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Pulse interactions in a colliding pulse mode-locked vertical external cavity surface emitting laser

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Abstract

The passive mode locking of vertical external cavity surface emitting lasers (VECSELs) enables the generation of high brightness ultrashort pulses at high repetition rates with unmatched performance. The peak power achievable with sub-200-fs pulse duration is mostly limited by the stability of the fundamental mode-locking regime as side pulses or harmonic mode locking emerges at high pump power. Here, we study a colliding pulse mode-locked VECSEL generating a pulse duration as short as 128 fs, with an average power of 90 mW per beam and a repetition rate of 3.27 GHz. The relevant laser parameters under different pumping regimes before and after the emergence of a side pulse are then used as input parameters for the simulation of the pulse interactions in the saturable absorber. We present a new comprehensive model for the calculation of saturable losses in the saturable absorber mirror and we study the energy transfer between the two counter-propagating pulses. This study reveals how a colliding pulse scheme reduces the saturation fluence of the absorber by a factor 2.9 and suppresses the mode competition between the two counterpropagating pulses of the ring cavity.

© 2017 Optical Society of America

1. INTRODUCTION

The passive mode locking of a vertical external cavity surface emitting laser (VECSEL) incorporating an optically pumped semiconductor gain element and a semiconductor saturable absorber mirror (SESAM) has proven to be a reliable and attractive technique for the generation of ultrashort pulses with high brightness, at repetition rates ranging from 85 MHz to 100 GHz [1,2]. The external free space cavity of VECSELs provides a power scaling capability leading to a high brightness circular fundamental transverse mode beam approaching the diffraction limit [3,4]. Furthermore, the operating wavelength of a mode-locked VECSEL can be broadly adjusted by changing the material system of the gain and absorber medium. To date, the operating wavelengths reported with a mode-locked VECSEL range from 665 [5] to 1960 nm [6], while the best performance in terms of power and pulse duration has been demonstrated between 960 and 1080 nm [7,8], where the semiconductor media benefit from the maturity and advantages of GaAs-based materials. The shortest pulse duration was recently demonstrated near 1033 nm, with a 107 fs pulse compressed to 96 fs at a repetition rate of 1.63 GHz and with 100 mW of output power [7]. The output power with such short pulses is often limited by the stability of the mode-locking regime, as a higher excitation leads to harmonic mode locking when the repetition rate is sufficiently low, and/or to side pulses with >1GHz repetition rates. It has been recently shown that, in the high excitation regime, a pulse duration of the order of 100 fs will bleach out the non-equilibrium carrier distributions to promote independent carrier reservoirs, leading to the emergence of multiple pulse waveforms [9], ultimately leading to a trade-off between the pulse duration and the average power achievable.

Laser sources combining femtosecond pulses with high peak power can benefit many applications, such as multi-photon imaging [10], high-resolution time domain terahertz spectroscopy with asynchronous optical sampling [11], or self-referenced gigahertz frequency combs [12]. VECSELs operating in the multi-gigahertz (GHz) regime are particularly promising for frequency combs, as they would provide a high comb-tooth spacing and a high power per mode, whereas other lasers using dielectric gain media generally suffer from Q-switching instabilities at high repetition rate due to their long upper-state lifetimes [13,14].

We recently introduced a robust mode-locking technique where the gain chip and the SESAM are placed in a ring cavity to create colliding pulses in the absorber, reducing the effective losses of the absorber while providing a symmetric gain for the two counterpropagating pulses [15]. This new geometry extended the range of the mode-locking stability and provided higher output power when compared to a more standard V-shaped cavity, yielding pulse durations of 195 fs with an average power of 225 mW per output beam at a repetition rate of 2.2 GHz. Here, we present a significant reduction of the pulse duration, down to 128 fs with a repetition rate increased to 3.27 GHz, and we study both experimentally and theoretically the pulse interactions in the absorber. The better performance demonstrated here is the result of a significant design optimization of the gain structure, which we describe in detail. The model used to simulate the saturable losses is also fully detailed, and we show how the effective saturation fluence of the SESAM is reduced in a colliding pulse VECSEL. We then discuss the importance of the carrier lifetime in the SESAM to avoid the formation of side pulses, which ultimately limits the peak power. Finally, we show that interactions in the SESAM also balance the output power of the two counterpropagating beams. These results provide valuable insight for the future development of high-power sub-100-fs mode-locked VECSELs in the GHz regime.

2. VECSEL SETUP

The VECSEL and the SESAM are placed in a ring cavity according to the geometry shown in Fig. 1. In order to provide a symmetrical amplification of the two counterpropagating pulses, the gain medium is placed at a quarter of the total cavity length L=92mm from the saturable absorber, assuring an equal pumping duration and gain recovery for both pulses. The cavity is completed with a highly reflective concave mirror with a radius of curvature of 50 mm, and a flat output coupler with a reflectivity of 99.2%. This gives a mode waist (radius) of 127 μm on the VECSEL and 67 μm on the SESAM, and the angle of incidence on the SESAM and VECSEL was kept as small as possible, at about 7°.

 figure: Fig. 1.

Fig. 1. Schematic layout of the VECSEL setup (right) and design of the full VECSEL structure (left).

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A. Design of the VECSEL Structure

The VECSEL structure was designed for an emission wavelength of 990 nm. It consists of a hybrid metal–semiconductor distributed Bragg reflector (DBR), followed by the active region, an InGaP cap layer, and a bi-layer anti-reflection coating.

The hybrid DBR contains 12 pairs of AlAs/AlGaAs quarter-wave layers. The reflectivity is enhanced by a pure gold reflector following the procedure described in Ref. [16]. This hybrid DBR provides high reflectivity at both the lasing and the pump wavelength, circumventing the need for an additional DBR to recycle the pump like in the structure used in Ref [15]. It also requires fewer quarter-wave layers pairs (12 instead of 23) to reach the reflectivity needed, providing a lower thermal impedance and a broader spectral bandwidth [16].

The active region contains 13 strain-compensated InGaAs quantum wells (QWs), placed non-uniformly around the anti-nodes of the standing electric field intensity, as shown in Fig. 1, and is pumped in the GaAsP barriers with an 808 nm fiber-coupled pump diode. The non-uniform placement of the QWs provides a flat field intensity enhancement spectrum, giving a broader modal gain than the structure used in our previous work [15], and increases the gain saturation fluence.

The structure is completed with a bi-layer dielectric coating of Ta2O5/SiO2 optimized to provide a broadband and flat group delay dispersion (GDD). The achievable spectral bandwidth over which the GDD is flat and near zero is significantly wider with a bi-layer coating than with a single layer coating, and should thus support shorter pulses.

Finally, for optimal thermal management, the structure is grown as a bottom emitter and is bonded to diamond following the procedure described in Ref. [4]. The reflectivity enhancement and broader bandwidth provided by the gold reflector is clearly visible in Fig. 2(a).

 figure: Fig. 2.

Fig. 2. (a) Reflectivity spectra of the VECSEL structure with and without the gold reflector measured at room temperature (black and gray lines, respectively), together with the simulated spectra (dotted lines). (b) Measured group delay dispersion spectrum of the SESAM and VECSEL gain structure. The dotted line represents the sum of the VECSEL and SESAM GDD, and the vertical bars indicate the standard deviation over 20 measures.

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B. Design of the SESAM Structure

The SESAM consists of 24 quarter-wave layer pairs of AlAs/GaAs followed by a single InGaAs QW placed 5 nm from the surface to provide a high carrier recombination velocity via tunneling to surface states. The wavelength of the SESAM QW absorption peak was blueshifted by 10 nm from the lasing wavelength to provide minimal absorption at room temperature, facilitating alignment. The GDD of the gain structure and SESAM measured at room temperature and normal incidence is shown in Fig. 2(b).

3. MODE-LOCKING RESULTS

A. Single Pulse Regime

With a colliding pulse mode-locking scheme, a stable mode-locking regime can be obtained over a wide range of pump powers and temperatures, as demonstrated previously [15]. The independent tuning of the SESAM and VECSEL temperature offers great flexibility to finely adjust the amount of absorption, the position of the gain maximum, and the total GDD of the cavity. With the specific gain and SESAM chips used here, we obtained a minimum pulse duration of 128 fs when the gain element was kept at 25°C and the SESAM at 55°C, with an output power of 90 mW per output beam for a pump power of 22 W. The output beams were both s-polarized. This polarization state is favored by the beam interference in the SESAM, since the intensity of the interference fringes will be maximum for s-polarized beams. Indeed, the intensity modulation generated by the superposition of p-polarized beams is smaller than for s-polarized beams for any angle of incidence θ>0, and vanishes at θ=45° (orthogonal polarizations). Since a higher field intensity reduces the saturation fluence of the absorber, the s-polarization state is naturally selected by the nonlinear dynamics of the high finesse VECSEL cavity.

The non-collinear second-harmonic generation (SHG) autocorrelation trace of the output shows an excellent agreement with a 128 fs sech2 pulse shape (Fig. 3). An autocorrelation scan over 20 ps was also performed to confirm the absence of any side pulses.

 figure: Fig. 3.

Fig. 3. Measured non-collinear SHG autocorrelation of the single pulse operation output, and simulated autocorrelation of a sech2 pulse with a FWHM of 128 fs.

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The optical spectrum of the output beam is shown on Fig. 4, together with the simulated spectrum of an ideal 128 fs sech2 pulse. The spectrum is centered at 994 nm with a FWHM of 9.05 nm, about 1.12 times the bandwidth of an unchirped 128 fs pulse. The shape of the spectrum is relatively smooth and close to the ideal spectrum, without any spikes. The presence of spikes would suggest a CW contribution.

 figure: Fig. 4.

Fig. 4. Measured optical spectrum of the output beam consisting of a single 128 fs pulse per round trip, and simulated spectrum of an unchirped 128 fs sech2 pulse.

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The microwave spectrum of the output was also recorded using an ultra-fast photodiode (Newport model 1014) and a high bandwidth electrical spectrum analyzer (Agilent model 8564E). Figure 5 shows a scan from DC to 40 GHz with a resolution bandwidth (RBW) of 100 kHz, and a zoom into the first harmonic with a span of 2 MHz and a RBW of 1 kHz. The repetition rate of the pulse is 3.724 GHz, and the higher harmonics, up to the 12th, are clearly visible with a constant amplitude. The zoom into the first harmonic shows a resolution-limited linewidth with a signal-to-noise ratio of 68 dB. With this high dynamic range, a pulse train instability or strong timing jitter would typically result in side peaks or pedestal around the microwave beatnote, which is not observed here. These pulse characterizations confirm a clean and stable mode-locking regime.

 figure: Fig. 5.

Fig. 5. Microwave spectrum of the laser output, with a RBW of 100 kHz and a 40 GHz span (left), and with a RBW of 1 kHz and a span of 2 MHz (right).

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B. Side Pulse Regime

When the pump power is increased up to 35 W, we observed a stable mode-locking regime with an output power of 152 mW per output beam. However, the autocorrelation trace reveals a side pulse containing 36% of the total energy. Figure 6 shows perfect agreement between the measured autocorrelation and the simulated autocorrelation of a sech2 pulse with a FWHM of 130 fs followed by a second 130 fs pulse delayed by 430 fs and a relative intensity of 56%. The transition between the single pulse and side pulse regimes occurs very abruptly at a pump power of about 24 W.

 figure: Fig. 6.

Fig. 6. Measured non-collinear autocorrelation of the side pulse operation output, and simulation of the autocorrelation of a sech2 pulse with a FWHM of 130 fs followed by a 130 fs side pulse delayed by 430 fs with a relative intensity of 56%.

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The optical spectrum of this regime is shown on Fig. 7. The spectrum exhibits a strong intensity modulation, resulting from the interference of the main pulse with the side pulse. The simulated spectrum of a 130 fs sech2 pulse followed by a second 130 fs pulse delayed by 430 fs, both centered at 994 nm, is also shown for reference. We should note that the interference pattern depends strongly on the phase and wavelength difference between the two pulses.

 figure: Fig. 7.

Fig. 7. Measured optical spectrum of the side pulse operation output, and simulation of the transform limited spectrum of two successive sech2 130 fs pulse delayed by 430 fs.

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The peak power of 238 W reached by the main pulse in this regime is higher than the peak power of 189 W reached in the single pulse regime, which can be useful for applications based on nonlinear processes. However, for metrology applications [11,12], a clean single pulse regime is usually desired. It is thus important to fully understand the physical processes leading to the formation of side pulses in order to push the limitations restricting the output power in a single pulse regime.

The following sections will explore this further and are focused on the interactions of the colliding pulses in the absorber. This will allow us to calculate the optical losses seen by various pulses, using experimental values as input parameters. We then discuss the benefits and limitations of a colliding pulse scheme.

4. DYNAMICS OF THE CARRIER DENSITY DISTRIBUTION IN THE SATURABLE ABSORBER

To analyze the effect of colliding pulses in the absorber, it is necessary to evaluate the spatial distribution of the carrier density during the passage of the pulses. First, we need to determine the expression for the field distribution evolution, then we will propose an adequate absorption model to calculate the temporal evolution of the carrier density.

A. Field Intensity Distribution

For our study, we will represent the optical field in the slowly varying envelope approximation. We assume two counterpropagating beams with a sech2 pulse envelope having the same central wavelength λ and duration τfwhm=1.76τ, and a Gaussian TEM00 transverse distribution. They propagate at a small angle θ to the z axis in the x-z plane and intersect within the saturable absorber located in the x-y plane at z=0. We assume that both beams are linearly polarized along the y axis (s-polarization). They are focused at z=0 with the same beam waist w0. In the paraxial approximation, the “right-handed” field Er and the “left-handed” field El may be written as [17]

Er(x,y,z,t)=Er0q0qejπλ((xθz)2+y2q+2θxθ2z)sech(tτ),
El(x,y,z,t)=El0q0qejπλ((x+θz)2+y2q2θxθ2z)sech(ttdτ),
where Er0 and El0 are the field amplitudes, td is the time delay between the pulses, q0=jπw02λ, and q=q0+z. The field intensity resulting from the collision of the two beams is given by
I(x,y,z,t)=[El+Er]×[El¯+Er¯].

The field intensity distribution of two synchronized beams colliding with an angle of 7° is represented in Fig. 8.

 figure: Fig. 8.

Fig. 8. Field intensity distribution of two Gaussian beams colliding with an angle of 7° at z=0.

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In the case of a thin absorber like a SESAM, i.e., where the interaction length with the absorber is negligible compared to the Rayleigh length, we can assume qq0, and Eq. (3) can be simplified to

I(x,y,t)=e2x2+y2w02[Er02sech2(tτ)+El02sech2(ttdτ)+2Er0El0sech(ttdτ)sech(tτ)cos(πθxλ)].

It is clear that the interference fringes created by the collision of the two beams will be maximum when they are synchronized, giving a maximum intensity 4 times higher than the intensity of a beam alone. The absorption of such a field distribution in the absorber will create a carrier grating, which is analyzed in the following sections.

B. Saturable Absorption Model

A very common way to model the saturation effects of the absorber is to introduce an empiric parameter referred as the saturation fluence, which is defined as the pulse energy per unit area necessary to reduce the absorption by 1/e (37%) of its initial value. This factor is usually determined experimentally via nonlinear reflectivity measurements [18]. This macroscopic parameter can be sufficient to describe the dynamic behavior of the absorber in the case of a clean single pulse operation [19], but it is not adequate for the simulation of multiple pulses or for colliding pulses. In order to describe the interaction of the pulses in the absorber, we need to account for the carriers generated by the previous pulses, which might not have fully recombined and will certainly affect the absorption seen by the delayed or side pulses. For synchronized colliding pulses, one would have to evaluate the saturation fluence with the same field distribution as in the laser cavity to account for the interference effects, which would be extremely challenging to measure.

For our simulations, we evaluate the SESAM absorption α as a function of the carrier density N, instead of the pulse intensity I. First, the QW absorption spectra are computed using a microscopic approach based on the semiconductor Bloch equation, which is described in Ref. [20] and references therein. Figure 9(a) shows the computed linear absorption of an InGaAs QW at a temperature of 350 K for various carrier densities.

 figure: Fig. 9.

Fig. 9. (a) Microscopically calculated QW absorption spectra for various carrier density N. (b) Simulated absorption losses as a function of the carrier density N of the SESAM.

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To account for the field enhancement of the structure, the full reflectivity spectra of the SESAM are simulated using conventional transfer-matrix methods, giving a realistic absorption evaluation. It has been shown recently that, for a better recovery time and less pulse distortion, an excitation energy higher than the excitonic bandgap of the QW is preferable [21]. Therefore, we evaluated the absorption at 990, 4 nm below the excitonic peak, which is also representative of the detuning between the experimental operating wavelength and the SESAM excitonic peak when its temperature is 350 K. Figure 9(b) shows the simulated absorption at 990 nm as a function of the carrier density, which can be fitted accurately with the following exponential function:

α(N)=2.244×exp(N1.585×1012)0.3,
where N is expressed in cm2. This equation is valid for only the specific SESAM structure used here, as the type of QW or the distance between the DBR and the QW will change the field strength and absorption. However, the pulse interaction effects and the conclusions drawn in the following sections could be generalized for other types of absorbers with a scaling of the fluence.

We should note that, with a finite spectral bandwidth around 990 nm, the spectral component of the pulse that is closer to the excitonic peak will saturate the absorption with a lower carrier density than the spectral component away from the excitonic peak. This is due to the higher density of energy states that needs to be filled at higher photon energy. The evaluation of the absorption at the central wavelength will average these effects with good accuracy as long as the absorption dispersion can be linearly approximated. However, for pulses with a very wide spectrum (>10nm), or when the SESAM is operated near its bandgap edge, a spectral integration of the absorption will become necessary.

To assess the carrier recovery dynamics of the absorber, we measured the transient reflectivity change of the SESAM in a conventional pump and probe setup. The pump pulses are focused onto the sample with a fluence of about 25μJ/cm2 under a 5° incidence angle. The probe pulses are focused onto the same spot with a fluence below 100nJ/cm2 and under a small angle for spatial separation of the beams. Figure 10 shows a recovery dynamic that can be fitted with a slow and fast time constant as follows:

R(t)=R0+ΔR×(A·et/τslow+(1A)·et/τfast),
where R0=97.9% is the linear reflectivity, ΔR=1.04% is the reflectivity change at t=0, and A=0.085 is the amplitude of the slow component. The fast decay rate τfast=400fs is governed by intraband electron–electron and electron–phonon scatterings of the spectrally localized carrier distribution created by the pulse and subsequently through phonon emission [21]. The second relaxation process has a decay rate τslow=20ps, and is governed by the tunneling of carriers into surface states.

 figure: Fig. 10.

Fig. 10. Experimentally measured and simulated reflectivity change in the SESAM after excitation with a 80 fs pulse at 990 nm with a fluence of 25μJ/cm2.

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C. Carrier Density Dynamic

To compute the carrier density evolution, we have to solve the carrier rate equations, taking into account the field distribution and the absorption properties described previously. For this simulation, we will assume that the optical power remains constant, which is a reasonable assumption considering the low level of losses in the SESAM (<2%). We will also neglect the carrier diffusion, as transverse diffusion will remain negligible while the pulses are present, and diffusion will show a strong saturation behavior and is much suppressed for high local intensities [22], which is the case in this study. In this simplified analysis, the governing rate equations are

N(x,y,t)=Ngen(x,y,t)+ANslow(x,y,t)+(1A)Nfast(x,y,t),
Ngent=ηhν×α(N)×I(x,y,t),
Nslowt=Ngen(x,y,t)+Nslow(x,y,t)τslow,
Nfastt=Ngen(x,y,t)+Nfast(x,y,t)τfast,
where Ngen is the carrier density generated from the absorption of the pulses, hν is the photon energy, and η is the photon conversion efficiency. Nslow and Nfast represent, respectively, the carriers relaxing with a slow and fast time constant. Here, we ignore ambipolar diffusion effects due to the local high intensities [22], and we will assume that every photon absorbed excites a carrier, i.e., η=1. This system of coupled equations was solved numerically using a Runge–Kutta method. Figure 11 shows a snapshot at t=0 of the spatial carrier density distribution in the case of the synchronous collision of two pulses having an equal energy of 50nJ/cm2 and 50μJ/cm2. The experimental pulse duration (128 fs), incident angle (7°), and beam waist radii (67 μm) are used.

 figure: Fig. 11.

Fig. 11. Carrier density in the SESAM QW generated by the colliding of two pulses of (a) 50nJ/cm2, and (b) 50μJ/cm2. The incident beams are centered at (x=0,y=0) and are axially symmetric.

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In the case of weak pulses [Fig. 11(a)], the carrier density distribution follows the interference pattern of the field intensity. However, with strong pulses [Fig. 11(b)], the carrier density at the field maximum becomes saturated, increasing the relative amplitude of the carrier density near the nodes and the tails of the field intensity distribution.

The time evolution of the carrier density at the center of the beam (x=y=0) is plotted in Fig. 12. For this simulation, we assumed a single 128 fs pulse with an energy of 51.8μJ/cm2, corresponding to the experimental output power of 90 mW. We also plotted the experimental case of the side pulse operation, with two 130 fs pulses delayed by 430 fs and an average output power of 152 mW.

 figure: Fig. 12.

Fig. 12. Simulated carrier density in the SESAM at the center of the beam (x=y=0), from a single 128 fs pulse of 51.8μJ/cm2 (90 mW average output power), and a double 130 fs pulse of 87.4μJ/cm2 (152 mW output power) separated by 430 fs.

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This result clearly shows the effect of the fast relaxation of carriers during the presence of the pulse, which makes the saturation fluence strongly dependent on the pulse duration. In the situation of a delayed pulse, it is also clear that it will benefit from the carriers generated by the earlier pulse, resulting in absorption losses decreasing with a short delay.

We should note that if the side pulse has a different central wavelength than the first pulse, it will only partially benefit from the saturation created by the earlier pulse. Indeed, if the pulses have a different spectral content, the first pulse will burn a kinetic hole in the carrier distribution that will partly overlap with the second pulse spectrum. However, after a delay of 430 fs, the initial kinetic holes will be significantly filled and smoothed out via intra-subband scatterings [23,24], which will reduce the spectral dependence of the side pulse interaction. Our model does not account for such phenomena as it would require a spatially resolved microscopic analysis of non-equilibrium dynamics in the semiconductor, and would be numerically too expensive.

D. Absorption Losses and Pulse Shaping

The optical power lost in the absorber Plost can be evaluated with the spatial integration of the carrier density generated as follows:

Plost(t)=hνη×t(xyNgen(x,y,t)dxdy).

Figure 13 shows the power lost in the SESAM for the two cases investigated. We can see that the power lost reaches a maximum located 25 fs before the main pulse maximum (centered at t=0s). The more intense the pulse, the more the maximum loss is shifted toward the leading edge of the pulse, as the saturation will occur earlier. This effect is obviously responsible for the pulse shortening occurring in the absorber, with a leading edge significantly more attenuated, as can be seen on Fig. 14. For a better visualization of the pulse shaping, we scaled the losses by a factor 30.

 figure: Fig. 13.

Fig. 13. Simulated absorption losses from a single pulse of 90 mW and a dual pulse of 152 mW separated by 430 fs.

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 figure: Fig. 14.

Fig. 14. Simulated pulse intensity before and after reflection on the SESAM for (a) single pulse operation and (b) side pulse operation. The SESAM losses are artificially increased by a factor 30 for illustration purposes.

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Finally, the total energy lost by the pulses is given by

Elost=Plost(t)dt.

In the case of the side pulse operation, the main pulse loses 0.89% of its energy, whereas the side pulse loses only 0.49%. The main pulse has thus transferred some of its energy to the side pulse through the interaction in the absorber. This energy transfer will obviously be balanced by the lower gain seen by the side pulse, since a similar gain recovery dynamic will occur in the gain medium.

E. Saturation Fluence

The total absorption losses are now calculated as a function of the fluence of the pulses. For this study, we assume a collision of two identical single pulses, with a pulse duration of 128 fs and the geometrical parameters given previously. We varied the delay between the pulses to assess the effect of the synchronization on the saturation fluence. Figure 15 shows a clear reduction of the saturation fluence when the pulses are delayed by less than 1 ps.

 figure: Fig. 15.

Fig. 15. Absorption losses from the SESAM as a function of intracavity fluence for different delays of the two counterpropagating pulses.

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For perfectly synchronized pulses, the saturation fluence is reduced by a factor 2.9, from Fsat1=50μJ/cm2 to Fsat2=17.2μJ/cm2. With a pulse fluence of 51.8μJ/cm2, corresponding to the 90 mW output power result, the absorption losses are reduced from 1.23% to 0.85% when the pulses are synchronized. The mode locking with synchronized colliding pulses is thus clearly favored. We should note that the interference pattern is also present in a CW regime, which helps to transition from the CW to the mode-locked regime since the absorber is saturated more easily. This explains the robustness of the mode-locking regime observed in our previous study [15], when compared to a standard V-shaped cavity.

In the case of the side pulse regime investigated, the saturation fluence is initially higher at Fsat1=65.1μJ/cm2 with a single beam. This is due to the longer time allowed for carrier relaxation while the pulse and side pulse are present. The saturation fluence is, however, reduced by a factor 2.8 at Fsat2=23.2μJ/cm2 when two beams are colliding. With the experimental pulse energy of 87.4μJ/cm2, the losses are reduced from 1.12% to 0.75% when the pulses are synchronized.

A possible strategy to avoid the emergence of side pulses at high pump power is to decrease the fast carrier recombination time constant of the absorber. It could be realized either by exciting the SESAM at a higher energy, where intraband electron–electron and electron–phonon scattering are faster, or by using a graphene-based absorber, which has a very fast carrier relaxation time due to the strong Coulomb and phonon interaction [21]. Another strategy would be to increase the recovery time of the gain medium. However, it would be very challenging with an intense short pulse since it would cause a deep spectral hole burning in the carrier distribution, which will recover quickly via intraband scattering [9].

We should note that, for longer pulses, in the 400 fs to 1 ps range, the saturation fluence will be much higher due to the extensive carrier relaxation occurring while the pulses are present, enabling much higher output powers without side pulses [8].

5. ENERGY TRANSFER IN A MODE-LOCKING REGIME

The interaction of the pulses in the absorber not only leads to a lower saturation fluence, but it also reduces the power imbalance between the two counterpropagating beams. Indeed, if one beam has more power than the other one, it will saturate the absorber faster, resulting in more absorption losses. Over the numerous round trips in the high-Q VECSEL cavity, the average power of each beam will naturally balance, and the mode competition frequently observed in a ring cavity will be strongly reduced.

Figure 16 shows an example of the mode competition and power imbalance observed in a ring cavity while in the CW regime, with a comparison to a mode-locked regime with the same cavity. The two output beams of a ring cavity VECSEL were recorded simultaneously at the same distance from the SESAM with two identical fast photodiodes and a 6 GHz bandwidth oscilloscope. To obtain the CW operation regime, the SESAM was simply cooled to 20°C to blueshift the absorption spectrum. The short time scale in Figs. 16(a) and 16(b) reveals a “noisy” CW regime where the fluctuations are not synchronized, while in the mode-locked regime the outputs are nearly identical and perfectly synchronized. Figures 16(c) and 16(d) represent the same outputs over a longer time window, confirming a “noisy” CW operation and perfectly stable and synchronized pulse trains when mode locked. In Figs. 16(e) and 16(f) we applied a low-pass filter to the signals. This reveals CW operation with a clear competition between the two beam directions while the total average power remains constant, whereas the mode-locked outputs reveal a very stable output power for each direction. The zoom in the inset of Fig. 16(f) shows the two beams fluctuating together rather than competing. This is clear evidence of the energy exchange occurring in a colliding pulse mode-locked regime.

 figure: Fig. 16.

Fig. 16. Time traces of the two counterpropagating output beams in a CW regime (left) and in a mode-locked regime (right).

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6. CONCLUSION

We presented significant improvement of performance from a colliding pulse mode-locking VECSEL, with a state-of-the-art pulse duration of 128 fs and an average power of 90 mW at a repetition rate of 3.27 GHz. We characterized the output in different mode-locking regimes: single pulse operation and double pulse operation at high excitation. The emergence of a side pulse at high power was further investigated with the simulation of the carrier dynamics in the SESAM. We proposed a new approach for the model of absorption saturation, permitting the calculation of absorption losses in a colliding pulse situation with and without side pulses. We demonstrated that the saturation fluence is reduced by a factor 2.9 with colliding pulses, and that side pulses are enabled by the energy transfer in the SESAM. Finally, we presented clear experimental evidence showing that the pulse interaction in the SESAM leads to a power balance of the two counterpropagating beams. This thorough analysis, carried out with experimental laser parameters, is a major step toward a full understanding of the physical processes limiting the power in the sub-200-fs regime.

Funding

Air Force Office of Scientific Research (AFOSR) (FA9550-14-1-0062).

Acknowledgment

We would like to thank Ganesh Balakrishnan and Sadhvikas Addamane of the University of New Mexico for providing the semiconductor saturable absorber, and Jason Jones of the University of Arizona for helpful discussions.

REFERENCES

1. M. Butkus, E. A. Viktorov, T. Erneux, C. J. Hamilton, G. Maker, G. P. A. Malcolm, and E. U. Rafailov, “85.7 MHz repetition rate mode-locked semiconductor disk laser: fundamental and soliton bound states,” Opt. Express 21, 25526–25531 (2013). [CrossRef]  

2. M. Mangold, C. A. Zaugg, S. M. Link, M. Golling, B. W. Tilma, and U. Keller, “Pulse repetition rate scaling from 5 to 100 GHz with a high-power semiconductor disk laser,” Opt. Express 22, 6099–6107 (2014). [CrossRef]  

3. F. Zhang, B. Heinen, M. Wichmann, C. Möller, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “A 23-watt single-frequency vertical-external-cavity surface-emitting laser,” Opt. Express 22, 12817–12822 (2014). [CrossRef]  

4. A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014). [CrossRef]  

5. R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013). [CrossRef]  

6. A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011). [CrossRef]  

7. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016). [CrossRef]  

8. K. G. Wilcox, A. C. Tropper, H. E. Beere, D. A. Ritchie, B. Kunert, B. Heinen, and W. Stolz, “4.35 kW peak power femtosecond pulse mode-locked VECSEL for supercontinuum generation,” Opt. Express 21, 1599–1605 (2013). [CrossRef]  

9. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014). [CrossRef]  

10. M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013). [CrossRef]  

11. J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015). [CrossRef]  

12. C. A. Zaugg, A. Klenner, M. Mangold, A. S. Mayer, S. M. Link, F. Emaury, M. Golling, E. Gini, C. J. Saraceno, B. W. Tilma, and U. Keller, “Gigahertz self-referenceable frequency comb from a semiconductor disk laser,” Opt. Express 22, 16445–16455 (2014). [CrossRef]  

13. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999). [CrossRef]  

14. A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23, 8532–8544 (2015). [CrossRef]  

15. A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016). [CrossRef]  

16. K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016). [CrossRef]  

17. A. E. Siegman, “Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating,” J. Opt. Soc. Am. 67, 545–550 (1977). [CrossRef]  

18. D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008). [CrossRef]  

19. O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013). [CrossRef]  

20. J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003). [CrossRef]  

21. J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016). [CrossRef]  

22. H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989). [CrossRef]  

23. J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014). [CrossRef]  

24. J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017). [CrossRef]  

References

  • View by:

  1. M. Butkus, E. A. Viktorov, T. Erneux, C. J. Hamilton, G. Maker, G. P. A. Malcolm, and E. U. Rafailov, “85.7 MHz repetition rate mode-locked semiconductor disk laser: fundamental and soliton bound states,” Opt. Express 21, 25526–25531 (2013).
    [Crossref]
  2. M. Mangold, C. A. Zaugg, S. M. Link, M. Golling, B. W. Tilma, and U. Keller, “Pulse repetition rate scaling from 5 to 100 GHz with a high-power semiconductor disk laser,” Opt. Express 22, 6099–6107 (2014).
    [Crossref]
  3. F. Zhang, B. Heinen, M. Wichmann, C. Möller, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “A 23-watt single-frequency vertical-external-cavity surface-emitting laser,” Opt. Express 22, 12817–12822 (2014).
    [Crossref]
  4. A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
    [Crossref]
  5. R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
    [Crossref]
  6. A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
    [Crossref]
  7. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
    [Crossref]
  8. K. G. Wilcox, A. C. Tropper, H. E. Beere, D. A. Ritchie, B. Kunert, B. Heinen, and W. Stolz, “4.35 kW peak power femtosecond pulse mode-locked VECSEL for supercontinuum generation,” Opt. Express 21, 1599–1605 (2013).
    [Crossref]
  9. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
    [Crossref]
  10. M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
    [Crossref]
  11. J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
    [Crossref]
  12. C. A. Zaugg, A. Klenner, M. Mangold, A. S. Mayer, S. M. Link, F. Emaury, M. Golling, E. Gini, C. J. Saraceno, B. W. Tilma, and U. Keller, “Gigahertz self-referenceable frequency comb from a semiconductor disk laser,” Opt. Express 22, 16445–16455 (2014).
    [Crossref]
  13. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
    [Crossref]
  14. A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23, 8532–8544 (2015).
    [Crossref]
  15. A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016).
    [Crossref]
  16. K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
    [Crossref]
  17. A. E. Siegman, “Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating,” J. Opt. Soc. Am. 67, 545–550 (1977).
    [Crossref]
  18. D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008).
    [Crossref]
  19. O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
    [Crossref]
  20. J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
    [Crossref]
  21. J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
    [Crossref]
  22. H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989).
    [Crossref]
  23. J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014).
    [Crossref]
  24. J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
    [Crossref]

2017 (1)

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

2016 (4)

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
[Crossref]

A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016).
[Crossref]

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

2015 (2)

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23, 8532–8544 (2015).
[Crossref]

2014 (6)

2013 (5)

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

K. G. Wilcox, A. C. Tropper, H. E. Beere, D. A. Ritchie, B. Kunert, B. Heinen, and W. Stolz, “4.35 kW peak power femtosecond pulse mode-locked VECSEL for supercontinuum generation,” Opt. Express 21, 1599–1605 (2013).
[Crossref]

M. Butkus, E. A. Viktorov, T. Erneux, C. J. Hamilton, G. Maker, G. P. A. Malcolm, and E. U. Rafailov, “85.7 MHz repetition rate mode-locked semiconductor disk laser: fundamental and soliton bound states,” Opt. Express 21, 25526–25531 (2013).
[Crossref]

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

2011 (1)

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

2008 (1)

2003 (1)

J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
[Crossref]

1999 (1)

1989 (1)

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989).
[Crossref]

1977 (1)

Alanko, J. P.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Alfieri, C. G. E.

Backus, S.

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

Baker, C.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

Beere, H. E.

Bek, R.

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

Bellancourt, A.-R.

Blake, G. A.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Butkus, M.

Carroll, P. B.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Durfee, C.

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

Emaury, F.

Erneux, T.

Finneran, I. A.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Gbele, K.

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

Gini, E.

Golling, M.

Good, J. T.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Grebing, C.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Guina, M.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Hader, J.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016).
[Crossref]

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
[Crossref]

J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
[Crossref]

Hamilton, C. J.

Härkönen, A.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Haug, H.

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989).
[Crossref]

Heinen, B.

Hoffmann, M.

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

Holland, D. B.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Hönninger, C.

Iwaniuk, D.

Jetter, M.

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

Kahle, H.

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

Keller, U.

D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
[Crossref]

A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23, 8532–8544 (2015).
[Crossref]

C. A. Zaugg, A. Klenner, M. Mangold, A. S. Mayer, S. M. Link, F. Emaury, M. Golling, E. Gini, C. J. Saraceno, B. W. Tilma, and U. Keller, “Gigahertz self-referenceable frequency comb from a semiconductor disk laser,” Opt. Express 22, 16445–16455 (2014).
[Crossref]

M. Mangold, C. A. Zaugg, S. M. Link, M. Golling, B. W. Tilma, and U. Keller, “Pulse repetition rate scaling from 5 to 100 GHz with a high-power semiconductor disk laser,” Opt. Express 22, 6099–6107 (2014).
[Crossref]

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008).
[Crossref]

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
[Crossref]

Kelley, M. J.

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Kilen, I.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

Klenner, A.

Koch, M.

Koch, S.

J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
[Crossref]

Koch, S. W.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989).
[Crossref]

Koskinen, R.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Kunert, B.

Laurain, A.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016).
[Crossref]

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
[Crossref]

Link, S. M.

Maas, D. J. H. C.

Maker, G.

Malcolm, G. P. A.

Mangold, M.

Marah, D.

Marchese, S. V.

Mart, C.

A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
[Crossref]

Mayer, A. S.

McInerney, J.

Michler, P.

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

Möller, C.

Moloney, J.

A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
[Crossref]

J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
[Crossref]

Moloney, J. V.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

A. Laurain, D. Marah, R. Rockmore, J. McInerney, J. Hader, A. R. Perez, W. Stolz, and J. V. Moloney, “Colliding pulse mode locking of vertical-external-cavity surface-emitting laser,” Optica 3, 781–784 (2016).
[Crossref]

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

Morier-Genoud, F.

Moser, M.

Paajaste, J.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Paschotta, R.

Perez, A. R.

Rafailov, E. U.

Rahimi-Iman, A.

Ritchie, D. A.

Rockmore, R.

Rudin, B.

Saraceno, C. J.

Scheller, M.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

Schwarzbäck, T.

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

Sieber, O.

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

Siegman, A. E.

Squier, J.

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

Steinmeyer, G.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Stolz, W.

Südmeyer, T.

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008).
[Crossref]

Suomalainen, S.

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

Tilma, B.

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

Tilma, B. W.

Tropper, A. C.

Viktorov, E. A.

Waldburger, D.

Wichmann, M.

Wilcox, K. G.

Wittwer, V.

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

Yang, H.-J.

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

Young, M. D.

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

Zaugg, C. A.

Zhang, F.

Appl. Phys. B (1)

O. Sieber, M. Hoffmann, V. Wittwer, M. Mangold, M. Golling, B. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113, 133–145 (2013).
[Crossref]

Appl. Phys. Lett. (2)

R. Bek, H. Kahle, T. Schwarzbäck, M. Jetter, and P. Michler, “Mode-locked red-emitting semiconductor disk laser with sub-250 fs pulses,” Appl. Phys. Lett. 103, 242101 (2013).
[Crossref]

J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104, 151111 (2014).
[Crossref]

Electron. Lett. (1)

A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 μm wavelength,” Electron. Lett. 47, 454–456 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (2)

K. Gbele, A. Laurain, J. Hader, W. Stolz, and J. V. Moloney, “Design and fabrication of hybrid metal semiconductor mirror for high-power VECSEL,” IEEE Photon. Technol. Lett. 28, 732–735 (2016).
[Crossref]

A. Laurain, C. Mart, J. Hader, J. Moloney, B. Kunert, and W. Stolz, “15 W single frequency optically pumped semiconductor laser with sub-MHz linewidth,” IEEE Photon. Technol. Lett. 26, 131–133 (2014).
[Crossref]

J. Appl. Phys. (1)

J. Hader, H.-J. Yang, M. Scheller, J. V. Moloney, and S. W. Koch, “Microscopic analysis of saturable absorbers: semiconductor saturable absorber mirrors versus graphene,” J. Appl. Phys. 119, 053102 (2016).
[Crossref]

J. Microsc. (1)

M. D. Young, S. Backus, C. Durfee, and J. Squier, “Multiphoton imaging with a direct-diode pumped femtosecond Ti:sapphire laser,” J. Microsc. 249, 83–86 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Opt. Express (7)

A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23, 8532–8544 (2015).
[Crossref]

C. A. Zaugg, A. Klenner, M. Mangold, A. S. Mayer, S. M. Link, F. Emaury, M. Golling, E. Gini, C. J. Saraceno, B. W. Tilma, and U. Keller, “Gigahertz self-referenceable frequency comb from a semiconductor disk laser,” Opt. Express 22, 16445–16455 (2014).
[Crossref]

D. J. H. C. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008).
[Crossref]

K. G. Wilcox, A. C. Tropper, H. E. Beere, D. A. Ritchie, B. Kunert, B. Heinen, and W. Stolz, “4.35 kW peak power femtosecond pulse mode-locked VECSEL for supercontinuum generation,” Opt. Express 21, 1599–1605 (2013).
[Crossref]

M. Butkus, E. A. Viktorov, T. Erneux, C. J. Hamilton, G. Maker, G. P. A. Malcolm, and E. U. Rafailov, “85.7 MHz repetition rate mode-locked semiconductor disk laser: fundamental and soliton bound states,” Opt. Express 21, 25526–25531 (2013).
[Crossref]

M. Mangold, C. A. Zaugg, S. M. Link, M. Golling, B. W. Tilma, and U. Keller, “Pulse repetition rate scaling from 5 to 100 GHz with a high-power semiconductor disk laser,” Opt. Express 22, 6099–6107 (2014).
[Crossref]

F. Zhang, B. Heinen, M. Wichmann, C. Möller, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “A 23-watt single-frequency vertical-external-cavity surface-emitting laser,” Opt. Express 22, 12817–12822 (2014).
[Crossref]

Optica (3)

Phys. Rev. A (1)

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1989).
[Crossref]

Rev. Sci. Instrum. (1)

J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
[Crossref]

Semicond. Sci. Technol. (1)

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32, 013002 (2017).
[Crossref]

Solid-State Electron. (1)

J. Hader, S. Koch, and J. Moloney, “Microscopic theory of gain and spontaneous emission in GaInNAs laser material,” Solid-State Electron. 47, 513–521 (2003).
[Crossref]

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Figures (16)

Fig. 1.
Fig. 1. Schematic layout of the VECSEL setup (right) and design of the full VECSEL structure (left).
Fig. 2.
Fig. 2. (a) Reflectivity spectra of the VECSEL structure with and without the gold reflector measured at room temperature (black and gray lines, respectively), together with the simulated spectra (dotted lines). (b) Measured group delay dispersion spectrum of the SESAM and VECSEL gain structure. The dotted line represents the sum of the VECSEL and SESAM GDD, and the vertical bars indicate the standard deviation over 20 measures.
Fig. 3.
Fig. 3. Measured non-collinear SHG autocorrelation of the single pulse operation output, and simulated autocorrelation of a sech 2 pulse with a FWHM of 128 fs.
Fig. 4.
Fig. 4. Measured optical spectrum of the output beam consisting of a single 128 fs pulse per round trip, and simulated spectrum of an unchirped 128 fs sech 2 pulse.
Fig. 5.
Fig. 5. Microwave spectrum of the laser output, with a RBW of 100 kHz and a 40 GHz span (left), and with a RBW of 1 kHz and a span of 2 MHz (right).
Fig. 6.
Fig. 6. Measured non-collinear autocorrelation of the side pulse operation output, and simulation of the autocorrelation of a sech 2 pulse with a FWHM of 130 fs followed by a 130 fs side pulse delayed by 430 fs with a relative intensity of 56%.
Fig. 7.
Fig. 7. Measured optical spectrum of the side pulse operation output, and simulation of the transform limited spectrum of two successive sech 2 130 fs pulse delayed by 430 fs.
Fig. 8.
Fig. 8. Field intensity distribution of two Gaussian beams colliding with an angle of 7° at z = 0 .
Fig. 9.
Fig. 9. (a) Microscopically calculated QW absorption spectra for various carrier density N . (b) Simulated absorption losses as a function of the carrier density N of the SESAM.
Fig. 10.
Fig. 10. Experimentally measured and simulated reflectivity change in the SESAM after excitation with a 80 fs pulse at 990 nm with a fluence of 25 μJ / cm 2 .
Fig. 11.
Fig. 11. Carrier density in the SESAM QW generated by the colliding of two pulses of (a)  50 nJ / cm 2 , and (b)  50 μJ / cm 2 . The incident beams are centered at ( x = 0 , y = 0 ) and are axially symmetric.
Fig. 12.
Fig. 12. Simulated carrier density in the SESAM at the center of the beam ( x = y = 0 ) , from a single 128 fs pulse of 51.8 μJ / cm 2 (90 mW average output power), and a double 130 fs pulse of 87.4 μJ / cm 2 (152 mW output power) separated by 430 fs.
Fig. 13.
Fig. 13. Simulated absorption losses from a single pulse of 90 mW and a dual pulse of 152 mW separated by 430 fs.
Fig. 14.
Fig. 14. Simulated pulse intensity before and after reflection on the SESAM for (a) single pulse operation and (b) side pulse operation. The SESAM losses are artificially increased by a factor 30 for illustration purposes.
Fig. 15.
Fig. 15. Absorption losses from the SESAM as a function of intracavity fluence for different delays of the two counterpropagating pulses.
Fig. 16.
Fig. 16. Time traces of the two counterpropagating output beams in a CW regime (left) and in a mode-locked regime (right).

Equations (12)

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E r ( x , y , z , t ) = E r 0 q 0 q e j π λ ( ( x θ z ) 2 + y 2 q + 2 θ x θ 2 z ) sech ( t τ ) ,
E l ( x , y , z , t ) = E l 0 q 0 q e j π λ ( ( x + θ z ) 2 + y 2 q 2 θ x θ 2 z ) sech ( t t d τ ) ,
I ( x , y , z , t ) = [ E l + E r ] × [ E l ¯ + E r ¯ ] .
I ( x , y , t ) = e 2 x 2 + y 2 w 0 2 [ E r 0 2 sech 2 ( t τ ) + E l 0 2 sech 2 ( t t d τ ) + 2 E r 0 E l 0 sech ( t t d τ ) sech ( t τ ) cos ( π θ x λ ) ] .
α ( N ) = 2.244 × exp ( N 1.585 × 10 12 ) 0.3 ,
R ( t ) = R 0 + Δ R × ( A · e t / τ slow + ( 1 A ) · e t / τ fast ) ,
N ( x , y , t ) = N gen ( x , y , t ) + A N slow ( x , y , t ) + ( 1 A ) N fast ( x , y , t ) ,
N gen t = η h ν × α ( N ) × I ( x , y , t ) ,
N slow t = N gen ( x , y , t ) + N slow ( x , y , t ) τ slow ,
N fast t = N gen ( x , y , t ) + N fast ( x , y , t ) τ fast ,
P lost ( t ) = h ν η × t ( x y N gen ( x , y , t ) d x d y ) .
E lost = P lost ( t ) d t .

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