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We demonstrate a direct observation of the coherent noise spectral hole in a saturated quantum dash amplifier. Its width 500-600 GHz is determined by the response time and is responsible for high speed regeneration properties.
©2008 Optical Society of America
1. Introduction
The noise properties of a semiconductor optical amplifier (SOA) are dictated by carrier and gain dynamics. An SOA operating in the saturated regime undergoes complicated dynamical processes which have a major effect on its output noise. First, saturation reduces the degree of inversion thereby increasing the spectral density across the entire broad band gain spectrum. Second, the saturating signal propagating along the SOA undergoes a four wave mixing like nonlinear interaction with the broad band noise resulting in a coherent spectral hole [1-4]. The coherent noise spectral hole was first predicted [1] and experimentally observed [2] in a bulk SOA. The width of the spectral hole is approximately equal to the inverse of the SOA response time which for the original bulk SOA was a few GHz and could therefore be observed, following detection, in the electrical domain [2].
In a quantum dot (QD) or quantum dash (QDash) gain medium, the response time is significantly faster (of the order of 1-2 ps) and therefore the coherent spectral hole was predicted to be much wider, 0.5 – 1 THz [3, 4]. While it is not feasible to observe such a wide spectral hole in the electrical domain, it should be straight forward to identify it directly in the amplified spontaneous emission (ASE) spectrum. The gain spectrum in the vicinity of a saturating signal has a similar signature of the unique dynamics of a QD or QDash SOA. The spectral hole in the gain was indeed demonstrated for a QD SOA operating near 1000 nm [5].
This paper describes a direct observation of a coherent spectral hole in the amplifier ASE spectrum of an InAs/InP QDash SOA operating near 1550 nm. The specific SOA has a relatively low saturation power which allows saturation without amplification of the input signal avoiding the noise spectral skirt that may mask the spectral hole [4]. The measured noise spectra show a clear hole with a typical asymmetry due to the Bogatov effect [6]. The shape of the hole is consistent with the prediction of [4]. Its width, 4-5 nm, represents a response time of 1.5-2 ps, consistent with pump probe measurement on similar SOAs [7].
2. Field propagation model
The model employed in this study is based on [4] and incorporates the following principals: (a) The Qdash amplifying media is modeled as a dense assembly of quantum wires [8] where the high energy tail of the density of states function is discretized [4]. (b) Inhomogeneous broadening due to the dash size variations is governed by Gaussian statistics. (c) Coupled carrier rate equations and two propagation equations for the electric field and the noise are used as described in (1) below. The solution is based on a small signal perturbation of the steady state.
Where A1 and A2 are given by
M is the number of same-size Qdash groups and N is the number of intradash energy levels [4]. E 0 is the steady state saturating electrical field and α int the internal losses. The constants Cjk 1,Cjk 2,Cjk 3,Cjk 4,Cjk 5 are given explicitly in [4]. τeff jk,0 and gpeak jk,0 are the effective response time and peak gain respectively of the kth intradash level in the jth group of dashes at steady state.
Equation (1) states that the small signal electrical field E1 at frequency ω is related to itself by the coefficient A1. The first term of A1 originates from the regular gain and absorption of all quantum dashes while the second term is due to a coherent interaction between the pump and the field E1(ω). The field at frequency ω contains also a contribution from the field at frequency (-ω) through the factor A2. This contribution originates solely from a coherent interaction between the pump and the field at frequency ω. The interactions become incoherent when the coherent terms vanish which can occur at large detuning, small gain or small pump powers. Note that (1) governs both the small signal electric field and the noise propagation along the amplifier.
3. Qdash amplifier structure and static characteristics
The SOA layer structure [9] was grown by MBE and consists of four InAs QDash layers with a nominal thickness of 5 monolayers separated by 10 nm AlGaInAs barriers embedded within a 250 nm GRINSCH waveguide structure. The upper 1.7 µm InP cladding layer was overgrown by MOVPE. The lateral waveguide was defined by a 2.5 mm long, 4 µm wide ridge whose end facets were anti reflection coated. The amplifier exhibits a peak gain of 21 dB at a bias of 300 mA and the saturation output power near the peak was ~15dBm. Bias dependent ASE spectra, shown in Fig. 1 reveal the expected wide bandwidth due to the gain inhomogeneity as well as the spectral shift due to the band filling effect [4].
A strong pump signal was injected from a tunable laser source, using a lens polished fiber, for the noise measurements. Fig. 2 shows measured and calculated spectral holes in the ASE. The hole in the spectra is seen very clearly in Fig. 2(a) and resembles exactly the prediction of (1) which is shown in Fig. 2(b). A more detailed view of the measured coherent spectral hole is presented in Fig. 3 which shows the bias dependence of the hole for an input signal having a power of +2 dBm. The pump wavelength was tuned to the gain peak for each bias.
Fig. 2. (a) Measured spectral hole, (b) Calculated spectral hole. Inset shows magnification of the hole. The red line signifies the spectral placing of the pump.
Fig. 3. Spectral hole for various bias levels. The width of the hole shows an equivalent life time of ~1/1.5ps.
The data in Fig. 3 reveals the clear asymmetry of the spectral hole. Based on the theoretical model and following the definition of [5], the width of the hole can be determined which implies here an effective SOA response time of 1 – 1.5 ps. This response time is consistent with an effective gain recovery time measurement in short pulse pump probe experiments performed on an identical SOA as describe in [7]. The bias dependence of the spectral hole shape is consistent with the prediction of (1). The coherent term of the coefficients Ai increases with bias because the peak gain gpeak jk,0 grows and hence the hole widens.
Figure 4 shows the coherent spectral hole for several saturating signal powers. The saturating pump power appears both in the numerator and the denominator of the coherent terms. According to the calculations presented in [4], the width of the hole should increase with rising saturating signal power and reach a maximum after which it ought to decrease with further increase in the saturating signal power. The increase in the depth of the hole and width are clearly seen in Fig. 4 but the maximum was not reached and hence the eventual decrease in width and depth was not observed in the present experiments.
The temperature dependence of the spectral hole was also examined and is described in Fig. 5. Temperature changes affect both the gain and the response time, both of which decrease with rising temperature. The dependence of the response time is of lower order meaning that the hole disappears with rising temperature as demonstrated in Fig. 5.
The properties of the gain spectra near the saturating signal are dictated by the same dynamics that determine the noise. Such gain spectra were measured using a static pump probe scheme [4] and the results are shown in Fig. 6. The pump wavelength was tuned once more to the gain peak for every bias level. While the gain measurements are rather noisy, it is clear that they exhibit the same asymmetric signature, due to the coherent interaction, as observed in the noise spectra.
Fig. 6. Gain spectra measurement using static pump probe setup. The red line signifies the spectral placing of the pump.
4. Conclusions
To conclude, we have demonstrated a direct observation of a coherent spectral hole in the noise spectrum of a QDash SOA. The very fast response time of the device (1-2 ps [7]) results in an extremely wide hole (500-600 GHz). A similar spectral hole is observable in highly saturated quantum well SOAs since the dynamics of those is governed by carrier capture time which has also a value of approximately 1 ps. [10]. In addition to the inherent value of confirming the predicted spectral hole, the observation has practical significance as the spectral hole is responsible for the high data rate regeneration capabilities of these types of SOAs [9].
Acknowledgements
This work originated from the European project Bigband.
References and links
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