_{\rm a, single}=1.1\times10^{-12}$ cm$^{3}$
Optical mode volume for single cavity $V_{\rm mode, single}=7.2\times10^{-14}$ cm$^{3}$
Lasing wavelength $\lambda _{l}=1.55\times10^{-4}$ cm
Pump laser wavelength $\lambda _{\rm p}=0.64\times10^{-4}$ cm
In our analysis the gain $G(N)$ is expressed as $G(N)=G_{0}c/n_{\rm eq}\log(N/N _{\rm tr})$, where $N$ is the carrier density, and $P$ is the photon density. The carrier and photon number are given by $NV _{\rm a}$ and $PV _{\rm mode}$, respectively. The output power is calculated by $L_{\rm out}=\hbar\omega _{l} PV _{\rm mode} /\tau _{\rm p}$. Figure 4 shows the output power as a function of the input power calculated by Eqs. (1) and (2). In our experiment, the pumping area of the coupled-cavity laser is about 5–6 times larger than that of the single-cavity laser, which means that $V_{\rm a,coupled}\approx 5V_{\rm a, single}$. However, the mode volume is increased with the number of coupled cavities $n_{\rm c}$ ($V_{\rm mode, coupled}=n_{\rm c}V_{\rm mode, single}$). The calculated results show that the threshold power of the coupled-cavity lasers is about five times larger than that of the single-cavity laser, while the threshold power among these coupled-cavity lasers is almost unchanged. This is because the threshold power depends on the pumping active volume $V_{\rm a}$. The results also show that the lasing efficiency increases with the number of coupled cavities. The reason is that with an increase of the cavities, the overlap between the pumping active region and the mode volume increases, thus the pumping efficiency increases. A more efficient pumping brings a higher lasing efficiency. The simulation results are consistent with the experimental results, showing that a coupled-cavity laser has a larger threshold power, output power and lasing efficiency. Comparing the theoretical results shown in Fig. 4 with our experimental data shown in Fig. 2, we can obtain that the majority of 25 cavities in the array are lasing simultaneously in our experiment. We can increase the number of cavities in the array to further enhance the output power and lasing efficiency.
cpl-34-2-024202-fig4.png
Fig. 4. Output power as a function of the input power calculated by rate equations based on our experimental conditions. Single-cavity result is shown in red, and coupled-cavity results are shown in blue. Here 10 times (square), 16 times (circle), and 25 times (triangle) $V_{\rm mode, single}$ are shown separately.
We next analyze the dynamic characteristics of PhC lasers. First we measure the time-resolved photoluminescence (PL) decay curve from the unpatterned InGaAsP QWs region to obtain the SpE rate (shown in Fig. 5). It shows that the PL decay lifetime from the unpatterned bulk region is 5.31 ns, corresponding to the SpE rate of $1.9\times10^{8}$ s$^{-1}$. Our data is comparable with that in Ref. [4]. Then we measured the dynamic behavior of both single- and coupled-cavity lasers at 1.3 times of their threshold current separately. The results are shown in Fig. 6. The pulse width (full width at half maximum) of the coupled-cavity laser is 201 ps while that of the single-cavity laser is 113 ps, close to the InGaAs APD resolution limit. An optical pumping with a spatial Gaussian-shaped beam results in inhomogeneous gain and asynchronous lasing action. Due to the asynchronous lasing action across the coupled-cavity array, the nanocavities are not phase locked, and the total response time is broadened. Moreover, the nonuniformity of the fabrication makes the cavities in the array not resonate simultaneously. The inhomogeneous pump[11] and the nonuniformity of fabrication, both of which cause asynchronous lasing action, are responsible for the longer duration of the coupled-cavity laser. The time duration for which the single-cavity pulse is greater than 10% is 206 ps. Consequently, our single-cavity laser is capable of a switching speed close to 5 GHz.
cpl-34-2-024202-fig5.png
Fig. 5. Time-resolved PL decay curve for the unpatterned area of InGaAsP QWs with an exponential fit (red).
cpl-34-2-024202-fig6.png
Fig. 6. Dynamic response of the PhC laser. Time response of the single-cavity laser (a) and the coupled-cavity laser (b) with a Gaussian fit.
In conclusion, we have fabricated both single- and coupled-cavity PhC lasers in an InGaAsP/InP material system and investigated the static and dynamic lasing action theoretically and experimentally. In the static analysis, both the maximum power and the lasing efficiency of the coupled-cavity laser are larger than those of the single-cavity laser due to a more efficient pumping (larger $V_{\rm mode}/V_{\rm a}$). In the dynamic analysis, the significant longer duration of the coupled-cavity laser indicates that it is important to obtain a uniform injection if the short pulse duration is desired. These results indicate that the PhC laser is a promising light source for a high-speed, photonic integrated circuit. References Toward fJ/bit optical communication in a chipResonance Absorption by Nuclear Magnetic Moments in a SolidSpontaneous-emission control by photonic crystals and nanocavitiesSimultaneous Inhibition and Redistribution of Spontaneous Light Emission in Photonic CrystalsObservation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperatureNanoparticle size and morphology control using ultrafast laser induced forward transfer of Ni thin filmsUltrafast photonic crystal nanocavity laserAnalysis of semiconductor microcavity lasers using rate equationsOxidation and sulfur passivation of GaInAsP(100)High Polarization Single Mode Photonic Crystal MicrolaserTime-resolved lasing action from single and coupled photonic crystal nanocavity array lasers emitting in the telecom band
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