Previously demonstrated slow light is still far from applications, particularly due to the limited bandwidth and control speed. Although semiconductor-based slow light has the high bandwidth and sub-nanosecond control speed, slow light was observed only in the absorption regime with attenuation, while fast light observed in the gain regime with amplification. The large power difference in two regimes makes the use of the optical delay impractical. We report novel slow light in the gain regime, with a high power comparable to that of fast light, utilizing the anomalous gain characteristic in a gain-clamped semiconductor optical amplifier. The slow light is tunable to fast light with the current as the only variable. Additional high speed operation, fast delay control, and wide range of operation wavelength make the present approach practical.
© 2009 OSA
Slowing down an optical signal is fundamentally interesting and has been an active research topic since a group velocity of 17 m/s was demonstrated in a cold gas using electromagnetically induced transparency below 435 nK . An optical signal propagates in a material with a group velocity, c/ng, where ng is the group index, which is the sum of the material index, n, and its dispersion term, ωdn/dω. It is difficult to change the material index by orders of magnitude. Therefore, the dispersion term is commonly utilized to significantly delay the optical signal. A large dispersion can be obtained by a narrow spectral dip in the absorption spectrum, induced by a narrow laser line, which in turn gives a significant dispersion through the Kramers-Kronig relation. As a result, the group index becomes large and the optical signal slows down near the laser frequency. Recently demonstrated slow light at room temperature also utilized the narrow spectral feature: slow down of group velocity to 57.5 m/s in a Ruby crystal based on coherent population oscillation (CPO) , a delay of 30 ns with a 100 ns optical pulse in kilometers of optical fiber based on stimulated Brillouin scattering .
Slow light is a good candidate as an optical buffer in flexible wavelength division multiplexing optical communications and optical processing. For these applications, the prerequisite is the high frequency bandwidth and fast delay control, which are inherently difficult for the above cases. Active control of slow light using a silicon chip with photonic crystal waveguides was reported, but the control speed was limited to 100 ns . Consequently, practical applications of slow light are far from realization with the reported techniques because of the difficult delay control and the limited bandwidth, even though large slow-down factors have been demonstrated [5-6].
Slow light based on semiconductors can have a high bandwidth and can also be electrically tunable at a high speed. Slow light has been demonstrated in the absorption regime using multiple quantum wells (QWs) , QW-  and quantum dot semiconductor optical amplifiers (SOAs) [9-10]. However, slow light in the absorption regime produced a small delay bandwidth product with significant attenuation .
In a gain regime, a strong pump induces a sharp dip in the gain spectrum as a result of CPO and four-wave mixing . The semiconductor gain leads to high output power for fast light, in contrast to the weak slow light in the absorption regime. Although switching from fast to slow light can give a large delay, the big difference in output power between slow and fast light limits the use of optical delay since it requires a very fast post power equalization process which is quite difficult. Ideally, we want to have the slow light with a high output power which is comparable to that of fast light, as well as the high bandwidth and fast control speed. Here we present slow light in the gain regime, with the desired characteristics.
2. Gain anomaly in a gain-clamped semiconductor optical amplifier
The gain-clamped semiconductor optical amplifier (GCSOA) used in this work contains a distributed-Bragg-reflector laser cavity at 1492 nm in an otherwise conventional SOA structure. Lasing at 1492 nm clamps the gain (and population inversion) of the SOA, and therefore, the gain at 1550 nm is the same regardless of input power up to the strength at which the lasing at 1492 nm stops. The device is anti-reflection coated in the 1550 nm band, and the gain difference on polarization is less than 1.0 dB.
Figure 1 shows the anomalous gain characteristic of the GCSOA: increase of gain with increasing input power in a limited range. Initially, at low input power, the gain of a GCSOA remains almost a constant (so-called gain-clamping) due to the lasing action at 1492 nm, which is in contrast to a conventional SOA in which the gain decreases monotonically with increasing input power even from a low input level, as shown in the inset. On the other hand, at a high input power, the gain of the GCSOA saturates, as in a conventional SOA, since the population inversion is decreased below the lasing threshold due to the strong stimulated emission at 1550 nm and so the lasing mode at 1492 nm cannot contribute to gain clamping. Near the transition between the gain-clamped and gain-saturated regimes, gain increases as the input power increases (gain-transition regime). This anomalous gain behavior has been observed in other GCSOAs we have tested and it has been predicted theoretically for this kind of DBR type GCSOA . The gain increase with increasing input power is likely to induce a gain peaking, instead of a gain dip which can be observed in materials with saturable gain, in the gain spectrum at the pump wavelength. This abrupt increase of gain in a narrow spectral range induces a large dispersion that can be estimated with the Kramers-Kronig relation. However, its slope is opposite to that of the dispersion for typical gain dip, providing the larger group index for the gain peaking. Thus, we expect slow light even in the high gain regime of a GCSOA, while a gain dip is induced in a conventional SOA, which will result in fast light due to the saturable gain.
Figure 2 shows gain spectra of the GCSOA measured by a weak tunable probe signal with a strong pump of different power at 1550 nm. The operation current was 250 mA. A lock-in amplifier was used to detect only the probe signal. At the highest pump power only a gain dip was observed (saturation regime), but at a reduced power (−1.1 dBm) a strong and sharp gain peaking was observed at the position of the pump (transition regime), which is very likely to be related to the anomalous gain characteristic in Fig. 1. As the pump power was further decreased (gain-clamped regime) the gain peaking was reduced, but there was still an increase of gain around the pump wavelength.
3. Results on optical delay and discussions
A single modulated beam method  was used to measure the phase delay, which is equivalent to the delay bandwidth product and bit delay, an important parameter in system applications. The modulated beam consists of a CW pump beam and two sidebands separated by the modulation frequency. The interaction of the sideband and pump beam induces CPO, and the interaction of one sideband and the other side band induces the four-wave mixing to result in the change in group velocity. In a real system, the power of input signal is typically fixed. Therefore, we changed the operation current of the GCSOA at a fixed input power to adjust the signal delay. An input power of −1.0 dBm was chosen since all three regimes (the saturation regime at low currents, transition regime at intermediate currents, and gain-clamped regime at high currents) can be covered by changing the operation current, as shown in Fig. 1.
Figure 3(a) shows the phase change as a function of the modulation frequency at various operation currents of the GCSOA with respect to the phase at the transparency current. At the transparency current, there exists neither material gain nor absorption, and, therefore, no change in gain or phase. The transparency current was determined to be 13 mA at 1550 nm by monitoring the gain invariance on the input signal power. Up to 220 mA, the trend was very similar to that of a conventional SOA; increase of gain [Fig. 3(b)] and phase advance (fast light) with the increase of current [9-10]. However, at 240 mA there were dramatic changes in the phase and the magnitude; a large phase delay of 45 degrees, instead of a phase advance, around 1 GHz and transition to fast light beyond 2.5 GHz. The phase change matches well with the change in the gain spectrum measured simultaneously by the network analyzer, through the Kramers-Kronig relation. As the current increased beyond 240 mA, the delay of slow light was reduced at low frequencies, but increased at high frequencies. Further increase of current reduced the amount of phase delay with a flat frequency response. An optical signal can be delayed by changing the current to the GCSOA and the difference in phase at two different currents is the relevant delay. The maximum phase difference between slow and fast light is 85 degrees at 1 GHz, which corresponds to 240 ps of time difference (61 degrees, 570 ps at 0.3 GHz). At the maximum delay, a significant distortion in waveform was observed at 1 GHz. However, distortion was negligible at higher frequencies (> 5 GHz), as well as away from the maximum.
Figure 4 shows the phase delay between 220 and 285 mA, reconstructed from Fig. 3(a), as a function of the modulation frequency. The total phase delay is 54 degrees at 5 GHz with a rather flat frequency response. The bandwidth is much higher (> 5 GHz) than a typical bandwidth of a conventional SOA, ~1 GHz  and is useful to delay high speed optical signals. The output power of the slow light at 285 mA, in the gain-clamped regime, was high and almost the same as that of the fast light at 220 mA, 20 mW, since 220 mA is already close to the clamping current. The comparable high output power for both slow and fast lights is a very good characteristic since it provides a high signal-to-noise ratio for the processed signal, and more importantly, we do not need any post equalization processes when an optical signal is switched from fast to slow light.
Figure 5 shows real time delays on a high bandwidth oscilloscope (Agilent 86100A) at (a) 5 GHz and (b) 10 GHz for various bias currents at a signal power of −1.1 dBm. The normalized trace at 30 mA at 5 GHz is close to that at the transparency (13 mA). From 30 to 210 mA, we observed the increase of phase advance, which is typical in the saturated gain regime. However, from 210 mA we clearly saw a transition to slow light, resulting in a phase delay beyond 240 mA, as shown in Fig. 5(a). Similarly, the phase advance was increased up to 200 mA and then reversed beyond 200 mA at 10 GHz, as shown in Fig. 5(b). The difference between the delay and advance, which can be used as the optical signal delay, was 24.4 ps, corresponding to 44 degrees at 5 GHz. The output power was comparable: the maximum power difference in the range between 210 and 300 mA was 3.1% at 5 GHz. The delay at 10 GHz was 34 degrees without signal distortion, and the output power variation stayed within 3.7%.
The slow light observed in the gain regime is related to the 1492 nm gain-clamped lasing mode. The 1550 nm band is not affected by the distributed-Bragg-reflector cavity since the reflection band is very narrow at 1492 nm, and the facets are anti-reflection coated for the 1550 nm band. In the measurements we did not observe multiple resonances from the Fabry-Perot cavity. In the present scheme, slow light can be obtained at other wavelengths in the gain band since there are no other restrictions on the location of the single modulated beam. We have tried at various wavelengths from 1530 to 1565 nm and obtained the comparable amount of delay at 5 GHz; 63 degrees at 1530 nm and 36 degrees at 1565 nm. Together with the same strong output power for both slow and fast light, large frequency bandwidth, and fast delay control, this property is beneficial to applications, in contrast to wavelength-specific slow light methods, such as electromagnetically induced transparency, stimulated Brillouin scattering, and coupled ring optical waveguide .
The strong slow light in the gain regime originates from the anomalous gain characteristic, increase of gain with increasing input power, which is contradictory to the common sense that the population inversion should be reduced with the increased stimulated emission. The anomalous gain characteristic comes from the spatial inhomogeneity of carrier distribution (spatial hole burning) in the GCSOA due to the uneven photon density of the gain-clamped lasing mode at 1492 nm, already predicted by a simulation. Because of the high photon density of the lasing field at 1492 nm, the population inversion (and the carrier concentration) is quite low at the input side (and output side), and so gain is reduced for the 1550 nm signal. However, when the input signal at 1550 nm becomes sufficiently strong the lasing field at 1492 nm reduces to provide a more favorable carrier distribution for the 1550 nm signal, which leads to the higher gain at the higher input signal, before it eventually disappears. A similar phenomenon was reported in a 980 nm pumped long-band erbium-doped fiber amplifier in which the gain at the stronger input signal was higher due to the lower conventional-band amplified spontaneous emission at the input side . Slow light in a long-band erbium-doped fiber amplifier are experimentally confirmed and to be published elsewhere. Consequently, slow light in the gain regime should be achievable in similar optical systems in which gain increases with the input signal power. Further increase of the delay-bandwidth product may be obtained by cascading several GCSOAs and the resulting size can be reduced by integrating such GCSOAs in a single chip. The concatenation of the GCSOAs is practical since the slow and fast lights have almost the same output power after each stage.
Slow light has been demonstrated in the high gain regime of a GCSOA with a high output power (20 mW) comparable to that of fast light. This slow light effect comes from the anomalous gain characteristic that the gain of GCSOA increases as the input power increases near the cessation of gain clamping. A significant distortion-free optical delay was obtained at 10 GHz, by switching from fast to slow light with the current as the only variable. The comparable delay was obtained in a wide wavelength range (> 30 nm), while other methods are typically wavelength-specific. These excellent characteristics may open a new road to slow light studies for practical applications.
We thank J. S. Lee and I. K. Yun of Samsung Electronics for providing GCSOAs used in this work. D. Lee is grateful for supports from the National Research Foundation of Korea [Grant No. 2009-0081380 and R11-2008-053-01001-0 (Quantum Metamaterials Research Center)], the Korea Research Foundation (Grant No. KRF-2008-314-C00148), and the KICOS (Grant No. M60605000007-6A0500-00710). Part of this work was performed when D. Lee was visiting the University of Illinois. The work at the University of Illinois was supported by the DARPA Slow Light Program and AFOSR Grant AF Sub UCB SA5612-11559.
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