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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 11 — May. 26, 2008
  • pp: 8269–8279
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Static gain saturation in quantum dot semiconductor optical amplifiers

Christian Meuer, Jungho Kim, Matthias Laemmlin, Sven Liebich, Amir Capua, Gadi Eisenstein, Alexey R. Kovsh, Sergey S. Mikhrin, Igor L. Krestnikov, and Dieter Bimberg  »View Author Affiliations


Optics Express, Vol. 16, Issue 11, pp. 8269-8279 (2008)
http://dx.doi.org/10.1364/OE.16.008269


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Abstract

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

1. Introduction

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

1. D. Bimberg, M. Kuntz, and M. Laemmlin, “Quantum Dot Photonic Devices for Lightwave Communication,” Appl. Phys. A 80, 1179–1182 (2005). [CrossRef]

, 2

2. D. Bimberg, N. Kirstaedter, N. N. Ledentsov, Z. I. Alferov, P. S. Kop’ev, and V. M. Ustinov, “InGaAs-GaAs Quantum-Dot Lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 196–204 (1997). [CrossRef]

]. 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 [3

3. D. Bimberg, M. Grundmann, N. N. Ledentsov, S. S. Ruvimov, P. Werner, U. Richter, J. Heydenreich, V. M. Ustinov, P. S. Kopev, and Z. I. Alferov, “Self-organization processes in MBE-grown quantum dot structures,” Thin Solid Films 267, 32–36 (1995). [CrossRef]

]. This broadening causes complex carrier and gain dynamics [3–8

3. D. Bimberg, M. Grundmann, N. N. Ledentsov, S. S. Ruvimov, P. Werner, U. Richter, J. Heydenreich, V. M. Ustinov, P. S. Kopev, and Z. I. Alferov, “Self-organization processes in MBE-grown quantum dot structures,” Thin Solid Films 267, 32–36 (1995). [CrossRef]

]. Important practical characteristics such as ultra-fast response, large saturation power [9

9. T. W. Berg, S. Bischoff, I. Magnusdottir, and J. Moerk, “Ultrafast gain recovery and modulation limitations in self-assembled quantum-dot devices,” IEEE Photon Technol. Lett. 13, 541–543 (2001). [CrossRef]

, 10

10. A. V. Uskov, E. P. O’Reilly, M. Laemmlin, N. N. Ledentsov, and D. Bimberg, “On gain saturation in quantum dot semiconductor optical amplifiers,” Opt. Commun. 248, 211–219 (2005). [CrossRef]

], pattern effect free amplification of fast signals under saturated conditions [11–13

11. A. V. Uskov, T. W. Berg, and J. Mork, “Theory of pulse-train amplification without patterning effects in quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. 40, 306–320 (2004). [CrossRef]

] and amplification of multi channel high bit rate signals with no cross talk [14

14. R. Alizon, D. Hadass, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, A. Somers, J. P. Reithmaier, A. Forchel, A. Calligaro, S. Bansropun, and A. Krakowski, “Multiple wavelength amplification in wide band high power 1550 nm quantum dash optical amplifier,” Electron. Lett. 40, 760–761 (2004). [CrossRef]

, 15

15. M. Sugawara, N. Hatori, T. Akiyama, Y. Nakata, and H. Ishikawa, “Quantum-Dot Semiconductor Optical Amplifiers for High Bit-Rate Signal Processing over 40 Gbit/s,” Jpn. J. Appl. Phys. 40, L488–L491 (2001). [CrossRef]

].

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

7. T. Akiyama, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, O. Wada, and H. Ishikawa, “Nonlinear gain dynamics in quantum-dot optical amplifiers and its application to optical communication devices,” IEEE J. Quantum Electron. 37, 1059 (2001). [CrossRef]

, 16

16. S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Laemmlin, and D. Bimberg, “Complete ground state gain recovery after ultrashort double pulses in quantum dot based semiconductor optical amplifier,” Appl. Phys. Lett. 90, 033508 (2007). [CrossRef]

], but the relaxation from ES to GS is much faster, ~130 fs [17

17. P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, H.-M. Mao, and D. Bimberg, “Spectral Hole-Burning and Carrier-Heating Dynamics in Quantum-Dot Amplifiers: Comparison with Bulk Amplifiers,” Phys. Status. Solidi. B 224, 419–423 (2001). [CrossRef]

].

The special properties of an inhomogeneously broadened gain spectrum manifest themselves clearly in the saturation characteristics [18

18. K. Kim, J. Urayama, T. B. Norris, J. Singh, J. Phillips, and P. Bhattacharya, “Gain dynamics and ultrafast spectral hole burning in In(Ga)As self-organized quantum dots,” Appl. Phys. Lett. 81, 670–672 (2002). [CrossRef]

]. 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 [19

19. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004). [CrossRef]

]. 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

9. T. W. Berg, S. Bischoff, I. Magnusdottir, and J. Moerk, “Ultrafast gain recovery and modulation limitations in self-assembled quantum-dot devices,” IEEE Photon Technol. Lett. 13, 541–543 (2001). [CrossRef]

, 11

11. A. V. Uskov, T. W. Berg, and J. Mork, “Theory of pulse-train amplification without patterning effects in quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. 40, 306–320 (2004). [CrossRef]

].

Saturation effects can be studied by continuous wave (c.w.) excitation using frequency domain modeling and experiments [20–22

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

]. 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 [16

16. S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Laemmlin, and D. Bimberg, “Complete ground state gain recovery after ultrashort double pulses in quantum dot based semiconductor optical amplifier,” Appl. Phys. Lett. 90, 033508 (2007). [CrossRef]

]. 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

19. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004). [CrossRef]

, 23

23. J. Kim, M. Laemmlin, C. Meuer, D. Bimberg, and G. Eisenstein, “Static Gain Saturation Model of Quantum-Dot Semiconductor Optical Amplifiers,” Accepted for publication in IEEE J. Quantum Electron. (2008). [CrossRef]

]). The model was adapted to correspond to the particular QD SOAs we investigated experimentally. We also studied the coherent noise spectral hole [20

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

, 24

24. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous Interaction of Spectral Modes in a Semiconductor Laser,” IEEE J. Quantum Electron. 11, 510–515 (1975). [CrossRef]

] 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

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

, 21

21. Y. Nambu, A. Tomita, H. Saito, and K. Nishi, “Effects of spectral broadening and cross relaxation on the gain saturation characteristics of quantum dot laser amplifiers,” Jpn. J.Appl. Phys. Part 1-Regular Papers Short Notes & Review Papers 38, 5087–5095 (1999).

].

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 [19

19. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004). [CrossRef]

].

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.

Fig. 1. Schematic representation of an inhomogeneously broadened QD distribution. Inset: The energy diagram of one QD in an excitonic representation.

The mutual dynamics and the optical properties are described in the following set of coupled equations.

dnwdt=Ie+jnu,jτuw,jjnwτuwGj(1nu,jNU,j)nwτr
(1)
dnu,jdt=nwτwuGj(1nu,jNU,j)nu,jτuw,j+ne,jτeu,j(1nu,jNU,j)nu,jτue(1ne,jNE,j)
+ng,jτgu,j(1nu,jNU,j)nu,jτug(1ng,jNG,j)nu,jτr
(2)
dne,jdt=nu,jτue,j(1ne,jNE,j)ne,jτeu,j(1nu,jNU,j)+ng,jτge,j(1ne,jNE,j)ne,jτeg(1ng,jNG,j)
ne,jτrLΓkgjkEPkћωk(2ne,jNE,j1)
(3)
dng,jdt=nu,jτug(1ng,jNG,j)ng,jτgu,j(1nu,jNU,j)+ne,jτeg(1ng,jNG,j)ng,jτge,j(1ne,jNE,j)
ng,jτrLΓkgjkGPkћωk(2ng,jNG,j1)
(4)

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.

τeg=τgeDgDeexp(ΔEegkT)
(5)

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.

Table 1:. Time constants, transition energies and degeneracies used for modeling.

table-icon
View This Table

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 [25

25. T. R. Nielsen, P. Gartner, and F. Jahnke, “Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers,” Phys. Rev. B 69, 235314 (2004). [CrossRef]

]. 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 [26

26. B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, “Rapid carrier relaxation in self-assembled InxGa1-xAs/GaAs quantum dots,” Phys. Rev. B 54, 11532–11538 (1996). [CrossRef]

] 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 [19

19. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004). [CrossRef]

]:

dP(ω,z)dz=[Γg(ω,z)α]P(ω,z)
(6)
dPsp(ω,z)dz=[Γg(ω,z)α]Psp(ω,z)+Γgsp(ω,z)Pvac(ω)
(7)

where α is the intrinsic loss and Pvac(ω) is the photon intensity of the vacuum field between frequency ω and ω+Δω.

Fig. 2. Calculated bias dependent ASE spectra for currents from 10 mA to 350 mA. A shift due to thermal heating which can be observed in Fig. 6 is not included in the calculations.

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.

Fig. 3. Calculated ASE difference for various pump powers. (a) 200 mA bias, (b) 350 mA bias current.

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.

Fig. 4. Pump wavelength dependence of ASE difference. Bias=200 mA, Pump power=4 dBm

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 [27

27. A. R. Kovsh, N. A. Maleev, A. E. Zhukov, S. S. Mikhrin, A. P. Vasil’ev, E. A. Semenova, Y. M. Shernyakov, M. V. Maximov, D. A. Livshits, V. M. Ustinov, N. N. Ledentsov, D. Bimberg, and Z. I. Alferov, “InAs/InGaAs/GaAs quantum dot lasers of 1.3 µm range with enhanced optical gain,” J. of Crystal Growth 251, 729–736 (2003). [CrossRef]

]. 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 [28

28. D. Ouyang, N. N. Ledentsov, D. Bimberg, A. R. Kovsh, A. E. Zhukov, S. S. Mikhrin, and V. M. Ustinov, “High performance narrow stripe quantum-dot lasers with etched waveguide,” Semicond. Sci. Technol. 18, L53–L54 (2003). [CrossRef]

]. 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

Fig. 5. (a) SEM micrograph of the output facet of the QD SOA. The 4µm wide ridge is shown which is deeply etched through the active region (white circle). (b) Schematic of the QD layer. The active region contains 10 layers of InAs QDs embedded in an InGaAs quantum well.

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).

Fig. 6. Measured ASE spectra at various drive currents showing the GS and ES peaks. At 125 mA the maximum ASE intensity is reached. For larger currents the peaks shift due to thermal effects.

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

5. S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Excited-state gain dynamics in InGaAs quantum-dot amplifiers,” IEEE Photon. Technol. Lett. 17, 2014–2016 (2005). [CrossRef]

, 29

29. K. Lüdge, M. Bormann, E. Malic, P. Hövel, M. Kuntz, D. Bimberg, A. Knorr, and E. Schöll, “Turn-on dynamics and modulation response in semiconductor quantum dot lasers,” Phys. Rev. B to be published (2008). [CrossRef]

]. This results in a significantly reduced ES saturation at high currents.

Fig. 7. Measured ASE difference for various pump powers from 4 dBm to -11 dBm. (a) 200 mA bias, (b) 350 mA bias

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 [21

21. Y. Nambu, A. Tomita, H. Saito, and K. Nishi, “Effects of spectral broadening and cross relaxation on the gain saturation characteristics of quantum dot laser amplifiers,” Jpn. J.Appl. Phys. Part 1-Regular Papers Short Notes & Review Papers 38, 5087–5095 (1999).

] 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 [20

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

] to be discussed below.

Fig. 8. (a) ASE difference for various pump wavelengths. (b) Zoom of ASE difference near the pump wavelength

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 [22

22. D. Hadass, A. Bilenca, R. Alizon, H. Dery, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, A. Somers, J. P. Reithmaier, A. Forchel, M. Calligaro, S. Bansropun, and M. Krakowski, “Gain and noise saturation of wide-band InAs-InP quantum dash optical amplifiers: model and experiments,” IEEE J. Sel. Top. Quantum Electron. 11, 1015–1026 (2005). [CrossRef]

]. The main difference lies in the fact that the quantum dash gain medium has quantum wire like properties [22

22. D. Hadass, A. Bilenca, R. Alizon, H. Dery, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, A. Somers, J. P. Reithmaier, A. Forchel, M. Calligaro, S. Bansropun, and M. Krakowski, “Gain and noise saturation of wide-band InAs-InP quantum dash optical amplifiers: model and experiments,” IEEE J. Sel. Top. Quantum Electron. 11, 1015–1026 (2005). [CrossRef]

] 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

30. M. Shtaif and G. Eisenstein, “Noise characteristics of nonlinear semiconductor optical amplifiers in the Gaussian limit,” IEEE J. Quantum Electron. 32, 1801–1809 (1996). [CrossRef]

, 31

31. M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: Relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34, 869–878 (1998). [CrossRef]

] and measured [32

32. M. Shtaif and G. Eisenstein, “Noise properties of nonlinear semiconductor optical amplifiers,” Opt. Lett. 21, 1851–1853 (1996). [CrossRef] [PubMed]

] 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 [20

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

]. A similar result was found experimentally for quantum dash SOAs [33

33. A. Capua, V. Mikhelashvili, G. Eisenstein, J. P. Reithmaier, A. Somers, A. Forchel, M. Calligaro, O. Parillaud, and M. Krakowski, “Direct observation of the coherent spectral hole in the noise spectrum of a saturated InAs/InP quantum dash amplifier operating near 1550 nm,” Opt. Express 16, 2141–2146 (2008). [CrossRef] [PubMed]

].

Fig. 9. Measured coherent noise spectral hole (a) bias dependence (b) detailed spectra for two bias levels

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

20. A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

, 22

22. D. Hadass, A. Bilenca, R. Alizon, H. Dery, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, A. Somers, J. P. Reithmaier, A. Forchel, M. Calligaro, S. Bansropun, and M. Krakowski, “Gain and noise saturation of wide-band InAs-InP quantum dash optical amplifiers: model and experiments,” IEEE J. Sel. Top. Quantum Electron. 11, 1015–1026 (2005). [CrossRef]

]. The asymmetry is due to the Bogatov effect [24

24. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous Interaction of Spectral Modes in a Semiconductor Laser,” IEEE J. Quantum Electron. 11, 510–515 (1975). [CrossRef]

] 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

4. P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, H.-M. Mao, and D. Bimberg, “Ultrafast Gain Dynamics in InAs-InGaAs Quantum-Dot Amplifiers,” IEEE Photon. Technol. Lett. 12, 594–596 (2000). [CrossRef]

, 7

7. T. Akiyama, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, O. Wada, and H. Ishikawa, “Nonlinear gain dynamics in quantum-dot optical amplifiers and its application to optical communication devices,” IEEE J. Quantum Electron. 37, 1059 (2001). [CrossRef]

, 16

16. S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Laemmlin, and D. Bimberg, “Complete ground state gain recovery after ultrashort double pulses in quantum dot based semiconductor optical amplifier,” Appl. Phys. Lett. 90, 033508 (2007). [CrossRef]

]. 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.

Fig. 10. Coherent noise spectral hole width and the corresponding QD SOA response time.

5. Conclusion

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 [6

6. P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, H.-M. Mao, and D. Bimberg, “Spectral Hole-Burning and Carrier-Heating Dynamics in InGaAs Quantum-Dot Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 6, 544–552 (2000). [CrossRef]

]) 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 [5

5. S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Excited-state gain dynamics in InGaAs quantum-dot amplifiers,” IEEE Photon. Technol. Lett. 17, 2014–2016 (2005). [CrossRef]

]. 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

34. J. Moerk, M. L. Nielsen, and T. W. Berg, “The Dynamics of Semiconductor Optical Amplifiers - Modeling and Applications,” Opt. Photon. News July, 43–50 (2003).

, 35

35. T. Vallaitis, C. Koos, R. Bonk, W. Freude, M. Laemmlin, C. Meuer, D. Bimberg, and J. Leuthold, “Slow and fast dynamics of gain and phase in a quantum dot semiconductor optical amplifier,” Opt. Express 16, 170–178 (2008). [CrossRef] [PubMed]

]. 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.

Acknowledgments

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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17.

P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, H.-M. Mao, and D. Bimberg, “Spectral Hole-Burning and Carrier-Heating Dynamics in Quantum-Dot Amplifiers: Comparison with Bulk Amplifiers,” Phys. Status. Solidi. B 224, 419–423 (2001). [CrossRef]

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A. Bilenca and G. Eisenstein, “On the Noise Properties of Linear and Nonlinear Quantum-Dot Semiconductor Optical Amplifiers: The Impact of Inhomogeneously Broadened Gain and Fast Carrier Dynamics,” IEEE J. Quantum Electron. 40, 690–702 (2004). [CrossRef]

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A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous Interaction of Spectral Modes in a Semiconductor Laser,” IEEE J. Quantum Electron. 11, 510–515 (1975). [CrossRef]

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31.

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33.

A. Capua, V. Mikhelashvili, G. Eisenstein, J. P. Reithmaier, A. Somers, A. Forchel, M. Calligaro, O. Parillaud, and M. Krakowski, “Direct observation of the coherent spectral hole in the noise spectrum of a saturated InAs/InP quantum dash amplifier operating near 1550 nm,” Opt. Express 16, 2141–2146 (2008). [CrossRef] [PubMed]

34.

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35.

T. Vallaitis, C. Koos, R. Bonk, W. Freude, M. Laemmlin, C. Meuer, D. Bimberg, and J. Leuthold, “Slow and fast dynamics of gain and phase in a quantum dot semiconductor optical amplifier,” Opt. Express 16, 170–178 (2008). [CrossRef] [PubMed]

OCIS Codes
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(250.5980) Optoelectronics : Semiconductor optical amplifiers
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Optoelectronics

History
Original Manuscript: March 13, 2008
Revised Manuscript: May 15, 2008
Manuscript Accepted: May 19, 2008
Published: May 22, 2008

Citation
Christian Meuer, Jungho Kim, Matthias Laemmlin, Sven Liebich, Amir Capua, Gadi Eisenstein, Alexey R. Kovsh, Sergey S. Mikhrin, Igor L. Krestnikov, and Dieter Bimberg, "Static gain saturation in quantum dot semiconductor optical amplifiers," Opt. Express 16, 8269-8279 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-8269


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