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Characteristics of 1.5 - µµµµm InAs/InP Quantum Dash Optical amplifiers
G. Eisenstein, R. Alizon, H.Dery, A. Bilenca, V. Mikhelashvili Electrical Engineering Dept. Technion Haifa 32000 Israel
R. Schwertberger, J.P. Reithmaier, A. Forchel
Technische Physik, Universitat Wurzburg 97074 Wurzburg Germany
Abstract: We describe InAs / InP quantum dash optical amplifiers operating near 1.5 µm. We present a model and experiments demonstrating that the quantum dash devices have quantum wire like properties. We describe fast dynamical characteristics within the homogeneously broadened gain as well as the complex wavelength dependent dynamical characteristics across the full inhomogeneously broadened gain spectrum.
OCIS codes: (250.5980) Semiconductor optical amplifiers
Introduction
Quantum dot and quantum dash lasers and amplifiers have numerous potential advantages over the widely used quantum well structures. Quantum dot devices based on GaAs and related material systems operating in the 1 to 1.3 µm wavelength range and exhibiting outstanding properties have been demonstrated by numerous groups [1-4]. Some successful results were also obtained with quantum dots operating in the important 1.55 µm range [5, 6] but more common are InAs/InP quantum dash structures [8-11].
Quantum dashes are nano structures which self assemble with a rather high density in a regular pattern. Fig. 1 shows an SEM picture of an ensemble of quantum dashes. The height of a typical quantum dashes is 2 - 4 nm yielding optoelectronic properties which are similar to those of shallow quantum dots. Fluctuations in cross sectional dimensions, mainly the height, result in inhomogeneously broadened gain spectra, very similar to the case of quantum dot gain media. One consequence of this is the availability of extremely broad gain spectra as seen in Fig. 2 which represents amplified spontaneous emission (ASE) spectra of an InAs/InP quantum dash optical amplifier [9, 10]. The spectra in Fig. 2 are for a pulsed bias range of 1.6 mA to 150 mA. The width of these ASE spectra in several hundreds of nm.
Fig. 1. SEM image of a quantum dash ensemble Fig. 2. Bias dependent pulsed ASE spectra
100 nm100 nm100 nm
This paper addresses two major issues; (1) the exact nature of the quantum dash gain media which we prove to have quantum wire ensemble like properties and (2) issues related to the dynamics of the homogeneously and inhomogeneously broadened gain spectrum.
The Nature Quantum Dash Gain Media Observation at the quantum dash structure � Fig. 1 suggests that these gain media comprise an ensemble of quantum wires. We calculate the gain of such an ensemble following the density-matrix formalism for a two level system in which the linear optical gain coefficient is derived from the linear susceptibility. The wires in the ensemble have some cross section size distribution where the homogeneous broadening of each wire is considered to be the same. The calculated gain takes the form
[ ]1)/)((
112
)}2/)(exp{1)()()()( 22
220
+−⋅
−
−−−+= ∫∫
∞+∞
∞− υγωπσ
σωωωω
cE i
iihe EEE
dEEEdEffCgi
hh (1)
where;
⋅
Γ=
σγη
ωπω
υω c
r
b
p
Ama
ncm
EeC
hh
12)(
0
2
(2)
The inhomogeneous broadening is centred at E0, which is extracted from ASE measurements at
high currents where no blue shift is taking place (not shown in Fig. 1). The broadening parameter σ is extracted from low temperature measurements and we assume that it is the same for room temperature operation. fe, fh are the distribution functions in the conduction and valence bands, respectively. υγ c is the dephasing rate which is taken to be 5 meV while Ep (~ 20 eV in most semiconductors) is the energy equivalent of the momentum matrix element. The first bracketed term in (2) contains the optical confinement factor, the fraction of the dipole moment due to the confinement of the envelope wave functions, the effective reduced mass, the dash coverage and the confinement area of an average wire. The effective mass was extracted from kp model calculations. For either a fully inverted system or absorption in a passive medium (fe(ω) + fh(ω) � 1 = ± 1), the linear optical gain coefficient spectrum is shown in Fig.3a. The asymmetry results from the fact that due to the shape of their DOS, quantum wires of different sizes have overlapping states with identical transition energies in the high-energy portion of their spectra. Fig. 3a shows also the inhomogeneously broadened, gaussian shaped spectrum whose peak and the gain peak are shifted relative to to each other by an amount that increases with the degree of inhomogeneity.
The parameters of the quantum dash gain media were extracted from the bias dependent ASE spectra shown in Fig. 2 using a newly developed procedure. The ground state emission does not saturate throughout the bias range considered and hence we assume that the gain is linear. The power spectrum of the ASE in then:
−
−−⋅⋅⋅=
LgLgffNCP he ))((
1}))(exp{()()()()( 1 αωαωωωωωω h (3)
where L is the length of the cavity, and α is the internal loss which is taken to be 7 cm-1 [11]. C1 changes slowly with wavelength and is proportional to the spontaneous emission rate and the output coupling. N(ω) denotes the number of dashes with the corresponding transition wavelength. Next we choose a
reference current (60mA in this case) and calculate a series of ratios between the ASE power spectra at the various bias levels and the spectrum at the reference current. In the present case we calculate eleven such ratios, which are shown as dashed lines in Fig. 3b to be discussed later. The horizontal line represents the trivial case of 60 mA.
We introduce two fitting parameters. The first, denoted by xe, is the value of the conduction band distribution function for the reference bias at the frequency of the central transition of the ensemble (ħωc = E0). The second denotes the conduction band to valence band mass ratio (y=me/mh). The square root of y represents the approximate ratio of the conduction to valence band density of states. Due to the deep carrier confinement, the energies of electrons and holes can be written as:
+++≈
++≈ 2
2
2
2
222
2
2
2
22
2)(
2)( z
yxegtrez
yxhtrh k
LLmEEk
LLmE ππωππω hh (4)
With the help of xe, y and (4) we deduce the distribution function at the reference current in the conduction band where for each transition energy we can use the fact that (Etr � E0)≈(Et r � E0)e/(1 + y) . Assuming charge neutrality in the confining region and using xe, y and (4); and since (Etr � E0)≈(Etr � E0 )h/(1 + y-1) we also extract (numerically) the valance band distribution at the reference current. In order to get the distribution functions for all other currents we make use of the fact that in the short wavelength range, the distribution functions are approximately Maxwell-Boltzmann distributions, because even near the spectra peak, the ASE is not saturated. The square bracketed term in (1) can then be replaced with �1, so that:
))()((exp{|),(),(
222
1 iiiPiP
SW µµβωω
−≈ (6)
where the subscript SW denotes short-wavelengths and the chemical potentials µ are the sums of the conduction and valence band potentials. Following a simple mathematical manipulation and taking i2 to be the reference current yields a geminate pair (fe(E0, iref), fh(E0, iref) ) for each current which leads to the distribution functions. This unique procedure allows then calculating the conduction and valence distribution functions for all currents and wavelengths using only two fitting parameters (xe and y). Fig.3b shows the best fitted case. The fit for all 10 non-trivial ratios is excellent with the peak optical power corresponding to the largest bias is about 5000 stronger than that of the lowest current.
Fig. 3a. Gain coefficient for a quantum wire ensemble Fig. 3b. Power ratio spectra normalized to 60 mA . shown as a solid line. The dashed line denotes the Dashed lines: experimental data Solid lines: Best fit inhomogeneous broadening. σ = 30 meV, ħγ = 5 meV. for the quantum wire ensemble model.
Repeating the analysis and using the gain profile of quantum dot ensemble failed to fit the experimental measurements for all sets of fitting parameters. We conclude therefore that the quantum dash gain media have indeed quantum wire ensemble like properties.
Quantum Dash SOA Characteristics within the Homogeneously Broadened Gain The gain spectrum of the quantum dash SOA comprises contributions from a large number of dash size populations making up the inhomogeneously broadened gain. Characterization within a small fraction of this spectrum yields properties which are dictated by the homogeneously broadened gain characteristics. Fig. 4 shows gain and gain saturation of a 2.2 mm long SOA as a function of bias and of the input power. The measurements were performed near the peak of the gain spectrum and using a CW bias. We notice the expected gain increase with bias reaching a maximum of 12 dB. The gain saturation also follows the predicted behavior with essentially no saturation observed at 75 mA and an output saturation power of about 20 mW at 160 mA.
Fig. 4. Gain saturation as a function of DC bias and input power
Dynamical properties of the SOA were studied using CW four wave mixing (FWM). The measurements were performed with a 1542nm wavelength pump operating at a power level of 0 dBm and a -11 dBm tunable probe whose frequency was scanned by more than ± 1000 GHz relative to the pump frequency.
10 1 10 2 10 3 10 4
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y [dB]
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1540 1542 1544
Probe
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5
α−pa
rameter
1505 1520 1535 1550 1565 1580 1595 1605Wavelength [nm]
α = 2.3
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Pump
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Probe
(a)
0
1
2
3
4
5
α−pa
rameter
1505 1520 1535 1550 1565 1580 1595 1605Wavelength [nm]
α = 2.3
Lasing
(b) Fig. 5. (a) CW FWM conversion efficiency dependence on detuning for a quantum dash SOA. (b) Wavelength dependent
linewidth enhancement factor of laser with an identical structure to the SOA.
0
5
10
15
0 50 100 150
Gai
n [d
B]
Current [mA]
(a) Gai
n [d
B]
-20 -15 -10 -5 0 5Optical Input Power [dBm]
160 mA
75 mA
2
4
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(b)0
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Gai
n [d
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Current [mA]
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-20 -15 -10 -5 0 5Optical Input Power [dBm]
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75 mA
2
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(b)
Fig. 5(a) shows the FWM conversion efficiency of the conjugate FWM product for positive and negative detuning. The insert shows a typical output spectrum with the two generated sidebands. The identical efficiency function slopes for positive and negative detuning are indicative of a low α-parameter, consistent with [12]. This was confirmed by measuring the α-parameter of quantum-dash lasers having identical structure. Those results, shown in Fig. 5(b) indicate a low value of 2.3 at lasing wavelength.
Further examination used FWM wavelength conversion using a train of 40 ps wide pulses, 6.2 nm away from the CW pump, namely a detuning which is within the homogeneously broadened gain. The converted product was filtered, detected and displayed on a fast oscilloscope. Fig. 6(a) shows very fast transitions of the converted pulse and a large signal-to-noise ratio. The very fast transitions are consistent with the gain dynamics in quantum dot SOA which were shown to be typically dominated by a gain recovery time of a few ps [13,14].
In order to confirm the speed of these SOA, data amplification of 10 Gbit/s NRZ signals was also
performed. A comparison between the eye diagram of the directly amplified signal and the input signal shown in Fig. 6(b), demonstrates the ability to amplify signals at 10 Gbit/s with no distortions.
(a)
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
Det
ecte
d Si
gnal
[a.u
.]
Time [ns]
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] 6.2 nmShort pulses
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ecte
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igna
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.]
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] 6.2 nmShort pulses
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igna
l (a.
u.)
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ecte
d S
igna
l (a.
u.)
Input Signal
50 ps/div
(b)
50 ps/div
Fig. 6. (a) Wavelength conversion of 40-ps pulses over a 6.2 nm detuning. Optical spectrum and time-domain description. (b)
Eye diagrams obtained for the amplification of a 10 Gbit/s signal through the QDash SOA.
Quantum Dash SOA Operating Across the Inhomogeneously Broadened Gain Spectrum The inhomogeneously broadened gain is an inherent property of quantum dash (and dot) SOAs. It is a unique property to those nano structured devices and has a profound impact on performance as well as on basic understanding of the gain media. In reality, the gain media are imperfect inhomogeneous media since different spectral regions are partially coupled via a common carrier reservoir from which they are fed. Therefore the SOA may in some cases enable multi wavelength amplification and in other cases it may allow for very wide band wavelength conversion.
A direct measurement of the inhomogeneous properties of the present quantum dash SOA was performed where we mapped out the saturation of the ASE spectrum in the presence of a saturating CW signal. Fig. 7 describes these spectra for four different input wavelength and three input powers for each.
1300 1350 1400 1450 1500 1550 1600 1650Wavelength [nm]
ASE
RA
TIO
(dB
)
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0
+5
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I=150 mAλλλλin=1460 nm
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Wavelength [nm]A
SE R
ATI
O (d
B)
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+5
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I=150 mAλλλλin=1470 nm
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(a) (b)
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)
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TIO
(dB
)
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+5
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+25
I=150 mAλλλλin=1460 nm
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SE R
ATI
O (d
B)
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+5
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I=150 mAλλλλin=1470 nm
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SE R
ATI
O (d
B)
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+5
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I=150 mAλλλλin=1470 nm
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B)
-5
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I=150 mAlin=1530 nm
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I=150 mAlin=1530 nm
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B)
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I=150 mAlin=1570 nm
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IO (d
B)
-5
0
+5
+10
+15
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+25
I=150 mAlin=1570 nm
(a) (b)
(c) (d)
Fig. 6. ASE ratios for a saturating signal at different wavelengths and three power levels for wach wavelength. The reference spectra with no input signal are also shown At every wavelength we injected a very small signal (which caused no saturation) followed by a moderate signal which saturated the SOA somewhat and finally a very strong signal. In each case we measured the complete ASE spectrum and divided it by the reference spectrum (with no input signal). The ratio displayed in the figures represents a direct presentation of the saturation properties. All measurements were done at a 150 mA DC bias and the reference ASE spectrum is also shown for clarity. The �spectral hole� is found to strongly depend on the saturating signal power and wavelength with saturation on the long wavelength side of the gain peak affecting a larger portion of the spectrum.
The dynamics across the inhomogeneously broadened gain spectrum was characterized by a cross gain modulation (XGM) experiment using short pulses. 40 ps wide pulses at 1560 nm and a peak power of 12 dBm were used as a pump. Fig. 8(a) shows four converted pulses presenting various efficiencies with detuning. Reasonably large pulse conversion efficiencies are observed at detunings of up to 80 nm (10 THz) but for 100 nm detuning, the conversion efficiency reduced almost completely. Observation of the converted pulses reveals that each has an initial fast rise time (actually not resolved here) followed by a slow (~ 200 ps) component of the recovery. The relative significance of the slow component increased as the probe wavelength shortened. This behavior is explained by a recovery whose dynamics is dominated by the detailed balance between carrier capture into the dashes and escape to the common reservoir comprising some quasi bound states and the barrier [15, 16]. Since the capture is almost constant but the escape time shortens with energy, a short wavelength probe senses energies levels which tend to thermalize against the quasi bound states and hence the response is reduced which manifests itself as a slow response.
1420 1460 1500 1540 1580 1620-80-75-70-65-60
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Signal output at λs=1575 nm Converted eye diagramfor BER=10-12
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Fig. 7. (a) Wavelength conversion of 40-ps pulses at 1560nm with conversion detunings of up to 80nm. ASE spectrum and time-domain description. (b) BER measurements of 2.5 Gbit/s pseudorandom data at a 50 nm detuning. (c)-(d) Detuning dependent small signal XGM bandwidth for a bias of 150 mA respectively for pump wavelengths of 1535 nm and 1462 nm.
The observed time constants suggest that moderate bit rates may be converted by XGM over a very wide range. Indeed we demonstrated low BER for 2.5 Gbit/s data conversion over 50 nm as shown in Fig.8(b). The shape of the curves indicates that the conversion process adds noise but doesn�t deteriorate the data.
Finally we quantified the XGM responses using small signal modulation. Fig. 8 (c) and (d) describe the small signal XGM response for a bias of 150 mA and pump wavelengths of 1535nm and 1462
nm respectively. At a pump wavelength of 1535 nm, the bandwidth increases as the probe energy decreases because of the decrease in carrier escape rate, improving the response of the gain [16]. The response at 1462 nm is significantly different than at 1535 nm with the bandwidth being narrower and probe-wavelength insensitive. Indeed at this wavelength, the pump is in the spectral surroundings of the quasi bound states so that the perturbation relaxes mainly by thermalization with the higher energy barrier. In addition, the inversion level at the short wavelength is reduced compared to the gain peak and therefore the response to the perturbation is weaker. Nevertheless, all dash populations are coupled to the high energy states, consequently, perturbing the gain region with a wavelength independent, narrow band and inefficient XGM response. Acknowledgement This work was supported by the EC through the BigBand project of the IST. H. Dery and A. Bilenca thank the Ministry of Science � Eshkol Fellowship � for its support.
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