The charge carrier dynamics of improved InP-based InAs/AlGaInAs quantum dot (QD) semiconductor optical amplifiers are examined employing the multi-wavelength ultrafast pump-probe measurement technique. The transient transmission response of the continuous wave probe shows interesting dynamical processes during the initial 2-3 ps after the pump pulse, when carriers originating from two photon absorption contribute the least to the recovery. The effects of optical excitations and electrical bias levels on the recovery dynamics of the gain in energetically different QDs are quantified and discussed. The experimental observations are validated qualitatively using a comprehensive finite-difference time-domain model by recording the time evolution of the charge carriers in the QDs ensemble following the pulse.

The three dimensional carrier confinement in semiconductor quantum dots (QDs) provides the optical gain material with vastly improved characteristics compared to those of higher dimensionality materials such as quantum wells. This manifests itself in many device properties such as low threshold,1,2 temperature insensitivity,3 high speed,3–5 low noise6 and narrow linewidth7 lasers as well as high gain,8,9 linear10 and low noise11,12 optical amplifiers. The superior device characteristics are related to the carrier and gain dynamics that are complex due to the effect of high energy unconfined carriers, which are coupled to the confined carriers in the QDs,13 and due to the gain inhomogeneity of the self-assembled QDs.14 

Carrier dynamics has been studied often in QD optical amplifiers using short pulse time domain techniques. For the 1300 nm wavelength range, InAs/GaAs QD amplifiers were characterized by single15 as well as multi-wavelength16 pump-probe systems. The first characterizations of amplifiers operating in the important telecom wavelength range of 1550 nm were performed in InP-based quantum dash (quantum wire like) systems. Gain and index dynamics were obtained in single wavelength coherent pump-probe experiments17 while multi wavelength experiments, which use a continuous wave (CW) probe signal,18,19 yielded energy dependent gain saturation and recovery rates18 as well as the phenomenon of instantaneous gain20 under high electrical and optical excitations. These multi-wavelength investigations of InP-based QD amplifiers also revealed the important role played by two photon absorption (TPA).18–20 A schematic description of the experimental arrangement reported here is shown in Fig. 1(a).

FIG. 1.

(a) Schematic view of the amplifier examined with the multi-wavelength pump-probe technique; the insets show an AFM image of self-assembled QDs and the layer structure. (b) Bias dependent ASE spectra (color curves) of the SOA with measured pump spectrum (black solid curve) and probed wavelengths (green arrows). (c) Measured relative transmission versus delay time at a probe wavelength of 1550 nm for a 150mA bias level and various pump pulse energies. The inset shows short time constant values versus pump energy for 1550nm at three examined levels of electrical excitation.

FIG. 1.

(a) Schematic view of the amplifier examined with the multi-wavelength pump-probe technique; the insets show an AFM image of self-assembled QDs and the layer structure. (b) Bias dependent ASE spectra (color curves) of the SOA with measured pump spectrum (black solid curve) and probed wavelengths (green arrows). (c) Measured relative transmission versus delay time at a probe wavelength of 1550 nm for a 150mA bias level and various pump pulse energies. The inset shows short time constant values versus pump energy for 1550nm at three examined levels of electrical excitation.

Close modal

InAs QDs can be grown on AlGaInAs lattice-matched to InP with high densities of 6 × 1010 cm-2 and an improved size homogeneity, as recently demonstrated.21 The improved QD material led to lasers with very high modal gain values of more than 15 cm-1 per QD layer22 and record modulation bandwidths with only a small temperature dependence.3 This report entails the investigation of the wavelength dependent carrier and gain dynamics of semiconductor optical amplifiers (SOAs) comprising this improved optical gain material. The ridge waveguide devices used here were fabricated from a laser structure with 6 QD layers (see inset of Fig. 1(a)) exhibiting a high modal gain3 of 90 cm-1. Both facets were anti-reflection coated to suppress lasing. The device length is 1.5 mm.

The experimental results are validated qualitatively by simulations, which are based on a comprehensive model previously developed in order to explain dynamical effects on a sub 200 fs time scale, where quantum coherent interactions23 take place. The model calculates, among other things, the population inversion across the QD gain spectrum during and following the pulse propagation along the SOA.

Detailed understanding of the carrier and gain dynamics in the inhomogeneously broadened QD SOAs requires a multi-wavelength investigation, where the response to a pulsed perturbation is investigated at any wavelength across the gain spectrum. The system we have employed18 uses a tunable CW probe that is sampled, after propagation through the SOA, by a replica of the pump pulse. A mode locked fiber laser served as the pump source, launching 150 fs long pulses with a repetition rate of 40 MHz and maximum output energy of 60 pJ. The pump spectrum, centered at 1580 nm, is depicted schematically in Fig. 1(b), superimposed on the bias dependent amplified spontaneous emission (ASE) spectra of the SOA. Three CW probe wavelengths (indicated by vertical arrows in Fig. 1(b)) were used: 1550 nm, which is close to the SOA gain peak, 1508 and 1620 nm. The latter two are at the edges of the gain spectrum and do not overlap the pump pulse spectrum. The SOA was electrically driven at 150, 200 and 250 mA bias levels. The absolute gain values for 1508, 1550 and 1620 nm, are respectively: 9, 21 and 5 dB at 150 mA; at 200 mA they are 14, 29 and 8 dB and at 250mA the gain values are 17, 32 and 8 dB.

Pump energy dependent responses of the CW probe transmission at 1550 nm for a DC bias of 150 mA, are shown in Fig. 1(c). The curves were normalized to their respective values prior to the pump pulse arrival. The zero delay time is defined here as the instance when the pump pulse is no longer present. This differs from common definitions of zero time which are usually taken as the center of the pump pulse. During the pump pulse, the probe does not measure the dynamics of recovery. The effect on the system during the pulse has to be measured by other means, most common by FROG.24 The real information in a pump probe set up is obtained after the perturbation is completed; therefore, we define zero time after the pump pulse. Moreover, there is additionally a technical problem in our system stemming from the fact that during the pump pulse, the detector is blinded (saturated) so that the measurement of the probe transmission is not reliable before the pulse has passed. The region of unreliable data is shown in the Figure 1(c) as hatched frame. At long delay times, for all but the lowest pump energy, the transmission reaches a level which exceeds the level prior to the pump pulse arrival. This is a well-known signature of TPA.19 

The nature of the response during the first 1-2 ps resembles several well documented15–17 previous results where following gain saturation, the recovery exhibits several time constants. In the present experiments, the initial fast recovery is masked somewhat by artifacts due to saturation of the detector. The relevant short time constants were obtained by fitting the recovery traces to a bi-exponential function (as in Ref. 19) and are summarized for the probe wavelength at 1550 nm in the inset of Fig. 1(c). The best fit is for the recovery at low bias. As the bias is increased, the bi-exponential fit becomes poorer as reflected in the larger error bars.

Strong bias and intensity dependencies are observed. The short time constants increase with the pump intensity and with a decrease in the bias level, as shown in the inset of Fig. 1(c) for 150 mA bias, which is the most reliable set of data. The behavior clarifies the origin of this recovery mechanism; the probability of charge carrier capture into the QDs from the higher energy carrier reservoir25 increases with the reservoir carrier density, which increases, in turn, with bias. Therefore, the gain recovers faster at high bias levels even for large pump energies. Moreover, the capture time shortens for short wavelengths as the small energetic distance to the reservoir states increases the capture probability. The long time constant, which represents the relaxation processes in the high energy carrier reservoir, is not shown here. It was found to be constant on average for different energies (with the variation of the root mean squared error in the range of 0.95-0.99) with a value of about 300 ps for 1550 nm of excitation at 150 mA.

During the first 2 ps of the transients following the pump pulse, we observe interesting dynamical processes indicated by a clearly observed plateau in the transmission, preceding its recovery to higher values by carrier capture into the QDs. Its origin is pursued and clarified by measuring the bias, wavelength, and excitation intensity dependencies of the transient transmission, as follows.

Bias dependent normalized recovery traces for all probe wavelengths and pump pulse energy of 31pJ are shown in Fig. 2. For 1508 nm (Fig. 2(a)) and 1550 nm (Fig. 2(b)) probes, we observe a slow recovery at a level below the steady state for the first 2 ps followed by a significant increase due to TPA generated carriers.

FIG. 2.

Measured relative transmission versus delay time for 150 mA, 200 mA and 250 mA bias levels and for 31pJ pump and (a) 1508 nm, (b) 1550 nm and (c) 1620 nm probe wavelengths.

FIG. 2.

Measured relative transmission versus delay time for 150 mA, 200 mA and 250 mA bias levels and for 31pJ pump and (a) 1508 nm, (b) 1550 nm and (c) 1620 nm probe wavelengths.

Close modal

The random spikes, which are more pronounced for probe wavelengths of 1508 and 1620 nm where the gain is low, originate from noise. The reduced gain at spectral edges leads to low probe levels. Additionally, the wavelength dependent sensitivity of the detector weakens the short wavelength signal further.

The instance at which the change in recovery rate occurs is determined by the relaxation time of the TPA generated carriers to the electron ground state which is probed. Since the carriers escape rate from the short wavelength QDs is strongly affected by the occupation of carriers in the reservoir, the 1508 nm probe recovers to a normalized value larger than the one at 1550 nm. At 250 mA, the response of the 1550 nm probe is essentially constant since neither the saturation due to the pump nor the TPA has a measurable effect on the large occupation probability dictated by the large bias level.

At 1620 nm (Fig. 2(c)), the probe transmission is almost unaffected by the pump pulse and the response is constant for all bias levels. A trace of an initial delay due to the depletion of the reservoir is observed but it is very small.

Figure 3 shows specifically the responses at 1508 nm for the three bias levels and two pump energies. Irrespective of the bias levels, we observe a plateau at a level below the steady state and then a recovery to high levels due to TPA generated carriers. The long term recovery level is highest at 150 mA since it is normalized to the lowest steady state level. The plateau, which is prone to occur in the short wavelength QDs, is a result of a balance between carrier capture and escape rates between the QDs and the common reservoir under the condition of a depleted reservoir and for times shorter than the relaxation time of TPA generated carriers. For the 5 pJ pump, the responses are constant since such a low pump level neither saturates the gain nor causes any appreciable TPA.

FIG. 3.

Measured relative transmission versus delay time for 1508 nm probe at three examined bias levels and for pump energies of 60 pJ (solid line) and 5 pJ (dashed line).

FIG. 3.

Measured relative transmission versus delay time for 1508 nm probe at three examined bias levels and for pump energies of 60 pJ (solid line) and 5 pJ (dashed line).

Close modal

The experimental observations were validated numerically using a comprehensive finite-difference time-domain (FDTD) model developed originally to analyze quantum coherent effects induced by ultra-short pulse propagation in QD amplifiers.23 Details of the model formalism are given in Ref. 26. Here we introduce a modification in which the rate equations for the electron and the hole reservoirs, equations (1) and (2) in Ref. 25, respectively, account for the non-unity barrier (high energy TPA levels) to reservoir volume ratio27 (VB/Vres):

Nrest=ηiJqdNresτres+(VBVres)(1NresDres)NTPAτTPArelaxNresND_totalτcapi=1MNDi(1Nexi4NDi)+VDVresi=1M(1NresDres)NexiτesciNresND_totalτd_capi=1MNDi(1ρ11i)+VDVres(1NresDres)i=1M2NDiρ11iτd_esci;
(1)
Prest=ηiJqdNresτresVDVresi=1MNexiτex+(VBVres)(1PresDres)hTPAτTPArelaxVDVresi=1M2NDi(γcρ11i+γνρ22i)Presτcaph1ND_totali=1MNDiρ22i+VDVres(1PresDres)1τeschi=1M2NDi(1ρ22i).
(2)

Other parameters of the equations have their usual meaning as explained in Ref. 26. The calculation used a transform limited Gaussian pulse of varying input energies. Some physical parameters used in the current paper, differ from what are listed in Ref. 26, are listed in Table I.

TABLE I.

Simulation parameters.

Simulation parameterValue
Length of the SOA 750 μm 
Dipole moment 0.5x10-28 C·m 
Peak of the gain spectrum 1550 nm 
Relaxation time of the TPA charge carriers 4 ps 
TPA recombination time 0.4 ns 
TPA coefficient 70 cm/GW 
Pulse central wavelength 1550 nm 
FWHM 150 fs 
VB/Vres 50 
Simulation parameterValue
Length of the SOA 750 μm 
Dipole moment 0.5x10-28 C·m 
Peak of the gain spectrum 1550 nm 
Relaxation time of the TPA charge carriers 4 ps 
TPA recombination time 0.4 ns 
TPA coefficient 70 cm/GW 
Pulse central wavelength 1550 nm 
FWHM 150 fs 
VB/Vres 50 

The spatial and spectral distribution of the difference in carrier occupation probabilities of the effective two-level systems (ρ11ρ22) is recorded along the simulated amplifier for each bias and excitation pulse energy when the pulse is close to the output facet of the amplifier. A typical example is shown in Fig. 4(a). Also calculated and recorded is the spatial distribution of the deviation of the refractive index from its unperturbed value. The refractive index variations result from the plasma effect induced by the changes in carrier density. An example for a bias of 150 mA is shown in Fig. 4(b). The spatial and spectral profiles of ρ11ρ22 behind the pulse with the knowledge of the spectrally resolved QD density can be translated to a time evolution of the gain since the two are directly related to each other. This is done (at any wavelength) using the refractive index information and this leads to the description of the time evolution of the probe transmission.

FIG. 4.

(a) Simulated spatial evolution of population inversion (color bar) (b) refractive index distribution along the length of the SOA at 150 mA bias for a 180 pJ pulse. Simulated population inversion values normalized to their respective values prior to the pulse entrance versus time are shown in (c, d, e) - 127 mA and (f, g, h) - 150 mA and corresponding pulse energies for (c, f) – 1507 nm, (d, g) – 1548 nm and (e, h) – 1620 nm.

FIG. 4.

(a) Simulated spatial evolution of population inversion (color bar) (b) refractive index distribution along the length of the SOA at 150 mA bias for a 180 pJ pulse. Simulated population inversion values normalized to their respective values prior to the pulse entrance versus time are shown in (c, d, e) - 127 mA and (f, g, h) - 150 mA and corresponding pulse energies for (c, f) – 1507 nm, (d, g) – 1548 nm and (e, h) – 1620 nm.

Close modal

Figures 4(ch) show the time evolution of population inversion normalized to its value prior to the pulse arrival at two bias levels 127 mA (upper row Fig. 4(ce)) and 150 mA (lower row Fig. 4(fh)) and for different pulse energies. At long wavelengths that do not overlap the pulse spectrum, i.e., 1620 nm (Fig 4(e, h)), the initial recovery starts from a value lower than one at both current values. This is consistent with the experimental observation (Fig. 2(c)). At longer times, the recovery barely exceeds its value prior to the pulse arrival verifying that long wavelength QDs, being energetically far from the reservoir, are affected the least by relaxations from the reservoir.

As depicted in Fig. 4(d, g), close to the SOA gain peak at 1548 nm, the initial depletion is deeper. At long times, TPA contribution to the recovery is consistent with the dependence on pulse energy; larger energy pulses induce more TPA carriers that relax to the QDs levels leading to higher recovery levels and, hence, the normalized inversion exhibits a larger energy dependence as compared to those in Fig. 4(e, h).

At the short wavelength side of the gain spectrum, i.e., at 1507 nm, the initial recovery shows a plateau or even a delayed depletion that extends up to 2 ps. This feature, which is also seen in the experiments, is reproduced in the simulations for a range of pulse energies that vary within 195±5 pJ at 127 mA and 245±5 pJ at 150 mA.

The density of short wavelength QDs is small and since they are energetically close to the reservoir, even a low energy pulse induces significant depletion. This leads to a dip in the recovery trace immediately after the pulse. Also, low energy pulses contribute insignificantly to the TPA induced reservoir carriers and it takes a relatively long time for this low number of carriers to affect the gain recovery. At long times, once a sufficient number of TPA induced carriers relax to the short wavelength QDs, they start to dominate the recovery as shown in Fig. 4(c,f). Higher energy pulses induce naturally more TPA carriers, which saturate the reservoir and mask any short time phenomenon. This ultimately leads to the TPA dominated recovery trace as shown in Fig. 4 (c) and 4 (f) for 230 pJ and 300 pJ pulses, respectively. Hence, the energy of the pulses plays a major role in balancing these two phenomena and this delicate balance (that is also bias dependent), which manifests itself as the plateau, is only achieved for a specific range of pulse energies. It is judicious to note that the large number of mutually dependent physical parameters allow for the simulations to fit the experiments only in a qualitative manner. Nevertheless, the physical principles governing the dynamical processes are clarified by the comparison between the two.

To conclude, we have investigated the temporal carrier and gain dynamics in an inhomogeneously broadened QD SOA using a multi wavelength pump-probe technique. Three key features were observed: (i) Fast processes reflecting intra-dot relaxations and carrier capture and escape, from and to high energy carrier reservoir were detected. (ii) Approximately 2 ps after the perturbation, the effect of TPA on the gain recovery starts to dominate. (iii) At the short wavelength edge of the gain spectrum, a delicate balance between escape and capture rates causes a constant transmission level termed as a plateau, that lasts for about 2 ps. This balance is disturbed when relaxation of TPA induced carriers to the carrier reservoir and consequently to the QD ground state becomes significant. The experimental results were confirmed by a comprehensive numerical model, which yields bias and pump pulse energy dependent time evolutions of the charge carriers in the QD ensemble (and hence the gain) at every wavelength and those resemble well the experimentally obtained probe transmissions.

This work was partially supported by the Israel Science Foundation and the European project SEQUOIA. I. K. acknowledges the fellowship from Russell Berrie Nanotechnology Institute at Technion. A. K. M. acknowledges the support in part at Technion by Israel Council for Higher Education. O. K. thanks the Adams Fellowship of the Israel Academy of Sciences and Humanities for financial support during this research.

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