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This PDF file contains the front matter associated with SPIE Proceedings Volume 7919, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.
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1300-nm, 1550-nm and 1480-nm wavelength, optically-pumped VECSELs based on wafer-fused InAlGaAs/InPAlGaAs/
GaAs gain mirrors with intra-cavity diamond heat-spreaders demonstrate very low thermal impedance of 4
K/W. Maximum CW output of devices with5 groups of quantum wells show CW output power of 2.7 W from 180μm
apertures in both 1300-nm and 1550-nm bands. Devices with 3 groups of quantum wells emitting at 1480 nm and with
the same aperture size show CW output of 4.8 W. These devices emit a high quality beam with M² beam parameter
below 1.6 allowing reaching a coupling efficiency into a single mode fiber as high as 70 %. Maximum value of output
power of 6.6 W was reached for 1300nm wavelength devices with 290μm aperture size.
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We compare an InAs quantum dot (QD) vertical external-cavity surface-emitting laser (VECSEL) design consisting of 4
groups of 3 closely spaced QD layers with a resonant periodic gain (RPG) structure, where each of the 12 QD layers is
placed at a separate field antinode. This increased the spacing between the QDs, reducing strain and greatly improving
device performance. For thermal management, the GaAs substrate was thinned and indium bonded to CVD diamond. A
fiber-coupled 808 nm diode laser was used as pump source, a 1% transmission output coupler completed the cavity. CW
output powers over 4.5 W at 1250 nm were achieved.
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We report a study investigating the power scaling properties of a single gain chip GaInNAs/GaAs semiconductor disk
laser emitting around 1180 nm. The power scaling was done by varying the pump spot diameter between 320 μm and
460 μm. The emission efficiency was assessed for output coupling ratios between 0.1% and 3%. A maximum output
power of 11 W was achieved with a 1.5 % output coupling ratio and a pump spot diameter of 390 μm. The heat from the
active region was extracted by an intracavity diamond heat spreader attached to a water-cooled copper mount.
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Vertical external cavity surface emitting lasers (VECSELs) provide a laser design platform in order to explore
a variety of systems, and their flexibility eases this exploration. Moreover, their high-brightness operation
makes them attractive for many applications. In considering the methods of coupling VECSELs as well as
their potential uses, we begin by reporting on the development of a gain coupled VECSEL for use in optical
switching. In particular, two VECSEL cavities share a common gain region; the competition for a common set
of carriers dictate how these cavities interact. The easiest manifestation to realize gain coupling is to utilize
a linear cavity as well as a v-cavity, built around a single half-vertical cavity surface-emitting laser (VCSEL)
chip. The cavity gain/loss of each cavity can be controlled independently through use of birefringent filters,
allowing us to explore the design space, which can be divided up into coarse behavior, easy to analyze through
comparing the two uncoupled lasers, and a fine behavior, where one cavity will affect the other and each cavity
can lase simultaneously, sometimes at dramatically different wavelengths. These two regions may be explained
with simple rate equations, and it will be shown that if prepared properly, spontaneous emission plays a large
role in balancing the two laser cavities within the fine regime, while may be completely neglected in the coarse
regime.
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Vertical external cavity surface emitting lasers (VECSELs) are attractive for many applications due to their high-power,
high-brightness outputs. In order to power scale the devices, the pump spot size should be increased. However, the large
pump area greatly amplifies the guided spontaneous emission in the epitaxial plane. In order to efficiently power scale
the devices, amplified spontaneous emission (ASE) and lateral lasing must be reduced. We begin by first reporting on
the temperature dependence of the phenomena. Particularly, since the quantum well gain and bandgap are functions of
temperature, ASE and lateral lasing are greatly dependent on the operating temperature as well as the pump power. The
easiest method of quantifying the affect of ASE and lateral lasing is by removing the Fabry-Perot cavity formed by the
chip edges. We have chosen two different methods: Reducing the Fresnel reflections by patterning the edges of the
sample, and depositing a layer of Ge on the edges of the VECSEL chip as the high index of refraction for Ge should
reduce the Fresnel reflections and the absorption properties in the NIR regime should also act to prevent feedback into
the pump area. Our research shows both of these methods have increased the performance and visibly decreased the
amount of lateral lasing seen in the devices.
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The design and experimental testing of an Optical Parametric Oscillator generating 2 Watts of continuous wave radiation
at 3.5 micron is presented.
The oscillator uses a KTA (Potassium Titanyl Arsenate) crystal as the nonlinear medium, pumped by the 1.06 mm
intracavity radiation of an Optically Pumped Semiconductor Laser (OPSL).
A review of the nonlinear characteristics of KTA is presented, and design criteria for the OPSL intra-cavity pumped
OPO are given.
The experimental results are presented and discussed.
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We present a non-resonantly pumped red-emitting vertical external cavity surface-emitting laser system based
on a multi-quantum-well structure with 20 compressively-strained GaInP quantum wells for an operation wavelength
between 645-675 nm. Five quantum well packages with four quantum wells are placed in a separate
confinement heterostructure in a resonant periodic gain design in quaternary AlGaInP barriers and cladding layers,
respectively. The 3 λ cavity is fabricated on a 55 λ/4 pairs Al0.50Ga0.50As/AlAs distributed Bragg reflector.
By bonding an intra-cavity diamond heatspreader to the chip, continuous-wave operation exceeding 700mW
output power at a wavelength of 662 nm with a low threshold power of 0.8W was achieved. A thermal resistance
value of R1 = 5K/W and R2 = 7K/W could be determined for our setup at operation heatsink temperatures
of Ths = -28°C and Ths = 16°C, respectively. Measurements of the slope efficiency within a v-type cavity with
different outcoupling mirror reflectivities lead to a cavity round-trip transmission factor of Tloss = 98.6% and an
absorption efficiency of ηabs = 17.6%. Using a birefringent filter in a folded cavity, a maximum tuning range
of 22 nm at a center wavelength of 667 nm could be shown. With this method wavelengths below 650 nm were
observed. Utilizing a non-linear crystal for intra-cavity frequency doubling in this cavity geometry, coherent
emission down to 322 nm could be detected. In the UV spectral range, a maximum tuning range of 10 nm could
be measured at a center wavelength of 330 nm, so we could match the HeCd laser line at 325 nm.
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Second harmonic generation (SHG) from near infrared (IR) diode lasers is an attractive solution for blue-light sources with high peak power and narrow linewidth. IR sources based on broad stripe devices with narrow linewidth makes it possible to achieve a wide range of wavelengths throughout the blue region. This paper summarizes recent results utilizing a configuration of external dual grating reflector coupled surface emitting laser array for blue light generation.
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Laser projectors integrated in portable devices offer a new platform for media display but put strong demands on the
laser sources in terms of efficiency, modulation band width, operating temperature range and device cost. Osram Opto
Semiconductors has developed and produces synthetic green lasers for projection applications on which the latest results
are reported. Based on vertical external cavity surface emitting laser (VECSEL) technology and second harmonic
generation an output power of >75mW has been achieved. The maximum output power is to a large extent limited by the
high thermal resistance of the monolithic VECSEL chip used. To overcome the thermal limitations a new thinfilm
VECSEL chip design is proposed where the epitaxial layers are transferred to a silicon carrier and processed on wafer
level, thus significantly lowering the thermal resistance and improving the maximum output power.
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Power Scaling VECSELs: Growth, Fabrication, and Electrical Pumping
VECSELs modelocked with SESAMs are promising lasers for numerous applications. The MIXSEL concept integrates
both laser gain and saturable absorber regions in one epitaxially grown semiconductor structure. This enables a
particularly simple cavity design: only an external output coupler is needed. In the current MIXSEL realizations, the full
structure is grown in one single growth run. This rises a number of epitaxial growth challenges, which we discuss in this
paper.
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We demonstrate a novel epitaxial process for the growth of low-dislocation density GaSb on GaAs. The
growth mode involves the formation of large arrays of periodic 90° misfit dislocations at the interface
between the two binary alloys which results in a completely strain relieved III-Sb epi-layer without the
need for thick buffer layers. This epitaxial process is used for the growth of antimonide active regions
directly on GaAs/AlGaAs distributed Bragg Reflectors (DBRs) resulting in 2 μm VECSELs on GaAs
substrates.
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Vertical external cavity surface emitting lasers (VECSELs) are excellent high power semiconductor lasers with
diffraction-limited circular output beam and outstanding modelocking performance even at tens of GHz repetition rate.
The output power can be scaled up by simply increasing the mode area on the gain region. It makes them very attractive
for numerous applications such as RGB displays, biomedical imaging or optical clocking of multi-core processors.
Passively modelocked optically-pumped VECSELs, using a semiconductor saturable absorber mirror (SESAM), have
generated shorter pulses and higher average powers than any other modelocked semiconductor laser (135-fs pulses at 35-
mW average power and 2.1-W in 4.7-ps pulses).
Electrical pumping (EP) of modelocked VECSELs is the obvious next step towards compact high-power ultrafast laser
sources. In 2003, Novalux Corporation reported a continuous wave (cw) output power of nearly one Watt from their
proprietary EP-VECSEL (NECSEL). The modelocking of a NECSEL has been demonstrated with 40 mW of average
power in 57-ps pulses. Since then, very few EP-VECSEL results have been reported. Recently, we started to develop EPVECSELs
designed for modelocking, which require an optimized balance between electrical resistance, optical losses,
dispersion and beam quality. We discuss our design approach and present initial EP-VECSEL devices generating
>100-mW cw power. Homogeneous current injection is achieved even for large devices, showing very good agreement
with our numerical simulations. Sufficient power in a diffraction-limited beam and a carefully designed SESAM are
required to modelock an EP-VECSEL.
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Fundamental mode operation along with high output power is a major challenge for an electrically pumped VECSEL
(EP-VECSEL) suitable for passive modelocking. We present an experimental study on the influence of the intermediate
DBR reflectivity on the beam quality and the output power of EP-VECSELs. For designs with reflectivities of 90%, 82%
and 71% the highest possible power for the best achievable beam quality was 15.1 mW (M2 = 1.1, 82% device). We can
demonstrate that a correctly chosen intermediate DBR reflectivity is necessary for both good beam quality and high
power, and that a trade-off in power has to be accepted.
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We report on demonstration of non-diffracting (Bessel) beams from Electrically Pumped Vertical External Cavity
Surface Emitting Lasers (EP-VECSELs), with output powers ranging up to hundreds of milliwatts and central lobe
diameters of 10-100 μm with propagation lengths up to few tens of centimeters. To our knowledge, this is the best result
for Bessel beams generated from semiconductor light sources and is comparable to that achievable from vibronic lasers.
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The design of electrically pumped vertical external cavity surface emitting lasers (EP-VECSELs) for high power
applications require a number of optimisations in design trade-offs, mainly that of doping for improved electrical
performance and optical loss. Devices with diameter greater than 70μm and current spreading layer thickness of 100μm
suffer from non-uniform carrier injection into the active region, below this diameter output power scales linearly with
device area. We show CW powers of 133mW from a 150μm device with 4x1017cm-3 substrate doping at 0°C can be
obtained.
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The future evolution of photonics, for a wide spectrum of applications ranging from
established optical telecommunications to emerging opportunities such as biotechnology,
reprographics and projection displays, will depend on availability of compact, rugged,
efficient and inexpensive lasers which deliver high power, good beam quality, excellent
wavelength stability, low noise and long lifetime in the near infrared and visible regions.
This combination is not readily available from either of the traditional classes of
semiconductor laser, edge-emitters and vertical cavity surface emitters (VCSELs). Here
we describe a novel class of laser based on geometry similar to VCSELs but controlled
by an extended coupled cavity. These devices are scalable to high powers while
maintaining fundamental spatial mode performance, a feature that is essential to efficient
coupling into a single mode optical fibre or waveguide, or long range propagation in free
space. They are also ideally suited to mode locking, gain-switching and intracavity
frequency conversion, among other applications.
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An approach based on fully microscopically computed material properties like gain/absorption, radiative
and Auger recombination rates are used to design, analyze and develop optimization strategies for Vertical
External Cavity Surface Emitting Lasers for the IR and mid-IR with high quantitative accuracy. The microscopic
theory is used to determine active regions that are optimized to have minimal carrier losses and
associated heating while maintaining high optical gain. It is shown that in particular for devices in the
mid-IR wavelength range the maximum output power can be improved by more than 100% by making rather
minor changes to the quantum well design. Combining the sophisticated microscopic models with simple onedimensional
macroscopic models for optical modes, heat and carrier diffusion, it is shown how the external
efficiency can be strongly improved using surface coatings that reduce the pump reflection while retaining the
gain enhancing cavity effects at the lasing wavelength. It is shown how incomplete pump absorption can be
reduced using optimized metallization layers. This increases the efficiency, reduces heating and strongly improves
the maximum power. Applying these concepts to VECSELs operating at 1010nm has already resulted
in more than twice as high external efficiencies and maximum powers. The theory indicates that significant
further improvements are possible - especially for VECSELs in the mid-IR.
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A microscopically consistent scheme for the nonequilibrium modelling of VECSELs is outlined. The theory
is based on the coupled Maxwell-semiconductor-Bloch equations describing the high-intensity light field in the
cavity coupled to the quantum-well gain material. Application examples are presented discussing quasi-stationary
two-color operation under high intracavity power conditions. It is demonstrated that kinetic hole-burning, i.e.
strong nonequilibrium deformations of the laser's carrier distributions, are responsible for the quasi-stationary
dual-mode emission.
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Vertical External Cavity Surface Emitting Lasers (VECSELs) feature scaling to large active areas and combine
surface emission with high optical power output. In principle, they can be designed with electrical pumping
operating in continuous wave or passively mode-locked operation. In this paper, our design and modeling
activities towards a high power passively mode-locked VECSEL are described. In particular, design towards
single mode high-power CW operation is discussed as prerequisite for passive mode-locking.
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The combination of high output power and femtosecond pulses from VECSELs and MIXSELs would be very attractive
for many applications. To explore the limitations, a quantitative understanding of the pulse formation processes is
required. Our numerical simulations showed a good qualitative agreement with experimental results in the picosecond
regime. By minimizing intracavity group delay dispersion (GDD) and improving gain bandwidth and SESAM
parameters, our model predicts pulses as short as 250 fs. As a first step we minimized GDD with a top coating which
provides values between ±10 fs2 over a range of 30 nm around the design wavelength.
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Quasi-soliton modelocking has been identified as the mechanism responsible for the formation of picosecond pulses
in passively mode-locked VECSELs, but neither this mechanism nor Kerr lens modelocking can account for the
formation of sub-picosecond pulses from these lasers. Numerical simulations have shown that the optical Stark effect
is capable of shortening pulses in the absence of bleaching, but to date no studies have been performed under
realistic operating conditions.
We model the interaction of an optical pulse with an absorbing quantum well using a semi-classical two
level atom approximation. As the bandwidth of a VECSEL pulse is small compared to the spread of energies within
a semiconductor band the population of two level atoms is divided into "live" atoms which interact with the optical
field, and "dead" atoms which do not. Live and dead states are coupled by carrier-carrier scattering.
Results from this model show an increase in pulse shortening above that due to saturable absorber bleaching
at pulse durations below one picosecond, implying that an additional effect is responsible for the formation of
femtosecond pulses. At these pulse durations the model predicts that the absorbing resonance broadens and decreases
in amplitude. This is recognisable as a result of the optical Stark effect.
The predictions of this model are compared to experimental results from several femtosecond VECSELs.
For some modelocked VECSELs an excellent match between simulation and experiment is found, but in other cases
the model cannot reproduce experimental results. We conclude that while the optical Stark effect may be the
dominant pulse shaping mechanism in some modelocked VECSELs, others appear to be dominated by other effects.
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Semiconductor lasers have the potential to drastically reduce complexity and cost of high power ultrafast lasers.
Optically-pumped VECSELs achieved >20 W cw-power in fundamental transverse mode. Passive modelocking with a
SESAM enabled 2.1-W average power, sub-100 fs duration, and 50-GHz repetition rate. In 2007, the integration of both
elements was demonstrated, the MIXSEL (modelocked integrated external-cavity surface-emitting laser). Here we
present a novel MIXSEL design based on a low-saturation fluence quantum dot (QD) absorber layer in an antiresonant
structure. Improved thermal management with a CVD-diamond enabled a >30-fold power increase to 6.4 W, higher than
any other ultrafast semiconductor laser.
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We present an overview of the quantum design, growth and lasing operation of both IR and mid-IR OPSL
structures aimed at extracting multi-Watt powers CW and multi-kW peak power pulsed. Issues related to
power scaling are identified and discussed. The IR OPSLs based on InGaAs QW bottom emitters targeted at
wavelengths between 1015nm and 1040nm are operated in CW mode (yielding a maximum power of 64W)
and pulsed (peak power of 245W). The mid-IR top emitter OPSLs designed to lase at 2μm are based on a
novel lattice mismatched growth using InGaSb QWs and yield a maximum peak power of 350W pulsed.
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Novel materials, notably quantum-dot (QD) semiconductor structures offer the unique possibility of combining
exploitable spectral broadening of both gain and absorption with ultrafast carrier dynamic properties. Thanks to these
characteristics QD-based devices have enhanced the properties of ultrashort pulse lasers and opened up new possibilities
in ultrafast science and technology. In this paper we review the recent progress on the development of novel quantumdot
SESAM structures for different lasers. We also demonstrate that QD structures can be designed to provide compact
and efficient ultrashort pulse laser sources with high and low repetition rates.
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Optically-pumped semiconductor disk lasers (SDLs) represent a proven approach for generation of multi-watt output
powers with excellent beam quality [1-6]. They combine many advantages of solid-state lasers with the added benefit of
wavelength tailoring provided by the semiconductor gain material. During the past few years a wafer fusion technique
has been used extensively in the producing of vertical-cavity surface-emitting lasers operating at the telecom
wavelengths of 1.3 - 1.55 μm. This technique allows the integration of non-lattice-matched semiconductor materials, e.g.
GaAs and InP, which cannot be grown monolithically. Here we describe the first wafer fused SDLs operating at the
wavelength of 1.3 and 1.57 μm in both continuous-wave and mode-locked regimes.
The quantum dot semiconductors provide an interesting alternative to quantum-well (QW) structures since these
materials alleviate the requirement for lattice matching. Recently, we have demonstrated first quantum dot based gain
medium in SDL architecture. Since then, different wavelengths have been demonstrated both in continuous-wave and
mode-locked regimes with a performance comparable to quantum-well-based lasers. The (AlGaIn)(AsSb) material
system establishes a steady platform for optoelectronic devices operating in the mid-infrared spectral range. Latticematched
or strain-compensated structures employing InGaAsSb as an active material and AlGaAsSb for barrier and
cladding layers grown on GaSb substrates are demonstrated to be compounds of choice for long-wavelength lasers and
photodetectors. In this study we report an optically-pumped semiconductor disk laser emitting radiation around 2.5 μm
tunable over 130 nm. To our knowledge, this is the widest spectral range reported to date at this wavelength.
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We present timing jitter measurements of a free-running SESAM modelocked VECSEL generating 8-ps pulses with
1.88-GHz repetition rate and 80-mW average output power. We observed very good performance comparable with iondoped
solid-state-lasers which typically show excellent stability. We measured the two-sided noise power spectral
density at the 10th harmonic of the laser output with the von der Linde method. The rms timing jitter integrated over an
offset frequency range from 100 Hz to 100 kHz gives a free-running timing jitter of ≈400 fs which is an upper limit
because the measurement was already system noise limited above 10 kHz.
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Using quantum well gain materials, ultrafast VECSELs have achieved higher output powers (2.1 W) and shorter pulses (60 fs) than any other semiconductor laser. Quantum dot (QD) gain materials offer a larger inhomogeneously broadened bandwidth, potentially supporting shorter pulse durations. We demonstrate the first femtosecond QD-based VECSEL using a QD-SESAM for modelocking, obtaining 63 mW at 3.2 GHz in 780-fs pulses at 960 nm. In continuous wave operation we obtained 5.2 W using an intra-cavity diamond heat spreader, which has been the highest output power from a QD-VECSEL so far. Further power scaling is thus expected also for modelocked operation.
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Diode-pumped solid state lasers, long dominant in many high power applications, now face a challenge from opticallypumped
semiconductor lasers, which add spectral versatility to the good beam quality and potential for power-scaling that
are characteristic of optically-pumped disc lasers. The vertical-external-cavity surface-emitting semiconductor laser, or
VECSEL, readily exhibits passive mode-locking with the inclusion of a semiconductor saturable absorber mirror (SESAM)
in the external cavity. These devices most often emit picosecond pulses, recruiting only a small fraction of the available
gain bandwidth of the quantum wells. If the dispersive and filtering effects of the multilayer gain and saturable absorber
structures are well-controlled, however, it is possible to observe clean sub-picosecond pulses of duration down to 100fs and
below. The presentation will describe SESAM-mode-locked VECSELs based on compressively strained InGaAs/GaAs
quantum wells that generate trains of near-transform-limited femtosecond pulses at wavelengths around 1 μm with average
power of 30 - 300 mW. The nonlinear optical response of the quantum well SESAM in this regime is investigated using a
numerical model in which the resonantly excited carriers are coupled by scattering to states outside the laser bandwidth.
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Adrian H. Quarterman, Keith G. Wilcox, Alex Perevedentsev, Vasilis Apostolopoulos, Zakaria Mihoubi, Aaron L. Chung, Harvey E. Beere, Ian Farrer, David A. Ritchie, et al.
High repetition rate passively mode-locked sources are of significant interest due to their potential for
applications including optical clocking, optical sampling, communications and others. Due to their
short excited state lifetimes mode-locked VECSELs are ideally suited to high repetition rate operation,
however fundamentally mode-locked quantum well-based VECSELs have not achieved repetition rates
above 10 GHz due to the limitations placed on the cavity geometry by the requirement that the
saturable absorber saturates more quickly than the gain. This issue has been overcome by the use of
quantum dot-based saturable absorbers with lower saturation fluences leading to repetition rates up to
50 GHz, but sub-picosecond pulses have not been achieved at these repetition rates.
We present a passively harmonically mode-locked VECSEL emitting pulses of 265 fs
duration at a repetition rate of 169 GHz with an output power of 20 mW. The laser is based around an
antiresonant 6 quantum well gain sample and is mode-locked using a semiconductor saturable absorber
mirror. Harmonic modelocking is achieved by using an intracavity sapphire etalon. The sapphire then
acts as a coupled cavity, setting the repetition rate of the laser while still allowing a tight focus on the
saturable absorber. RF spectra of the laser output show no peaks at harmonics of the fundamental
repetition rate up to 26 GHz, indicating stable harmonic modelocking. Autocorrelations reveal groups
of pulses circulating in the cavity as a result of an increased tendency towards Q-switched modelocking
due to the low pulse energies.
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Keith G. Wilcox, Aaron Chung, Adrian H. Quarterman, Zakaria Mihoubi, Ian Farrer, Harvey E. Beere, David A. Ritchie, Vasilis Apostolopoulos, Anne C. Tropper
We report on a high peak power femtosecond modelocked VECSEL and its application as a drive laser for an all
semiconductor terahertz time domain spectrometer. The VECSEL produced near-transform-limited 335 fs sech2 pulses at
a fundamental repetition rate of 1 GHz, a centre wavelength of 999 nm and an average output power of 120 mW. We
report on the effect that this high peak power and short pulse duration has on our generated THz signal.
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OPS lasers have found applications in various industrial and scientific laser applications due to their power scaling
capability, their wide range of emission wavelengths, physical size and their superior reliability. This paper provides an
overview of commercially available OPS lasers and the applications in which they are used including biotechnology,
medical, holography, Titanium-Sapphire laser pumping, non-lethal defense, forensics, and entertainment.
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We demonstrate high power (multiwatt) low noise single frequency operation of tunable compact verical-external-
cavity surface-emitting-lasers exhibiting a low divergence high beam quality, of great interest for photonics
applications. The quantum-well based lasers are operating in CW at RT at 1μm and 2.3μm exploiting GaAs
and Sb technologies. For heat management purpose the VECSEL membranes were bonded on a SiC substrate.
Both high power diode pumping (using GaAs commercial diode) at large incidence angle and electrical pumping
are developed. The design and physical properties of the coherent wave are presented. We took advantage
of thermal lens-based stability to develop a short (0.5 < 5mm) external cavity without any intracavity filter.
We measured a low divergence circular TEM00 beam (M2 = 1.2) close to diffraction limit, with a linear light
polarization (> 30 dB). The side mode suppression ratio is > 45 dB. The free running laser linewidth is 37 kHz
limited by pump induced thermal fluctuations. Thanks to this high-Q external cavity approach, the frequency
noise is low and the dynamics is in the relaxation-oscillation-free regime, exhibiting low intensity noise (< 0.1%),
with a cutoff frequency > 41MHz above which the shot noise level is reached. The key parameters limiting the
laser power and coherence will be discussed. These design/properties can be extended to other wavelengths.
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