1. Introduction

The dynamical properties of quantum dot lasers have been studied theoretically [1, 2, 4 –7] and experimentally [3, 4, 8–12] for many years. The nature of the small signal modulation response in quantum dot lasers is known to be highly damped [3, 7] with rather moderate bandwidths (usually below 10 GHz). The large nonlinear gain compression was shown to be due to the inhomogeneous gain broadening as well as the balance between the carrier capture and escape processes [7]. Also, the state filling effect, together with the carrier capture time reduces the differential gain [6, 13], further limiting the high frequency modulation capabilities.

The modulation characteristics and the noise spectra are governed by the same dynamical processes. The highly damped limited bandwidth modulation response of quantum dot lasers offers therefore unique low noise characteristics. This was demonstrated first in InP based quantum dash lasers operating near 1550 nm which exhibited relative intensity noise (RIN) levels as low as -160 dB/Hz [14]. Similar results were reported recently for high power GaAs based 1300 nm quantum dot lasers [15]. The very low RIN levels make quantum dot lasers suitable substitute sources to solid state lasers (whose RIN is also in the range of -160 dB/Hz) for use in analog transmission applications [16].

This paper reports on the direct correlation between the damped modulation response and a low RIN in GaAs/InGaAs quantum dot lasers emitting near 1300 nm. We demonstrate very flat modulation responses with a 3dB bandwidth of ~6.5 GHz and correspondingly a very low RIN. At a power of 27 mW per facet, the laser exhibits a RIN of -158 ÷ -160 dB/Hz at frequencies up to 10 GHz. We carefully separate the laser noise from the detection system thermal and shot noise components [16] in order to arrive at an accurate laser RIN spectrum. The RIN values we demonstrate are significantly lower than those of commercial quantum well lasers specially designed for microwave applications [17]. For relatively narrow bandwidths used in the cable TV industry (~10 MHz to 850 MHz), some lasers have been demonstrated which have similar RIN levels [18].

2. Quantum dot laser structure and static characteristics

The laser structure is similar to the one reported in Ref. [19]. It comprises 15 layers of InGaAs quantum dots having nominal thicknesses of 2.5 monolayers, separated by 33 nm GaAs barriers. The wide barriers ensure electronic decoupling of the quantum dot layers which enhances the role of carrier transport between dot layers and lengthens the capture time, both of which result in an increased nonlinear gain compression coefficient [13]. The waveguide is defined by a deeply etched 2 μm wide mesa and the cavity length is 1 mm. The laser chips were mounted in a microwave test fixture with separate DC and RF current inputs. Partial microwave matching was achieved by connecting a 35Ω resistor in series with the RF current line.

Figure 1(a) shows a CW L-I curve measured at 18°C. The threshold current was 9 mA and the output power increased linearly with a slope efficiency of 0.18 W/A, up to a bias of ~150 mA and then saturated slightly due to heating. The output power at a bias of 200 mA was 27 mW per facet. Figure 1(b) shows measured low resolution spectra at three bias levels with a typical broad spectral extent due to the inhomogeneously broadened gain of the quantum dot active region [20, 21].

 

Fig. 1. (a). L-I curve measured at 18° C, (b). Measured spectra at three output power levels.

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3. Dynamic properties

Small signal modulation responses and noise spectra were measured using a receiver comprising a photo-detector followed by a trans-impedance amplifier. The receiver transfer function M(f) in units of V/W (output peak to peak voltage (into 50 Ω) per input peak to peak optical power) was carefully characterized using an optical network analyzer. An RF spectrum analyzer was employed for measurements of the noise spectra while the modulation responses were measured in a conventional manner with a network analyzer.

Measured small signal modulation responses at several average power levels are shown in Fig. 2. The expected highly damped nature of the responses is clearly confirmed. Even at a low power of 1.7 mW, the resonance peak is very shallow (1.5 dB) and at higher power levels it disappears. The maximum observed 3 dB bandwidth is ~6.5 GHz at 20 mW. The bandwidth does not increase at higher optical powers, as expected in a laser having a very large nonlinear gain compression coefficient.

 

Fig. 2. Measured modulation responses at different optical power levels.

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Figure 3 shows noise spectral densities measured by driving the laser at different DC bias levels. The resolution bandwidth was 3 MHz. The lowest (blue colored) curve represents the receiver thermal noise which was obtained with no optical input signal. The periodic response at high frequencies stems from an electronic oscillatory response of the amplifying stage.

 

Fig. 3. Measured noise spectral densities for different optical power levels.

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In order to obtain a correct RIN spectrum, each measured noise spectral density function has to be corrected for the thermal and shot noise contributions and then transformed from the output electrical power domain to an input optical noise power. Figure 4(a) shows for example the various noise contributions (plotted in a linear scale) at an optical facet power of 27 mW.

The thermal noise is input power independent. The shot noise, generated in the photo-detector, has a white Gaussian statistical distribution and an RMS spectral density <i ²>= 2qI_DC = 2qρ <P>. IDC is the average photo current andρ is the detector responsivity which takes on the value of 0.85 ± 0.05A/W and is assumed to be frequency independent in the relevant range of 0 to 10 GHz. q is the elementary electronic charge and <P> is the average optical power at the receiver input.

 

Fig. 4. (a). Noise spectral density components at an output power level of 27 mW, (b). Corrected noise spectra at different power levels.

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The shot noise is amplified and spectrally modified by the trans-impedance transfer function. The shot noise contribution becomes then $N_{\mathrm{shot}}=\frac{<i^2>M^2\left(f\right)}{{\rho }^{2}R}=\frac{2q{M}^2\left(f\right)<P>}{\mathrm{\rho R}}$ where R = 50Ω is the input impedance of the spectrum analyzer.

Figure 4(b) shows the corrected noise spectral densities (N_laser (f)) which together with an accurate measurement of the average power at the receiver input, enables the determination of the $\mathrm{RIN}=\frac{<{\Delta p}^2>}{{<P>}^2}$ spectra described in Fig. 5, where Δp represents the optical power fluctuations at the receiver input: $\mathrm{RIN}\left(f\right)=\frac{{\mathrm{RN}}_{\mathrm{laser}}\left(f\right)}{{M{\left(f\right)}^2<p>}^2}$

 

Fig. 5. RIN spectra for different laser power levels.

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The spectra in Fig. 5 reveal flat RIN spectra reaching extremely low levels at high optical powers. The actual RIN is somewhat masked by the electrical resonances at high frequencies but it is easy to extract a RIN of -158 ÷ -160 at frequencies up to 10 GHz. We have observed a lower RIN at higher frequencies but the limited response of the receiver prevents a reliable quantification beyond 10 GHz. At low frequencies, the RIN level increases with part of the increase being an artifact of the detection system and part representing a true low frequency laser noise.

4. Conclusions

To conclude, we have addressed the impact of the large nonlinear gain compression coefficient in quantum dot lasers on the small signal modulation response and the RIN. The RIN spectra were obtained after a careful correction of the measured noise spectra for the shot noise and the receiver thermal noise. For a laser emitting up to 27 mW per facet, we have demonstrated a modulation bandwidth of ~6.5 GHz in a response which at moderate and high powers exhibits no resonance. Correspondingly, the RIN spectra are flat reaching values of -158 ÷ -160 dB/Hz at frequencies up to 10 GHz. These values are similar to the RIN of narrow band lasers aimed at analog cable TV transmission and are lower by several dB than those common in microwave photonics quantum well lasers. The low RIN was observed to extend beyond 10 GHz but higher frequencies were not quantified due to the limited response of the receiver. Such low RIN values rival those of solid state lasers designed to be used in advanced analog fiber optics transmission systems [16].