Gain-switching dynamics in optically pumped single-mode InGaN vertical-cavity surfaceemitting lasers Shaoqiang Chen,1,* Akifumi Asahara,1 Takashi Ito,1 Jiangyong Zhang,2 Baoping Zhang,2 Tohru Suemoto,1 Masahiro Yoshita,1 and Hidefumi Akiyama1 1
Institute for Solid State Physics (ISSP), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan 2 Department of Electronic Engineering, Xiamen University, Xiamen 361005, Fujian, China * [email protected]
Abstract: The gain-switching dynamics of single-mode pulses were studied in blue InGaN multiple-quantum-well vertical-cavity surface-emitting lasers (VCSELs) through impulsive optical pumping. We measured the shortest single-mode pulses of 6.0 ps in width with a method of upconversion, and also obtained the pulse width and the delay time as functions of pump powers from streak-camera measurements. Single-mode rate-equation calculations quantitatively and consistently explained the observed data. The calculations indicated that the pulse width in the present VCSELs was mostly limited by modal gain, and suggested that subpicosecond pulses should be possible within feasible device parameters. ©2014 Optical Society of America OCIS codes: (140.5960) Semiconductor lasers; (140.3570) Lasers, single-mode; (140.7090) Ultrafast lasers; (320.5390) Picosecond phenomena.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989). H. E. Pudavar, M. P. Joshi, P. N. Prasad, and B. A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74(9), 1338–1340 (1999). K. Yamasaki, S. Juodkazis, M. Watanabe, H.-B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76(8), 1000–1002 (2000). S. Tashiro, Y. Takemoto, H. Yamatsu, T. Miura, G. Fujita, T. Iwamura, D. Ueda, H. Uchiyama, K. S. Yun, M. Kuramoto, T. Miyajima, M. Ikeda, and H. Yokoyama, “Volumetric optical recording using a 400 nm allsemiconductor picosecond laser,” Appl. Phys. Express 3(10), 102501 (2010). S. Kono, T. Oki, T. Miyajima, M. Ikeda, and H. Yokoyama, “12 W peak-power 10 ps duration optical pulse generation by gain switching of a single-transverse-mode GaInN blue laser diode,” Appl. Phys. Lett. 93(13), 131113 (2008). S. Q. Chen, M. Okano, B. P. Zhang, M. Yoshita, H. Akiyama, and Y. Kanemitsu, “Blue 6-ps short-pulse generation in gain-switched InGaN vertical-cavity surface-emitting lasers via impulsive optical pumping,” Appl. Phys. Lett. 101(19), 191108 (2012). J. Y. Zhang, L. E. Cai, B. P. Zhang, S. Q. Li, F. Lin, J. Z. Shang, D. X. Wang, K. C. Lin, J. Z. Yu, and Q. M. Wang, “Low threshold lasing of GaN-based vertical cavity surface emitting lasers with an asymmetric coupled quantum well active region,” Appl. Phys. Lett. 93(19), 191118 (2008). T. Someya, R. Werner, A. Forchel, M. Catalano, R. Cingolani, and Y. Arakawa, “Room temperature lasing at blue wavelengths in gallium nitride microcavities,” Science 285(5435), 1905–1906 (1999). C. J. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 57(3), 218–220 (1990). S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, and H. Yokoyama, “Gain-switched pulses from InGaAs ridge-quantum-well lasers limited by intrinsic dynamical gain suppression,” Opt. Express 21(6), 7570– 7576 (2013). L. G. Melcer, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Picosecond dynamics of optical gain switching in vertical cavity emitting lasers,” IEEE J. Quantum Electron. 27(6), 1417–1425 (1991). K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988). J. R. Karin, L. G. Melcer, R. Nagarajan, J. E. Bowers, S. W. Corzine, P. A. Morton, R. S. Geels, and L. A. Coldren, “Generation of picosecond pulses with a gain-switched GaAs surface-emitting laser,” Appl. Phys. Lett. 57(10), 963–965 (1990).
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4196
14. S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys. 51, 098001 (2012). 15. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999). 16. K. Domen, K. Kondo, A. Kuramata, and T. Tanahashi, “Gain analysis for surface emission by optical pumping of wurtzite GaN,” Appl. Phys. Lett. 69(1), 94–96 (1996). 17. T. Oki, K. Saito, H. Watanabe, T. Miyajima, M. Kuramoto, M. Ikeda, and H. Yokoyama, “Passive and hybrid mode-locking of an external-cavity GaInN laser diode incorporating a strong saturable absorber,” Appl. Phys. Express 3(3), 032104 (2010).
1. Introduction One of the most important applications of semiconductor laser diodes (LDs) is reading and recording data in optical disks. The increasing requirements for higher density optical storage have promoted the shortening of wavelengths from 780 nm for AlGaAs LDs for CDs to 650 nm for AlGaInP LDs for DVDs, and then to 405 nm for InGaN LDs for Blu-ray discs. The next generation of 3D optical storage [1–3] is expected to have much higher density and capacity. However, its introduction necessarily needs optical-pulse light sources with short pulse widths for reading and recording [2–4]. Therefore, gain-switched short wavelength semiconductor lasers [5, 6] might be possible candidates because of three advantages of being simple, low cost, and compactable. Consequently, studying the generation of short pulses from gain-switched GaN based semiconductor lasers is of great interest. Although the high reflectivity of distributed-Bragg reflectors (DBRs) may dramatically increase the photon lifetime of nitride-based blue VCSELs [6–8], the intrinsic short length of cavities can still produce short photon lifetimes that are very useful for generating short pulses if there are appropriate designs for cavities. In fact, we previously demonstrated optical pulses as short as 6.0 ps from a gain-switched InGaN VCSEL [6], indicating that nitridebased blue VCSELs are indeed very good prospects for generating short pulses. However, lasing only occurred in multi-modes, which made it very difficult to quantitatively and theoretically analyze it. Consequently, generation dynamics of the 6 ps pulses was not clarified. A quantitative study of gain-switching dynamics is crucial to understand or design nitride-based gain-switched VCSELs that generate short output pulses. For this purpose, single-mode gain-switched pulses that are convenient for physical analysis are on demand. In this paper, we obtained single-mode gain-switched short pulses from an InGaN VCSEL under impulsive optical pumping. We studied the lasing characteristics of the single-mode pulses through detailed measurements of pulse widths and delay times as functions of pump power. Single-mode rate-equation calculations with a nonlinear-gain model were undertaken to quantitatively analyze and also predict gain-switching dynamics. Quantitative simulations indicated that subpicosecond pulses could be generated in nitride-based VCSELs through structural improvements of the devices. 2. Experimental setup The sample used in this study was the same as that in previous studies [6, 7], which consisted of two (top and bottom) Ta2O5/SiO2 distributed Bragg reflector (DBR) layers and an optical cavity with a length of 2.3 μm. The active region consisted of three sets of In0.2Ga0.8N asymmetric quantum wells (with thicknesses of 2.5, 3.0 and 3.5 nm) and 5-nm GaN spacer layers. There is a schematic of the experiment setup in Fig. 1. The sample was optically pumped with a 1-kHz pulse laser beam of 400 nm at 300 fs that was focused on the sample’s surface with a beam size of ~50 μm with an optical lens. The 400-nm laser beam was the second harmonic generation (SHG) of an 800-nm laser beam with a duration of 120 fs from a regenerative amplifier. The time-integrated emission spectra were measured with a spectrometer system with a liquid-nitrogen-cooled charge-coupled device (CCD). The timeresolved emission spectra were measured with a streak camera with a system resolution of 5.2 ps. Since the system resolution of the streak camera may not have been sufficient to measure pulse width, a system of supplementary up-conversion measurements with a time
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4197
resolution of 0.12 ps (limited by the 800-nm gate pulse width) was used to measure the pulse width with elevated pump powers. Streak camera system or up-conversion system
Up-conversion system PMT
Gain-switched output pulse
SF BBO
400-nm Pump pulse
BS Lens
Gain-switched output pulse
DBR Cavity
120-fs 800-nm gate pulse
DBR
InGaN VCSEL
Fig. 1. Schematic of experimental setup for gain-switching dynamics of InGaN VCSELs. BS: Beam splitter, SF: Sum frequency, BBO: Beta-Ba2BO4 (Beta-Barium Borate) crystal, and PMT: Photonmultiplier tube.
(b)
444.5 nm
10
FWHM 0.2 nm 200 μ W
38.2μ W
Output power (nW)
Emission intensity with offset (arb.unit)
(a)
10
-1
10
-2
10
-3
20.8 μ W 15.0 μ W 420 430 440 450 460 470 Wavelength (nm) 1.0
Normalized Intensity
0
2
4
5.0 ps @ 200 μW 6.0 ps @ 200 μW 15.0 ps @ 52 μW 18.0 ps @ 38 μW
(c)
0.8
2
4
2
4
1 10 100 Average pump power (μW) by simultion by up-conversion by streak camera by streak camera
0.6 Tail
0.4 0.2 0.0
0
20
40 Delay time (ps)
60
80
Fig. 2. (a) Time-integrated spectra of gain-switched VCSEL with various pump powers. (b) Plot of output power vs. input power of VCSEL. (c) Waveforms of gain-switched pulses with various pump powers. Dashed line plots simulation results for waveform with pump power of 200 μW.
3. Experimental results and discussion The time-integrated emission spectra with various pump powers are plotted in Fig. 2(a). Single-mode lasing at 444.5 nm started at 20.8 μW (average power and subsequently the #197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4198
following power) and continued the single mode even at elevated pump powers. Multiplemode lasing was observed in a previous study with an excitation beam size of ~500 μm. The single mode lasing observed in the present study demonstrated that reducing the excitation beam size was indeed helpful to obtain single-mode lasing [9]. We know from the log plot of input-power vs. output-power in Fig. 2(b) that the spontaneous emission coupling factor of the VCSEL is ~3.0 × 10−2, which is in good agreement with the previous results [7]. Figure 2(c) plots the time-resolved waveforms of the single-mode output pulses of the VCSEL with pump powers of 38, 52 and 200 μW. These results indicate that gain-switched pulses have a long pulse width of 18 ps and a long delay time of 48 ps with pump powers at around the threshold, while they have a short pulse width of 6.0 ps (full width at half maximum) and a delay time of 16 ps with a pump power of 200 μW. The spectral width of the time-integrated spectrum of the 6.0-ps short pulses is around 0.2 nm (resolution ~0.15 nm). The time-bandwidth product of the pulse is around 1.9, which is much larger than the Fourier-transform-limited value of 0.44 (Gaussian) or 0.31 (Sech2), indicating that the single-mode 6.0-ps pulses we obtained are strongly chirped. This was also in good agreement with the results obtained from previous Kerr-gate experiments [6].
Pulse width & delay time (ps)
50 Delay time by streak camera Delay time by simulation
40
Pulse width by streak camera Pulse width by upconversion Pulse width by simulation
30 20 10 0
0
50
100 150 200 Average pump power (μW)
250
Fig. 3. Delay times and pulse widths of gain-switched pulses with various pump powers. Dashed lines plot simulation results.
The delay times and pulse widths of pulses with different pump powers are summarized in Fig. 3. It can be seen that the delay times and the pulse widths gradually decreased with increasing pump powers and then simultaneously stayed at certain values at pump powers over 100 μW. The shortest delay time was limited to 16 ps and the shortest pulse width was limited to 6.0 ps independently of the pump power. The power dependencies of the delay time and pulse width are similar to those in other gain-switched semiconductor lasers [10–13]. These typical features indicate that gain switching indeed occurred in the VCSEL. The power dependencies of the delay time and pulse width of the gain-switched pulses were quantitatively simulated with a model of a single-mode-laser rate equation [10, 14] given below to clarify the gain-switching dynamics and factors in the pulse-width limitations of the VCSEL. dn 2 D P (t ) Γ g n2 D 2D =η − vg s − . dt hν mA m 1 + ε s 2 D τr
(1)
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4199
ds 2 D g s2D n2 D 2D = Γvg − + β . s m τp τr dt 1 + ε s2D
g = g 0 (n 2 D − n02 D ) / [1 +
g 0 (n 2 D − n02 D ) gs
].
(2)
(3)
Here, n2D is the two-dimensional carrier density in one quantum well, s2D is the twodimensional photon density for all active layers, and g0 is the differential gain. ε is the gain compression factor, gs is the saturated material gain of the InGaN quantum well, and P(t) denotes the transient pumping power given by a Gaussian distribution with a pulse duration of 0.3 ps. η = 0.41 is the power absorption rate, m = 3 is the quantum-well period, and A = 2.5 × 10−5 cm2 is the spot size of the pump laser beam. L = 2.3 µm is the cavity length, n0 = 2.0 × 1012 cm2 is the transparence carrier density, and β = 0.03 is the spontaneous emission coupling factor. τr = 5 ns is the carrier lifetime, τp = 0.6 ps is the photon lifetime (also called the cavity lifetime), Γ = 4.6 × 10−3 is the confinement factor (estimated from Γ = md / L , d is the quantum-well thickness), and vg = 1.1 × 10−2 cm/ps is the group velocity. Differential gain g0, gain compression factor ε, and saturated material gain gs are the three main fitting parameters. Best agreement with the experimental results was obtained when a value for differential gain g0 = 2.0 × 10−10 cm, a very small value for gain compression factor ε = 2.0 × 10−16 cm2, and a high value for saturated material gain gs = 4.9 × 104 cm−1 were used. The order of saturated material gain was in very good agreement with the theoretical calculations [15, 16], and was considerably larger than the values for (In)GaAs lasers [10], indicating that the material gain of nitrides is indeed very large. The large gain of the nitrides was considered to have resulted from the three bands in the valence band close to the band edge and the large reduced-effective mass of each valence band [16]. This reasonable value for the saturated gain of the nitrides we obtained and the good agreement between the experimental results and quantitative simulation demonstrated that the rate-equation model we used was indeed suitable to describe the gain-switching dynamics of InGaN VCSELs. We discuss possible ways toward accomplishing even shorter pulses in what follows. According to Eq. (2), the shortest pulse width (PW) with strong excitations is approximately given by:
PW ≈ ( ln 2)τ p (1+
1
τ p vg g smod al −1
)
(4)
where τ p vg g smod al > 1 is a requirement to generate pulses, saturated modal gain g smod al is determined by g smod al = Γg s = ( md / L) g s , and photon lifetime τp is determined by equation τ p = 2 L / [vg ln( R1 R2 ) −1 ] . Here, R1 and R2 are the reflectivity of DBR on the top and bottom of the cavity. We know from Eq. (4) that the photon lifetime and saturated modal gain are two essential factors that limit the shortest pulse width of the gain-switched pulses. Since the 6.0-ps pulse width is ten times longer than the 0.6-ps photon lifetime of the VCSEL, the 6.0-ps pulse width is not limited by the photon lifetime but saturated modal gain. We also know from Eq. (4) that increasing saturated modal gain g smod al by increasing the number of quantum wells or the confinement factor should be useful for generating even shorter pulses. If the number of quantum wells in the present InGaN VCSEL could be increased to 20, corresponding to an increase in modal gain to ~1500 cm−1 according to the quantitative rate-equation simulations, the shortest pulse would be expected to be as short as ~0.9 ps, which is near the photon-lifetime limit. Therefore, reducing photon lifetime τp could help to obtain even shorter pulses. Note that while the photon lifetime decreases with decreasing cavity length, the product of τ p vg g smod al does not depend on cavity length;
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4200
therefore, the shortest pulse width repeatedly decreases with decreasing cavity length. The simulation indicated that if the cavity length could be decreased to 1.0 μm, the shortest pulse width could be ~400 fs. Therefore, we can obtain subpicosecond photon-lifetime-limited short pulses by decreasing the cavity length and increasing the number of quantum wells in VCSELs. We should comment that the decay tail of the gain-switched pulses could not be simulated well while most of the experimental results were quantitatively simulated with the rate equations. We can see that the decay tail at the end of the experimentally obtained pulses is much longer than that in the simulation results by comparing the pulse shape in the experiment with that in the simulation (shown as a dashed curve in Fig. 2(c)) with a high pump power of 200 μW. The decay time of the pulse with a high pump power should theoretically be mainly limited by the photon lifetime in the cavity of the VCSEL. Although the exact origin of the long tail is still unknown, the long tail should also be suppressed or removed to obtain even shorter gain-switched pulses. Finally, we examined the necessary output power of the InGaN VCSEL for some applications. A previous data-recording experimental results [4] have shown that data recording can be performed with a 405-nm 3-ps pulse laser with a maximum peak power of 100 W via amplification of a 3-W peak power from a mode-locked laser oscillator [17]. The maximum peak power of the pulses for present sample was 0.2 W. Assuming the beam size of the output pulses was similar to the excitation beam size of 50 μm in diameter, the peak power density was then estimated to be 10 kW/cm2. To generate a peak power of 3 W for applications of data recording, we may increase the single-mode lasing area of the VCSEL to around 200 μm in diameter, or use a higher amplification. 7. Conclusion
In summary, a single-mode 6.0 ps blue pulse was generated by gain switching from an optically pumped InGaN VCSEL. Single-mode gain-switching dynamics in the VCSEL was quantitatively analyzed by both experimentally and theoretically investigating the pumppower dependencies of delay time and pulse width of gain-switched output pulses. The results from simulation demonstrated that subpicosecond short gain-switched pulses could be expected from nitride-based VCSELs by increasing the number of quantum wells and decreasing the cavity length. These results as well as the quantitative rate-equation model are expected to provide very significant reference values to future designs of samples and basic studies on nitride-based VCSELs. Acknowledgments
This work was partly supported by Kakenhi grant no. 20104004 from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), no. 23360135 from the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology-Core Research for Evolutional Science and Technology (JST-CREST) (FY2011–2016), and the Photon Frontier Network Program of MEXT in Japan.
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4201
Institute for Solid State Physics (ISSP), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan 2 Department of Electronic Engineering, Xiamen University, Xiamen 361005, Fujian, China * [email protected]
Abstract: The gain-switching dynamics of single-mode pulses were studied in blue InGaN multiple-quantum-well vertical-cavity surface-emitting lasers (VCSELs) through impulsive optical pumping. We measured the shortest single-mode pulses of 6.0 ps in width with a method of upconversion, and also obtained the pulse width and the delay time as functions of pump powers from streak-camera measurements. Single-mode rate-equation calculations quantitatively and consistently explained the observed data. The calculations indicated that the pulse width in the present VCSELs was mostly limited by modal gain, and suggested that subpicosecond pulses should be possible within feasible device parameters. ©2014 Optical Society of America OCIS codes: (140.5960) Semiconductor lasers; (140.3570) Lasers, single-mode; (140.7090) Ultrafast lasers; (320.5390) Picosecond phenomena.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989). H. E. Pudavar, M. P. Joshi, P. N. Prasad, and B. A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74(9), 1338–1340 (1999). K. Yamasaki, S. Juodkazis, M. Watanabe, H.-B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76(8), 1000–1002 (2000). S. Tashiro, Y. Takemoto, H. Yamatsu, T. Miura, G. Fujita, T. Iwamura, D. Ueda, H. Uchiyama, K. S. Yun, M. Kuramoto, T. Miyajima, M. Ikeda, and H. Yokoyama, “Volumetric optical recording using a 400 nm allsemiconductor picosecond laser,” Appl. Phys. Express 3(10), 102501 (2010). S. Kono, T. Oki, T. Miyajima, M. Ikeda, and H. Yokoyama, “12 W peak-power 10 ps duration optical pulse generation by gain switching of a single-transverse-mode GaInN blue laser diode,” Appl. Phys. Lett. 93(13), 131113 (2008). S. Q. Chen, M. Okano, B. P. Zhang, M. Yoshita, H. Akiyama, and Y. Kanemitsu, “Blue 6-ps short-pulse generation in gain-switched InGaN vertical-cavity surface-emitting lasers via impulsive optical pumping,” Appl. Phys. Lett. 101(19), 191108 (2012). J. Y. Zhang, L. E. Cai, B. P. Zhang, S. Q. Li, F. Lin, J. Z. Shang, D. X. Wang, K. C. Lin, J. Z. Yu, and Q. M. Wang, “Low threshold lasing of GaN-based vertical cavity surface emitting lasers with an asymmetric coupled quantum well active region,” Appl. Phys. Lett. 93(19), 191118 (2008). T. Someya, R. Werner, A. Forchel, M. Catalano, R. Cingolani, and Y. Arakawa, “Room temperature lasing at blue wavelengths in gallium nitride microcavities,” Science 285(5435), 1905–1906 (1999). C. J. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 57(3), 218–220 (1990). S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, and H. Yokoyama, “Gain-switched pulses from InGaAs ridge-quantum-well lasers limited by intrinsic dynamical gain suppression,” Opt. Express 21(6), 7570– 7576 (2013). L. G. Melcer, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Picosecond dynamics of optical gain switching in vertical cavity emitting lasers,” IEEE J. Quantum Electron. 27(6), 1417–1425 (1991). K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988). J. R. Karin, L. G. Melcer, R. Nagarajan, J. E. Bowers, S. W. Corzine, P. A. Morton, R. S. Geels, and L. A. Coldren, “Generation of picosecond pulses with a gain-switched GaAs surface-emitting laser,” Appl. Phys. Lett. 57(10), 963–965 (1990).
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4196
14. S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys. 51, 098001 (2012). 15. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999). 16. K. Domen, K. Kondo, A. Kuramata, and T. Tanahashi, “Gain analysis for surface emission by optical pumping of wurtzite GaN,” Appl. Phys. Lett. 69(1), 94–96 (1996). 17. T. Oki, K. Saito, H. Watanabe, T. Miyajima, M. Kuramoto, M. Ikeda, and H. Yokoyama, “Passive and hybrid mode-locking of an external-cavity GaInN laser diode incorporating a strong saturable absorber,” Appl. Phys. Express 3(3), 032104 (2010).
1. Introduction One of the most important applications of semiconductor laser diodes (LDs) is reading and recording data in optical disks. The increasing requirements for higher density optical storage have promoted the shortening of wavelengths from 780 nm for AlGaAs LDs for CDs to 650 nm for AlGaInP LDs for DVDs, and then to 405 nm for InGaN LDs for Blu-ray discs. The next generation of 3D optical storage [1–3] is expected to have much higher density and capacity. However, its introduction necessarily needs optical-pulse light sources with short pulse widths for reading and recording [2–4]. Therefore, gain-switched short wavelength semiconductor lasers [5, 6] might be possible candidates because of three advantages of being simple, low cost, and compactable. Consequently, studying the generation of short pulses from gain-switched GaN based semiconductor lasers is of great interest. Although the high reflectivity of distributed-Bragg reflectors (DBRs) may dramatically increase the photon lifetime of nitride-based blue VCSELs [6–8], the intrinsic short length of cavities can still produce short photon lifetimes that are very useful for generating short pulses if there are appropriate designs for cavities. In fact, we previously demonstrated optical pulses as short as 6.0 ps from a gain-switched InGaN VCSEL [6], indicating that nitridebased blue VCSELs are indeed very good prospects for generating short pulses. However, lasing only occurred in multi-modes, which made it very difficult to quantitatively and theoretically analyze it. Consequently, generation dynamics of the 6 ps pulses was not clarified. A quantitative study of gain-switching dynamics is crucial to understand or design nitride-based gain-switched VCSELs that generate short output pulses. For this purpose, single-mode gain-switched pulses that are convenient for physical analysis are on demand. In this paper, we obtained single-mode gain-switched short pulses from an InGaN VCSEL under impulsive optical pumping. We studied the lasing characteristics of the single-mode pulses through detailed measurements of pulse widths and delay times as functions of pump power. Single-mode rate-equation calculations with a nonlinear-gain model were undertaken to quantitatively analyze and also predict gain-switching dynamics. Quantitative simulations indicated that subpicosecond pulses could be generated in nitride-based VCSELs through structural improvements of the devices. 2. Experimental setup The sample used in this study was the same as that in previous studies [6, 7], which consisted of two (top and bottom) Ta2O5/SiO2 distributed Bragg reflector (DBR) layers and an optical cavity with a length of 2.3 μm. The active region consisted of three sets of In0.2Ga0.8N asymmetric quantum wells (with thicknesses of 2.5, 3.0 and 3.5 nm) and 5-nm GaN spacer layers. There is a schematic of the experiment setup in Fig. 1. The sample was optically pumped with a 1-kHz pulse laser beam of 400 nm at 300 fs that was focused on the sample’s surface with a beam size of ~50 μm with an optical lens. The 400-nm laser beam was the second harmonic generation (SHG) of an 800-nm laser beam with a duration of 120 fs from a regenerative amplifier. The time-integrated emission spectra were measured with a spectrometer system with a liquid-nitrogen-cooled charge-coupled device (CCD). The timeresolved emission spectra were measured with a streak camera with a system resolution of 5.2 ps. Since the system resolution of the streak camera may not have been sufficient to measure pulse width, a system of supplementary up-conversion measurements with a time
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4197
resolution of 0.12 ps (limited by the 800-nm gate pulse width) was used to measure the pulse width with elevated pump powers. Streak camera system or up-conversion system
Up-conversion system PMT
Gain-switched output pulse
SF BBO
400-nm Pump pulse
BS Lens
Gain-switched output pulse
DBR Cavity
120-fs 800-nm gate pulse
DBR
InGaN VCSEL
Fig. 1. Schematic of experimental setup for gain-switching dynamics of InGaN VCSELs. BS: Beam splitter, SF: Sum frequency, BBO: Beta-Ba2BO4 (Beta-Barium Borate) crystal, and PMT: Photonmultiplier tube.
(b)
444.5 nm
10
FWHM 0.2 nm 200 μ W
38.2μ W
Output power (nW)
Emission intensity with offset (arb.unit)
(a)
10
-1
10
-2
10
-3
20.8 μ W 15.0 μ W 420 430 440 450 460 470 Wavelength (nm) 1.0
Normalized Intensity
0
2
4
5.0 ps @ 200 μW 6.0 ps @ 200 μW 15.0 ps @ 52 μW 18.0 ps @ 38 μW
(c)
0.8
2
4
2
4
1 10 100 Average pump power (μW) by simultion by up-conversion by streak camera by streak camera
0.6 Tail
0.4 0.2 0.0
0
20
40 Delay time (ps)
60
80
Fig. 2. (a) Time-integrated spectra of gain-switched VCSEL with various pump powers. (b) Plot of output power vs. input power of VCSEL. (c) Waveforms of gain-switched pulses with various pump powers. Dashed line plots simulation results for waveform with pump power of 200 μW.
3. Experimental results and discussion The time-integrated emission spectra with various pump powers are plotted in Fig. 2(a). Single-mode lasing at 444.5 nm started at 20.8 μW (average power and subsequently the #197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4198
following power) and continued the single mode even at elevated pump powers. Multiplemode lasing was observed in a previous study with an excitation beam size of ~500 μm. The single mode lasing observed in the present study demonstrated that reducing the excitation beam size was indeed helpful to obtain single-mode lasing [9]. We know from the log plot of input-power vs. output-power in Fig. 2(b) that the spontaneous emission coupling factor of the VCSEL is ~3.0 × 10−2, which is in good agreement with the previous results [7]. Figure 2(c) plots the time-resolved waveforms of the single-mode output pulses of the VCSEL with pump powers of 38, 52 and 200 μW. These results indicate that gain-switched pulses have a long pulse width of 18 ps and a long delay time of 48 ps with pump powers at around the threshold, while they have a short pulse width of 6.0 ps (full width at half maximum) and a delay time of 16 ps with a pump power of 200 μW. The spectral width of the time-integrated spectrum of the 6.0-ps short pulses is around 0.2 nm (resolution ~0.15 nm). The time-bandwidth product of the pulse is around 1.9, which is much larger than the Fourier-transform-limited value of 0.44 (Gaussian) or 0.31 (Sech2), indicating that the single-mode 6.0-ps pulses we obtained are strongly chirped. This was also in good agreement with the results obtained from previous Kerr-gate experiments [6].
Pulse width & delay time (ps)
50 Delay time by streak camera Delay time by simulation
40
Pulse width by streak camera Pulse width by upconversion Pulse width by simulation
30 20 10 0
0
50
100 150 200 Average pump power (μW)
250
Fig. 3. Delay times and pulse widths of gain-switched pulses with various pump powers. Dashed lines plot simulation results.
The delay times and pulse widths of pulses with different pump powers are summarized in Fig. 3. It can be seen that the delay times and the pulse widths gradually decreased with increasing pump powers and then simultaneously stayed at certain values at pump powers over 100 μW. The shortest delay time was limited to 16 ps and the shortest pulse width was limited to 6.0 ps independently of the pump power. The power dependencies of the delay time and pulse width are similar to those in other gain-switched semiconductor lasers [10–13]. These typical features indicate that gain switching indeed occurred in the VCSEL. The power dependencies of the delay time and pulse width of the gain-switched pulses were quantitatively simulated with a model of a single-mode-laser rate equation [10, 14] given below to clarify the gain-switching dynamics and factors in the pulse-width limitations of the VCSEL. dn 2 D P (t ) Γ g n2 D 2D =η − vg s − . dt hν mA m 1 + ε s 2 D τr
(1)
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4199
ds 2 D g s2D n2 D 2D = Γvg − + β . s m τp τr dt 1 + ε s2D
g = g 0 (n 2 D − n02 D ) / [1 +
g 0 (n 2 D − n02 D ) gs
].
(2)
(3)
Here, n2D is the two-dimensional carrier density in one quantum well, s2D is the twodimensional photon density for all active layers, and g0 is the differential gain. ε is the gain compression factor, gs is the saturated material gain of the InGaN quantum well, and P(t) denotes the transient pumping power given by a Gaussian distribution with a pulse duration of 0.3 ps. η = 0.41 is the power absorption rate, m = 3 is the quantum-well period, and A = 2.5 × 10−5 cm2 is the spot size of the pump laser beam. L = 2.3 µm is the cavity length, n0 = 2.0 × 1012 cm2 is the transparence carrier density, and β = 0.03 is the spontaneous emission coupling factor. τr = 5 ns is the carrier lifetime, τp = 0.6 ps is the photon lifetime (also called the cavity lifetime), Γ = 4.6 × 10−3 is the confinement factor (estimated from Γ = md / L , d is the quantum-well thickness), and vg = 1.1 × 10−2 cm/ps is the group velocity. Differential gain g0, gain compression factor ε, and saturated material gain gs are the three main fitting parameters. Best agreement with the experimental results was obtained when a value for differential gain g0 = 2.0 × 10−10 cm, a very small value for gain compression factor ε = 2.0 × 10−16 cm2, and a high value for saturated material gain gs = 4.9 × 104 cm−1 were used. The order of saturated material gain was in very good agreement with the theoretical calculations [15, 16], and was considerably larger than the values for (In)GaAs lasers [10], indicating that the material gain of nitrides is indeed very large. The large gain of the nitrides was considered to have resulted from the three bands in the valence band close to the band edge and the large reduced-effective mass of each valence band [16]. This reasonable value for the saturated gain of the nitrides we obtained and the good agreement between the experimental results and quantitative simulation demonstrated that the rate-equation model we used was indeed suitable to describe the gain-switching dynamics of InGaN VCSELs. We discuss possible ways toward accomplishing even shorter pulses in what follows. According to Eq. (2), the shortest pulse width (PW) with strong excitations is approximately given by:
PW ≈ ( ln 2)τ p (1+
1
τ p vg g smod al −1
)
(4)
where τ p vg g smod al > 1 is a requirement to generate pulses, saturated modal gain g smod al is determined by g smod al = Γg s = ( md / L) g s , and photon lifetime τp is determined by equation τ p = 2 L / [vg ln( R1 R2 ) −1 ] . Here, R1 and R2 are the reflectivity of DBR on the top and bottom of the cavity. We know from Eq. (4) that the photon lifetime and saturated modal gain are two essential factors that limit the shortest pulse width of the gain-switched pulses. Since the 6.0-ps pulse width is ten times longer than the 0.6-ps photon lifetime of the VCSEL, the 6.0-ps pulse width is not limited by the photon lifetime but saturated modal gain. We also know from Eq. (4) that increasing saturated modal gain g smod al by increasing the number of quantum wells or the confinement factor should be useful for generating even shorter pulses. If the number of quantum wells in the present InGaN VCSEL could be increased to 20, corresponding to an increase in modal gain to ~1500 cm−1 according to the quantitative rate-equation simulations, the shortest pulse would be expected to be as short as ~0.9 ps, which is near the photon-lifetime limit. Therefore, reducing photon lifetime τp could help to obtain even shorter pulses. Note that while the photon lifetime decreases with decreasing cavity length, the product of τ p vg g smod al does not depend on cavity length;
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4200
therefore, the shortest pulse width repeatedly decreases with decreasing cavity length. The simulation indicated that if the cavity length could be decreased to 1.0 μm, the shortest pulse width could be ~400 fs. Therefore, we can obtain subpicosecond photon-lifetime-limited short pulses by decreasing the cavity length and increasing the number of quantum wells in VCSELs. We should comment that the decay tail of the gain-switched pulses could not be simulated well while most of the experimental results were quantitatively simulated with the rate equations. We can see that the decay tail at the end of the experimentally obtained pulses is much longer than that in the simulation results by comparing the pulse shape in the experiment with that in the simulation (shown as a dashed curve in Fig. 2(c)) with a high pump power of 200 μW. The decay time of the pulse with a high pump power should theoretically be mainly limited by the photon lifetime in the cavity of the VCSEL. Although the exact origin of the long tail is still unknown, the long tail should also be suppressed or removed to obtain even shorter gain-switched pulses. Finally, we examined the necessary output power of the InGaN VCSEL for some applications. A previous data-recording experimental results [4] have shown that data recording can be performed with a 405-nm 3-ps pulse laser with a maximum peak power of 100 W via amplification of a 3-W peak power from a mode-locked laser oscillator [17]. The maximum peak power of the pulses for present sample was 0.2 W. Assuming the beam size of the output pulses was similar to the excitation beam size of 50 μm in diameter, the peak power density was then estimated to be 10 kW/cm2. To generate a peak power of 3 W for applications of data recording, we may increase the single-mode lasing area of the VCSEL to around 200 μm in diameter, or use a higher amplification. 7. Conclusion
In summary, a single-mode 6.0 ps blue pulse was generated by gain switching from an optically pumped InGaN VCSEL. Single-mode gain-switching dynamics in the VCSEL was quantitatively analyzed by both experimentally and theoretically investigating the pumppower dependencies of delay time and pulse width of gain-switched output pulses. The results from simulation demonstrated that subpicosecond short gain-switched pulses could be expected from nitride-based VCSELs by increasing the number of quantum wells and decreasing the cavity length. These results as well as the quantitative rate-equation model are expected to provide very significant reference values to future designs of samples and basic studies on nitride-based VCSELs. Acknowledgments
This work was partly supported by Kakenhi grant no. 20104004 from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), no. 23360135 from the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology-Core Research for Evolutional Science and Technology (JST-CREST) (FY2011–2016), and the Photon Frontier Network Program of MEXT in Japan.
#197987 - $15.00 USD Received 19 Sep 2013; revised 7 Nov 2013; accepted 3 Feb 2014; published 18 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004196 | OPTICS EXPRESS 4201
