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Amplification of kW peak power femtosecond pulses in single quantum well InGaAs tapered amplifiers
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Optics Communications 281 (2008) 2160–2166 www.elsevier.com/locate/optcom
Amplification of kW peak power femtosecond pulses in single quantum well InGaAs tapered amplifiers Thorsten Ulm a,*, Harry Fuchs a, Johannes A. L’huillier a, Andreas Klehr b, Bernd Sumpf b, Edeltraud Gehrig c a
Department of Physics, Technical University of Kaiserslautern, Erwin-Schro¨dinger-Straße 46, 67663 Kaiserslautern, Germany b Ferdinand-Braun-Institut fu¨r Ho¨chstfrequenztechnik, Gustav-Kirchhoff-Straße 4, 12489 Berlin, Germany c Advanced Technology Institute, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom Received 20 August 2007; received in revised form 23 November 2007; accepted 23 November 2007
Abstract The amplification of ps and fs pulses with peak powers of up to 4.5 kW has been investigated in a single quantum well InGaAs tapered amplifier. The pulses with durations of 100 fs or 2 ps were generated by a modelocked titanium–sapphire laser. The amplified pulses indicate strong gain saturation and carrier generation due to photon absorption in the laser active region which causes a temporal broadening of the amplified pulses as well as modifications of the optical spectrum. The gain recovery time was measured by a pump–probe experiment. The experimental results are analyzed with respect to the sub-ps gain dynamics which is described by a relaxation time approximation. Ó 2007 Elsevier B.V. All rights reserved. PACS: 42.55.Px; 42.60.Da; 42.65.Jx Keywords: Ultrafast optics; Semiconductor optics; Diode lasers; Femtosecond lasers; Semiconductor optical amplifiers; Intraband relaxation; Self-phase modulation
1. Introduction Semiconductor tapered amplifiers are of advantage for amplifying ultrashort pulses, due to high gain, direct electrical pumping [1] and a large spectral bandwidth of up to 30 nm [2]. In addition the spectral position of the gain profile can be chosen by an adequate chemical composition of the epitaxial structure. For these reasons semiconductor amplifiers have been investigated and used for many years in short-pulse semiconductor laser systems [3–8]. In this paper we report on the amplification of 920 nm picosecond and femtosecond pulses with high peak powers of up to 4.5 kW in a single quantum-well (QW), InGaAs tapered amplifier (TA). The fourier-limited pulses with the duration *
Corresponding author. Tel.: +49 631 2017407; fax: +49 631 205 3906. E-mail address: [email protected] (T. Ulm).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.11.062
of 130 fs or 2 ps were generated by a modelocked titanium– sapphire (Ti:Sa) laser (Spectra-Physics, model Tsunami) with a repetition rate of 82 MHz. The aim of these experiments was to investigate how the temporal and spectral shape of the amplified pulses is influenced by the fast transient changes of the carrier density, the refractive index and the gain [9,10]. The experimental results are analyzed with respect to the sub-ps dynamics as described by a relaxation time approximation. 2. Refractive index and carrier dynamics In the laser-active region, the carrier density is reduced by stimulated emission. The changes in the carrier density modify the gain and the refractive index [11]. The fast transient variation of the refractive index changes the phase of the emitted light field. Since this phase modulation is not
T. Ulm et al. / Optics Communications 281 (2008) 2160–2166
caused by an external field but by the light field itself, this effect is known as self-phase modulation (SPM) [9]. SPM changes the temporal and the spectral shape of the amplified pulse [12]. A fast replacement of the recombined carriers damps the dynamics of the refractive index variations. A fast carrier transport into the QW therefore damps also the SPM. Depending on the epitaxial and geometrical structure of the semiconductor amplifier several electronic states are involved in this carrier transport. Fig. 1 shows the electronic states in the single QW, InGaAs tapered amplifier. The double heterojunction [1] is formed by a p-doped, an intrinsic and an n-doped layer. Electrons and holes are injected from the p- and n-doped regions into bulk states located in the intrinsic layer. The carriers relax into the QW states by intraband scattering processes, such as carrier–carrier and carrier-phonon scattering [13]. This process is called intraband relaxation. In good approximation the relaxation processes can be described by assuming a fixed carrier relaxation time, which is also called intraband relaxation time si . In the QW states, the carriers then decay via stimulated emission processes. As the intraband relaxation is not an instantaneous process, the value of the intraband relaxation time si is essential for the gain dynamics, if the pulse duration becomes comparable to si [14]. As outlined by Chow et al. [13], the carrier heating and the carrier relaxation occur on the fs timescale and are far from the thermal equilibrium. The simulation of non-equilibrium processes would require large computational efforts [13]. Since we restrict ourselves to a qualitative analysis of the experimental results, we will use the relaxation time approximation as described above. The error resulting from the relaxation time approximation is below the error in measurement. We would like to note, however, that more detailed theories (including the full non-equilibrium carrier dynamics) have to be used if one aims at a calculation of the pulse shape or the spectra which are strongly dependent on the ultrafast carrier dynamics.
Fig. 1. The epitaxial structure of the tapered amplifier is a double heterojunction [1], consisting of a p-doped, an intrinsic and a n-doped layer. The double heterojunction structure provides carrier and optical confinement.
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After presenting the experimental set-up, we will discuss the influence of the gain dynamics on the temporal and spectral shape of the amplified pulse. In Sections 4–6 the experimental results related to gain saturation, spectral distortion and temporal broadening are presented. The results are analyzed qualitatively by considering the sub-ps gain dynamics. Section 7 describes a pump–probe experiment that allowed to measure the intraband relaxation time. 3. Experimental setup As a pulse source, we used the commercially available modelocked titanium–sapphire (Ti:Sa) laser (Spectra-Physics, model Tsunami). This laser system generates fourier limited pulses with durations of either 2 ps or 100 fs in a diffraction limited beam with a repetition rate of 82 MHz. This offers the opportunity to investigate and compare the distortion of pulses with durations less or larger than si . The center wavelength of the Ti:Sa laser was tuned to 920 nm, the spectral gain maximum of the TA. The experimental setup is shown in Fig. 2. The pulses emitted by the Ti:Sa laser pass an optical isolator. The isolator blocks radiation emitted backwards from the TA which might disturb the mode-locking of the Ti:Sa laser. This radiation consists of amplified spontaneous emission (ASE). ASE is emitted, if the gain is not saturated completely by injected radiation [15]. Thus the amplifier emits ASE in particular between consecutive input pulses, but also at low cw input powers. In the optical isolator, chromatic dispersion stretches the pulse from about 100 fs to about 130 fs. Because of the narrow spectral width, an increase of the pulse duration was not observed for the 2 ps pulses. These Ti:Sa laser pulses are amplified in a 2.75 mm long TA, manufactured by the Ferdinand-Braun-Institut fu¨r Ho¨chstfrequenztechnik based in Berlin, Germany. The active region consists of a 0.75 mm long ridge waveguide section for pre-amplification and a 2 mm long tapered section for the generation of the high power output. The tapered region is used to spatially expand the optical power, to keep the spatial power density below the damage threshold. The taper angle is 6° and close to the diffraction angle at the end of the ridge waveguide. The QW consists of InGaAs, the optical waveguide is 1 lm high and consists of AlGaAs. The dimensions of the output facet are 200 lm 1 lm. To prevent lasing inside the amplifier both facets were AR coated and have a residual reflectivity of < 3 104 . A spherical and a cylindrical lens collimate the output beam and compensate for the astigmatism caused by the rectangular output facet. The vertical divergence of the output beam is less than 28°. In cw operation, 74% of the optical output power is emitted in a near-diffraction limited beam ðM 2 ¼ 1:15Þ. The mounting base of the TA is thermo-electrically cooled to a temperature of 20 °C. The laser pulses were characterized before and after amplification. An optical isolator prevents back reflections from the diagnostic tools into the TA. For diag-
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Fig. 2. The experimental setup includes a power meter, an auto-correlator and a spectrometer to characterize the pulse properties of the input and the amplified output pulse. To measure the intraband relaxation time in a pump–probe experiment, an optional beam splitter with an adjustable delay time was added. For further details see text.
nostics a power meter (MellesGriot, model: 13PEM001), a SHG auto-correlator (APE, model: Pulse-Check) and a double-grating spectrometer (Ando Electronics, model: AQ6317B) were used. To measure the magnitude of si in a pump–probe experiment the pulses pass a beam splitter (see Fig. 2). One of the spatially separated pulse trains is delayed before both pulse trains are re-united at the beam splitter and injected into the TA. In this way a train of double-pulses with a variable temporal separation of up to 30 ps was generated. 4. Gain saturation As mentioned in Section 2, the ratio of the pulse duration and si is crucial for the gain dynamics. One of the system parameters that strongly depends on the gain dynamics is the output power: If the pulse duration becomes comparable to or shorter than si then the output power is expected to decrease significantly. In such a case, the QW states cannot be re-populated during the pulse duration which leads to strong gain saturation.
pulsed operation, we can subtract the ASE power emitted by the free-running amplifier in good approximation. But in the cw regime P ase out is not constant, because the gain is saturated by the amplified signal radiation [15]. From the fact that P total out consists of ASE and amplified signal power, we obtain ase sig P total out ¼ P out þ P out P in ase ase P out ¼ P max exp P sat P in sig sig P out ¼ P max 1 exp P sat
ð2Þ ð3Þ ð4Þ
with the saturation power P sat and the maximum ASE and sig signal output power, P ase max and P max . For the cw measurease ments P out was subtracted from P total out after fitting Eq. (4) to the data. As can be seen from Fig. 3, the highest gain values are obtained for cw input. In the cw regime, the amount of carriers in the QW states is given by the equilibrium of injected carriers and stimulated recombination. The gain increases with the injection current, as long as no thermal roll-over
To confirm this expectation, cw radiation from a diode laser as well as modelocked pulses were amplified in the TA. The output powers achieved with the same average input powers were compared to each other. The experimental results are shown in Fig. 3. In general, laser amplifiers are characterized by their gain g (dB) given by ! P in g ðdBÞ ¼ 10 log10 sig ð1Þ P out where P in and P sig out are the signal input and output power, respectively. In the following discussion, we assumed the Ti:Sa laser to be free of ASE. Please note that the ASE power P ase out has to be subtracted from the total output sig power P total out to obtain the signal output power P out . For
gain [dB]
4.1. Experimental results
average input power [mW] Fig. 3. Dependence of the amplifier gain on the average input power and on the injection current measured for cw and pulsed laser radiation.The injection current is either 3 A (solid symbols) or 5 A (open symbols).
T. Ulm et al. / Optics Communications 281 (2008) 2160–2166
4.2. Gain depletion by ASE The influence of ASE may be understood by the fact that the amplifier emits ASE between two consecutive pulses. The gain depletion by ASE results in a poor storage of energy in the bulk states and in the QW states. ASE is emitted, when the inversion is sufficiently large to amplify the radiation generated by spontaneous emission. If the current is increased, the additional amount of carriers is depleted by ASE and is thus not available to amplify the next pulse [16]. Therefore, the inversion is limited by the ASE, and not the current. At the time when the next pulse arrives the inversion is the same at all the currents. In the fs regime additionally, the influence of the intraband relaxation becomes observable. 4.3. The influence of the intraband relaxation Due to the non-instantaneous intraband relaxation a delayed gain recovery occurs in pulsed operation. The gain recovery inside the QW takes place on a timescale of about si 500 fs [10]. A 130 fs long pulse is much shorter than si and is affected in a different manner by the carrier dynamics than a 2 ps long pulse (which is four times longer than si ). For 2 ps long pulses one expects that a partial gain recovery occurs during the pulse duration, since carriers
relax from the bulk states into the QW states. A 2 ps long pulse therefore depletes not only the QW states, but also the bulk states. For 130 fs long pulses no gain recovery during pulse propagation is expected, because the intraband relaxation processes are too slow to re-populate the QW states. For the amplification of a 130 fs long pulse only the initial inversion in the QW is available, which results in strong gain saturation even for low input powers. Since a larger amount of carriers is available to amplify a 2 ps long pulse, it experiences more gain than a 130 fs long pulse (see Fig. 3). 5. Spectral distortions As mentioned in Section 2, depletion of the carriers causes not only gain saturation but also SPM. As the refractive index is changing while the pulse propagates within the amplifier, the relative phases of different spectral components of the pulse are changed and new spectral components are generated [12]. The spectral as well as the temporal shape of a pulse is created by the interference of its spectral components. Changes in the phase of the light field therefore lead to spectral distortions [9,12]. To obtain further information on the influence of the ultrafast gain dynamics on the output pulses we have measured and compared the spectral shape of the pulses with the durations of 2 ps and 130 fs, i.e. longer and shorter than si . The spectra of the amplified 2 ps long pulses are shown in Fig. 4. The pulse induced carrier depletion leads (via the real part of the susceptibility) to a corresponding increase in the spectral index dispersion. In combination with the saturation of the gain this leads to a red shift [17] of 0.5 nm and to the generation of a spectral satellite peak at a distance of 0.6 nm to the main peak [9–11]. Since no absorption occurs for ps pulses with input powers below 50 mW, the spectral distortions are limited to
normalized intenstiy
occurs. At an injection current of 5 A, the small signal gain for cw radiation is 25 dB. In the experiment the current was limited to 5 A to limit the thermal load of the amplifier. For ps pulses, the small signal gain is reduced by a factor of 2. We attribute this to the low repetition rate (82 MHz) of the Ti:Sa laser, which leads to high peak powers and causes strong gain saturation within the TA. For ps pulses with average input powers up to 50 mW the gain remains positive. The small signal gain for 130 fs long pulses is comparable to the value observed for ps pulses, but absorption occurs, if the input power exceeds 12 mW. For higher input powers one could expect that the TA becomes transparent due to absorption saturation which corresponds to a gain of zero. In contrast to this expectation zero gain is not observed, but the gain becomes negative. This is a direct consequence of the ultrafast carrier dynamics. For high input powers, two processes occur within the pulse envelope: First, the leading edge of the pulse depletes the inversion in the QW states. Second, the trailing parts of the pulse causes a dynamic carrier excitation. As a consequence, absorption of light occurs, i.e. the gain becomes negative. For cw operation, we found an increase of the gain with increasing injection currents. (Please note the logarithmic scaling of g, i.e. small variations of g correspond to large changes in the output power.) The situation is different, if the amplifier is used for pulse amplification. There are two reasons why higher gain currents do not provide higher gain for short optical input pulses: The gain depletion by the ASE and the non-instantaneous gain recovery.
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wavelength [nm] Fig. 4. Spectra of amplified ps pulses (thin lines) measured for different optical input powers (solid line: 5 mW, dash-dotted line: 20 mW, dashed line: 50 mW) in comparison to the spectrum emitted by the Ti:Sa laser (thick gray line).
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wavelengths longer than the center wavelength [11]. Higher input powers lead to stronger depletion of the inversion and therefore cause stronger SPM effects. As expected, the amplitude of the satellite peak increases with input power (see Fig. 4). The results of the experiments performed with 130 fs long pulses are shown in Fig. 5. The peak power of a pulse with a duration of 130 fs is approximately 15 times higher than the peak power of a 2 ps long pulse for the same average power. Additionally, the intraband relaxation is too slow to transfer carriers from the bulk states into the QW states. Unlike for ps pulses, for the amplification of the 130 fs pulses only the initial inversion in the QW states is available. Therefore, one can expect much stronger gain saturation and consequently stronger spectral distortions than in the ps regime. The experimental results shown in Fig. 5 reveal that – compared to the amplification of ps pulses – a fs pulse experience larger spectral broadening. The spectral width Dk of the output pulses was calculated using the following formula for the second moment: ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 1 2 Dk ¼ 2 ðk kc Þ SðkÞdk N ð5Þ Z Z 1 k SðkÞdk; N ¼ SðkÞdk kc ¼ N
6. Temporal broadening The nonlinear chirp caused by the SPM not only results in spectral distortions but also in a temporal broadening of the pulses. Temporal broadening in amplifiers is critical for a wide range of applications that require short pulses with high peak powers (e.g. SHG). A detailed measurement of the temporal broadening in the QW tapered amplifier is thus of high importance for the development of optimized amplifier systems. To describe the temporal broadening we introduce the temporal broadening factor f, defined by the ratio of the FWHM sACF of the autocorrelation functions (ACF) before and after the amplification of the laser pulses. sACF;out ð6Þ f¼ sACF;in In general, temporal broadening in the amplifier can be caused by dispersion and by SPM. To obtain information on the magnitude of these influencing factors we have systematically measured the temporal broadening of ps and fs pulses in dependence on the average input power and the amplifier current. The results are summarized in Fig. 6. The temporal pulse broadening increases with the input power and saturates for large input powers. This is obvious from the fact that the largest transient change of the refractive index occurs if the inversion is totally depleted. The contribution of the dispersive broadening can be identified by extrapolating f to zero input power. For very low input powers the gain depletion is negligible and no SPM occurs. Extrapolating the data in Fig. 6 to zero input power we found a dispersive broadening factor of 1.6–1.7 for ps pulses and 1.3–2.0 for fs pulses.
normalized intenstiy
temporal broadening factor
SðkÞ denotes the spectral power distribution, values smaller than 3% of the maximum were considered to be noise and set to zero for the integration. Related to the FWHM of the input pulses (Dk = 10.48 nm) the output pulses are broadened spectrally by a factor of 1.52 (3 A) and 1.59 (5 A). Another important consequence of the SPM is the large redshift of about 5.1 nm. A 130 fs long pulse causes both carrier depletion by stimulated emission and carrier generation by photon absorption in the active layer, as indicated by the gain characteristics shown in Fig. 3. The amplified fs pulses thus shows a characteristic spectral broadening towards both shorter and longer wavelengths [11].
As the pulse duration is much shorter than si , the distortions are also supposed to be independent from the carrier density in the bulk bands and from the injection current. This expectation is confirmed by the results shown in Fig. 5.
wavelength [nm] Fig. 5. Spectra of amplified 130 fs pulses measured for two amplifier currents of 3 A (thin solid line) and 5 A (thin dashed line) in comparison to the spectrum of the input pulse (thick gray line).
average input power [mW] Fig. 6. Temporal broadening of the ps pulses (solid symbols) and the fs pulses (open symbols), measured for different injection currents. For the definition of f, see text.
T. Ulm et al. / Optics Communications 281 (2008) 2160–2166
7. Pump–probe experiments As described above, the intraband relaxation time si represents a key feature in the amplification of ultrashort pulses. In particular, it has a strong influence on the output power as well as on the temporal and spectral pulse characteristics. To obtain further information on the value of si we have set up a pump–probe experiment (similar to those described in Refs. [14,18,19]). This method allows to measure si directly. To generate pump and probe pulses, a beam splitter with adjustable pulse delay (shown in Fig. 2) was used. Pump and probe pulses were injected into the TA with delay times between 0 and 30 ps. The first pulse is used to saturate the gain. The available gain for the second pulse depends on the delay time and the dynamics of the gain recovery. We expect the output power to increase as soon as the delay time becomes comparable to si , because the QW states are re-populated during the delay time and the second pulse will experience more gain. An average input power of 1 mW was used for both the pump and the probe pulse train to prevent substantial temporal broadening (see Fig. 6 for comparison). The current was set to 3 A to keep the thermal load of the amplifier and the influence of the ASE at a low level. To determine the delay time between the pump and the probe pulses, two different methods were used, depending on the size of the delay time. The first method is based on the auto-correlation function (ACF). A double-pulse generates an ACF with three peaks. For delay times larger than 0.5 ps, the delay between the pump and the probe pulse was obtained directly from the satellite maxima of the ACF. For delay times comparable to the output pulse duration, this method fails because the three maxima are not resolved in the ACF. Therefore, delay times smaller than 0.5 ps were obtained from amplitude modulations in the spectra of the output pulse. Therefore, we consider the
two pulses as a superposition of plane waves within a certain spectral range. Spectral components with the same wavelength can interfere constructively or destructively with each other. The periodicity Dx of interference minima and maxima in the output spectrum is therefore Dx Dt ¼ 2p
ð7Þ
where Dt denotes the delay time. Both methods were demonstrated to yield consistent results for those delay times, for which both methods were applicable. As presented in Section 2, si denotes the decay time of the bulk states for electronic transitions into the QW states. If the QW states had been depleted completely, the population N QW of the QW states after a time interval Dt should be Dt N QW ðDtÞ ¼ N QW ð1Þ 1 exp ð8Þ si with N QW ð1Þ denoting the final inversion for Dt ! 1. Since the gain and the output power is (approximately) proportional to the amount of carriers, the function Dt sig sig P out ðDtÞ ¼ P out ð1Þ AP exp ð9Þ si was fitted to the experimental results to obtain si . P sig out ð1Þ denotes the maximum output power achieved for an infinite pulse delay. The amplitude AP is the difference between the maximum and the minimum output power. Fig. 7 shows the average output power in dependence of the delay time between the pump and the probe pulse. The experimental data are in good agreement with the model described by Eq. (9). From the data shown in Fig. 7 we obtained si ¼ ð540 60Þ fs: An intraband relaxation time of 540 fs is in good agreement with microscopic calculations using Boltzmann collision terms for the intraband scattering processes [10,20].
average output power [mW]
Fig. 6 reveals a significantly stronger broadening for fs pulses than for ps pulses. This originates from the higher peak power and larger spectral bandwidth of the fs pulses. In addition, the shorter pulse length leads to a faster transient change of the refractive index. For higher currents the amount of carriers interacting with the light field is larger, leading to stronger index modulations and an increase in temporal broadening. In contrast to the amplification of ps pulses, the gain dynamics induced by fs pulses includes carrier generation by photon absorption, which causes additional index changes. As can be seen in Fig. 6, the broadening of the 2 ps pulses decreases slightly with increasing injection current. We attribute this effect to higher temperatures in the active layer due to the higher current. Higher temperatures cause slightly faster carrier relaxation into the QW states, because the intraband relaxation is partially driven by carrier-phonon scattering [13].
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measured data points exponential ascent
pulse delay [ps] Fig. 7. Pump–probe experiment performed with pairs of 130 fs long pulses of equal power with delay times in the range of 0–30 ps. The average input power of each the pump and the probe pulses is 1 mW. The amplifier current is 3 A.
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Generally, the relaxation rate is influenced by the amplifier injection current and by the electronic band structure of a given semiconductor device [20]. A measurement of this dependence is, however, beyond the accuracy of our experimental setup and thus is planned for future investigations. Our experimental result can only be interpreted as an upper limit for si , since the temporal pulse broadening has to be taken into account. The temporal resolution of the presented experiment is given by the temporal broadening of the pulse in the TA. Although pump and probe pulses have an average input power of only 1 mW, they experience a broadening from 130 fs to 480 fs, as shown in Fig. 6. Therefore, relaxation processes on time scales shorter than 480 fs cannot be measured with the used setup, and the value of 540 fs has to be considered as an upper limit for si . (Values for si obtained by pump– probe experiments in high power TA’s are strongly affected by temporal broadening, as known from other experiments with high power semiconductor amplifiers [18].) In future investigations, we plan to perform pump– probe experiments within shorter amplifiers, since the shorter gain length should reduce the temporal broadening and might provide more precise results. 8. Summary We investigated the amplification of modelocked pulses in a single quantum well InGaAs tapered amplifier. The pulses were generated with a titanium–sapphire laser with a repetition rate of 82 MHz. For a qualitative analysis of the gain dynamics in the tapered amplifier, a relaxation time approximation was used. In pulsed operation high peak powers, carrier depletion by ASE and a delayed gain recovery in the QW states cause gain saturation even at low input powers. Gain depletion results in self-phase modulation evident from spectral and temporal pulse distortions. Picosecond pulses are broadened to longer wavelength because of gain depletion, while fs pulses also experience broadening towards shorter wavelengths as a result of absorption. Femtosecond pulses experience larger temporal broadening than ps pulses due to the higher peak powers and faster changes of the refractive index. In the ps regime, the temporal broadening might be decreased by high injection currents due to faster carrier relaxation at high temperatures. This is not possible in the fs regime, as the QW and the bulk states are not coupled efficiently by the intraband relaxation in this case.
The measured values of the intraband relaxation time were in good agreement with theoretical predictions, but suffer from large systematical errors. An upper limit for the intraband relaxation time of 540 fs was found. A more precise value should be obtained by using amplifiers with shorter gain length. Acknowledgements The authors would like to thank Richard Wallenstein for his continuous support and many helpful and instructive discussions. We also thank the German Ministry of Research and Education for financial support (Project No. 13N8568). References [1] R. Diehl (Ed.), High-Power Diode Lasers, Topics in Applied Physics, Springer, Berlin, 2000. [2] M. Chi, O.B. Jensen, J. Holm, C. Pedersen, P.E. Andersen, G. Erbert, B. Sumpf, P.M. Petersen, Opt. Express 13 (26) (2005) 10589. [3] P.J. Delfyett, C.-H. Lee, G.A. Alphonsse, J.C. Connolly, Appl. Phys. Lett. 57 (10) (1990) 971. [4] P.J. Delfyett, A. Dienes, J.P. Heritage, M.Y. Hong, Y.H. Chang, Appl. Phys. B 58 (1994) 183. [5] H. Fuchs, M.A. Tremont, O. Casel, D. Woll, T. Ulm, J.A. L’huillier, R. Wallenstein, Appl. Phys. B 87 (2007) 425. [6] D. Woll, J. Schumacher, A. Robertson, M.A. Tremont, R. Wallenstein, Opt. Lett. 27 (12) (2002) 1055. [7] L. Goldberg, D. Mehuys, Appl. Phys. Lett. 65 (5) (1994) 522. [8] C.T.A. Brown, M.A. Cataluna, A.A. Lagatsky, E.U. Rafailov, M.B. Agate, C.G. Leburn, W. Sibbett, New J. Phys. 6 (175) (2004). [9] N.A. Olsson, G.P. Agrawal, Appl. Phys. Lett. 55 (1) (1989) 13. [10] E. Gehrig, O. Hess, A. Volland, G. Jennemann, I. Fischer, W. Elsa¨ßer, J. Opt. Soc. Am. B 21 (9) (2004) 1638. [11] R.S. Grant, W. Sibbett, Appl. Phys. Lett. 58 (11) (1991) 1119. [12] E. Gehrig, D. Woll, M.A. Tremont, A. Robertson, R. Wallenstein, O. Hess, J. Opt. Soc. Am. B 17 (8) (2000) 1452. [13] W.W. Chow, H.C. Schneider, W. Koch, C.-H. Chang, L. Chrostowski, C.J. Chang-Hasnain, IEEE J. Quantum Electron. 38 (4) (2002) 402. [14] J. Mark, J. Mørk, Appl. Phys. Lett. 61 (19) (1992) 2281. [15] D. Woll, B. Beier, K.J. Boller, M. Hagberg, S. O’Brien, R. Wallenstein, Opt. Lett. 24 (10) (1999) 691. [16] E. Gehrig, O. Hess, Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers, Springer, Heidelberg, 2003. [17] C. Lin, T.P. Lee, C.A. Burrus, Appl. Phys. Lett. 42 (2) (1982) 141. [18] J. Kaiser, I. Fischer, W. Elsa¨ßer, E. Gehrig, O. Hess, IEEE J. Quantum Electron. 42 (4) (2006) 363. [19] S. Dommers, V.V. Temnov, U. Woggona, J. Gomis, J. MartinezPastor, M. Laemmlin, D. Bimberg, Appl. Phys. Lett. 90. [20] O. Hess, T. Kuhn, Phys. Rev. A 54 (4) (1996) 3347.
Optics Communications 281 (2008) 2160–2166 www.elsevier.com/locate/optcom
Amplification of kW peak power femtosecond pulses in single quantum well InGaAs tapered amplifiers Thorsten Ulm a,*, Harry Fuchs a, Johannes A. L’huillier a, Andreas Klehr b, Bernd Sumpf b, Edeltraud Gehrig c a
Department of Physics, Technical University of Kaiserslautern, Erwin-Schro¨dinger-Straße 46, 67663 Kaiserslautern, Germany b Ferdinand-Braun-Institut fu¨r Ho¨chstfrequenztechnik, Gustav-Kirchhoff-Straße 4, 12489 Berlin, Germany c Advanced Technology Institute, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom Received 20 August 2007; received in revised form 23 November 2007; accepted 23 November 2007
Abstract The amplification of ps and fs pulses with peak powers of up to 4.5 kW has been investigated in a single quantum well InGaAs tapered amplifier. The pulses with durations of 100 fs or 2 ps were generated by a modelocked titanium–sapphire laser. The amplified pulses indicate strong gain saturation and carrier generation due to photon absorption in the laser active region which causes a temporal broadening of the amplified pulses as well as modifications of the optical spectrum. The gain recovery time was measured by a pump–probe experiment. The experimental results are analyzed with respect to the sub-ps gain dynamics which is described by a relaxation time approximation. Ó 2007 Elsevier B.V. All rights reserved. PACS: 42.55.Px; 42.60.Da; 42.65.Jx Keywords: Ultrafast optics; Semiconductor optics; Diode lasers; Femtosecond lasers; Semiconductor optical amplifiers; Intraband relaxation; Self-phase modulation
1. Introduction Semiconductor tapered amplifiers are of advantage for amplifying ultrashort pulses, due to high gain, direct electrical pumping [1] and a large spectral bandwidth of up to 30 nm [2]. In addition the spectral position of the gain profile can be chosen by an adequate chemical composition of the epitaxial structure. For these reasons semiconductor amplifiers have been investigated and used for many years in short-pulse semiconductor laser systems [3–8]. In this paper we report on the amplification of 920 nm picosecond and femtosecond pulses with high peak powers of up to 4.5 kW in a single quantum-well (QW), InGaAs tapered amplifier (TA). The fourier-limited pulses with the duration *
Corresponding author. Tel.: +49 631 2017407; fax: +49 631 205 3906. E-mail address: [email protected] (T. Ulm).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.11.062
of 130 fs or 2 ps were generated by a modelocked titanium– sapphire (Ti:Sa) laser (Spectra-Physics, model Tsunami) with a repetition rate of 82 MHz. The aim of these experiments was to investigate how the temporal and spectral shape of the amplified pulses is influenced by the fast transient changes of the carrier density, the refractive index and the gain [9,10]. The experimental results are analyzed with respect to the sub-ps dynamics as described by a relaxation time approximation. 2. Refractive index and carrier dynamics In the laser-active region, the carrier density is reduced by stimulated emission. The changes in the carrier density modify the gain and the refractive index [11]. The fast transient variation of the refractive index changes the phase of the emitted light field. Since this phase modulation is not
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caused by an external field but by the light field itself, this effect is known as self-phase modulation (SPM) [9]. SPM changes the temporal and the spectral shape of the amplified pulse [12]. A fast replacement of the recombined carriers damps the dynamics of the refractive index variations. A fast carrier transport into the QW therefore damps also the SPM. Depending on the epitaxial and geometrical structure of the semiconductor amplifier several electronic states are involved in this carrier transport. Fig. 1 shows the electronic states in the single QW, InGaAs tapered amplifier. The double heterojunction [1] is formed by a p-doped, an intrinsic and an n-doped layer. Electrons and holes are injected from the p- and n-doped regions into bulk states located in the intrinsic layer. The carriers relax into the QW states by intraband scattering processes, such as carrier–carrier and carrier-phonon scattering [13]. This process is called intraband relaxation. In good approximation the relaxation processes can be described by assuming a fixed carrier relaxation time, which is also called intraband relaxation time si . In the QW states, the carriers then decay via stimulated emission processes. As the intraband relaxation is not an instantaneous process, the value of the intraband relaxation time si is essential for the gain dynamics, if the pulse duration becomes comparable to si [14]. As outlined by Chow et al. [13], the carrier heating and the carrier relaxation occur on the fs timescale and are far from the thermal equilibrium. The simulation of non-equilibrium processes would require large computational efforts [13]. Since we restrict ourselves to a qualitative analysis of the experimental results, we will use the relaxation time approximation as described above. The error resulting from the relaxation time approximation is below the error in measurement. We would like to note, however, that more detailed theories (including the full non-equilibrium carrier dynamics) have to be used if one aims at a calculation of the pulse shape or the spectra which are strongly dependent on the ultrafast carrier dynamics.
Fig. 1. The epitaxial structure of the tapered amplifier is a double heterojunction [1], consisting of a p-doped, an intrinsic and a n-doped layer. The double heterojunction structure provides carrier and optical confinement.
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After presenting the experimental set-up, we will discuss the influence of the gain dynamics on the temporal and spectral shape of the amplified pulse. In Sections 4–6 the experimental results related to gain saturation, spectral distortion and temporal broadening are presented. The results are analyzed qualitatively by considering the sub-ps gain dynamics. Section 7 describes a pump–probe experiment that allowed to measure the intraband relaxation time. 3. Experimental setup As a pulse source, we used the commercially available modelocked titanium–sapphire (Ti:Sa) laser (Spectra-Physics, model Tsunami). This laser system generates fourier limited pulses with durations of either 2 ps or 100 fs in a diffraction limited beam with a repetition rate of 82 MHz. This offers the opportunity to investigate and compare the distortion of pulses with durations less or larger than si . The center wavelength of the Ti:Sa laser was tuned to 920 nm, the spectral gain maximum of the TA. The experimental setup is shown in Fig. 2. The pulses emitted by the Ti:Sa laser pass an optical isolator. The isolator blocks radiation emitted backwards from the TA which might disturb the mode-locking of the Ti:Sa laser. This radiation consists of amplified spontaneous emission (ASE). ASE is emitted, if the gain is not saturated completely by injected radiation [15]. Thus the amplifier emits ASE in particular between consecutive input pulses, but also at low cw input powers. In the optical isolator, chromatic dispersion stretches the pulse from about 100 fs to about 130 fs. Because of the narrow spectral width, an increase of the pulse duration was not observed for the 2 ps pulses. These Ti:Sa laser pulses are amplified in a 2.75 mm long TA, manufactured by the Ferdinand-Braun-Institut fu¨r Ho¨chstfrequenztechnik based in Berlin, Germany. The active region consists of a 0.75 mm long ridge waveguide section for pre-amplification and a 2 mm long tapered section for the generation of the high power output. The tapered region is used to spatially expand the optical power, to keep the spatial power density below the damage threshold. The taper angle is 6° and close to the diffraction angle at the end of the ridge waveguide. The QW consists of InGaAs, the optical waveguide is 1 lm high and consists of AlGaAs. The dimensions of the output facet are 200 lm 1 lm. To prevent lasing inside the amplifier both facets were AR coated and have a residual reflectivity of < 3 104 . A spherical and a cylindrical lens collimate the output beam and compensate for the astigmatism caused by the rectangular output facet. The vertical divergence of the output beam is less than 28°. In cw operation, 74% of the optical output power is emitted in a near-diffraction limited beam ðM 2 ¼ 1:15Þ. The mounting base of the TA is thermo-electrically cooled to a temperature of 20 °C. The laser pulses were characterized before and after amplification. An optical isolator prevents back reflections from the diagnostic tools into the TA. For diag-
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Fig. 2. The experimental setup includes a power meter, an auto-correlator and a spectrometer to characterize the pulse properties of the input and the amplified output pulse. To measure the intraband relaxation time in a pump–probe experiment, an optional beam splitter with an adjustable delay time was added. For further details see text.
nostics a power meter (MellesGriot, model: 13PEM001), a SHG auto-correlator (APE, model: Pulse-Check) and a double-grating spectrometer (Ando Electronics, model: AQ6317B) were used. To measure the magnitude of si in a pump–probe experiment the pulses pass a beam splitter (see Fig. 2). One of the spatially separated pulse trains is delayed before both pulse trains are re-united at the beam splitter and injected into the TA. In this way a train of double-pulses with a variable temporal separation of up to 30 ps was generated. 4. Gain saturation As mentioned in Section 2, the ratio of the pulse duration and si is crucial for the gain dynamics. One of the system parameters that strongly depends on the gain dynamics is the output power: If the pulse duration becomes comparable to or shorter than si then the output power is expected to decrease significantly. In such a case, the QW states cannot be re-populated during the pulse duration which leads to strong gain saturation.
pulsed operation, we can subtract the ASE power emitted by the free-running amplifier in good approximation. But in the cw regime P ase out is not constant, because the gain is saturated by the amplified signal radiation [15]. From the fact that P total out consists of ASE and amplified signal power, we obtain ase sig P total out ¼ P out þ P out P in ase ase P out ¼ P max exp P sat P in sig sig P out ¼ P max 1 exp P sat
ð2Þ ð3Þ ð4Þ
with the saturation power P sat and the maximum ASE and sig signal output power, P ase max and P max . For the cw measurease ments P out was subtracted from P total out after fitting Eq. (4) to the data. As can be seen from Fig. 3, the highest gain values are obtained for cw input. In the cw regime, the amount of carriers in the QW states is given by the equilibrium of injected carriers and stimulated recombination. The gain increases with the injection current, as long as no thermal roll-over
To confirm this expectation, cw radiation from a diode laser as well as modelocked pulses were amplified in the TA. The output powers achieved with the same average input powers were compared to each other. The experimental results are shown in Fig. 3. In general, laser amplifiers are characterized by their gain g (dB) given by ! P in g ðdBÞ ¼ 10 log10 sig ð1Þ P out where P in and P sig out are the signal input and output power, respectively. In the following discussion, we assumed the Ti:Sa laser to be free of ASE. Please note that the ASE power P ase out has to be subtracted from the total output sig power P total out to obtain the signal output power P out . For
gain [dB]
4.1. Experimental results
average input power [mW] Fig. 3. Dependence of the amplifier gain on the average input power and on the injection current measured for cw and pulsed laser radiation.The injection current is either 3 A (solid symbols) or 5 A (open symbols).
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4.2. Gain depletion by ASE The influence of ASE may be understood by the fact that the amplifier emits ASE between two consecutive pulses. The gain depletion by ASE results in a poor storage of energy in the bulk states and in the QW states. ASE is emitted, when the inversion is sufficiently large to amplify the radiation generated by spontaneous emission. If the current is increased, the additional amount of carriers is depleted by ASE and is thus not available to amplify the next pulse [16]. Therefore, the inversion is limited by the ASE, and not the current. At the time when the next pulse arrives the inversion is the same at all the currents. In the fs regime additionally, the influence of the intraband relaxation becomes observable. 4.3. The influence of the intraband relaxation Due to the non-instantaneous intraband relaxation a delayed gain recovery occurs in pulsed operation. The gain recovery inside the QW takes place on a timescale of about si 500 fs [10]. A 130 fs long pulse is much shorter than si and is affected in a different manner by the carrier dynamics than a 2 ps long pulse (which is four times longer than si ). For 2 ps long pulses one expects that a partial gain recovery occurs during the pulse duration, since carriers
relax from the bulk states into the QW states. A 2 ps long pulse therefore depletes not only the QW states, but also the bulk states. For 130 fs long pulses no gain recovery during pulse propagation is expected, because the intraband relaxation processes are too slow to re-populate the QW states. For the amplification of a 130 fs long pulse only the initial inversion in the QW is available, which results in strong gain saturation even for low input powers. Since a larger amount of carriers is available to amplify a 2 ps long pulse, it experiences more gain than a 130 fs long pulse (see Fig. 3). 5. Spectral distortions As mentioned in Section 2, depletion of the carriers causes not only gain saturation but also SPM. As the refractive index is changing while the pulse propagates within the amplifier, the relative phases of different spectral components of the pulse are changed and new spectral components are generated [12]. The spectral as well as the temporal shape of a pulse is created by the interference of its spectral components. Changes in the phase of the light field therefore lead to spectral distortions [9,12]. To obtain further information on the influence of the ultrafast gain dynamics on the output pulses we have measured and compared the spectral shape of the pulses with the durations of 2 ps and 130 fs, i.e. longer and shorter than si . The spectra of the amplified 2 ps long pulses are shown in Fig. 4. The pulse induced carrier depletion leads (via the real part of the susceptibility) to a corresponding increase in the spectral index dispersion. In combination with the saturation of the gain this leads to a red shift [17] of 0.5 nm and to the generation of a spectral satellite peak at a distance of 0.6 nm to the main peak [9–11]. Since no absorption occurs for ps pulses with input powers below 50 mW, the spectral distortions are limited to
normalized intenstiy
occurs. At an injection current of 5 A, the small signal gain for cw radiation is 25 dB. In the experiment the current was limited to 5 A to limit the thermal load of the amplifier. For ps pulses, the small signal gain is reduced by a factor of 2. We attribute this to the low repetition rate (82 MHz) of the Ti:Sa laser, which leads to high peak powers and causes strong gain saturation within the TA. For ps pulses with average input powers up to 50 mW the gain remains positive. The small signal gain for 130 fs long pulses is comparable to the value observed for ps pulses, but absorption occurs, if the input power exceeds 12 mW. For higher input powers one could expect that the TA becomes transparent due to absorption saturation which corresponds to a gain of zero. In contrast to this expectation zero gain is not observed, but the gain becomes negative. This is a direct consequence of the ultrafast carrier dynamics. For high input powers, two processes occur within the pulse envelope: First, the leading edge of the pulse depletes the inversion in the QW states. Second, the trailing parts of the pulse causes a dynamic carrier excitation. As a consequence, absorption of light occurs, i.e. the gain becomes negative. For cw operation, we found an increase of the gain with increasing injection currents. (Please note the logarithmic scaling of g, i.e. small variations of g correspond to large changes in the output power.) The situation is different, if the amplifier is used for pulse amplification. There are two reasons why higher gain currents do not provide higher gain for short optical input pulses: The gain depletion by the ASE and the non-instantaneous gain recovery.
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wavelength [nm] Fig. 4. Spectra of amplified ps pulses (thin lines) measured for different optical input powers (solid line: 5 mW, dash-dotted line: 20 mW, dashed line: 50 mW) in comparison to the spectrum emitted by the Ti:Sa laser (thick gray line).
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wavelengths longer than the center wavelength [11]. Higher input powers lead to stronger depletion of the inversion and therefore cause stronger SPM effects. As expected, the amplitude of the satellite peak increases with input power (see Fig. 4). The results of the experiments performed with 130 fs long pulses are shown in Fig. 5. The peak power of a pulse with a duration of 130 fs is approximately 15 times higher than the peak power of a 2 ps long pulse for the same average power. Additionally, the intraband relaxation is too slow to transfer carriers from the bulk states into the QW states. Unlike for ps pulses, for the amplification of the 130 fs pulses only the initial inversion in the QW states is available. Therefore, one can expect much stronger gain saturation and consequently stronger spectral distortions than in the ps regime. The experimental results shown in Fig. 5 reveal that – compared to the amplification of ps pulses – a fs pulse experience larger spectral broadening. The spectral width Dk of the output pulses was calculated using the following formula for the second moment: ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 1 2 Dk ¼ 2 ðk kc Þ SðkÞdk N ð5Þ Z Z 1 k SðkÞdk; N ¼ SðkÞdk kc ¼ N
6. Temporal broadening The nonlinear chirp caused by the SPM not only results in spectral distortions but also in a temporal broadening of the pulses. Temporal broadening in amplifiers is critical for a wide range of applications that require short pulses with high peak powers (e.g. SHG). A detailed measurement of the temporal broadening in the QW tapered amplifier is thus of high importance for the development of optimized amplifier systems. To describe the temporal broadening we introduce the temporal broadening factor f, defined by the ratio of the FWHM sACF of the autocorrelation functions (ACF) before and after the amplification of the laser pulses. sACF;out ð6Þ f¼ sACF;in In general, temporal broadening in the amplifier can be caused by dispersion and by SPM. To obtain information on the magnitude of these influencing factors we have systematically measured the temporal broadening of ps and fs pulses in dependence on the average input power and the amplifier current. The results are summarized in Fig. 6. The temporal pulse broadening increases with the input power and saturates for large input powers. This is obvious from the fact that the largest transient change of the refractive index occurs if the inversion is totally depleted. The contribution of the dispersive broadening can be identified by extrapolating f to zero input power. For very low input powers the gain depletion is negligible and no SPM occurs. Extrapolating the data in Fig. 6 to zero input power we found a dispersive broadening factor of 1.6–1.7 for ps pulses and 1.3–2.0 for fs pulses.
normalized intenstiy
temporal broadening factor
SðkÞ denotes the spectral power distribution, values smaller than 3% of the maximum were considered to be noise and set to zero for the integration. Related to the FWHM of the input pulses (Dk = 10.48 nm) the output pulses are broadened spectrally by a factor of 1.52 (3 A) and 1.59 (5 A). Another important consequence of the SPM is the large redshift of about 5.1 nm. A 130 fs long pulse causes both carrier depletion by stimulated emission and carrier generation by photon absorption in the active layer, as indicated by the gain characteristics shown in Fig. 3. The amplified fs pulses thus shows a characteristic spectral broadening towards both shorter and longer wavelengths [11].
As the pulse duration is much shorter than si , the distortions are also supposed to be independent from the carrier density in the bulk bands and from the injection current. This expectation is confirmed by the results shown in Fig. 5.
wavelength [nm] Fig. 5. Spectra of amplified 130 fs pulses measured for two amplifier currents of 3 A (thin solid line) and 5 A (thin dashed line) in comparison to the spectrum of the input pulse (thick gray line).
average input power [mW] Fig. 6. Temporal broadening of the ps pulses (solid symbols) and the fs pulses (open symbols), measured for different injection currents. For the definition of f, see text.
T. Ulm et al. / Optics Communications 281 (2008) 2160–2166
7. Pump–probe experiments As described above, the intraband relaxation time si represents a key feature in the amplification of ultrashort pulses. In particular, it has a strong influence on the output power as well as on the temporal and spectral pulse characteristics. To obtain further information on the value of si we have set up a pump–probe experiment (similar to those described in Refs. [14,18,19]). This method allows to measure si directly. To generate pump and probe pulses, a beam splitter with adjustable pulse delay (shown in Fig. 2) was used. Pump and probe pulses were injected into the TA with delay times between 0 and 30 ps. The first pulse is used to saturate the gain. The available gain for the second pulse depends on the delay time and the dynamics of the gain recovery. We expect the output power to increase as soon as the delay time becomes comparable to si , because the QW states are re-populated during the delay time and the second pulse will experience more gain. An average input power of 1 mW was used for both the pump and the probe pulse train to prevent substantial temporal broadening (see Fig. 6 for comparison). The current was set to 3 A to keep the thermal load of the amplifier and the influence of the ASE at a low level. To determine the delay time between the pump and the probe pulses, two different methods were used, depending on the size of the delay time. The first method is based on the auto-correlation function (ACF). A double-pulse generates an ACF with three peaks. For delay times larger than 0.5 ps, the delay between the pump and the probe pulse was obtained directly from the satellite maxima of the ACF. For delay times comparable to the output pulse duration, this method fails because the three maxima are not resolved in the ACF. Therefore, delay times smaller than 0.5 ps were obtained from amplitude modulations in the spectra of the output pulse. Therefore, we consider the
two pulses as a superposition of plane waves within a certain spectral range. Spectral components with the same wavelength can interfere constructively or destructively with each other. The periodicity Dx of interference minima and maxima in the output spectrum is therefore Dx Dt ¼ 2p
ð7Þ
where Dt denotes the delay time. Both methods were demonstrated to yield consistent results for those delay times, for which both methods were applicable. As presented in Section 2, si denotes the decay time of the bulk states for electronic transitions into the QW states. If the QW states had been depleted completely, the population N QW of the QW states after a time interval Dt should be Dt N QW ðDtÞ ¼ N QW ð1Þ 1 exp ð8Þ si with N QW ð1Þ denoting the final inversion for Dt ! 1. Since the gain and the output power is (approximately) proportional to the amount of carriers, the function Dt sig sig P out ðDtÞ ¼ P out ð1Þ AP exp ð9Þ si was fitted to the experimental results to obtain si . P sig out ð1Þ denotes the maximum output power achieved for an infinite pulse delay. The amplitude AP is the difference between the maximum and the minimum output power. Fig. 7 shows the average output power in dependence of the delay time between the pump and the probe pulse. The experimental data are in good agreement with the model described by Eq. (9). From the data shown in Fig. 7 we obtained si ¼ ð540 60Þ fs: An intraband relaxation time of 540 fs is in good agreement with microscopic calculations using Boltzmann collision terms for the intraband scattering processes [10,20].
average output power [mW]
Fig. 6 reveals a significantly stronger broadening for fs pulses than for ps pulses. This originates from the higher peak power and larger spectral bandwidth of the fs pulses. In addition, the shorter pulse length leads to a faster transient change of the refractive index. For higher currents the amount of carriers interacting with the light field is larger, leading to stronger index modulations and an increase in temporal broadening. In contrast to the amplification of ps pulses, the gain dynamics induced by fs pulses includes carrier generation by photon absorption, which causes additional index changes. As can be seen in Fig. 6, the broadening of the 2 ps pulses decreases slightly with increasing injection current. We attribute this effect to higher temperatures in the active layer due to the higher current. Higher temperatures cause slightly faster carrier relaxation into the QW states, because the intraband relaxation is partially driven by carrier-phonon scattering [13].
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measured data points exponential ascent
pulse delay [ps] Fig. 7. Pump–probe experiment performed with pairs of 130 fs long pulses of equal power with delay times in the range of 0–30 ps. The average input power of each the pump and the probe pulses is 1 mW. The amplifier current is 3 A.
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Generally, the relaxation rate is influenced by the amplifier injection current and by the electronic band structure of a given semiconductor device [20]. A measurement of this dependence is, however, beyond the accuracy of our experimental setup and thus is planned for future investigations. Our experimental result can only be interpreted as an upper limit for si , since the temporal pulse broadening has to be taken into account. The temporal resolution of the presented experiment is given by the temporal broadening of the pulse in the TA. Although pump and probe pulses have an average input power of only 1 mW, they experience a broadening from 130 fs to 480 fs, as shown in Fig. 6. Therefore, relaxation processes on time scales shorter than 480 fs cannot be measured with the used setup, and the value of 540 fs has to be considered as an upper limit for si . (Values for si obtained by pump– probe experiments in high power TA’s are strongly affected by temporal broadening, as known from other experiments with high power semiconductor amplifiers [18].) In future investigations, we plan to perform pump– probe experiments within shorter amplifiers, since the shorter gain length should reduce the temporal broadening and might provide more precise results. 8. Summary We investigated the amplification of modelocked pulses in a single quantum well InGaAs tapered amplifier. The pulses were generated with a titanium–sapphire laser with a repetition rate of 82 MHz. For a qualitative analysis of the gain dynamics in the tapered amplifier, a relaxation time approximation was used. In pulsed operation high peak powers, carrier depletion by ASE and a delayed gain recovery in the QW states cause gain saturation even at low input powers. Gain depletion results in self-phase modulation evident from spectral and temporal pulse distortions. Picosecond pulses are broadened to longer wavelength because of gain depletion, while fs pulses also experience broadening towards shorter wavelengths as a result of absorption. Femtosecond pulses experience larger temporal broadening than ps pulses due to the higher peak powers and faster changes of the refractive index. In the ps regime, the temporal broadening might be decreased by high injection currents due to faster carrier relaxation at high temperatures. This is not possible in the fs regime, as the QW and the bulk states are not coupled efficiently by the intraband relaxation in this case.
The measured values of the intraband relaxation time were in good agreement with theoretical predictions, but suffer from large systematical errors. An upper limit for the intraband relaxation time of 540 fs was found. A more precise value should be obtained by using amplifiers with shorter gain length. Acknowledgements The authors would like to thank Richard Wallenstein for his continuous support and many helpful and instructive discussions. We also thank the German Ministry of Research and Education for financial support (Project No. 13N8568). References [1] R. Diehl (Ed.), High-Power Diode Lasers, Topics in Applied Physics, Springer, Berlin, 2000. [2] M. Chi, O.B. Jensen, J. Holm, C. Pedersen, P.E. Andersen, G. Erbert, B. Sumpf, P.M. Petersen, Opt. Express 13 (26) (2005) 10589. [3] P.J. Delfyett, C.-H. Lee, G.A. Alphonsse, J.C. Connolly, Appl. Phys. Lett. 57 (10) (1990) 971. [4] P.J. Delfyett, A. Dienes, J.P. Heritage, M.Y. Hong, Y.H. Chang, Appl. Phys. B 58 (1994) 183. [5] H. Fuchs, M.A. Tremont, O. Casel, D. Woll, T. Ulm, J.A. L’huillier, R. Wallenstein, Appl. Phys. B 87 (2007) 425. [6] D. Woll, J. Schumacher, A. Robertson, M.A. Tremont, R. Wallenstein, Opt. Lett. 27 (12) (2002) 1055. [7] L. Goldberg, D. Mehuys, Appl. Phys. Lett. 65 (5) (1994) 522. [8] C.T.A. Brown, M.A. Cataluna, A.A. Lagatsky, E.U. Rafailov, M.B. Agate, C.G. Leburn, W. Sibbett, New J. Phys. 6 (175) (2004). [9] N.A. Olsson, G.P. Agrawal, Appl. Phys. Lett. 55 (1) (1989) 13. [10] E. Gehrig, O. Hess, A. Volland, G. Jennemann, I. Fischer, W. Elsa¨ßer, J. Opt. Soc. Am. B 21 (9) (2004) 1638. [11] R.S. Grant, W. Sibbett, Appl. Phys. Lett. 58 (11) (1991) 1119. [12] E. Gehrig, D. Woll, M.A. Tremont, A. Robertson, R. Wallenstein, O. Hess, J. Opt. Soc. Am. B 17 (8) (2000) 1452. [13] W.W. Chow, H.C. Schneider, W. Koch, C.-H. Chang, L. Chrostowski, C.J. Chang-Hasnain, IEEE J. Quantum Electron. 38 (4) (2002) 402. [14] J. Mark, J. Mørk, Appl. Phys. Lett. 61 (19) (1992) 2281. [15] D. Woll, B. Beier, K.J. Boller, M. Hagberg, S. O’Brien, R. Wallenstein, Opt. Lett. 24 (10) (1999) 691. [16] E. Gehrig, O. Hess, Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers, Springer, Heidelberg, 2003. [17] C. Lin, T.P. Lee, C.A. Burrus, Appl. Phys. Lett. 42 (2) (1982) 141. [18] J. Kaiser, I. Fischer, W. Elsa¨ßer, E. Gehrig, O. Hess, IEEE J. Quantum Electron. 42 (4) (2006) 363. [19] S. Dommers, V.V. Temnov, U. Woggona, J. Gomis, J. MartinezPastor, M. Laemmlin, D. Bimberg, Appl. Phys. Lett. 90. [20] O. Hess, T. Kuhn, Phys. Rev. A 54 (4) (1996) 3347.