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This article describes a new approach to cancel the pulse broadening in a cascaded slow-light system. With the help of a simple experimental setup a method with significant potential to achieve a high pulse delay at almost zero pulse broadening is shown. Since the pulse reshaping is done inside a single delaying segment, this method can be used in connection with any other Brillouin based slow-light system.
©2009 Optical Society of America
1. Introduction
The realization of optical buffers in so called slow-light systems is a quantum leap toward the realization of all-optical communication networks. Beyond that, the manipulation of the velocity of optical pulses offers a way to applications such as time resolved spectroscopy and optical signal processing. The nonlinear optical effect of stimulated Brillouin scattering (SBS) is a promising method to alter the group index in a material system [1, 2]. Besides undeniable advantages of SBS slow-light systems such as working in the whole transparency range of every fiber, high delay times at small pump powers and the opportunity of adaptive adjustment of the delaying bandwidth [3], the pulse delaying is always accompanied by distortions, which lead to a pulse broadening. Recently, different approaches to minimize this broadening were investigated [4,5,6,7]. Beyond that, first experimental proves were given, that it is possible to fully cancel the broadening [8,9].
In this article we investigate theoretically and in experiment, that the pulse broadening owed to any conventional SBS based slow-light system could be cancelled in the presented manner. While the conventional system is represented by a single SBS gain delay, a second stage consists of a double gain line setup. Contrary to the approach in [6], this second stage is not used for a gain bandwidth enhancement, but for a pulse spectrum reshaping. Both lines form a saturated gain distribution as described in [9], but in the linear SBS amplifier regime and therefore at significant lower pump powers. However, any demanded almost distortion free time delay could be achieved by an additional cascading of such a slow-light system.
2. Theory
Stimulated Brillouin scattering in a waveguide is an interaction between counter propagating optical waves mediated by an acoustic wave. A narrow bandwidth pump wave, propagating in one direction inside an optical waveguide, can produce a gain and a loss for a frequency shifted counter propagating wave via the acoustic wave. The acoustic wave defines the frequency shift and the spectrum of gain and loss.
Fig. 1. Experimental setup. MZM: Mach-Zehnder modulator, SSMF: standard single mode fiber, C: circulator, EDFA: Erbium doped fiber amplifier, VOA: variable optical attenuator, PD: photo diode, OSA: optical spectrum analyzer, Osci: oscilloscope.
From a practical point of view a SBS based slow-light system can be seen as a Brillouin amplifier. A strong pump wave with a frequency ωP, which propagates in one direction generates a gain for a counter propagating Stokes wave at a frequency around ωP − ωB, and a loss for a wave at ωP + ωB. Consider a two stage SBS delay line as shown in Fig. 1. In the first stage just one single broadened pump wave produces a gain. To simplify the theoretical view we assume that it has a Lorentzian shape and can be written as:
With g 0 = gPPPLeff / Aeff as the gain in the center, gP as the peak value of the SBS gain coefficient, PP as the input power of the pump wave, Leff and Aeff as the effective length and area of the fiber and Ω = ω/γ 0 as a frequency normalized to the half 3-dB-bandwidth of the gain distribution.
According to the Kramers-Kronig relations, the gain distribution leads to a group index change and therefore a time delay, which is:
A normalized Gaussian input pulse can be written as In = exp [−ln(2)(Ω/W)2], where W = ΔωIn/γ 0 is the relation between the half FWHM input pulse width and the gain bandwidth. The pulse will be delayed and amplified in the first stage. If we neglect the phase change, the corresponding output pulse is:
Fig. 2. Normalized gain (a) and time delay (b) of the first stage, generated by one single pump wave (solid lines; g 0 = γ 0 = 1). The dashed lines show the normalized input and the dotted the normalized output pulse spectra (W = 1).
The gain bandwidth and corresponding time delay of the first stage is shown in Fig. 2. Since the gain bandwidth acts like a filter for the input pulse, the output pulse will be broadened. Another reason for the broadening of the output pulse is the group velocity dispersion (GVD). This GVD-dependent broadening can be approximated to a difference between time delays at the center frequency ΔT (ω 0) and at the FWHM bandwidth ΔT (±Δω), hence [7]: BGVD = ΔωIn [ΔT (ω 0) − ΔT,(±Δω)]/ln(2). But, such an approximation is only valid, if the distortions are not too strong. As can be seen from Fig. 2(b), the time delay in the line center of the pulse is higher than at the FWHM bandwidth. Hence, the GVD dependent broadening of the pulse is positive. Both effects lead to a broadening of the output pulse. As can be seen, this broadening can be reduced by an enhancement of the SBS bandwidth and by an adaptation of the pulse spectrum [3,4,5]. However, according to Eq. (2), a broadening of the gain spectrum leads to a reduction of the achievable time delay. Since the maximum gain is restricted by the threshold of pump depletion to g 0 < 12 [10], this time delay reduction cannot be mitigated by higher pump powers. This can only be done by a cascading of several stages.
In the second stage of the delay line (Fig. 1) the gain is produced by two pump waves with a frequency shift of δ in respect to the center frequency of the gain in the first stage. Then the normalized gain of the second stage can be written as:
Here m = g 1/g 0 is the relation between the gains of the first and the second stage, k = γ 1/γ 0 is the relation between their bandwidths and d = δ/γ 0 is the normalized frequency shift of the gains of the second stage. The corresponding time delay is than:
Fig. 3. Normalized gain (a) and time delay (b) of the second stage, generated by two pump waves (solid lines; g 0 =γ 0 =1, m = 2, k = 1, d = 0.9). The dotted lines show the normalized output pulse spectra of the first stage (W = 1).
The gain bandwidth and the corresponding time delay of the second stage, together with the output pulse spectrum of the first are shown in Fig. 3. As can be seen from Fig. 3(b), the time delay in the center of the pulse is smaller than that at the FWHM-bandwidth. Therefore, the GVD-dependent broadening is negative, which can mitigate the GVD broadening of the first stage. In the line center Ω = 0, the time delay is:
Hence as long as k > d, the second stage will add a time delay to the pulse. If the output pulse of the first stage is attenuated with the first variable optical attenuator (VOA) and than amplified in the second stage, the output of the two stage system is:
where we have neglected the phase change as well and D is the attenuation due to the VOA (Fig. 1).
Figure 4 shows the overall gain bandwidth of the two stages. The free parameters can be adjusted in a manner that the overall gain of both stages is flat within the bandwidth of the pulse. As the theoretical discussion has shown, due to the opposite behavior of the second stage it can mitigate the gain and the GVD dependent broadening of the first. A similar shape of the gain spectrum can be obtained in just one delay line if three pump lines are superimposed. But, for m = 2 it follows that g 0 = g 1/2. Since the maximum gain is restricted by the pump depletion, this leads to much lower time delays.
3. Experiment
In Fig. 1 the principle experimental setup was shown. For the experiment we used a Gaussian shaped pulse with a temporal width of approximately 1.4 ns and 10 km standard single mode fibers (SSMF) for both stages. The first stage is pumped by a direct noise modulated pump laser, which produces a single gain region to slow down the pulse. Such a system is used to prove our concept, but could be replaced by any other conventional SBS based slow-light system. Besides a direct noise modulation, the pump source of the second stage is externally modulated in a suppressed carrier regime to emulate the gain shape of a saturated zero-broadening system described in [9]. The VOA between the stages adjusts the output pulse amplitude of the first stage. To prevent the photo diode (PD) from damage we used another VOA at the output of the second stage. The system output pulse is detected by a PD and monitored by an oscilloscope (Osci).
Fig. 5. Output pulses at every stage in comparison to the reference pulse for a FWHM gain bandwidth of the first stage of 550 MHz and an additional attenuation between both segments of 0 dB.
Figure 5 shows the reference (output pulse of the system without SBS activity), the output of the first and the second stage exemplarily for one measurement. By using just the first stage, a significant pulse broadening can be seen. However, the second stage reshapes the pulse to its initial temporal width, although the added time delay is small.
The first slow-light stage was adjusted in a manner to reach the maximum time delay at the given gain bandwidth. Therefore, the stage’s pump power was 21 dBm for all measurements. To achieve a high pulse width compression within the second stage, we used a FWHM gain bandwidth of 400 MHz, a modulation frequency for the external modulation of 280 MHz and a pump power of 19 dBm.
Fig. 6. Fractional time delay (a) and fractional pulse width (b) as a function of the attenuation between the slow-light stages. The given Parameters at the measurement graphs are the fractional output values and the gain bandwidth of the first stage.
In Fig. 6 the measurement results for the full working cascaded slow-light system at different gain bandwidths in the first stage are shown. The given parameters at every single graph correspond to the first stage’s gain bandwidth and the fractional output values (i.e. fractional time delay and fractional pulse width, respectively) with only first stage working. Since the saturation in a SBS delay depends on the pump power as well as the power of the input pulse [11] and the first stage acts as an amplifier, we changed the attenuation between the stages to control the saturation behavior of the second stage. As can be seen in Fig. 6(b), the pulse width decreases with decreasing attenuation. Due to the increasing saturation in the center of the pulse spectrum, this behavior follows the results in [9]. However, the time delay remains almost constant for all attenuation values (Fig. 6(a)).
4. Conclusion
Following our theoretical considerations, the experiment shows that it is possible to overcome the pulse broadening in SBS based slow-light delays with the help of the described cascaded system. As can be seen from Fig. 6(a), more than 20 % of the pulse broadening is compensated inside the system, while the mitigation has little effect on the pulse delay. Since the main part of the time delay is caused by the first stage, this stage could be replaced by a SBS slow-light system with a higher delay factor to increase the overall delay. Contrary to a zero-broadening system based on a saturation by high pump powers [9], significant smaller pump powers are required here. Since the pulse accumulates almost no distortion during the delaying process, a cascading of the described system would give the opportunity to achieve any demanded time delay.
Acknowledgments
We gratefully acknowledge the financial support of the German Federal Ministry of Education and Research funding program Optical Technologies (contract number: 13N9355). R. Henker and A. Wiatrek gratefully acknowledge the financial support of Deutsche Telekom and the support of M. J. Ammann and A. T. Schwarzbacher of the Dublin Institute of Technology. Additionally the authors would like to thank J. Klinger of HfT Leipzig.
References and links
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