1. Introduction

Optical fibers have emerged as the media of choice for slow and fast light systems since they employ resonant gain (rather than loss) while enabling large bandwidths which are compatible with Gbit/s data signals. The majority of reported fiber based slow light systems employ stimulated Brillouin scattering (SBS) [1–7]. Conventional SBS systems exhibit a narrow bandwidth of about 30 MHz together with a relatively large delay bandwidth product of close to 1. The SBS gain and bandwidth can be traded for each other by employing pump modulation as has been reported in several recent publications [4–7] enabling to delay narrow pulses.

A different fiber based slow light system based on Raman assisted narrow band optical parametric amplification (OPA) was described in [8]. That system offers extremely wide bandwidths, in the tens of GHz range, which can be varied by tuning the pump wavelength and power. The first report on that slow light system [8] demonstrated slow and fast light propagation of single 70 ps wide pulses in dispersion shifted fibers ranging in length from 200 m to 3 km. A later experiment [9] also used OPA to delay a 10 Gbit/s packet. That experiment used broad band OPA which limited the achievable delay.

The ability to delay single pulses with low distortions [4, 6, 8] indicates the availability of sufficiently wide and flat gain and delay spectra. However, proper characterization requires the use of random data streams [7, 9] because all narrow band fiber gain processes tend to saturate easily and therefore the fidelity of a delayed signal may be pattern dependent. This paper reports on a tunable delay of 10 to 60 ps with very low distortions of a 10 Gbit/s pseudo random bit stream (PRBS) propagating in a narrow band fiber parametric amplifier based on a 1 km long dispersion shifted fiber. The experimental results are consistent with a theoretical prediction which takes into account variations of the propagation parameters along the fiber. These parameter distributions are extracted from measured amplified spontaneous emission (ASE) spectra which are analyzed using a special optimization procedure.

2. Estimation of the spatial distribution of propagation parameters

The detailed characteristics of the narrow band OPA spectrum (and hence the delay spectrum) are very sensitive to the longitudinal variations of the fiber propagation parameters. In order to theoretically predict the delay and exact temporal shape of the delayed signal, it is imperative that the distribution of propagation parameters be known accurately. To that end, we have developed a high resolution parameter extraction procedure which yields the spatial distribution of the zero dispersion wavelength λ₀(z) as well as β₃(z), β₄(z) and the effective mode area A_eff(z). The starting point is a measured amplified spontaneous emission (ASE) spectrum of the OPA. Figure 1(a) shows in a blue line an exemplary ASE spectrum obtained for an average pump level of 20 dBm.

The distribution of dispersion parameters along the fiber is computed by segmenting the fiber into sections, each being several meters long. The dispersion parameters are assumed to be constant within each segment so it is possible to determine an analytic complex parametric gain spectrum for each segment. Combining the contribution of all the segments yields the cumulative complex gain spectrum of the fiber. The mean values of dispersion parameters in each segment are set by deterministic functions which are assumed to be continuous and hence can be spanned by a sine/cosine basis of finite size [10]. A small noise is added so as to account for the short-scale perturbations induced by mechanical and environmental fluctuations of the fiber [11]. The vector consisting of span coefficients and the exact pump power that yields the best match of the gain function to the measured ASE spectrum (in the mean square error sense) are obtained via the so called Particle Swarm Optimization algorithm [12]. The distributions of λ₀(z), β₃(z), β₄(z) and A_eff(z), calculated from the ASE spectrum of Fig. 1(a) are shown in Fig. 1(b).

 

Fig. 1. (a). Blue line–measured ASE spectrum, green line–estimated gain spectrum, red line–calculated delay spectrum (b) Estimated distributions of propagation parameters, λ₀(z), β₃(z), β₄(z), A_eff(z)

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The green line in Fig. 1(a) describes the parametric gain of the fiber calculated using the best attained parameters, Fig. 1(b), while the red line represents the calculated delay. Both have been averaged among an ensemble of 20 distribution perturbations. The delay and temporal shape of the output data sequence can be predicted theoretically in two ways. First, the extracted distribution of propagation parameters [Fig. 1(b)] can be incorporated in a simulated solution of the propagation equation. Alternatively, the gain and delay spectra [Fig. 1(a)] can be used to linearly transform any input signal to the fiber output.

3. Theoretical and experimental results

The experimental set up shown in Fig. 2 is similar to the one used in Ref. [8].

 

Fig. 2. Experimental set up

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An amplified pulsed pump source (8 nsec pulses with a duty cycle of 1%), is tuned to λ_p=1535 nm, which is 4 nm shorter than the fiber zero dispersion wavelength. The pump establishes a narrow spectral region near 1428 nm where phase matching conditions are satisfied and narrow band parametric gain occurs. The pump is combined with a 10 Gbit/s PRBS at 1428 nm which is filtered at the output and characterized using a fast photodetector and a sampling oscilloscope. The portion of the 10 Gbit/s bit stream which coincides with the pump and experiences delay is easily identified.

The ability to tune the delay of a 10 Gbit/s PRBS while maintaining a high signal fidelity is demonstrated in Fig. 3 for a signal at 1428 nm [λ₁ in Fig. 1(a)]. Shown is a segment within the subset of the data sequence which falls within the 8 nsec wide pump pulse.

 

Fig. 3. Delayed 10 Gb/s PRBS for different OPA gain levels, (a) -3dB, (b) 2.8dB, (c) 4.4dB, (d) 7.5dB

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The output with no pump is shown in each case as a blue curve. The red curves represent the delayed data for different OPA gain levels. The delay varied from 10 ps to 60 for gain levels of -8 dB to 8 dB, respectively. The green squares are a calculation based on a full simulation which uses the extracted distribution of propagation parameters, Fig. 1(b). In the negative gain regime, the system is dominated by Raman loss [8] and a small degree of pattern dependent distortion is apparent. For the large gain and delay values, the data sequence suffers little if any distortion. Significantly larger delays can be obtained with larger pump levels [8]. However, the OPA gain exhibits in those cases some saturation which also leads to pattern dependent data distortion.

The delay dependence on OPA gain is summarized in Fig. 4.

 

Fig. 4. Delay versus OPA gain. Blue curve–calculation, green curve–measured results

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An accurate determination of the delay requires considering changes in the pulse temporal shape due to propagation in the slow light medium. For moderate distortions, the delay is best defined in terms of the optimum sampling point that yields the largest eye opening [7]. The measured delay (shown in green) and the calculation (shown in blue) fit very well for large gain values but less so in the negative gain regime where the process is dominated by Raman loss [8]. In the negative gain regime, the signals are somewhat noisy and an accurate determination of the optimum sampling point requires averaging over many bits. However, only a relatively small number of bits are available (in the present system) within the pump pulse duration and this limited statistical ensemble causes some inaccuracies. Nevertheless, even the largest error is relatively small.

The results shown in Figs. 3 and 4 were obtained for a signal wavelength λ₁=1428 nm. Next we demonstrate the ability to use other wavelengths across the OPA gain spectrum. Figure 5 shows simulated results for signals at λ₂=1427.7 nm and λ₃=1428.4 nm [see Fig. 1(a)].

 

Fig. 5. Simulated 10 Gb/s eye patterns at two wavelengths and two OPA gain levels. Blue curve-pump off, red curves pump on. (a) λ₂=1427.7 nm, G=-5.3 dB, (b) λ₂=1427.7 nm, G=5.5 dB, (c) λ₃=1428.4 nm, G=-4.1 dB, (d) λ₃=1428.4 nm, G=8.3 dB.

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The simulations used a long data sequence where the nature of individual pulses resembles closely the pulses used for the experiments. For each wavelength, we compare two gain levels to the case with the pump off. Similarly to the case of λ₁, a low gain level results in a slight distortion which all but disappears at high gain levels. Similar levels of delay with low distortions are achievable within a wide range of wavelengths. Hence, the mechanism used here can be employed to delay signals at higher data rates, having much broader spectra. Indeed, theoretical results for large delays of a 40 Gb/s data stream are reported in Ref. [13].

4. Conclusion

To conclude, we have demonstrated a large tunable all optical delay with very low distortion of a 10 Gbit/s data stream propagating in a slow light system based on narrow band fiber parametric amplification. Delays of 10 ps to 60 ps have been demonstrated experimentally and theoretically. Simulated results suggest that equally high quality results are obtainable at several wavelengths across the OPA gain spectrum. We present a procedure to estimate the spatial distribution of the fiber propagation parameters with a high resolution. These distributions are used to predict theoretically the temporal shape and the delay of the data streams. The theoretical predictions fit the experimental results very well.