Measurements of saturated amplified spontaneous emission-spectra of quantum dot semiconductor optical amplifiers demonstrate efficient replenishment of the quantum-dot ground state population from excited states. This saturation behavior is perfectly modeled by a rate equation model. We examined experimentally the dependence of saturation on the drive current and the saturating optical pump power as well as on the pump wavelength. A coherent noise spectral hole is observed with which we assess dynamical properties and propose optimization of the SOA operating parameters for high speed applications.
©2008 Optical Society of America
Photonic devices based on Quantum Dots (QDs) in the GaAs material system are promising for fiber optic communication in the 1.3 µm wavelength range [1, 2]. Quantum dot semiconductor optical amplifiers (QD SOAs) offer unique features, the most important being the inhomogeneous gain broadening which is due to the dot size and strain distribution of self organized QDs . This broadening causes complex carrier and gain dynamics [3–8]. Important practical characteristics such as ultra-fast response, large saturation power [9, 10], pattern effect free amplification of fast signals under saturated conditions [11–13] and amplification of multi channel high bit rate signals with no cross talk [14, 15].
QD SOA properties benefit from their discrete electronic structure consisting of a ground (GS) and excited states (ES). Complex carrier dynamics governs the coupling between the confined states and high energy states through which carriers are fed to the QD. In the structures studied here, the high energy states are mainly those of a quantum well (QW) that surrounds the QDs. Additional states that may influence the dynamical properties belong to the barrier.
The amplification process brings the ground state into resonance with the input signal. Upon saturation, the GS is replenished by carriers originating from the higher energy states which serve as a carrier reservoir. It has been shown in various pump-probe measurements that the gain recovery of the QD ground state occurs on a time scale of 1–2 ps [7, 16], but the relaxation from ES to GS is much faster, ~130 fs .
The special properties of an inhomogeneously broadened gain spectrum manifest themselves clearly in the saturation characteristics . QD gain media are in reality only partially inhomogeneously broadened. Carriers with energies close to the pump energy (within the homogeneously broadened gain region) are strongly coupled but widely spaced spectral regions are only coupled indirectly via carrier capture and escape processes from and to the various high energy states . A saturated GS is replenished efficiently by carriers from the ES which also saturates and is replenished, in turn, by carriers from the reservoir states. The saturation of the quantum well and barrier layers (which are common to all dots) couples the entire dot population. This coupling process is slow, however, and is negligible for fast saturating excitations [9, 11].
Saturation effects can be studied by continuous wave (c.w.) excitation using frequency domain modeling and experiments [20–22]. This paper reports on such an investigation of a 1.3 µm QD SOA. We study the dependence of amplified spontaneous emission (ASE) at the GS and ES energies on the operating conditions. We demonstrate that the QD excited states act as an effective reservoir for the ground states, consistent with . The saturation of the high energy states is shown to limit the overall gain dynamics. The experimental results are consistent with a theoretical model which includes both GS and ES carriers (similar to [19, 23]). The model was adapted to correspond to the particular QD SOAs we investigated experimentally. We also studied the coherent noise spectral hole [20, 24] which is a direct signature of the ultra-fast gain dynamics because its width is proportional to the reciprocal of the SOA response time [20, 21].
2. Theoretical model
Static gain saturation of a QD SOA was simulated using a standard model consisting of a set of coupled rate equations that describe carrier dynamics and optical interaction with input signals .
Figure 1 shows the schematic diagram of an assembly of inhomogeneously broadened QDs. The ensemble of dots is divided into M types which differ in size and hence in confined energies. The continuous (Gaussian) distribution of confined energies is discretized in the model with a resolution of 1 meV. Each QD is assumed to have two spin-degenerate GS, a fourfold degenerate ES, and a many-fold continuum-like US. An electron - hole pair is treated in the model as an exciton. The device has a so called dot-in-a-well (DWELL) structure, where InAs dots are embedded within an InGaAs QW layer which serves as a common carrier reservoir for all sizes of QDs as shown in the inset of Fig. 1. We assume that the carrier relaxation from the upper state (US) to ES or GS occurs only among the same QDs.
The mutual dynamics and the optical properties are described in the following set of coupled equations.
where I is the injection current, e is the electron unit charge. The terms nw, nu,j, ne,j, and ng,j are the number of carriers in the QW layer, the jth group of US, the jth group of ES, and the jth group of GS, respectively. The term Gj is the fraction of the jth QD group within an inhomogeneous QD ensemble, which is assumed to have a Gaussian distribution. The terms NU,j, NE,j and NG,j are the maximum allowable carrier numbers at the jth group of US, ES and GS, expressed as NU,j=30NDVAGj, NE,j=4NDVAGj and NG,j=2NDVAGj. The US degeneracy of 30, which represents all the continuum-like QD upper states, is chosen to give the best fitting to the experimental results such as ASE spectra and saturation output power. The terms ND and VA are the total QD density and the active region volume. Pk, and ħωk are the optical power and photon energy of the kth mode. The term gE,Gjk is the linear optical gain that the jth-group of QDs give to the kth-mode of photons. Finally, L and Γ are the cavity length and the optical confinement factor.
The time constants are the carrier relaxation from the QW to the US (τwu), from the US to the ES (τue), from the US to the GS (τug), and the ES to the GS (τeg), respectively. The radiative recombination time is τr. The relation between relaxation and escape times is dictated by the principle of detailed balance . For example, τeg and τge, are related as:
where Dg=2 and De=4 are the degeneracy of the GS and the ES and ΔEeg is the energy difference between the ES and the GS.
The various time constants are taken from published pump-probe experiments . The most important ones are the carrier relaxation time from the QW layer to the QD US (τwu) and from the QD ES to GS (τeg). The values of the simulation parameters related with carrier relaxation and escape are summarized in Table 1.
Carrier capture/relaxation in QD SOAs is determined by the Auger scattering, which depends on both the energy difference and the envelope function overlap between the initial and final states . The direct carrier capture from the QW to the QD GS is not included in this model because it is very small compared to other carrier relaxation/capture rates. This supports the claim in  that sequential Auger processes are more efficient than a single Auger process for direct carrier capture to the QD GS.
The propagation of the optical signal and the ASE along the QD SOA is described by :
where α is the intrinsic loss and Pvac(ω) is the photon intensity of the vacuum field between frequency ω and ω+Δω.
In order to solve (6) and (7), the QD SOA is divided into ten sections. In each section, the traveling-wave equations are solved along with the appropriate optical gain in the section, which is obtained by the solving coupled rate equations (1)–(4). ASE spectra for different bias levels are shown in Fig. 2, where thermal effects are not included. Clear saturation of the ground state is observed while the emission from the excited state continues to increase with bias beyond 350 mA.
Calculated saturation characteristics are described in Fig. 3 for different pump powers and two bias levels. Plotted are the ASE differences, defined as the ratio (difference in dB) of the saturated ASE spectra, and the corresponding spectra with no pump. Because the gain reduction due to thermal effects at I=350 mA is not included, the calculated ASE difference spectra in Fig. 3(b) have relatively larger values than the measured data, which will be shown later.
The calculated saturation characteristics clearly demonstrate the role of the ES as carrier reservoir for the depleted GS. Since the coupling from ES to GS is significantly more efficient (faster) than the coupling of the quantum well and wetting layer to the ES, the ES saturates deeper than the GS as seen in Fig. 3. The population of the GS is not completely replenished for the largest pump power and a bias of 200 mA, but for 350 mA the saturation is minimal because the large ES population replenishes the GS carriers with large efficiency. Finally, since the GS occupation is saturated even at 200 mA and since for larger bias levels, the ES population increases, the ES saturation is reduced at 350 mA.
The calculated dependence of the ASE saturation on pump wavelength is shown in Fig. 4. The assumed bias and pump power were 200 mA and +4 dBm, respectively. The ASE spectra in Fig. 4 reveal the complexity of the saturation process. The GS dip of the ASE difference in Fig. 4(b) matches the corresponding pump wavelength which can be attributed to spectral hole burning. Additionally, broad band saturation occurs due to total carrier depletion. Because of the strong coupling from ES to GS the dip of the ES ASE difference in Fig. 4(a) also depends on the pump wavelength. This is ascribed to the inhomogeneous gain nature of spatially isolated QDs and a finite QD carrier capture time with respective strong carrier depletion induced by signal amplification. Furthermore, the wavelength dependence of the unsaturated gain determines the absolute ASE difference for different pump wavelength, i.e. lower gain leads to less ASE difference.
3. Device structure and experimental setup
An Al0.35Ga0.65As/GaAs waveguide structure with 10 layers of InAs QDs in a GaAs core, placed between AlGaAs cladding layers was grown by molecular beam epitaxy. Each QD layer was formed by self-organized growth in the Stranski-Krastanow mode following growth interruption after deposition, at 485 °C, of 2.5 monolayers of InAs directly on a GaAs matrix. The dots were covered by a 5 nm thick In0.15Ga0.85As layer which ensures reduced QD strain and activated alloy phase separation between the cover layer and the dots. This extends the emission wavelength to 1.3 µm . A 33 nm thick GaAs p-doped spacer separating the QD layers ensures strain relaxation and thus minimization of defects in the 10 stacks of QDs.
The 2 mm long SOAs were processed to deeply etched ridge waveguide structures of 4 µm width. The ridge was dry etched through the active core layer containing the QDs to provide strong index guiding of the optical mode while suppressing current spreading . The waveguide end facets were tilted at 6.8° and were anti-reflection coated. A scanning electron microscopy image of the structure is shown in Fig. 5
The characterization set up included tapered fibers for coupling in and out of the SOA waveguide. The measured coupling loss per facet was 4 dB. The maximum linear chip gain and saturation output power were 19 dB and +14 dBm, respectively. The residual gain ripple was smaller than 2 dB.
The saturating optical pump signal was generated by a tunable external cavity laser (Agilent 81672B) in combination with an attenuator module. The maximum power was +4 dBm which was sufficient to drive the SOA into saturation. The external cavity laser ensured a narrow input linewidth which does not mask any details in the spectral vicinity of the pump. The output spectra were recorded using an optical spectrum analyzer (ANDO, AQ 6317 C) with a resolution set to 0.2 nm.
The signature of the saturating pump signal was removed from the measured spectra and the data were smoothed in order to minimize the effect of the gain ripple. These spectra were compared to the unsaturated ASE spectrum for each drive current.
4. Experimental results
Figure 6 shows measured ASE spectra for various drive currents. The GS exhibits a clear red shift as the bias increases in contrast to the expected blue shift due to band filling as calculated in Fig. 2. This red shift results from parasitic thermal effects. The GS emission saturates at a bias of about 125 mA, but exact determination of this saturation is difficult, because it is masked by the thermal effects. As for the ES, at a low drive current of 50 mA, it is almost unpopulated. The ES emission increases with increasing injection current beyond 125 mA up to 350 mA, where it is nearly saturated.
Saturation characteristics are described in Fig. 7 and Fig. 8. For a given bias, the pump wavelength was tuned to the peak of the unsaturated ASE spectrum and the ASE spectrum was recorded for several pump powers in the range of -11 dBm to +4 dBm. The results for a bias of 200 mA (where the pump wavelength was set to 1300 nm) are shown in Fig. 7(a). The ASE difference for the GS is negligible at low and moderate pump powers but for deep saturation it reaches about 2dB since the limited ES population at 200 mA is insufficient for efficiently fast carrier replenishment. This is also seen clearly in the ES ASE difference which is very large for deep GS saturation. The results in Fig. 7(a) confirm very well the predictions of the model shown in Fig. 2(a).
At 350 mA, the peak of the unsaturated ASE spectrum shifts to 1310 nm (Fig. 6). The pump wavelength was adjusted accordingly and the obtained ASE differences are shown in Fig. 7(b). The large ES population ensures very efficient GS carrier replenishment so that the ASE difference is very small (1 dB) for all pump powers while the ES ASE difference is smaller than in Fig. 7(a). The results of Fig. 7(b) are consistent with the predictions of the model shown in Fig. 2(b). The ES recovers faster with increasing current due to the strong dependence of the Auger scattering mechanism of the QW to the ES relaxation on the carrier density [5, 29]. This results in a significantly reduced ES saturation at high currents.
The dependence of ASE difference on pump wavelength was examined at a bias current of 125 mA and a pump power of +4 dBm. The results are shown in Fig. 8. The GS saturation is determined in this case by the complex carrier dynamics of the QD SOA but also by the saturation power dependence on the signal wavelength. In particular, pumping at short wavelengths, for example at 1270 nm, where the saturation power is low, causes a spectral red shift  which completely masks the ASE difference dip and actually yields a positive ASE difference, as seen in Fig. 8(a). For longer wavelengths, the GS ASE difference dip is in general symmetric around the pump wavelength. The peak in the ES ASE difference varies for the different pump wavelengths, but does not coincide with the ES peak observed in Fig. 6. This is caused by the strong coupling of the ES to the QW due to the small energy difference especially at short wavelengths leading to higher escape rates than for ES at longer wavelengths. The slight shift of the ES ASE difference dip shows that the spectral hole burning also occurs in the ES demonstrating that the carrier relaxation from ES to GS is only within the same QD possible. Finally, we show in Fig. 8(b) a zoom of the GS ASE difference for a few pumping wavelengths. The complex asymmetric spectra with the shifts of the corresponding peaks due to spectral hole burning are clearly seen and demonstrate the fact that saturation is governed by many simultaneous processes. Also seen in Fig. 8(b) are signatures of the coherent noise spectral hole  to be discussed below.
The experimental data presented in Fig. 7 and 8 (as well as the predictions of Fig. 2 and 3) resemble theoretical and experimental results of static saturation in 1550 nm quantum dash SOAs . The main difference lies in the fact that the quantum dash gain medium has quantum wire like properties  and hence its density of state function is highly asymmetric. Consequently, saturation spectra are correspondingly asymmetric highlighting the high energy tail characterizing quantum wires.
4.1 The coherent noise spectral hole
The noise spectrum of a saturated SOA contains, in addition to the obvious spectral hole due to carrier removal, a coherent spectral hole. The coherent spectral hole results from a four wave mixing (FWM) like interaction between the saturating signal and the broadband ASE. The coherent noise spectral hole was first predicted [30, 31] and measured  in bulk SOAs where its spectral width is of the order of a few GHz determined by the SOA response time. A recent theoretical prediction suggested that in QD SOAs the spectral width should increase to hundreds of GHz . A similar result was found experimentally for quantum dash SOAs .
Measurements of the coherent noise spectral hole in the present QD SOA are described in Fig. 9. Using five bias levels and tuning the pump wavelength with +4 dBm in each case to the unsaturated ASE peak, we recorded the ASE spectra as seen in Fig. 9(a). A clear asymmetric hole whose width and depth increase with bias is observed as predicted in [20, 22]. The asymmetry is due to the Bogatov effect  and testifies to the fact that the hole is indeed due to a coherent FWM like process. Figure 9(b) shows detailed spectra at the smallest (50 mA) and largest (350 mA) bias levels. The width dependence on bias is clearly seen and a summary of the coherent noise spectral hole width on bias is presented in Fig. 10.
The observed spectral hole width can be used to estimate the bias dependence of the overall QD SOA response time. In the present case, the width in Fig. 10 varies from 5.0±0.7 nm at 50 mA to 7.0±0.7 nm at 350 mA. This corresponds to SOA response times on the order of hundreds of GHz or of 0.8±0.1 ps to 1.1±0.2 ps, respectively. These values are consistent with pump probe measurements of similar gain structures [4, 7, 16]. The reduction in response time with increasing bias is further evidence of the important role of ES to GS carrier replenishment. It is important to note, that the response times are not influenced by the response time of the saturated quantum well and barrier layers since they are extracted from static experiments. QW and barrier layer response times will affect the response to high speed signals which drive the SOA into deep saturation.
The saturation behavior of a QD SOA is governed by a complex combination of different processes related to both the homogeneous and the inhomogeneous gain broadening. The most important contribution to GS carrier replenishment in saturation is the efficient coupling to the ES. The ES is replenished in turn by carrier capture from the higher reservoir states, e.g. the QW states, a process which is less efficient. Moreover, since the gain is inhomogeneously broadened, various spectral regions are coupled via the quantum well and the barrier layer which serve as a common reservoir. These various carrier replenishing processes have complex dynamics but many of their details can be understood from frequency domain models and experiments using CW excitations.
The key parameters influencing the saturation characteristics are the relaxation and thermalization time constants between the different relevant states. The ES to GS relaxation is the most efficient (and fastest, ~130 fs ) process in the system and hence the GS saturation is easily recovered in all cases where the ES is highly populated. Carrier relaxation from the quantum well states to the ES is slower, but can be enhanced by increased carrier injection . This leads to a reduced ASE saturation of the ES and an overall decrease of the response time of the amplifier as can be deduced from the broadening of the coherent noise spectral hole. The dynamics of the high energy states themselves are the slowest, typical in the order of several hundred picoseconds [34, 35]. Strong high speed signals which cause saturation of the QW states experience therefore pattern effects, since the gain recovery is limited by the slow dynamics. These effects are not observable in the static case described in this paper.
We would like to acknowledge the funding of this work by the SANDiE NoE of the European Commission, contract number NMP4-CT-2004-500101, the TRIUMPH project IST-027638 STP, and the State of Berlin (ProFIT MonoPic and OptiDot) and SFB 787 of the German Research Council (DFG). G. Eisenstein, who is the recipient of a Humboldt Foundation Award at TU Berlin, thanks the Foundation for its support. J. Kim acknowledges the financial support from the Alexander von Humboldt Foundation and the Marie Curie Incoming International Fellowship (MIF1-CT-2006-040250).
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