Room temperature quantum-well semiconductor optical amplifier with large input power is utilized in both the absorption and gain regime as an optical group delay and advance (slow and fast light), respectively. Material resonance created by coherent population oscillation and four wave mixing is tuned by electrical injection current, which in turn controls the speed of light. The four-wave mixing and population oscillation model explains the slow-to-fast light switching. Experimentally, the scheme achieves 200 degrees phase shift at 1 GHz, which corresponds to 0.56 delay-bandwidth product. The device presents a feasible building block of a multi-bit optical buffer system.
© 2007 Optical Society of America
For a long time, controlling the propagation speed of light has been considered a challenging problem. Recently, several experiments have demonstrated that the group velocity of light can be reduced to as small as 17 meters per second . Today, slow light research has caught a lot of attention for both its intriguing physics and potential applications. These include all-optical buffers, variable true-time delay lines , and nonlinear optics , which may become essential components for all-optical signal processing and optical communication systems in the near future. From an application point of view, the so called delay-bandwidth product is more important than the absolute delay time. The delay-bandwidth product indicates how many bits can be delayed through the slow-light medium. In order to modify the group velocity of light in an optical medium, a large waveguide dispersion or material dispersion needs to be induced. Recent experiments have demonstrated that a large signal delay of more than 10 bits can be achieved from waveguide dispersion using photonic crystals . However, delay tuning ability and relatively slow switching time are typically disadvantages of using waveguide dispersion. We have been studying slow light and fast light using the material dispersion approach by coherent population oscillation (CPO) and four wave mixing (FWM) in quantum well (QW) and quantum dot (QD) semiconductor optical amplifiers (SOA) [5, 6, 7]. Our studies coincide to pioneering work using material resonances of CPO and FWMeffects in crystals [8, 9, 10]. Semiconductors have several advantages such as compactness, large bandwidth, and easy and quick response of delay tuning by direct current injection or optical pumping. We recently studied that a single microwave modulated optical beam in a SOA gives a relatively large signal delay due to strong signal to conjugate coupling effect (FWM) . This is in contrast to the two beam experiment (a pump and a probe in counter-propagating directions) in which only the coherent population effect due to the pump beam dominates while FWM is negligible due to phase-matching consideration [7, 12]. In this paper, we investigate both slow light and fast light in a QW-SOA using a single co-propagating modulated beam (the pump is the carrier and the probe is the sidebands created by modulation). Similar studies have been demonstrated previously in a single quantum-dot devices  and in a monolithically integrated device consisting of two SOA-EA pairs (which show a device with net gain) . Other studies show very large bandwidths and consider limitations of CPO/FWM in active semiconductors [15, 16].
In this work, we experimentally present more than half-cycle optical advance-delay at GHz bandwidth. This observation of large delay-bandwidth product is attributed to a large variation in saturation power with current controlled QW-SOA. The scheme presents a discrete optical delay block, which could be utilized in a cascaded setup (with coupled optical attenuators and optical filters) as an active optical delay capable of multi-bit delays. The experimental results and theoretical models with mean filed approximations are coherently compared for analysis.
2. Device and experimental investigation
The device considered in this work, shown in Fig. 1, is made up of a current driven variable QW-SOA, whose optical input (pump [5 dBm at 1310 nm] and probe sidebands) is pre-amplified using a booster SOA. The electrically varied QW-SOA is about 2.5 mm in length with about 25 dB small-signal gain at 500 mA. An isolator, in the path of the optical modulated signal guarantees that the spontaneous emission from the variable QW-SOA does not affect the booster pre-amplifier. The amplified optical signal is large in power (larger or on the order of the saturation power Psat of the variable QW-SOA), therefore, the modulated carrier response can be measured under very strong absorption. The pump-probe interaction via FWMand CPO within the QW-SOA active medium is responsible for electrically (current injection) tuned large optical delay or advance.
The experimental analysis is performed at fixed frequency (1 GHz), where the optical transfer function, the magnitude of small signal gain and its RF phase, is measured. The analysis is equivalent to an optical network thru S- parameter analysis with the current bias control into the QW-SOA. Figure 1 is a representation of a discrete device capable of a large delay-bandwidth product at GHz frequencies. Hence, this scheme can be used in a cascaded setup, coupled with isolators and signal filters, to produce multi-bit, large variable optical delays at GHz bandwidths.
3. Model analysis
The analysis of the frequency behavior of this slow-to-fast light scheme is based on the FWM and CPO theory previously developed [17, 18] with analytically refined solutions for variable light with a modal gain variation in a single QW-SOA device . The model parameter space includes: αint - unsaturable (intrinsic) waveguide loss (11–22 cm -1), Γg - modal gain tuned by current injection, t - carrier lifetime (1–0.6 ns), Pin and Pout - input and output power normalized to saturation power. The output power is evaluated using the saturation characteristics of the QW-SOA (based on Γg, αint, and Pin/Psat) .
The observation of large experimental phase shift (or delay) is explained by large variation in input power normalized to saturation, Pin/Psat, into the current controlled QW-SOA. This normalized input power is actually drastically changing (even though the actual experimental input power [pre-amplified by booster SOA]) is constant. The behavior of Psat with current variation and over absorption to gain switching was recently investigated for QWand QD active media . The saturation power below transparency of the QW-SOA is small, and, therefore, Pin/Psat is very large for our analysis. Prior to the QW-SOA reaching transparency modal gain, the saturation power is substantially increased, therefore, Pin/Psat is drastically reduced. Under large current injection (large gain), the saturation power is nearly pinned. Similar is the case for low current injection (large absorption). The transition of saturation power roughly occurs around zero modal gain (Γg=0) to transparency (Γg=αint) .
The RF phase versus frequency model is plotted with increasing intervals of modal gain and varying normalized input power in Fig. 2. The data shows the phase behavior vs. frequency as the device is tuned from absorption (negative modal gain) to gain (positive modal gain). Note that the model shows the slow-to-fast light transition not at zero net modal gain, Γg-αint=0, but when the modal gain is zero. An extracted RF phase at 1 GHz (fixed frequency scatter) is plotted in Fig. 3. The modeled 1 GHz RF phase is plotted vs. linearly variable modal gain (bottom axis) and input power (top axis). The phase delay of the probe is seen to switch from absorption to gain, or slow to fast light. On the top axis, the input power (normalized to saturation) is large and decreasing as the modal gain is tuned. The large variation of Pin/Psat is chosen to match the amplitude and variation of the experimental data (shown in Fig. 4 vs. current injection). The inset of the figure pictorially explains the broad band modal gain behavior of the electrically biased QW-SOA. Below intrinsic absorption, the device is a saturable absorber and hence produces slow light (delay). Near intrinsic absorption of the QW-SOA (Γg=0), the slow light changes to fast light, were the device becomes a gain medium exhibiting saturation characteristics. The current tuning of the modal gain and the implicit changes in saturation power give an explanation of the large delay-bandwidth variability in this QW-SOA slow-to-fast light scheme.
4. Experimental results
The presented model is utilized in the following explanation of experimental observations. The bottom of Figure 4 shows experimental (scatter) and model (lines) of 1 GHz RF phase (left axis) or time delay (right axis) for the current controlled QW-SOA. The delay is evaluated by τd=ΔϕRF/(2πfmod). The delay-bandwidth for these data is easily evaluated because modulation frequency is fixed at 1 GHz. Therefore, delay (right axis in nano-seconds) can be directly translated to a unit-less delay-bandwidth product. Note that the bandwidth in this product is the maximum spectral band for the modulated signal to travel through at a reduced/increased velocity without significant distortion. In our case it is the fixed modulation frequency of 1 GHz used in the experiment. The current at which the QW-SOA is at material transparency is about 60 mA, and thus we fix the relative RF phase to be around zero before transparency current (≃30 mA), where device is at modal gain transparency. The top of Fig. 4 shows the experimental and model of 1 GHz probe gain behavior with increasing current into QW-SOA. When the current into QW-SOA is near zero, the medium is an absorber producing slow light (see inset of Fig. 3). With increasing current, the device modal gain reaches a zero point (Γg=0), which translates to net modal gain being equal to Γg-αint=-αint. At this point of modal gain transparency, the medium switches from slow-to-fast light (at about 30 mA in the model). The delay (right axis of Fig. 4), which is also relative, is switching from delay (slow light) in absorptive medium to advance (fast light) in gain medium. A total of about 200 degrees in RF phase shift is observed experimentally (at 1 GHz, 0.56 ns). This translates to a total of 0.56 delay-bandwidth product for this ~2 mm QW-SOA with a large optical input power. A close match of experimental phase and gain in comparison to model with current is evident.
In correlation to the RF network analysis, a high speed optical oscilloscope is utilized to obtain both, time waveforms and observable tunable delay of this scheme. The oscilloscope traces for a 1 GHz modulation (1 ns period), shown in Fig. 5, are plotted at various currents into the QW-SOA. The time waveform data, by using methods of cross-correlation, can be used to extract the time delay, and also the RF phase. The extracted time delays (and RF phase) from the time domain measurement are shown (as square scatter) for comparison to the RF analysis in Fig. 4. A good match between the two observations is evident. Moreover, this time analysis clearly shows the relative slow-to-fast light scheme because in the extraction a comparison of all subsequent current traces is made to 25 mA data. Since the 25 mA waveform is the smallest current (absorptive SOA) at which the oscilloscope detector can resolve the waveforms, a smaller total relative delay of 0.475 ns is observed.
In conclusion, a unique scheme for slow-to-fast light by means of absorption to gain switching in QW-SOA was presented. The device consists of a current controlled QW-SOA. The optical input power is larger or on the order of the saturation power of the variable QW-SOA. We find that the CPO and FWM effects is enhanced because of the inherent saturation power variation with changing current (or modal gain) into the QW-SOA. Experimentally, we have shown that a modulated pump can experience more than half cycle relative delay through absorption to gain switching. We show time-domain and frequency-domain experiments that correlate well to theoretical model, which includes nonlinear CPO and FWMeffects. The scheme presented is capable of a 0.56 delay-bandwidth product at 1 GHz, which makes it a feasible building block of a multi-bit variable light system.
We thank previous technical discussions with Dr. Hui Su. This work was supported by DARPA Slow Light Program.
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