Tunable delays in semiconductor optical amplifiers are achieved via four wave mixing between a strong pump beam and a modulated probe beam. The delay of the probe beam can be controlled both electrically, by changing the SOA bias, and optically, by varying the pump power or the pump-probe detuning. For sinusoidal modulated signal at 0.5 GHz, a tunable delay of 1.6 ns is achieved. This corresponds to a RF phase change of 1.6 π. For 1.3 ns optical pulses propagating through the SOA a delay of 0.59 ns is achieved corresponding to a delay-bandwidth product exceeding 0.45. For both the cases, slow light and superluminal light are observed as the pump-probe detuning is varied.
© 2006 Optical Society of America
Slow and Superluminal (fast) light has gained considerable interest with applications ranging from optical clock distribution, beam steering to RF phased array antennas. Of particular interest is its application in realizing an all-optical buffer [1,2]. Slow light has been demonstrated by several mechanisms, including electromagnetically induced transparency (EIT) [1, 3], coherent population oscillations (CPO) [4, 5], stimulated Brillouin scattering [6, 7], stimulated Raman scattering (SRS) , optical parametric amplification assisted by SRS .
Tunable delay using semiconductor devices attracts special attention because it offers the advantage of compactness, room temperature operation and easy integration with existing optical communication systems [10–17]. In , slow-down of light via wave-mixing in a semiconductor waveguide absorber has been demonstrated. Slow light can also arise from sharp gain spectra, e.g. using a VCSEL Semiconductor Optical Amplifiers (SOA)  or in a FP filter employing a DFB geometry . In , tunable delay in Quantum Dot SOAs has been demonstrated. Due to ultrafast nature of the nonlinearities, very large bandwidths (2.6THz) are obtained. However, these large bandwidths are obtained at an expense of small delays (~17 fs). Recently, we proposed realizing slow and superluminal light via four wave-mixing (FWM) in SOA [14, 15]. In , fast light in semiconductor optical amplifiers using FWM is demonstrated. In prior research works [10,17], tunable delays are achieved by applying an RF modulation to a constant pump signal. The two side bands that are created act as probe and conjugate. The phase change of the modulated signal propagating through semiconductor medium can thus be controlled by changing the current. So, they have observed either slow light  or fast light effect  depending on whether it’s loss medium or gain medium. Our work differs from the earlier works, where for the first time a separate modulation is applied on a probe laser which is different from the pump laser. This distinction results in the observation of both slow light and fast light on the same device.
In this paper, we demonstrate tunable delays for a sinusoidal modulated signal and also for an optical pulse propagating through the SOA in the presence of a strong pump beam. The dependence of this delay on various parameters: pump power, pump-probe detuning and SOA bias is investigated. Tunable delays exceeding 1.6 ns is obtained for a sinusoidal modulated signal at 0.5 GHz. For a 1.3 ns pulse, delays exceeding 0.59 ns is observed corresponding to a delay-bandwidth product (DBP) exceeding 0.45.
2. Physical principle
The theory of four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) has been discussed extensively (see, for instance,  and references therein). Four-wave mixing between a strong pump beam and a weak probe beam in an SOA results in carrier density pulsations at the difference frequency (usually referred to as detuning frequency), Ω=ωprobe-ωpump. This leads to creation of gain and refractive index gratings at the detuning frequency. The gratings, in turn, lead to two effects: the generation of the conjugate signal , the modification of the dispersion-relationship for the probe [14, 15] depending on the pump power. The modification of the probe dispersion implies change of the group refractive index for the probe. Correspondingly, a modulated probe beam traveling through the SOA experiences delay which is dependent on the pump power, pump-probe detuning, and SOA bias. This particular aspect is not different from slow light through semiconductor absorbers via coherent CPO and FWM [5, 10, 14–15, 19]. However, unique for a semiconductor gain medium, both slow and fast light can be achieved depending on the frequency detuning due to a large linewidth enhancement factor. Our theoretical studies [14–15] showed that slow light for the probe beam can be achieved in SOA for negative frequency detuning while fast light can be achieved for positive frequency detuning. Hence, the group delay of the signal can be controlled electrically by changing the SOA bias and optically by changing the pump power or pump-probe detuning.
3. Experimental set-up
The experimental setup is shown in Fig. 1. A quantum-well SOA from JDS Uniphase Corporation is used in this experiment. The parameters of the SOA are as follows: the fiber-to-fiber unsaturated gain is 28 dB, the saturation power is 13 dBm, and the operating band is 1.52–1.57 µm. The SOA is operated at the maximum current of 300 mA and is temperature controlled.
The outputs of two DFB lasers are used as the pump and probe respectively. The probe is modulated at RF frequency fm by a LiNbO3 external modulator before being combined with the pump by a fiber directional coupler. A polarization controller is used to maintain the polarization of probe beam parallel to the pump beam. A band-pass electrical filter (0.5~1 GHz) is used to select the modulation frequency component and suppress all the beating components between the pump, probe and conjugate. The inset in Fig. 1 shows the schematic of optical spectrum at the input and output. Typically, the power in the modulated side bands of probe is maintained at least 15–20 dB lower than the pump power to avoid the possibility of gain saturation effects due to modulated probe. At the output, in addition to pump and probe, conjugate is also present. Hence, the detected RF signal at the output will also have contributions from modulation side bands of conjugate.
4. Results and discussion
Four-wave mixing between the pump and probe beams in SOA creates a conjugate at the frequency ωconj=2ωpump-ωprobe. Fig. 2 shows the optical spectrum as the pump-probe detuning is varied. It can be seen that the conjugate power at the output can be higher than the probe power for small positive frequency detuning values that is in agreement with the theory of FWM in SOA . One should note that the predictions for slow and superluminal light in SOA was done in  in assumption that the conjugate signal is negligible in comparison with the probe (that take place near to SOA input, for instance).
The green curve in Fig. 3 shows the delay ΔT of the modulation in the probe wave due to FWM in the SOA, calculated with this assumption, as function of the detuning Ω between the probe and pump (τS is the carrier lifetime in the SOA). However, Fig. 2 shows that the probe and conjugate signals can be comparable to each other, at least, near to SOA output, and the conjugate wave can effect the probe propagation. Based on the general theory of FWM , we calculated the probe propagation in SOA taking into account the influence of generated conjugate signal. The red curve in Fig. 3 shows the delay of a modulated probe taking into account the effect of the conjugate signal. It is clear that the generated conjugate signal is also modulated, and the modulation in the conjugate wave propagates in the SOA with a delay. In real experiments, the probe and conjugate are difficult to separate optically for very small detuning values, and correspondingly, the observed signal at the modulation frequency contains the contributions from both the modulated probe and the modulated conjugate.
The blue curve shows the delay in observed modulated signal taking into account the contributions from both modulated probe and conjugate. One sees from Fig. 3, that in contrast to the case when the conjugate signal generation is suppressed completely (green curve), and the dependence of the delay on the detuning is “asymmetric” (positive delay at Ω<0, and negative delay at Ω>0), the generation of conjugate signal lead to “symmetrization” of the dependence. Namely, it becomes possible to observe slow light for small positive detuning values, see red and blue curves in Fig. 3. Our calculations also show that an increase in the optical length of SOA, ΓgoL (L is the SOA length, go is the SOA material gain, Γ is the confinement factor) leads, in fact, to complete “symmetrization” of the curve, where in the opportunity of observing fast light at positive detuning disappears.
4.1. Delay of sinusoidal modulated signal
Figure 4 shows tunable delay of a sinusoidally modulated signal. The probe beam is externally modulated to produce a sinusoidal signal at the desired frequency. The amplitude of modulation is maintained well below the saturation power of SOA to avoid gain fluctuations due to modulated signal.
Figure 4 shows time-domain traces of a detected modulated signal for different values of the detuning Ω. As expected from the theory (Fig. 3), the delay/advancement, measured relatively to the trace, obtained for large (-150GHz) pump-probe detuning, is nonzero only if the detuning is not very large in comparison with the inverse carrier lifetime (~1ns). This behavior is related to the origin of the delay which is FWM via carrier density pulsations, which take place only at the small detuning values. Both slow light and fast light are observed as the detuning is varied from negative values to positive values. Considering both the delay and the advancement of the signal, a maximum tunable range of 1.6 ns is observed for a 0.5 GHz signal. This corresponds to a RF Phase change of 1.6 π, or a DBP of 0.8. We also observed that the delay is dependant on the precise polarization matching of the pump and the probe beams. The inability to maintain the precise polarization in a single mode fiber results in fluctuations of the observed signal at the output. Hence, the results reported here are time averaged values of the delay.
Figure 5 shows the delay as function of detuning for different values of the pump power. Higher pump power results in more efficient four wave mixing and hence larger delay. However, if the pump power is much higher than the saturation power of SOA (>13 dB), then the gain of the SOA decreases resulting in smaller delays. Further, slow light is observed at small positive detuning due to the contribution from the conjugate (compare with Fig. 3).
4.2. Pulse delays
In the previous section, we discussed the tunable delay of the sinusoidal modulated signals. These results are important for applications like RF Phased antennas and optical clock distribution. In this section, we discuss the tunable delay of the pulses in SOA which has direct application in realizing an all-optical buffer.
We use a bit-error-rate test set (HP70841) to generate 1.3 ns electrical pulses. The square pulses are subsequently shaped using an electrical filter to achieve an optimum shape suitable for pulse measurements. The pulses are not transform-limited and, hence, its bandwidth is not optimized for the SOA slow light device. The electrical pulses are fed to an external Mach-Zender modulator where the CW probe light is modulated to generate the optical pulses.
Figure 6 shows the output time traces of the pulse as the detuning is varied. The Pump power at the input of the SOA is 3 dBm and the probe power is -9 dBm. Both slow light and fast light are observed as the detuning is changed. Also, the pulse shape distorts significantly at small detuning values resulting in a dip at the trailing edge (Green curve). A total delay of 0.59 ns is attained corresponding to DBP of 0.46. The enhanced distortion and reduced DBP are likely to be due to cross-gain modulation between the probe and the pump beams. Further study is currently under-way to understand and reduce the effect of cross gain modulation.
Figure 7 shows the delay curves as the pump power is changed. The curves shown in this figure correspond to three different pump powers: -3 dBm, 0 dBm, 3 dBm. Similar to sinusoidal modulation results, the delay in general increases as the pump power is increased. Both fast light and slow light are observed as the detuning is varied. However at small detunings (< 2.5GHz), beating signal between the pump and probe whose frequency equals the detuning frequency Ω, is comparable to modulation frequency of signal fm (see inset of Fig.1). This interferes with the detection of the signal. Hence, we couldn’t measure delay at these small detuning values. As mentioned before, the pulse undergoes distortion and significant broadening as it passes through the SOA. Hence, to compute the delays we followed the following scheme. The reference signal data is cross correlated with the delayed signal data. The peak in the cross correlation data corresponds to maximum overlap between the reference pulse and the delayed pulse. The shift in time corresponding to the peak of cross correlation is taken as the delay at that particular condition.
Finally, the SOA bias is varied to investigate its effect on the delay. These measurements are performed for a pump power of 0 dBm and a probe power of -11 dBm at a detuning of -3 GHz. As the SOA bias is increased, the gain of the SOA increases in this regime. This results in strong beating between the pump and the probe giving rise to larger delays as seen from the Fig. 8. However, the gain of the SOA does not increase significantly at higher SOA bias and reaches a maximum value at 300 mA. At this bias, increasing the SOA current does not increase the gain significantly as the SOA operates in saturation regime.
We present the first experimental demonstration of both slow light and superluminal light in the same device via four wave mixing processes in SOA. We show that tunable delay at room temperature can be achieved either by the tuning the wavelength of the pump or by changing the power of the pump or by changing the SOA bias. Time delays of 1.6 ns is achieved for a sinusoidal modulation at 0.5 GHz, corresponding to a delay-bandwidth product of 0.8. For a 1.3 ns pulse, tunable delays exceeding 0.59 ns is demonstrated, corresponding to a smaller DBP of 0.45. Though the increase in bandwidth may account for some reduction in DBP, the DBP is much less than expected and this discrepancy is currently under investigation. It is, however, likely to be due to the presence of conjugate signal and cross gain modulation on the pump beam, both affect the results significantly. The current study shows that the bandwidth of this scheme is limited by the carrier life time (~1ns) in semiconductors. The bandwidth can be increased by two-three orders of magnitude by using higher order non-linearities including carrier heating and spectral hole burning, which is the subject currently under investigation.
The authors thank Ms. Xiaoxue Zhao for her help in the experiments. We thank the support of DARPA grants F30602-02-2-0096 and Airforce contract FA 9550-04-1-0196.
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