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Heterodyne pump-probe and four-wave mixing in semiconductor optical amplifiers using balanced lock-in detection
1 October 1999
Optics Communications 169 Ž1999. 317–324 www.elsevier.comrlocateroptcom
Full length article
Heterodyne pump-probe and four-wave mixing in semiconductor optical amplifiers using balanced lock-in detection P. Borri ) , W. Langbein 1, J. Mørk, J.M. Hvam Research Center COM, The Technical UniÕersity of Denmark, Building 349, DK-2800 Lyngby, Denmark Received 26 April 1999; accepted 12 July 1999
Abstract We demonstrate a new detection scheme for pump-probe and four-wave mixing heterodyne experiments, using balanced detection and a dual-phase lock-in for spectral filtering. The technique allows the use of low repetition-rate laser systems, as is demonstrated on an InGaAsPrInP bulk optical amplifier at 1.53 m m. Ultrafast pump-induced changes in the amplitude and phase of the transmitted probe signal are simultaneously measured, going from small to large signal changes and with no need of an absolute phase calibration, showing the versatility and the sensitivity of this detection scheme. The results for small perturbations are consistent with previous pump-probe experiments reported in literature. Time-resolved four-wave mixing in the absorption regime of the device is measured, and compared with numerical simulations, indicating a 100 fs dephasing time. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.55.Px; 78.47.q p Keywords: Ultrafast spectroscopy; Semiconductor laser
1. Introduction Optical pump-probe experiments can provide direct information on the ultrafast dynamics of gain and refractive index in semiconductor optical amplifiers ŽSOAs., as shown in several works in the past w1–8x. Recently a novel pump-probe heterodyne technique was introduced, where pump and probe can propagate co-linearly and with equal polarization ) Corresponding author. Fax: q45 4588 7762; e-mail: [email protected] or [email protected] 1 Present address: Lehrstuhl fur ¨ Experimentelle Physik EIIb, Universitat ¨ Dortmund, Otto-Hahn Str.4, 44221 Dortmund, Germany.
w2,5x. This technique measures the electric field of the probe, and can provide information on both amplitude and phase changes induced by the pump pulse. It has also been used for non-degenerate measurements, where pump and probe are at different wavelengths w6,7x. In both cases the experiments were performed with high repetition-rate laser-systems, using a high-frequency radio-receiver to detect the 1 MHz beat between reference and probe pulses. Switching between the AM or FM operation of the radio receiver it was possible to detect alternatively amplitude or phase changes induced by the pump pulse. For differential measurements, modulations were induced by chopping the pump beam and their amplitude was measured by a lock-in after the radio
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 3 9 1 - 0
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P. Borri et al.r Optics Communications 169 (1999) 317–324
receiver w5x. For the phase change measurements, a calibration with respect to a known optical phase change was necessary. Also, both techniques used a Michelson-interferometer to recombine probe and reference, with a single detector. In this way, the full amplitude noise of pump and probe beams affects the measurements. In this paper we demonstrate a novel heterodyne detection scheme, where a Mach-Zehnder interferometer, a balanced detection, and a dual-phase lockin is used for signal recovery. The lock-in provides amplitude and phase measurements at the same time, with no need of absolute phase calibration. The balanced detection is suppressing the amplitude noise from the laser source, making it feasible to work with a 300 kHz laser system of 10% amplitude noise. Results are shown for an InGaAsP bulk SOA, in both the weak and strong perturbation regime. With the same set-up the four-wave mixing signal induced by two exciting pulses can be detected and time-resolved.
2. Experimental set-up The heterodyne detection scheme works by imposing a small ŽMHz. frequency shift between the pump and the probe beam. By mixing the output mode of the device with a third, reference pulse at yet another frequency, the probe beam can be separated out by detecting at the proper beat frequency between probe and reference. Acousto-optic modulators ŽAOMs. are appropriate for frequency shifting the beams in the range of tens of MHz. In the case of laser systems with repetition rates larger than the AOM frequency shifts, such as investigated in Refs. w5,6x, the detection process can be understood by considering the shifts imposed by the AOMs on each of the laser mode frequency components individually. In the case of a laser system with a repetition rate much lower than the AOM induced frequency shifts, the beat frequency acquires a large number of lower sidebands, closely spaced by the repetition rate. Also, the duty cycle is much lower, and both
Fig. 1. Ža. Experimental set-up. C1 and C2: broadband non-polarizing cube beam-splitters; A: 200 m m aperture, L: lens, AC: autocorrelator, SOA: semiconductor optical amplifier. Žb. Scheme of the electrical mixing to generate the reference signal for lock-in. LP: low-pass filter, HP: high-pass filter.
P. Borri et al.r Optics Communications 169 (1999) 317–324
issues require a higher selectivity and sensitivity for the detection process. We show here, that the use of a balanced detection in combination with lock-in frequency filtering satisfies these demands and additionally provides a direct measurement of phase and amplitude. The experimental set-up is shown in Fig. 1a. The laser source is the idler of an Optical Parametric Amplifier that uses the output of a Ti:sapphire regenerative amplifier system to produce 140 fs pulses tunable from 0.9 to 2.5 m m at 295 kHz repetition rate. The large number of nonlinear processes Žwhite-light generation, frequency doubling and parametric amplification. leads to a large amplitude noise Žf 10%. of the system. Linear chirp compensation is achieved by a pulse-shaper. The pump pulse is obtained by deflecting the laser beam with an AOM driven at 40 MHz with a large maximum deflection efficiency Ž92% at 1.5 m m wavelength.. This AOM can be made of dispersive glass because the induced chirp can be precompensated by the pulse-shaper. This precompensation is monitored by optimizing the temporal pulsewidth with an autocorrelator ŽAC.. By controlling the radio-frequency ŽRF. power driving the AOM, the intensity of the pump pulse can be adjusted with high precision over four orders of magnitude. The probe pulse is obtained by deflecting the beam transmitted through the first AOM with a second AOM driven at 39 MHz. This AOM is made of fused-silica that does not introduce a significant pulse broadening but has a low maximum deflection efficiency Ž20% at 1.5 m m.; since the probe beam has to be weak in order not to perturb the system, this is not a limitation of the experiment. The probe intensity is controlled by the RF power driving the second AOM. Pump and probe beams are recombined by a non-polarizing cube beam-splitter ŽC1. and focused into the device by a high numerical-aperture ŽNA. aspheric lens. The light at the output of the device is collected with an equal high NA lens, focused into a 200 m m aperture ŽA. for spatial selection of the waveguide mode, collimated by a lens ŽL. and directed into a Mach-Zehnder interferometer. The transmitted beam from the second AOM is the reference beam that can be optionally injected into the device by a second cube beamsplitter ŽC2. Žand it has to precede the pump and probe by ; 1ns in order not to perturb the SOA., or
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can travel outside the device and be combined, using cube beam-splitters, in the Mach-Zehnder interferometer with the signal from the device. The probe signal transmitted through the device, which is frequency shifted by 39 MHz, interferes with the reference beam; both beams are pulse-trains at the laser repetition rate, i.e., are composed in the frequency domain of modes frequency spaced by 295 kHz. The lowest interference frequency between the probe modes and the reference modes, which is the only one in the range of the low-frequency lock-in, is 39 MHz down-shifted by 132 times the repetition rate, i.e. 60 kHz. This interference signal is detected in the intensity difference of the two output beams from the Mach-Zehnder interferometer by a balanced InGaAs detector of 125 kHz 3 dB-bandwidth. The balanced detection rejects the common-mode laser noise 2 . The interference signal is recovered by a dual-phase low-frequency lock-in ŽF 100 kHz.. The synchronized electric signal for the reference channel of the lock-in is obtained by down-mixing the sinusoidal electrical reference signal from the probe AOM driver with a high harmonic in the synchronous TTL signal at 295 kHz repetition rate from the laser driver, as shown in Fig. 1b. The TTL signal is high-pass filtered in order to reject lowfrequency components in the range of the lock-in reference signal. The mixed signals at higher frequencies are rejected by low-pass filters after the mixer. To detect the FWM signal, which has a frequency of two times the probe minus the pump frequency, the electrical reference signal is obtained by frequency-doubling the reference signal from the probe AOM driver Ž v 2 ; 39 MHz., then down-mixing
2
Actually, the noise level in our differential measurements was still limited by the laser noise and it was therefore depending on the stability of the laser source. In case of best performance we have reached less than 1% noise over a single scan. Shot noise at 300 KHz repetition rate, 10 fJ output probe pulse energy, and our detection quantum efficiency of about 20% is 1.5P10y5 r'Hz . The balanced detector used in the experiment ŽNew Focus Nirvana a 2017. was actually not rejecting the common mode laser noise sufficiently, i.e. to the shot noise limit, probably due to the small duty cycle of the pulses Ž2P10y7 ., which might lead to a transient overload of the detector Žpulse peak power of the reference pulse is ;1 KW.. Note that the 1% noise level in the differential transmission corresponds to 0.1 dB as the minimum measurable gain change, well in the small signal regime.
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it with an electric signal from the pump AOM driver Ž v 1; 40 MHz., and finally down-mixing the resulting frequency Ž38 MHz. with a high harmonic of the laser repetition rate from the laser TTL output. In Fig. 1b HP and LP indicate high-pass and low-pass filters, used in order to isolate the desired frequency component. The used frequency doublerrmixers and filters were cheap commercially available components. The whole optical set-up is covered to reject air-flow and thus provide phase-stability. Slow thermal drift is eliminated in the differential recording. The stability of the set-up allows for long delay scans and averaging over multiple scans, with no need of active stabilization. The set-up is shown for co-linearly polarized pump and probe pulses, the cross-linear case is obtained by rotating the pumppolarization by 90 degrees using a lr2 waveplate. All experimental results presented in this paper were obtained for co-linear polarization corresponding to the TE mode of the waveguide. For each pump-probe delay amplitude and phase of the transmitted probe is measured with and without the presence of the pump, for differential measurements, by changing the pump AOM RF-power. The phase measurement is directly given by the angle between the X and Y components in the lock-in, with no need of absolute phase calibration, while the amplitude is given by detecting R s 'X 2 q Y 2 . In this way, amplitude and phase are detected simultaneously during the same measurement. Moreover, the direct comparison between amplitude and phase in presence and absence of the pump allows to measure signal changes far from the small perturbation regime, not possible with a radio receiver which is relying on small amplitude and frequency modulations. 3. Pump-probe experiment An example of pump-probe measurements on a commercially available InGaAsrInP bulk amplifier at room temperature is shown in Fig. 2. The amplifier is 250 m m long and has a small signal gain of 13 dB at 120 mA bias current and 1.53 m m wavelength. The measurements are performed at different bias currents, corresponding to gain Ža., transparency Žb. and absorption Žc. at 1.53 m m, and for different
Fig. 2. Pump-induced change of the gain in a pump-probe experiment, at a wavelength of 1.53 m m and different bias currents corresponding to Ža. gain, Žb. transparency and Žc. absorption in the device. Both small and high signal changes, as obtained for different pump intensities, are shown. Nearly instantaneous gain changes, carrier heating effects and long-lived changes are visible, and strongly affected by the pump intensity Žsee text for details..
pump pulse energies. In Fig. 2a the changes in the gain at 120 mA bias current induced by a pump pulse with energy of 11 fJ and 460 fJ are shown. The probe pulse energy was less than 1 fJ. The change of the intensity gain in dB is calculated from the differential electric field transmission DTrT using DGŽdB. s 20logŽ1 q DTrT .. In the small perturbation regime Ž11 fJ., the results show an ultrafast gain reduction due to stimulated emission induced by the pump Žspectral-hole burning. and a recovery on a picosecond time-scale due to the recovery of carrier heating ŽCH., as reported in literature w3,5x. In the strong perturbation regime Ž460 fJ., a large ultrafast gain reduction exceeding the 13 dB small signal gain of the device is measured, indicating that an ultrafast
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loss channel additional to the pump-induced stimulated emission is present, since the stimulated emission can at maximum lead to transparency. This could be consistent with the occurrence of two-photon absorption ŽTPA. of the probe and pump photons, which almost follows the pulse autocorrelation time dependence w9x, as already reported in several pump-probe experiments. The recovery of the gain compression clearly occurs with two different time scales: an initial fast recovery that can be attributed to TPA and spectral-hole burning ŽSHB., and a slower recovery due to CH. At transparency ŽFig. 2b. for 35 mA bias current, no net stimulated transitions can occur. The two curves shown refer to pump energies of 0.58 pJ and 5 pJ and a probe pulse energy of 20 fJ, still in the region of negligible probe-induced gain changes. Both at high and small pump energy an initial fast negative-going transient is observed. This has been reported previously w3,5,8x and attributed to TPA. For small pump energies the recovery of this negative transient occurs in two parts: an initial instantaneous recovery of the TPA Ži.e., following the pump pulse., and a delayed slower recovery due to free carrier heating w5,8x. For large pump energies the dynamic at small delay times is more complicated, with stronger ondulation and delay in the onset of the carrier heating recovery. Similar effects have been observed in the literature and explained with the occurrence of spectral artifacts w8x, i.e., due to pump-induced changes of the refractive index in combination with gain dispersion, even if a link between large pump energies and stronger spectral artifacts is not reported and has to be further investigated. It is interesting to note that the long-lived changes of the gain for high pump energy is positiÕe indicating an increased carrier density induced by TPA. For 6 dB absorption ŽFig. 2c. at 20 mA bias current, the pump energies were 0.58 pJ and 10 pJ and the probe energy was 40 fJ. For small pump energies a fast positive gain change due to SHB followed by a slower recovery due to carrier cooling and a positive long-lived change, due to the increased carrier density, is observed in agreement with previous results w8x. At high pump energy a first negative fast transient, likely due to TPA, is followed by a strong positive peak up to full bleaching
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of the absorption by SHB. These effects are probably also strongly enhanced by the spectral artifact w8x. TPA induces significant heating by real carrier excitation in this strong pump regime w4x and the hot distribution subsequently cools, giving the slow positive transient. In Fig. 3 the phase dynamics measured together with the data of Fig. 2 are shown. Since the refractive index is sensitive to non-resonant changes in oscillator strength, it gives complementary information to the resonant absorption shown in Fig. 2. In Fig. 3a the long-lived positive phase-change corresponds to a reduction of the carrier density, in agreement with pump-induced stimulated emission. The initial fast positive change of the phase corresponds to the CH effect, that recovers on a picosecond time-scale. In transparency ŽFig. 3b. the negative
Fig. 3. Pump-induced phase changes for the same conditions as in Fig. 2. Instantaneous nonlinearities, carrier heating effects on a picosecond time-scale, and long-lived changes are clearly observed and strongly influenced by the pump intensity Žsee text for details..
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ultrafast phase change is due to instantaneous nonlinearities of the refractive index, associated with TPA but also electronic Raman and optical Stark effects w10,8x. Note that in the high pump-energy case the long-lived phase change is negative, indicating an increase in carrier density in agreement with the optically induced inversion via TPA, observed in the gain change. In absorption ŽFig. 3c. the TPA is observed together with a strong instantaneous index nonlinearity at large pump energy, both in the carrier heating and in a strong long-lived phase change due to carrier density increase. We notice that the present experiments are carried out for parallel pump and probe polarizations, where the coherent coupling due to pump-probe interference leads to an instantaneous so-called ‘‘coherent’’ artifact, which is a coherent interaction of pump and probe at the probe frequency, that has to be subtracted when comparing with orthogonal pump and probe measurements w5x. The influence of the coherent artifact was theoretically analyzed in Ref. w11x for the heterodyne scheme, although only in the adiabatic limit of fast polarization dephasing and small pump-induced changes. Further investigations of these coherent phenomena are required and can be accomplished using the FWM technique presented in the next section.
detection scheme. Pulse 1 is frequency shifted by v 1 s 40 MHz in the first AOM and corresponds to the pump beam in the pump-probe experiment Žsee Fig. 1.. Pulse 2 is delayed by t with respect to pulse 1, is frequency shifted by v 2 s 39 MHz in the second AOM and corresponds to the probe beam in the pump-probe experiment. The interference between the FWM signal and the reference pulse is detected by the balanced detector and the lock-in at the lowest side band of the frequency 2 v 2 y v 1 modulo the 295 KHz repetition rate Žsee Fig. 1b.. The measured FWM signal is the time-average over the product of the reference pulse electric field and the FWM electric field. The time resolution is thus given by the reference pulse duration, and the timedynamics of the FWM signal is measured as a function of the reference delay t for each value of t . In Fig. 4 the TR–FWM signal in the absorption region Žfor 20 mA bias current. is shown at different delay times t of the two exciting beams, as indicated. The pulse energies were 0.62 pJ for pulse 1 and 1.25 pJ for pulse 2. In the inset the time-integrated FWM ŽTI–FWM. field amplitude is also
4. Time-resolved four-wave mixing The use of the heterodyne technique for time-resolved four-wave mixing ŽTR–FWM. with collinear exciting beams was proposed by Mecozzi et al. w11x and experimentally demonstrated by Hofmann et al. w12x. This technique avoids the phase-matching restriction present in the commonly used non-collinear geometries and enables the use of waveguide devices such as semiconductor optical amplifiers. In this way long interaction lengths are accessible, which allows to measure weak nonlinearities. We have recently demonstrated this advantage measuring the time-resolved FWM response in III-V semiconductor quantum-dot amplifiers w13x. The FWM signal is created by two exciting pulses with time delays of yt y t and yt relative the reference pulse, respectively, and is detected by its interference with the reference pulse using the lock-in
Fig. 4. Time-resolved four-wave mixing field amplitude at a wavelength of 1.53 m m and 20 mA bias current, for different delay times of the two exciting beams, as indicated. The dotted curves are at 0 and 50 fs delay. In the inset the time-integrated FWM Žclosed square. together with a numerical simulation Žsolid line. assuming 100 fs dephasing time.
P. Borri et al.r Optics Communications 169 (1999) 317–324
shown Žfilled square.. Note that the real-time FWM was not shown by Hofmann et al. w12x where only a scan over t was performed for t s 0. The results of Fig. 4 clearly show that the FWM signal is not a photon echo w14x. This indicates that in the investigated inhomogeneously broadened band-band transition, the homogeneous broadening is larger than the used spectral pulse width. We have simulated the experimental results by solving the optical Bloch equation for a two-level model assuming Gaussian excitation pulses and an inhomogeneous broadening much larger than the spectral pulse width. Propagation effects were neglected assuming that we are effectively in the thin-film limit of small induced changes. The calculated electric field amplitude of the FWM is then convoluted with a Gaussian reference pulse to simulate our detection scheme. The solid curve in the inset of Fig. 4 represents the
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calculated TI-FWM for a homogeneous broadening of 13.2 meV Ži.e. a dephasing time of 100 fs. and assuming a population lifetime of 50 fs, as supported by the fast SHB recovery time due to carrier-carrier scattering observed in the pump-probe experiment, at the limit of our time resolution. The simulation reproduces the experimental data with a value of the homogeneous broadening comparable to the pulse spectral width, as expected. The stronger deviation at negative delay times might be due to the simplifications of the model, namely the neglected Coulomb correlations w15,16x and possibly also propagation effects. In Fig. 5a a two-dimensional contour plot of the data over both the real-time t and the delay-time t is shown. The corresponding calculated signal ŽFig. 5b. shows reasonable agreement with the experimental data. 5. Summary In summary, we have demonstrated a novel detection scheme for heterodyne pump-probe and FWM, using a balanced detection and a dual-phase lock-in for signal recovery. We demonstrate its performance using a low repetition rate laser system with large intensity noise on a InGaAsP bulk semiconductor optical amplifier ŽSOA.. Pump-induced amplitude and phase changes of the transmitted probe were measured at different bias currents corresponding to gain, transparency and absorption in the device; the results are in agreement with previous findings reported in the literature. The measurements were performed at different pump intensities, going from small to large signal changes, with simultaneous acquisition of probe amplitude and phase and without the need of absolute phase calibration. Also time-resolved four-wave mixing measurements were demonstrated, and their numerical simulation indicates a 100 fs dephasing time in the investigated SOA. Acknowledgements
Fig. 5. Župper plot. Two-dimensional contour plot in linear scale of the FWM measurements as a function of both the reference delay time and the delay between the two exciting beams. Žlower plot. Numerical simulation using 100 fs dephasing time and 50 fs state lifetime.
This work was supported by the Danish Technical Research Council in the framework of SCOOP. The authors acknowledge Tele Danmark R & D for the donation of part of the equipment.
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References w1x C.T. Hultgren, E.P. Ippen, Appl. Phys. Lett. 59 Ž1991. 635. w2x K.L. Hall, G. Lenz, E.P. Ippen, G. Raybon, Opt. Lett. 17 Ž1992. 874. w3x J. Mark, J. Mørk, Appl. Phys. Lett. 61 Ž1992. 2281. w4x J. Mørk, J. Mark, C.P. Seltzer, Appl. Phys. Lett. 64 Ž1994. 2206. w5x K.L. Hall, G. Lenz, A.M. Darwish, E.P. Ippen, Opt. Commun. 111 Ž1994. 589. w6x C.-K. Sun, B. Golubovic, H.-K. Choi, C.A. Wang, J.G. Fujimoto, Appl. Phys. Lett. 66 Ž1995. 1650. w7x C.-K. Sun, B. Golubovic, J.G. Fujimoto, H.K. Choi, C.A. Wang, Opt. Lett. 20 Ž1995. 210. w8x J. Mørk, A. Mecozzi, C. Hultgren, Appl. Phys. Lett. 68 Ž1996. 449; J. Mørk, A. Mecozzi, J. Opt. Soc. Am. B 13 Ž1996. 1803.
w9x Y. Tomita, M.-A. Shibata, J. Bergquist, J. Appl. Phys. 71 Ž1992. 2102. w10x M. Sheik-Bahae, E.W.V. Stryland, Phys. Rev. B 50 Ž1994. 14171. w11x A. Mecozzi, J. Mørk, J. Opt. Soc. Am. B 13 Ž1996. 2437. w12x M. Hofmann, S.D. Brorson, J. Mørk, A. Mecozzi, Appl. Phys. Lett. 68 Ž1996. 3236. w13x P. Borri, W. Langbein, J. Mørk, J.M. Hvam, F. Heinrichsdorff, M.-H. Mao, D. Bimberg, Phys. Rev. B., in press, 1999. w14x J. Shah, in Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, Springer, Berlin, 1996, Chap. 2. w15x S. Hughes, Opt. Lett. 23 Ž1998. 948. w16x W.W. Chow, S.W. Koch, M. Sargent, Semiconductor-Laser Physics, Springer, Berlin, 1994.
Optics Communications 169 Ž1999. 317–324 www.elsevier.comrlocateroptcom
Full length article
Heterodyne pump-probe and four-wave mixing in semiconductor optical amplifiers using balanced lock-in detection P. Borri ) , W. Langbein 1, J. Mørk, J.M. Hvam Research Center COM, The Technical UniÕersity of Denmark, Building 349, DK-2800 Lyngby, Denmark Received 26 April 1999; accepted 12 July 1999
Abstract We demonstrate a new detection scheme for pump-probe and four-wave mixing heterodyne experiments, using balanced detection and a dual-phase lock-in for spectral filtering. The technique allows the use of low repetition-rate laser systems, as is demonstrated on an InGaAsPrInP bulk optical amplifier at 1.53 m m. Ultrafast pump-induced changes in the amplitude and phase of the transmitted probe signal are simultaneously measured, going from small to large signal changes and with no need of an absolute phase calibration, showing the versatility and the sensitivity of this detection scheme. The results for small perturbations are consistent with previous pump-probe experiments reported in literature. Time-resolved four-wave mixing in the absorption regime of the device is measured, and compared with numerical simulations, indicating a 100 fs dephasing time. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.55.Px; 78.47.q p Keywords: Ultrafast spectroscopy; Semiconductor laser
1. Introduction Optical pump-probe experiments can provide direct information on the ultrafast dynamics of gain and refractive index in semiconductor optical amplifiers ŽSOAs., as shown in several works in the past w1–8x. Recently a novel pump-probe heterodyne technique was introduced, where pump and probe can propagate co-linearly and with equal polarization ) Corresponding author. Fax: q45 4588 7762; e-mail: [email protected] or [email protected] 1 Present address: Lehrstuhl fur ¨ Experimentelle Physik EIIb, Universitat ¨ Dortmund, Otto-Hahn Str.4, 44221 Dortmund, Germany.
w2,5x. This technique measures the electric field of the probe, and can provide information on both amplitude and phase changes induced by the pump pulse. It has also been used for non-degenerate measurements, where pump and probe are at different wavelengths w6,7x. In both cases the experiments were performed with high repetition-rate laser-systems, using a high-frequency radio-receiver to detect the 1 MHz beat between reference and probe pulses. Switching between the AM or FM operation of the radio receiver it was possible to detect alternatively amplitude or phase changes induced by the pump pulse. For differential measurements, modulations were induced by chopping the pump beam and their amplitude was measured by a lock-in after the radio
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 3 9 1 - 0
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P. Borri et al.r Optics Communications 169 (1999) 317–324
receiver w5x. For the phase change measurements, a calibration with respect to a known optical phase change was necessary. Also, both techniques used a Michelson-interferometer to recombine probe and reference, with a single detector. In this way, the full amplitude noise of pump and probe beams affects the measurements. In this paper we demonstrate a novel heterodyne detection scheme, where a Mach-Zehnder interferometer, a balanced detection, and a dual-phase lockin is used for signal recovery. The lock-in provides amplitude and phase measurements at the same time, with no need of absolute phase calibration. The balanced detection is suppressing the amplitude noise from the laser source, making it feasible to work with a 300 kHz laser system of 10% amplitude noise. Results are shown for an InGaAsP bulk SOA, in both the weak and strong perturbation regime. With the same set-up the four-wave mixing signal induced by two exciting pulses can be detected and time-resolved.
2. Experimental set-up The heterodyne detection scheme works by imposing a small ŽMHz. frequency shift between the pump and the probe beam. By mixing the output mode of the device with a third, reference pulse at yet another frequency, the probe beam can be separated out by detecting at the proper beat frequency between probe and reference. Acousto-optic modulators ŽAOMs. are appropriate for frequency shifting the beams in the range of tens of MHz. In the case of laser systems with repetition rates larger than the AOM frequency shifts, such as investigated in Refs. w5,6x, the detection process can be understood by considering the shifts imposed by the AOMs on each of the laser mode frequency components individually. In the case of a laser system with a repetition rate much lower than the AOM induced frequency shifts, the beat frequency acquires a large number of lower sidebands, closely spaced by the repetition rate. Also, the duty cycle is much lower, and both
Fig. 1. Ža. Experimental set-up. C1 and C2: broadband non-polarizing cube beam-splitters; A: 200 m m aperture, L: lens, AC: autocorrelator, SOA: semiconductor optical amplifier. Žb. Scheme of the electrical mixing to generate the reference signal for lock-in. LP: low-pass filter, HP: high-pass filter.
P. Borri et al.r Optics Communications 169 (1999) 317–324
issues require a higher selectivity and sensitivity for the detection process. We show here, that the use of a balanced detection in combination with lock-in frequency filtering satisfies these demands and additionally provides a direct measurement of phase and amplitude. The experimental set-up is shown in Fig. 1a. The laser source is the idler of an Optical Parametric Amplifier that uses the output of a Ti:sapphire regenerative amplifier system to produce 140 fs pulses tunable from 0.9 to 2.5 m m at 295 kHz repetition rate. The large number of nonlinear processes Žwhite-light generation, frequency doubling and parametric amplification. leads to a large amplitude noise Žf 10%. of the system. Linear chirp compensation is achieved by a pulse-shaper. The pump pulse is obtained by deflecting the laser beam with an AOM driven at 40 MHz with a large maximum deflection efficiency Ž92% at 1.5 m m wavelength.. This AOM can be made of dispersive glass because the induced chirp can be precompensated by the pulse-shaper. This precompensation is monitored by optimizing the temporal pulsewidth with an autocorrelator ŽAC.. By controlling the radio-frequency ŽRF. power driving the AOM, the intensity of the pump pulse can be adjusted with high precision over four orders of magnitude. The probe pulse is obtained by deflecting the beam transmitted through the first AOM with a second AOM driven at 39 MHz. This AOM is made of fused-silica that does not introduce a significant pulse broadening but has a low maximum deflection efficiency Ž20% at 1.5 m m.; since the probe beam has to be weak in order not to perturb the system, this is not a limitation of the experiment. The probe intensity is controlled by the RF power driving the second AOM. Pump and probe beams are recombined by a non-polarizing cube beam-splitter ŽC1. and focused into the device by a high numerical-aperture ŽNA. aspheric lens. The light at the output of the device is collected with an equal high NA lens, focused into a 200 m m aperture ŽA. for spatial selection of the waveguide mode, collimated by a lens ŽL. and directed into a Mach-Zehnder interferometer. The transmitted beam from the second AOM is the reference beam that can be optionally injected into the device by a second cube beamsplitter ŽC2. Žand it has to precede the pump and probe by ; 1ns in order not to perturb the SOA., or
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can travel outside the device and be combined, using cube beam-splitters, in the Mach-Zehnder interferometer with the signal from the device. The probe signal transmitted through the device, which is frequency shifted by 39 MHz, interferes with the reference beam; both beams are pulse-trains at the laser repetition rate, i.e., are composed in the frequency domain of modes frequency spaced by 295 kHz. The lowest interference frequency between the probe modes and the reference modes, which is the only one in the range of the low-frequency lock-in, is 39 MHz down-shifted by 132 times the repetition rate, i.e. 60 kHz. This interference signal is detected in the intensity difference of the two output beams from the Mach-Zehnder interferometer by a balanced InGaAs detector of 125 kHz 3 dB-bandwidth. The balanced detection rejects the common-mode laser noise 2 . The interference signal is recovered by a dual-phase low-frequency lock-in ŽF 100 kHz.. The synchronized electric signal for the reference channel of the lock-in is obtained by down-mixing the sinusoidal electrical reference signal from the probe AOM driver with a high harmonic in the synchronous TTL signal at 295 kHz repetition rate from the laser driver, as shown in Fig. 1b. The TTL signal is high-pass filtered in order to reject lowfrequency components in the range of the lock-in reference signal. The mixed signals at higher frequencies are rejected by low-pass filters after the mixer. To detect the FWM signal, which has a frequency of two times the probe minus the pump frequency, the electrical reference signal is obtained by frequency-doubling the reference signal from the probe AOM driver Ž v 2 ; 39 MHz., then down-mixing
2
Actually, the noise level in our differential measurements was still limited by the laser noise and it was therefore depending on the stability of the laser source. In case of best performance we have reached less than 1% noise over a single scan. Shot noise at 300 KHz repetition rate, 10 fJ output probe pulse energy, and our detection quantum efficiency of about 20% is 1.5P10y5 r'Hz . The balanced detector used in the experiment ŽNew Focus Nirvana a 2017. was actually not rejecting the common mode laser noise sufficiently, i.e. to the shot noise limit, probably due to the small duty cycle of the pulses Ž2P10y7 ., which might lead to a transient overload of the detector Žpulse peak power of the reference pulse is ;1 KW.. Note that the 1% noise level in the differential transmission corresponds to 0.1 dB as the minimum measurable gain change, well in the small signal regime.
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it with an electric signal from the pump AOM driver Ž v 1; 40 MHz., and finally down-mixing the resulting frequency Ž38 MHz. with a high harmonic of the laser repetition rate from the laser TTL output. In Fig. 1b HP and LP indicate high-pass and low-pass filters, used in order to isolate the desired frequency component. The used frequency doublerrmixers and filters were cheap commercially available components. The whole optical set-up is covered to reject air-flow and thus provide phase-stability. Slow thermal drift is eliminated in the differential recording. The stability of the set-up allows for long delay scans and averaging over multiple scans, with no need of active stabilization. The set-up is shown for co-linearly polarized pump and probe pulses, the cross-linear case is obtained by rotating the pumppolarization by 90 degrees using a lr2 waveplate. All experimental results presented in this paper were obtained for co-linear polarization corresponding to the TE mode of the waveguide. For each pump-probe delay amplitude and phase of the transmitted probe is measured with and without the presence of the pump, for differential measurements, by changing the pump AOM RF-power. The phase measurement is directly given by the angle between the X and Y components in the lock-in, with no need of absolute phase calibration, while the amplitude is given by detecting R s 'X 2 q Y 2 . In this way, amplitude and phase are detected simultaneously during the same measurement. Moreover, the direct comparison between amplitude and phase in presence and absence of the pump allows to measure signal changes far from the small perturbation regime, not possible with a radio receiver which is relying on small amplitude and frequency modulations. 3. Pump-probe experiment An example of pump-probe measurements on a commercially available InGaAsrInP bulk amplifier at room temperature is shown in Fig. 2. The amplifier is 250 m m long and has a small signal gain of 13 dB at 120 mA bias current and 1.53 m m wavelength. The measurements are performed at different bias currents, corresponding to gain Ža., transparency Žb. and absorption Žc. at 1.53 m m, and for different
Fig. 2. Pump-induced change of the gain in a pump-probe experiment, at a wavelength of 1.53 m m and different bias currents corresponding to Ža. gain, Žb. transparency and Žc. absorption in the device. Both small and high signal changes, as obtained for different pump intensities, are shown. Nearly instantaneous gain changes, carrier heating effects and long-lived changes are visible, and strongly affected by the pump intensity Žsee text for details..
pump pulse energies. In Fig. 2a the changes in the gain at 120 mA bias current induced by a pump pulse with energy of 11 fJ and 460 fJ are shown. The probe pulse energy was less than 1 fJ. The change of the intensity gain in dB is calculated from the differential electric field transmission DTrT using DGŽdB. s 20logŽ1 q DTrT .. In the small perturbation regime Ž11 fJ., the results show an ultrafast gain reduction due to stimulated emission induced by the pump Žspectral-hole burning. and a recovery on a picosecond time-scale due to the recovery of carrier heating ŽCH., as reported in literature w3,5x. In the strong perturbation regime Ž460 fJ., a large ultrafast gain reduction exceeding the 13 dB small signal gain of the device is measured, indicating that an ultrafast
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loss channel additional to the pump-induced stimulated emission is present, since the stimulated emission can at maximum lead to transparency. This could be consistent with the occurrence of two-photon absorption ŽTPA. of the probe and pump photons, which almost follows the pulse autocorrelation time dependence w9x, as already reported in several pump-probe experiments. The recovery of the gain compression clearly occurs with two different time scales: an initial fast recovery that can be attributed to TPA and spectral-hole burning ŽSHB., and a slower recovery due to CH. At transparency ŽFig. 2b. for 35 mA bias current, no net stimulated transitions can occur. The two curves shown refer to pump energies of 0.58 pJ and 5 pJ and a probe pulse energy of 20 fJ, still in the region of negligible probe-induced gain changes. Both at high and small pump energy an initial fast negative-going transient is observed. This has been reported previously w3,5,8x and attributed to TPA. For small pump energies the recovery of this negative transient occurs in two parts: an initial instantaneous recovery of the TPA Ži.e., following the pump pulse., and a delayed slower recovery due to free carrier heating w5,8x. For large pump energies the dynamic at small delay times is more complicated, with stronger ondulation and delay in the onset of the carrier heating recovery. Similar effects have been observed in the literature and explained with the occurrence of spectral artifacts w8x, i.e., due to pump-induced changes of the refractive index in combination with gain dispersion, even if a link between large pump energies and stronger spectral artifacts is not reported and has to be further investigated. It is interesting to note that the long-lived changes of the gain for high pump energy is positiÕe indicating an increased carrier density induced by TPA. For 6 dB absorption ŽFig. 2c. at 20 mA bias current, the pump energies were 0.58 pJ and 10 pJ and the probe energy was 40 fJ. For small pump energies a fast positive gain change due to SHB followed by a slower recovery due to carrier cooling and a positive long-lived change, due to the increased carrier density, is observed in agreement with previous results w8x. At high pump energy a first negative fast transient, likely due to TPA, is followed by a strong positive peak up to full bleaching
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of the absorption by SHB. These effects are probably also strongly enhanced by the spectral artifact w8x. TPA induces significant heating by real carrier excitation in this strong pump regime w4x and the hot distribution subsequently cools, giving the slow positive transient. In Fig. 3 the phase dynamics measured together with the data of Fig. 2 are shown. Since the refractive index is sensitive to non-resonant changes in oscillator strength, it gives complementary information to the resonant absorption shown in Fig. 2. In Fig. 3a the long-lived positive phase-change corresponds to a reduction of the carrier density, in agreement with pump-induced stimulated emission. The initial fast positive change of the phase corresponds to the CH effect, that recovers on a picosecond time-scale. In transparency ŽFig. 3b. the negative
Fig. 3. Pump-induced phase changes for the same conditions as in Fig. 2. Instantaneous nonlinearities, carrier heating effects on a picosecond time-scale, and long-lived changes are clearly observed and strongly influenced by the pump intensity Žsee text for details..
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ultrafast phase change is due to instantaneous nonlinearities of the refractive index, associated with TPA but also electronic Raman and optical Stark effects w10,8x. Note that in the high pump-energy case the long-lived phase change is negative, indicating an increase in carrier density in agreement with the optically induced inversion via TPA, observed in the gain change. In absorption ŽFig. 3c. the TPA is observed together with a strong instantaneous index nonlinearity at large pump energy, both in the carrier heating and in a strong long-lived phase change due to carrier density increase. We notice that the present experiments are carried out for parallel pump and probe polarizations, where the coherent coupling due to pump-probe interference leads to an instantaneous so-called ‘‘coherent’’ artifact, which is a coherent interaction of pump and probe at the probe frequency, that has to be subtracted when comparing with orthogonal pump and probe measurements w5x. The influence of the coherent artifact was theoretically analyzed in Ref. w11x for the heterodyne scheme, although only in the adiabatic limit of fast polarization dephasing and small pump-induced changes. Further investigations of these coherent phenomena are required and can be accomplished using the FWM technique presented in the next section.
detection scheme. Pulse 1 is frequency shifted by v 1 s 40 MHz in the first AOM and corresponds to the pump beam in the pump-probe experiment Žsee Fig. 1.. Pulse 2 is delayed by t with respect to pulse 1, is frequency shifted by v 2 s 39 MHz in the second AOM and corresponds to the probe beam in the pump-probe experiment. The interference between the FWM signal and the reference pulse is detected by the balanced detector and the lock-in at the lowest side band of the frequency 2 v 2 y v 1 modulo the 295 KHz repetition rate Žsee Fig. 1b.. The measured FWM signal is the time-average over the product of the reference pulse electric field and the FWM electric field. The time resolution is thus given by the reference pulse duration, and the timedynamics of the FWM signal is measured as a function of the reference delay t for each value of t . In Fig. 4 the TR–FWM signal in the absorption region Žfor 20 mA bias current. is shown at different delay times t of the two exciting beams, as indicated. The pulse energies were 0.62 pJ for pulse 1 and 1.25 pJ for pulse 2. In the inset the time-integrated FWM ŽTI–FWM. field amplitude is also
4. Time-resolved four-wave mixing The use of the heterodyne technique for time-resolved four-wave mixing ŽTR–FWM. with collinear exciting beams was proposed by Mecozzi et al. w11x and experimentally demonstrated by Hofmann et al. w12x. This technique avoids the phase-matching restriction present in the commonly used non-collinear geometries and enables the use of waveguide devices such as semiconductor optical amplifiers. In this way long interaction lengths are accessible, which allows to measure weak nonlinearities. We have recently demonstrated this advantage measuring the time-resolved FWM response in III-V semiconductor quantum-dot amplifiers w13x. The FWM signal is created by two exciting pulses with time delays of yt y t and yt relative the reference pulse, respectively, and is detected by its interference with the reference pulse using the lock-in
Fig. 4. Time-resolved four-wave mixing field amplitude at a wavelength of 1.53 m m and 20 mA bias current, for different delay times of the two exciting beams, as indicated. The dotted curves are at 0 and 50 fs delay. In the inset the time-integrated FWM Žclosed square. together with a numerical simulation Žsolid line. assuming 100 fs dephasing time.
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shown Žfilled square.. Note that the real-time FWM was not shown by Hofmann et al. w12x where only a scan over t was performed for t s 0. The results of Fig. 4 clearly show that the FWM signal is not a photon echo w14x. This indicates that in the investigated inhomogeneously broadened band-band transition, the homogeneous broadening is larger than the used spectral pulse width. We have simulated the experimental results by solving the optical Bloch equation for a two-level model assuming Gaussian excitation pulses and an inhomogeneous broadening much larger than the spectral pulse width. Propagation effects were neglected assuming that we are effectively in the thin-film limit of small induced changes. The calculated electric field amplitude of the FWM is then convoluted with a Gaussian reference pulse to simulate our detection scheme. The solid curve in the inset of Fig. 4 represents the
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calculated TI-FWM for a homogeneous broadening of 13.2 meV Ži.e. a dephasing time of 100 fs. and assuming a population lifetime of 50 fs, as supported by the fast SHB recovery time due to carrier-carrier scattering observed in the pump-probe experiment, at the limit of our time resolution. The simulation reproduces the experimental data with a value of the homogeneous broadening comparable to the pulse spectral width, as expected. The stronger deviation at negative delay times might be due to the simplifications of the model, namely the neglected Coulomb correlations w15,16x and possibly also propagation effects. In Fig. 5a a two-dimensional contour plot of the data over both the real-time t and the delay-time t is shown. The corresponding calculated signal ŽFig. 5b. shows reasonable agreement with the experimental data. 5. Summary In summary, we have demonstrated a novel detection scheme for heterodyne pump-probe and FWM, using a balanced detection and a dual-phase lock-in for signal recovery. We demonstrate its performance using a low repetition rate laser system with large intensity noise on a InGaAsP bulk semiconductor optical amplifier ŽSOA.. Pump-induced amplitude and phase changes of the transmitted probe were measured at different bias currents corresponding to gain, transparency and absorption in the device; the results are in agreement with previous findings reported in the literature. The measurements were performed at different pump intensities, going from small to large signal changes, with simultaneous acquisition of probe amplitude and phase and without the need of absolute phase calibration. Also time-resolved four-wave mixing measurements were demonstrated, and their numerical simulation indicates a 100 fs dephasing time in the investigated SOA. Acknowledgements
Fig. 5. Župper plot. Two-dimensional contour plot in linear scale of the FWM measurements as a function of both the reference delay time and the delay between the two exciting beams. Žlower plot. Numerical simulation using 100 fs dephasing time and 50 fs state lifetime.
This work was supported by the Danish Technical Research Council in the framework of SCOOP. The authors acknowledge Tele Danmark R & D for the donation of part of the equipment.
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References w1x C.T. Hultgren, E.P. Ippen, Appl. Phys. Lett. 59 Ž1991. 635. w2x K.L. Hall, G. Lenz, E.P. Ippen, G. Raybon, Opt. Lett. 17 Ž1992. 874. w3x J. Mark, J. Mørk, Appl. Phys. Lett. 61 Ž1992. 2281. w4x J. Mørk, J. Mark, C.P. Seltzer, Appl. Phys. Lett. 64 Ž1994. 2206. w5x K.L. Hall, G. Lenz, A.M. Darwish, E.P. Ippen, Opt. Commun. 111 Ž1994. 589. w6x C.-K. Sun, B. Golubovic, H.-K. Choi, C.A. Wang, J.G. Fujimoto, Appl. Phys. Lett. 66 Ž1995. 1650. w7x C.-K. Sun, B. Golubovic, J.G. Fujimoto, H.K. Choi, C.A. Wang, Opt. Lett. 20 Ž1995. 210. w8x J. Mørk, A. Mecozzi, C. Hultgren, Appl. Phys. Lett. 68 Ž1996. 449; J. Mørk, A. Mecozzi, J. Opt. Soc. Am. B 13 Ž1996. 1803.
w9x Y. Tomita, M.-A. Shibata, J. Bergquist, J. Appl. Phys. 71 Ž1992. 2102. w10x M. Sheik-Bahae, E.W.V. Stryland, Phys. Rev. B 50 Ž1994. 14171. w11x A. Mecozzi, J. Mørk, J. Opt. Soc. Am. B 13 Ž1996. 2437. w12x M. Hofmann, S.D. Brorson, J. Mørk, A. Mecozzi, Appl. Phys. Lett. 68 Ž1996. 3236. w13x P. Borri, W. Langbein, J. Mørk, J.M. Hvam, F. Heinrichsdorff, M.-H. Mao, D. Bimberg, Phys. Rev. B., in press, 1999. w14x J. Shah, in Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, Springer, Berlin, 1996, Chap. 2. w15x S. Hughes, Opt. Lett. 23 Ž1998. 948. w16x W.W. Chow, S.W. Koch, M. Sargent, Semiconductor-Laser Physics, Springer, Berlin, 1994.