We demonstrate superluminal propagation of optical pulses with amplification in optical fibers based on stimulated Brillouin scattering. A triple gain peak configuration is used for the generation of narrowband anomalous dispersion in 2 m tellurite glass fiber, where the group index change as much as -1.19 is achieved with 6.9 dB amplification in 34 ns Gaussian pulses, leading to the group index of 0.84.
© 2008 Optical Society of America
Recent studies on the group-index control of optical pulses, i.e. slow and fast light, in optical fibers have attracted much attention in photonics societies, and a number of interesting results have been reported based on stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), Raman-assisted optical parametric amplification, and coherent population oscillation (CPO) [1–7]. For most of potential applications of the slow and fast light such as optical buffers, optical variable delay lines, phased-array antennas, and optical memories, the amount of the fractional delay, i.e. the product of the bandwidth and the time delay, is regarded as a key parameter rating the device performance. However, the amount of the group index change (Δng) also plays an important role in some applications like a passive resonator gyroscope where the rotational sensitivity is inversely proportional to ng , therefore so called ‘superluminal’ (ng<1) propagation can lead to the enhancement of the sensing performance.
In order to induce large Δng in optical fibers, an experimental scheme based on SBS or CPO is advantageous because of the inherently narrow bandwidth. In particular, SBS can offer a simpler and more flexible system compared to CPO in which the operation highly depends on the saturation property of the medium . In the previous work, the superluminal propagation based on SBS has been reported under the condition of large Brillouin loss as much as -12 dB , which could be a drawback in practical applications. A gain-assisted or a zero-gain fast light based on SBS also has been demonstrated using Brillouin double-pump configurations [9, 10]; however the efficiencies were not high enough to reach the superluminal condition. In the meantime, specialty fibers with a large Brillouin gain coefficient (gB) made of bismuth-oxide, chalcogenide glass, and tellurite glass have been shown to provide high-efficiency slow and fast light due to their large Brillouin gain coefficients [11–13]. Among them, the un-doped tellurite-glass fiber has a unique advantage of low propagation loss as small as 0.054 dB/m , and can provide the Brillouin gain coefficient 2~3 times larger than that of a bismuth-oxide fiber as well as higher input power capacity than that of chalcogenide glass fiber. Thus it could be referred to as a good candidate for the fiber-based slow and fast light medium.
In this paper, we demonstrate gain-assisted fast light propagation in a tellurite-glass fiber based on SBS. A triple Brillouin pump is applied to a 2 m tellurite-glass fiber to introduce anomalous dispersion between gain peaks, and Δn g of -1.19 with 6.93 dB amplification is achieved using 34 ns Gaussian pulses, resulting in the n g of 0.84. To the best of our knowledge, this is the first demonstration of gain-assisted superluminal propagation based on SBS.
Figure 1 shows the relation between Brillouin gain, the phase index change (Δn), and Δng based on the Kramers-Kronig relation. As depicted in Fig. 1(a), a Lorentzian gain with a bandwidth (FWHM) of ΔνB induces sudden changes of Δn and Δng with local maxima δn and δng which are expressed as following equations:
where c, ν0, gB, and Ip are speed of light in vacuum, center frequency of Brillouin gain, Brillouin gain coefficient, and intensity of pump wave, respectively.
For the generation of gain-assisted fast light, the frequency region of the minimum Δn g is used which is located at with the amplitude of -δng/8. In order to reduce the pulse distortion, a double-peak configuration is usually adopted with the peak separation of √3·ΔνB, and the resultant Δng is an addition of the contributions from two peaks as shown in Fig. 1(b) based on the linearity of the Kramers-Kronig relation. Since the efficiency of the double peak is only 1/8 of that of the single peak under the same pump power, the superluminal condition (ng<1) in a conventional single-mode fiber requires over 40 dBm (10 W) of pump power considering the former parameters (Δng~-2 with pump power ~37 dBm) of a single peak experiment , which is beyond practical pump power level. In this work, a 2 m tellurite-glass fiber with small effective area (9.2 µm2) is used to enhance the efficiency of SBS, and the gain-assisted superluminal condition is demonstrated under the pump power less than 30 dBm (1 W).
3. Experiments and results
The experimental setup is shown in Fig. 2. A 1550-nm laser diode was used as a light source and the output power was divided by a 50/50 coupler. In one arm, a single-sideband modulator (SSBM) and a microwave generator were used to generate a stable Stokes wave detuned from the carrier wave by stable frequency offset (Δν) near the Brillouin frequency (νB) of a fiber under test (FUT). The output from the SSBM was launched into an intensity modulator (IM) to generate probe pulses. In the other arm, a phase modulator (PM) and a RF generator were used to build multiple-peak Brillouin pump waves, and the output was amplified by a high power Er-doped fiber amplifier (EDFA) and launched into the FUT through a circulator in the opposite direction to the probe waves. The time waveforms of the probe pulses were recorded using a photodiode (PD) and an oscilloscope with the amplitude of the pulses maintained constant by a variable optical attenuator (VOA). In the measurement of Brillouin gain spectrum (BGS), we changed the role of the IM into a chopper for the CW probe wave and a lock-in detection technique was applied (dashed line), while sweeping Δν around νB.
As a FUT, a 2 m tellurite-glass single-mode fiber was used with the parameters of Δ (≡Δn/n)~1.6%, refractive index ~2.03, and Aeff ~9.2 µm2. The core was doped with erbium at a concentration of about 1000 ppm, and the propagation loss under saturation condition (power >15 dBm) was about 0.51 dB/m. The splice loss to a lead fiber was about 0.6 dB. From the reported value of gB (1.47~2.16×10-10 m/W) , the efficiency of SBS (gB/Aeff) in the FUT was estimated to be about 20 times larger than that of a conventional silica fiber.
We measured the BGS of the FUT using the lock-in detection with the CW probe wave chopped into a rectangular shape at 100 kHz. As depicted in Fig. 3(a), the νB and the Δν B of a single Brillouin gain peak were measured to be 7.883 GHz and 23.4 MHz, respectively with the PM turned off. Fig. 3(b) shows the BGS with the pump wave phase-modulated at 72 MHz (2Δf) through the PM. A triple Brillouin gain peak with equal amplitude was obtained by controlling the RF power input to the PM, and the Brillouin gain of 20 dB each was achieved with the pump power of 28 dBm.
The measurement of the pulse delay and advancement was carried out after spectrally positioning the probe wave to the middle of two gain peaks (dashed line in Fig. 3(b)). In the previous work , a double peak configuration was used with the suppression of the carrier wave, however it was practically difficult to keep high suppression ratio over 25 dB. In current experiment, large Brillouin gain peaks (>30 dB each) were required, for which we adopted the triple peak configuration that is free from the suppression problem at the cost of low power efficiency. Gaussian probe pulses with a width (FWHM) of 34 ns were generated by the IM at 113 kHz repetition rate with a peak power of -13 dBm.
In order to find the optimum value of Δf, the time delay of the pulse was measured sweeping Δf from 0 to 48 MHz in 4 MHz step with a constant pump power of 25.3 dBm (340 mW). Figure 4(a) shows the time delay and the gain of the probe pulse as a function of Δf. It is noticeable that fast light propagation with negative time delay was observed from Δf of 24 MHz and the maximum advancement was achieved at Δf=36 MHz (dashed arrow), while the Brillouin gain was maintained positive. Some of normalized time waveforms are depicted in Fig. 4(b) where the original peak position is indicated by dashed line. The delay and the advancement by Δf control are clearly seen with resultant broadening and narrowing of the pulses .
In order to achieve the maximum advancement of the pulse, Δf was fixed to 36 MHz and the pump power was increased up to 29.8 dBm (960 mW). As shown in Fig. 5(a), both the amount of advancement and the gain were gradually increased with the pump power, and the maximum advancement of -7.95 ns was obtained with the gain of 6.93 dB. The maximum pump power was limited to 29.8 dBm due to the onset of SBS noise from the CW pump wave. The time waveforms of the probe pulses with different Brillouin gains are depicted in Fig. 5(b) with the amplitude relatively scaled to the initial value. The advancement of the pulse with gain is clearly seen as the initial and the final position indicated by the dashed lines. Some distortion of the pulse is also observed in the case of large pump power (>29 dBm) which seems to have come from the limited bandwidth accompanied by the gain saturation due to large peak gain (>30 dB for each peak).
Figure 6 shows the time delay and the calculated Δng with respect to the Brillouin gain. The result matches well with the linear fit (red line), and Δng at the maximum gain is -1.19 which corresponds to a condition of superluminal propagation with ng of 0.84 from the reported refractive index 2.03 .
We have demonstrated gain-assisted advancement of optical pulses based on Stimulated Brillouin scattering in a 2 m tellurite fiber. A group index of 0.84, corresponding to the condition of superluminal propagation, has been achieved using a triple gain peak configuration with the pump power level less than 30 dBm (1 W). Although the onset of SBS from the CW pump wave has limited the maximum value (-1.19) of the group index change, it will be avoidable by reducing the fiber length on which the group index change does not have dependence. Therefore the pulse propagation with zero group index with amplification would be possible with shorter length (~1 m) of the tellurite fiber with the pump power level of 30~33 dBm (1~2 W), which may provide a significant contribution to the sensor applications based on the slow and fast light.
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-331-C00116), and this experiment was done in Department of Electronic Engineering, The University of Tokyo.
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