Generation of sub-100 ps pulses tunable over 48 nm is demonstrated by optically gain-switching a MEMS-vertical-cavity surface-emitting laser (VCSEL). A minimum pulse width of 61 ps and a maximum, unamplified peak power of 28 mW are demonstrated. The polarization stability of the VCSELs allows amplification with a polarization-dependent semiconductor optical amplifier, resulting in pulse compression to 57 ps with a peak power of 932 mW. The low threshold power (average <1 mW) enables simultaneous pumping of multiple lasers for the generation of synchronized, independently tunable picosecond pulses.

Wavelength-tunable, ultrafast lasers drive a variety of applications, such as coherent Raman spectroscopy (CRS),1–3 two-photon excitation fluorescence microscopy (TPEF),4–6 fluorescence lifetime imaging (FLIM),7 and scan-free time-of-flight LiDAR.8 In particular, picosecond sources offer a compromise between high peak power and narrow linewidth, both critical parameters for high-resolution CRS. Wavelength tunability enables efficient, single-source excitation of multiple fluorophores in TPEF and FLIM and is typically achieved through mode-locked Ti:Sapphire lasers.4 For CRS, continuously tunable, synchronized, dual-wavelength outputs are required to scan over molecular roto-vibrational modes. Conventional implementations leverage the wide tunability and synchronized pump, signal, and idler outputs of optical parametric amplifiers (OPAs) or optical parametric oscillators (OPOs) to avoid complex electronic synchronization circuits.1 However, Ti:Sapphire lasers, OPAs, and OPOs have a large footprint, require persistent maintenance, and cost upward of $250 k, restricting the application space of contingent systems.

Recent interest in implementing various multiphoton microscopy modalities directly in a hospital setting has spurred efforts to replace Ti:Sapphire lasers, OPAs, and OPOs with compact, low cost, alignment-free alternatives, such as mode-locked fiber lasers and fiber-based supercontinuum generation.2,9,10 Mode-locked fiber lasers have achieved reliable, self-starting mode-locking, 100 s of unamplified peak power, and up to 152 nm of tuning.11–14 However, the accessible wavelengths are limited by the narrow bands of rare-earth doped fiber gain. Furthermore, these demonstrations required the use of broadband free-space components and switching between bandwidth-limiting intracavity elements. Alignment-free, all-fiber mode-locked lasers are typically restricted to <50 nm due to the limited bandwidths of fiber components and the difficulty in maintaining stable mode-locking across the full tuning range.14 To increase the spectral coverage and generate synchronized, dual-wavelength outputs, mode-locked fiber lasers have been used to pump supercontinuum generation in photonic crystal fibers. These systems enable all-fiber, octave-spanning spectra but suffer from low conversion efficiencies, requiring kilowatts of pump peak power to generate average power spectral densities of a few mW/nm.15,16

Alternatively, wavelength-tunable gain-switched diode lasers have been investigated due to their reduced source footprint, flexible repetition rate, and ease of synchronization. Gain-switching takes advantage of high frequency relaxation oscillations when the carrier density first crosses the threshold to rapidly modulate the gain, producing a series of short output pulses. By periodically modulating the excitation above and below the threshold, a train of single pulses is generated. Previously, 28 ps pulses tunable over a 65 nm bandwidth were demonstrated by gain-switching two Fabry–Perot lasers injection-locked with a tunable CW laser.17 However, wavelength tuning required the use of a tunable external cavity laser and a tunable Bragg grating filter, limiting system integrability.

Efforts to develop monolithic, broadly tunable semiconductor lasers have driven rapid improvements in the performance of MEMS-vertical-cavity surface-emitting lasers (VCSELs). These lasers have achieved up to 150 nm of continuous, single-mode tuning in CW operation while supporting compact, co-packaged integration with a semiconductor optical amplifier (SOA) in a butterfly package.18,19 MEMS-VCSELs benefit from the high scalability of VCSELs, which consume less real estate on the wafer than in-plane lasers and allow for wafer-scale testing. However, there has been limited exploration of the pulsed operation of tunable VCSELs to date. Previous demonstrations used direct current modulation to achieve 5 Gb/s transmission over 24 nm of tuning in an 850 nm MEMS-VCSEL (200 ps pulses)20 and 10 Gb/s transmission over 47 nm of tuning in a 1550 nm MEMS-VCSEL (100 ps pulses).21 

Optical pumping offers several key advantages in achieving both shorter gain-switched pulses and broader tunability.18,22–25 Because carriers are generated directly by the pump light absorbed in the active region, optical pumping bypasses the electrical parasitics that inhibit efficient, high frequency carrier modulation. Furthermore, the use of fixed wavelength ultrafast pump lasers minimizes the overlap between the pump pulse and the output pulse, allowing gain-switched pulse widths to approach the theoretical limit imposed by the photon lifetime.23,26 Uncompressed pulse widths less than 4 ps have been demonstrated in a fixed-wavelength MQW VCSEL pumped by a 6 ps dye laser.22 Pulses as short as 670 fs pulses were achieved in an in-plane double heterostructure VCSEL at 5 K using a 360 fs pump laser and a spectral filter to remove the long-wavelength tail.25 Design for wide, mode-hop free tuning in a MEMS-VCSEL requires maximizing the free spectral range (FSR) and gain bandwidth. The optically pumped cavity design eliminates the need for thick current spreading layers and doping of the cavity and mirror layers, shortening the cavity length and reducing free carrier absorption.18 This increases the FSR while reducing cavity losses and resistive heating, lowering the threshold gain, and increasing the useable gain spectrum. Consequently, optical gain-switching of MEMS-VCSELs is expected to enable shorter pulse generation, wider tunability, and higher optical powers with low threshold pump powers.

In this letter, we demonstrate stable pulses over a 56 nm tuning range by optically gain-switching a MEMS-VCSEL. The MEMS-VCSELs used in this demonstration employ a strained InP multi-quantum well-active region and wideband AlxOy-GaAs mirrors.18 The top distributed Bragg reflector (DBR) is suspended over the active region by a MEMS trampoline, as illustrated in Fig. 1(a). In CW operation, the device achieves continuously tunable, single-mode lasing over an 80 nm range (1280–1360 nm) while maintaining a polarization extinction ratio (PER) of 20 dB. Wavelength tuning is achieved by applying a voltage to the suspended top DBR, which causes the cavity to contract via electrostatic actuation. The device is integrated with a thermoelectric cooler (TEC) into a fiber-coupled butterfly package. A fused fiber wavelength division multiplexer (WDM) directs pump light to the VCSEL output fiber and separates out the lasing emission.

FIG. 1.

(a) Structure of the optically pumped MEMS-VCSEL. (b) Gain-switched tuning spectrum. (c) Normalized pulses at 1340, 1300, and 1250 nm.

FIG. 1.

(a) Structure of the optically pumped MEMS-VCSEL. (b) Gain-switched tuning spectrum. (c) Normalized pulses at 1340, 1300, and 1250 nm.

Close modal

Optical gain-switching is performed with a 1040 nm mode-locked Ytterbium-doped fiber laser producing 84 ps pulses at a 35 MHz repetition rate. Under these pump conditions, lasing threshold occurs at a pump average power between 0.13 and 1 mW across the tuning range, corresponding to a peak power of 43 and 345 mW, respectively. While a mode-locked fiber laser is used in this demonstration, the low threshold power of the VCSELs allows the pump laser to be replaced by an electrically gain-switched diode laser and an SOA generating <50 pJ pulses.27,28 Output pulses are longpass filtered to remove the lingering pump light before measurement with a 45 GHz detector (Newport Model 1014) and a 50 GHz sampling oscilloscope (HP 54750A). The pulse peak power is calculated from the measured average power and pulse width. A diagram of the gain-switching setup is shown in Fig. 2(a).

FIG. 2.

(a) Diagram of the gain-switching setup. ML-YDFL – mode-locked Ytterbium-doped fiber laser, PD – photodetector, VOA – variable optical attenuator, LP – longpass. (b) Pulse width and VCSEL peak power vs pump peak power at 1252 nm (solid line) and 1330 nm (dashed line). (c) Pulse evolution with pump power at 1252 nm. (d) Pulse width vs pump power normalized to threshold power across the tuning range, with the minimum pulse width across wavelength shown in the inset. (e) 8.1 ps rms jitter at 1250 nm, calculated from the standard deviation of the histogram of half-maxima crossing times (inset). (f) 3 dB-linewidth with increasing pump peak power at 1250 nm (solid line) and 1350 nm (dashed line), with the corresponding OSA traces shown in the inset.

FIG. 2.

(a) Diagram of the gain-switching setup. ML-YDFL – mode-locked Ytterbium-doped fiber laser, PD – photodetector, VOA – variable optical attenuator, LP – longpass. (b) Pulse width and VCSEL peak power vs pump peak power at 1252 nm (solid line) and 1330 nm (dashed line). (c) Pulse evolution with pump power at 1252 nm. (d) Pulse width vs pump power normalized to threshold power across the tuning range, with the minimum pulse width across wavelength shown in the inset. (e) 8.1 ps rms jitter at 1250 nm, calculated from the standard deviation of the histogram of half-maxima crossing times (inset). (f) 3 dB-linewidth with increasing pump peak power at 1250 nm (solid line) and 1350 nm (dashed line), with the corresponding OSA traces shown in the inset.

Close modal

Under gain-switched operation, the tuning range is reduced to 56 nm, with premature snap-down of the suspended top DBR occurring at 1290 nm. Stable tuning is achieved from 1300 to 1350 nm (and 1246–1252 nm). The pulse FWHM and peak power are plotted as a function of pump power in Fig. 2(b) for the modes at 1252 and 1330 nm. The mode at 1252 nm achieves both shorter pulse widths and higher peak powers than the mode at 1330 nm. The lateral displacement in the curves across wavelengths arises from the increase in threshold peak (average) power from 43 mW (0.13 mW) at 1330 nm to 345 mW (1 mW) at 1252 nm as the mode tunes away from the gain peak and DBR center. After normalization to the threshold pump power, the minima of the curves converge to ∼5 times the threshold pump power [Fig. 2(d)]. The S-shaped curve at 1350 nm arises from a mode hop back to the 1250 nm mode for pump powers exceeding 10× the threshold power. The minimum pulse width monotonically decreases with decreasing wavelength. This wavelength dependence could result from a decrease in the photon lifetime with wavelength from the combined effects of the cavity contraction and the reduced reflectivity along the DBR edge. A minimum pulse width of 61 ps is attained for the mode at 1250 nm, with a corresponding rms jitter of 8.1 ps [Fig. 2(e)]. At low pump powers, the increase in pump power drives a decrease in the pulse width, as expected from the increase in the relaxation oscillation frequency with increasing photon density. However, as the pump power continues to increase, the slope of the curve changes sign, and pulses begin to broaden. This behavior arises from the decrease in turn-on delay with increasing pump power, which causes a growing temporal overlap between the output pulse and the falling edge of the pump pulse. The continued injection of carriers after the onset of stimulated emission only pumps the tail of the output pulse, causing pulses to broaden.23 Shorter pulses could be achieved by reducing the overlap between the pump pulse and the output pulse, either by using a shorter pump pulse or by designing for a longer turn-on delay.

As with all gain-switched devices, the output pulse is chirped by the variation in active region carrier density. The linewidth increases with pump power, as expected from the coupling of refractive index to gain through the Kramers–Kronig relations.29 At the leading edge of the pump pulse, the gain increases rapidly due to the rise in the carrier density, inducing a negative change in the refractive index. At the falling edge of the pump pulse, the gain decreases rapidly, inducing a positive change in the refractive index. Consequently, the effective cavity length first decreases, then increases throughout the duration of the pulse, negatively chirping the output pulse. The dependence of linewidth on pump power is shown in Fig. 2(f) for the modes at 1250 and 1350 nm. The 3 dB-linewidth of the main peak decreases at high pump powers for wavelengths near 1350 nm due to the transfer of power to a blue-shifted side peak. As the wavelength decreases, the side peak diminishes for the equivalent excitation above the threshold. This is due to the decrease in the linewidth enhancement factor with decreasing wavelength, as derived in Ref. 30. The corresponding peak power spectral densities are 16.6 mW/nm (41 μW/nm average) at 1250 nm and 10.5 mW/nm (41 μW/nm average) at 1350 nm.

The polarization extinction ratio (PER) reduces slightly under gain-switched operation, attaining a maximum value of 17 dB near 1350 nm and falling off to a minimum of 8.6 dB near 1250 nm. The 8.6 dB PER is nonetheless sufficient for pulse amplification with a semiconductor optical amplifier (SOA), with only a slight increase in the rms jitter to 9.6 ps. The SOA imposes a positive chirp on the pulse due to the saturation of the SOA gain by the pulse leading edge,31 compressing the negatively chirped gain-switched pulses from 61 ps to a minimum of 49 ps [Fig. 3(b)]. Tuning the SOA current shifts the saturation power of the amplifier, varying the magnitude of the positive chirp and the level of amplification. A maximum peak power of 932 mW is obtained at a pulse width of 57 ps.

FIG. 3.

(a) (Top) Unamplified pulse (black trace) and the shortest amplified pulse (red trace). (Bottom) Diagram of the polarization bench to the SOA. The free-space components can be replaced by fiber polarization controllers for an all-fiber setup. LP – longpass filter, HWP – half-wave plate, QWP – quarter-wave plate, PBS – polarizing beam splitter. (b) Pulse width and amplified VCSEL peak power vs SOA current. (c) 9.6 ps rms jitter at 1250 nm after amplification with the SOA, with the jitter of the half-maxima crossings shown in the inset.

FIG. 3.

(a) (Top) Unamplified pulse (black trace) and the shortest amplified pulse (red trace). (Bottom) Diagram of the polarization bench to the SOA. The free-space components can be replaced by fiber polarization controllers for an all-fiber setup. LP – longpass filter, HWP – half-wave plate, QWP – quarter-wave plate, PBS – polarizing beam splitter. (b) Pulse width and amplified VCSEL peak power vs SOA current. (c) 9.6 ps rms jitter at 1250 nm after amplification with the SOA, with the jitter of the half-maxima crossings shown in the inset.

Close modal

To take advantage of the low threshold pump power requirements, two MEMS-VCSELs are synchronized by splitting a total pump average power of 2.8 mW between the two devices. In the context of TPEF or FLIM, the added flexibility of two or more independently tunable sources allows efficient, simultaneous excitation and single-scan image acquisition of fluorophores with detuned absorption peaks, reducing image acquisition time and eliminating sample-drift misalignment between sequential images. Furthermore, two MEMS-VCSELs with offset center wavelengths could be used to extend the spectral coverage. A schematic of the setup is shown in Fig. 4(a) for two 1310 nm MEMS-VCSELs. Sampling oscilloscope traces and the spectrum of the synchronized pulses are shown in Figs. 4(b) and 4(c), respectively, as the wavelength of one VCSEL is tuned relative to the other. At a fixed pump power, the delay between the two pulses shifts with wavelength due to the wavelength-dependent shift in the threshold. This can be compensated by adjusting the relative pump power between devices.

FIG. 4.

(a) Setup for synchronous pumping of two VCSELs. (b) Synchronized pulses and (c) spectrum of two synchronized devices as one device is tuned relative to the other. Each wavelength is labeled with a different color.

FIG. 4.

(a) Setup for synchronous pumping of two VCSELs. (b) Synchronized pulses and (c) spectrum of two synchronized devices as one device is tuned relative to the other. Each wavelength is labeled with a different color.

Close modal

In conclusion, optical gain-switching of MEMS-VCSELs is demonstrated to generate a minimum pulse width of 61 ps with an 84 ps pump laser. Pulses maintain sub-100 ps pulse widths over 48 nm of wavelength tuning and a PER exceeding 8 dB, allowing amplification to 932 mW peak power with a SOA. While a mode-locked fiber laser is used in this demonstration, the low pump power requirements (average power <1 mW) allow the fiber laser to be replaced with a gain-switched diode laser and SOA for compact, on-demand, tunable picosecond pulse generation. For high power applications, optically gain-switched MEMS-VCSELs can serve as flexible, tunable seeds for fiber amplifiers, enabling variable repetition rates and single-shot pulses. This eliminates the need for pulse-pickers to reduce repetition rate, a scheme commonly used in TPEF systems to avoid sample damage. In addition, the ease of synchronizing multiple MEMS-VCSELs makes these seed sources promising for multimodal microscopy, facilitating simultaneous excitation of multiple fluorophores or coherent Raman spectral acquisition. The demonstrated tuning range is competitive with commercial mode-locked fiber lasers and offers higher polarization purity than most commercial fiber-based supercontinuum sources. While the large linewidth enhancement factor in semiconductor lasers chirps pulses well above the transform limit, previous studies have compressed fixed-wavelength, gain-switched VCSEL pulses to the transform-limit by propagating through a length of normally dispersive fiber.32 However, pulse compression across the full MEMS-VCSEL wavelength range requires tunable or broadband dispersion compensation methods. Alternatively, shorter pulses can be pursued by using a shorter pulsed pump laser and optimizing the cavity design for a lower photon lifetime. Future work needs to be performed to extend the tuning range to the full CW tuning range and to evaluate the long-term stability under gain-switched operation. In addition, further investigations into the mechanism behind the wavelength dependence of the pulse width could provide valuable insight into the design for shorter pulses. Potential for substantial improvements in pulse width, tuning range, and peak power exists through appropriate device optimization.

The authors are grateful for the funding from the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its Campus for Research Excellence and Technological Enterprise (CREATE) program. The Disruptive and Sustainable Technologies for Agricultural Precision (DiSTAP) is an interdisciplinary research group (IRG) of the Singapore MIT Alliance for Research and Technology (SMART) center.

The authors have no conflicts to disclose.

Elise Uyehara: Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Rajeev J. Ram: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Christopher Burgner: Resources (equal). Vijay Jayaraman: Resources (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
C. W.
Freudiger
et al, “
Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy
,”
Science
322
,
1857
1861
(
2008
).
2.
C. W.
Freudiger
et al, “
Stimulated Raman scattering microscopy with a robust fibre laser source
,”
Nat. Photonics
8
,
153
159
(
2014
).
3.
T.
Steinle
et al, “
Synchronization-free all-solid-state laser system for stimulated Raman scattering microscopy
,”
Light: Sci. Appl.
5
,
e16149
(
2016
).
4.
R. K. P.
Benninger
and
D. W.
Piston
, “
Two-photon excitation microscopy for the study of living cells and tissues
,”
Curr. Protoc. Cell Biol.
59
,
4.11.1
(
2013
).
5.
J.
Ryu
et al, “
In vivo monitoring of intracellular chloroplast movements in intact leaves of C4 plants using two-photon microscopy
,”
Microsc. Res. Tech.
77
,
806
813
(
2014
).
6.
S. G.
Stanciu
et al, “
Experimenting liver fibrosis diagnostic by two photon excitation microscopy and bag-of-features image classification
,”
Sci. Rep.
4
,
4636
(
2014
).
7.
R.
Datta
,
T. M.
Heaster
,
J. T.
Sharick
,
A. A.
Gillette
, and
M. C.
Skala
, “
Fluorescence lifetime imaging microscopy: Fundamentals and advances in instrumentation, analysis, and applications
,”
J. Biomed. Opt.
25
,
071203
(
2020
).
8.
X. S.
Yao
,
X.
Liu
, and
P.
Hao
, “
Scan-less 3D optical sensing/Lidar scheme enabled by wavelength division demultiplexing and position-to-angle conversion of a lens
,”
Opt. Express
28
,
35884
(
2020
).
9.
A.
Zach
,
M.
Mohseni
,
C.
Polzer
,
J. W.
Nicholson
, and
T.
Hellerer
, “
All-fiber widely tunable ultrafast laser source for multimodal imaging in nonlinear microscopy
,”
Opt. Lett.
44
,
5218
(
2019
).
10.
S.
Karpf
et al, “
Two-photon microscopy using fiber-based nanosecond excitation
,”
Biomed. Opt. Express
7
,
2432
(
2016
).
11.
O. G.
Okhotnikov
,
L.
Gomes
,
N.
Xiang
,
T.
Jouhti
, and
A. B.
Grudinin
, “
Mode-locked ytterbium fiber laser tunable in the 980–1070-nm spectral range
,”
Opt. Lett.
28
,
1522
(
2003
).
12.
S.
Chen
et al, “
All-fiber short-wavelength tunable mode-locked fiber laser using normal dispersion thulium-doped fiber
,”
Opt. Express
28
,
17570
(
2020
).
13.
Z.
Xu
,
Z.-Y.
Dou
,
J.
Hou
, and
X.-J.
Xu
, “
All-fiber wavelength-tunable Tm-doped fiber laser mode locked by SESAM with 120 nm tuning range
,”
Appl. Opt.
56
,
5978
(
2017
).
14.
B.
Nyushkov
,
S.
Kobtsev
,
A.
Antropov
,
D.
Kolker
, and
V.
Pivtsov
, “
Femtosecond 78-nm tunable Er:fibre laser based on drop-shaped resonator topology
,”
J. Lightwave Technol.
37
,
1359
1363
(
2019
).
15.
J. M.
Dudley
,
G.
Genty
, and
S.
Coen
, “
Supercontinuum generation in photonic crystal fiber
,”
Rev. Mod. Phys.
78
,
1135
1184
(
2006
).
16.
C.
Poudel
and
C. F.
Kaminski
, “
Supercontinuum radiation in fluorescence microscopy and biomedical imaging applications
,”
J. Opt. Soc. Am. B
36
,
A139
(
2019
).
17.
A. M.
Clarke
,
P. M.
Anandarajah
, and
L. P.
Barry
, “
Generation of widely tunable picosecond pulses with large SMSR by externally injecting a gain-switched dual laser source
,”
IEEE Photonics Technol. Lett.
16
,
2344
2346
(
2004
).
18.
V.
Jayaraman
,
G. D.
Cole
,
M.
Robertson
,
A.
Uddin
, and
A.
Cable
, “
High-sweep-rate 1310 nm MEMS-VCSEL with 150 nm continuous tuning range
,”
Electron. Lett.
48
,
867
(
2012
).
19.
C.
Burgner
et al, “
Reliable widely tunable electrically pumped 1050 nm MEMS-VCSELs with amplifier in single butterfly co-package
,”
Proc. SPIE
11228
,
1122809
(
2020
).
20.
B.
Kogel
et al, “
Integrated MEMS-tunable VCSELs using a self-aligned reflow process
,”
IEEE J. Quantum Electron.
48
,
144
152
(
2012
).
21.
S.
Paul
et al, “
10-Gb/s direct modulation of widely tunable 1550-nm MEMS VCSEL
,”
IEEE J. Sel. Top. Quantum Electron.
21
,
1700908
(
2015
).
22.
J. R.
Karin
et al, “
Generation of picosecond pulses with a gain-switched GaAs surface-emitting laser
,”
Appl. Phys. Lett.
57
,
963
965
(
1990
).
23.
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
,
1417
1425
(
1991
).
24.
S.
Chen
et al, “
Spectral dynamics of picosecond gain-switched pulses from nitride-based vertical-cavity surface-emitting lasers
,”
Sci. Rep.
4
,
4325
(
2014
).
25.
T.
Ito
et al, “
Femtosecond pulse generation beyond photon lifetime limit in gain-switched semiconductor lasers
,”
Commun. Phys.
1
,
42
(
2018
).
26.
K. Y.
Lau
, “
Gain switching of semiconductor injection lasers
,”
Appl. Phys. Lett.
52
,
257
259
(
1988
).
27.
Y.
Yokoyama
et al, “
1064-nm DFB laser diode modules applicable to seeder for pulse-on-demand fiber laser systems
,”
Opt. Fiber Technol.
20
,
714
724
(
2014
).
28.
M.
Poelker
, “
High power gain-switched diode laser master oscillator and amplifier
,”
Appl. Phys. Lett.
67
,
2762
2764
(
1995
).
29.
L. A.
Coldren
,
S. W.
Corzine
, and
M. L.
Mašanović
,
Diode Lasers and Photonic Integrated Circuits
(
Wiley
,
Hoboken, NJ
,
2012
).
30.
T.
Yamanaka
,
Y.
Yoshikuni
,
K.
Yokoyama
,
W.
Lui
, and
S.
Seki
, “
Theoretical study on enhanced differential gain and extremely reduced linewidth enhancement factor in quantum-well lasers
,”
IEEE J. Quantum Electron.
29
,
1609
1616
(
1993
).
31.
G. P.
Agrawal
, “
Effect of gain dispersion on ultrashort pulse amplification in semiconductor laser amplifiers
,”
IEEE J. Quantum Electron.
27
,
1843
1849
(
1991
).
32.
M.
Nakazawa
,
H.
Hasegawa
, and
Y.
Oikawa
, “
10-GHz 8.7-ps pulse generation from a single-mode gain-switched AlGaAs VCSEL at 850 nm
,”
IEEE Photonics Technol. Lett.
19
,
1251
1253
(
2007
).