1. Introduction

Fiber chromatic dispersion is one of the major fiber impairments that limit the performance of the high bit-rate and long-haul optical transmission system. Faster and longer transmission links can be achieved by accurate dispersion map planning and effective dispersion compensation. These tasks cannot be carried out easily without the ability to monitor the residual dispersion effectively. Additionally, dynamic dispersion compensation becomes necessary in order to give optimal signal quality in reconfigurable optical networks as the accumulated dispersion becomes a non-static parameter. Hence, dispersion monitoring becomes an essential function for the deployment and operation of optical networks.

Several previously proposed dispersion monitoring schemes utilize a single RF monitoring tone and the RF fading characteristics with varying dispersion [1–4]. These techniques are simple, but are unable to distinguish the sign of the residual dispersion and have limited monitoring ranges. Other techniques such as [5–8] are able to monitor the dispersion sign. However, these techniques use complicated setups and special components. In addition, they are often bit-rate and data-format dependent. N. Liu et al proposed a technique that uses a dispersion offset to enable the sign of the residual dispersion to be monitored [9]. However, this technique requires two RF monitoring tones to be transmitted simultaneously as it measures the ratio of the RF tone powers.

We propose an improved chromatic dispersion monitoring technique that is able to monitor the residual dispersion sign, but uses only a single RF monitoring tone. Additionally, the monitoring range of our proposed technique doubles that proposed in [9] for a similar value of dispersion offset. Alternatively, for comparable monitoring range, the dispersion offset required for our technique is less than 50% of the dispersion offset required in [9].

Our proposed technique utilizes the RF fading caused by chromatic dispersion and two photodetectors. A dispersion offset is inserted before one of the detectors to create a horizontally shifted RF fading characteristic. Unlike the RF power ratio technique, where two RFmonitoring tones are required to remove the effect on the monitoring accuracy caused by the loss or gain experienced by the optical signal, our technique is based on an accurate measurement of the modulation depth of the RF monitoring tone. The modulation depth of this tone is independent of the optical signal power level.

2. Operation principle and experiment setup

When an optical signal is modulated by a RF signal, chromatic dispersion causes the the detected RF tone power to have a periodic fading characteristic that is given by [1, 2]

where P ₀ is the averaged transmitted optical power, A is a constant governed by the loss and gain experienced by the signal, α is the fiber loss per unit length, L is the fiber span length, m is the modulation index of the RF tone, D is the dispersion coefficient of the fiber, λ is the optical carrier wavelength, f_RF is the RF tone frequency, and c is the speed of light.

The RF tone power, P_RF from (1) is dependent on the residual dispersion (DL) as well as the system loss or gain (Ae ^-αL). Thus, in order to remove the impact of loss or gain variations on the measurement, we instead measure the normalized power (i.e. the modulation depth) of the received tone rather than simply its power. The modulation depth of the RF tone, M_RF , can be expressed as

where P_ROP =P ₀ Ae ^-αL is the averaged received power and M_eff is the effective modulation index.

 

Fig. 1. Conceptual diagram of our experimental setup for dispersion monitoring using single in-band RF tone and two detection paths.

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The value of $M_{\mathit{\text{eff}}}^2$ depends on the driving parameters of the modulator at the transmitter, including the RF monitoring tone amplitude, the baseband data signal amplitude, and the modulator bias level. Initial calibration is done where the driving parameters of the modulator are configured to give a predetermined value of M_RF for back-to-back transmission. Thus, for a given channel and monitoring tone frequency, the residual dispersion can be determined from the measured modulation depth of the RF tone.

Due to the periodic nature of (1), dispersion monitoring techniques based on a single RF tone have a limited monitoring range given by [2]

This range can be extended by lowering the frequency of the RF tone, f_RF , however, the sensitivity of the measurement is then reduced. Furthermore, since the response given by (1) is symmetric about the origin, it cannot determine the sign of the measured dispersion. Our proposed method reduces both these limitations by introducing an additional optical path, with a dispersion offset, at the monitor. This modification can extend the monitoring range by a factor of two, monitor the sign of the dispersion while also increase the measurement accuracy.

Fig. 1 illustrates the principle and an experiment used to demonstrate the proposed technique. The RF monitoring tone is electrically combined with a 10 Gb/s baseband signal before modulating onto a continuous wave laser. The modulated signal is then passed through various lengths of single-mode-fibre (SMF) to simulate different amounts of residual dispersion. At the dispersion monitor, the optical signal is divided into two paths. The signal in the first path is detected and the modulation depth of the RF tone is measured, while in the second path an additional dispersion offset is inserted before the photodetector. In the experiment described here, a chirped-fibre-bragg-grating (CFBG) with a -500 ps/nm nominal dispersion is used as the dispersion offset.

At the monitor, the signal at the first path is detected and the modulation depth of the RF tone, given by (2), is measured. The signal on the second path is passed through a dispersion offset before being detected. The modulation depth of the RF tone from the second path is given by

where D_offset is the amount of dispersion offset inserted.

 

Fig. 2. Unambiguous monitoring range for the proposed technique and the conventional technique using a single monitoring tone. The monitoring tone fading characteristics are shown for the path with (dashed curve) and without (solid curve) the dispersion offset.

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The dispersion offset shifts the fading characteristic horizontally. This is illustrated in Fig. 2, which plots the fading characteristics for each detection path. The solid (Path 1) and dashed (Path 2) curves represent the fading characteristic of the monitoring tone observed from the first and second monitoring path respectively.

The unambiguous monitoring range is the range of residual dispersion that allows a one-to-one mapping of the measured RF modulation depth to the residual dispersion. For conventional techniques that use a single RF monitoring tone, both negative residual dispersion and residual dispersion beyond the first null of the RF fading characteristic would result in an ambiguous mapping of the measured RF modulation depth to the residual dispersion.

The combined measurement from the basic (Path 1) and offset RF fading characteristic (Path 2) increases the range of unique one-to-one mapping to the residual dispersion. As shown in Fig. 2, the theoretical improved unambiguous monitoring range is twice as the conventional unambiguous monitoring range. In addition, the combined modulation depth measurements from the two paths can be used to remove the dispersion sign ambiguity. As indicated in Fig. 2, the absolute values of the theoretical signed and unsigned unambiguous monitoring ranges are the same. The theoretical improved unambiguous monitoring range is given by

(6)

We now compare (6) with the monitoring range in [9]. The monitoring range is c/(2λ ² $f_1^2$)-c/(2λ ²f²₂) for f ₁<f ₂. If we set f_RF =f ₁, the monitoring range of our proposed technique is greater than two times of themonitoring range presented in [9]. Alternatively, if we set f_RF =f ₂, the monitoring range becomes comparable, but the dispersion offset required for our proposed technique is less than half the amount required in [9].

 

Fig. 3. (a) RF fading due to dispersion for a 9.8 GHz tone from the two detection paths at the dispersion monitor. The lines are simulation results and the points are experimental results. (b) BER versus Received Optical Power. The solid line represents the back-to-back measurements with no monitoring tone, where the dashed line represents the case of having the 9.8 GHz monitoring tone with the modulator biased below quadrature.

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3. Experimental results and discussion

Our experiment was configured to demonstrate an unambiguous dispersion monitoring range of 1300 ps/nm. Fig. 3(a) shows our experimental results plotted together with simulation results. In our experiment, the observed error of the estimated residual dispersion is within ±35 ps/nm of the actual residual dispersion from 0 ps/nm to 1300 ps/nm.

One advantage of the proposed technique is that both the data and the monitoring tone are modulated onto the continuous wave laser through a single amplitude modulator. However, a power penalty is introduced to the system due to the additional monitoring tone. In the experiment reported here, the modulation index of the the monitoring tone is 15 %. The modulator is biased at 85% of the quadrature level to minimise the penalty effect caused by the added monitoring tone. Fig. 3(b) shows the BER curves of the back-to-back case, as well as the cases when the 9.8 GHz monitoring tone is presented with the modulator biased at 85% of the quadrature level. The power penalty caused by the addition of the monitoring tone is observed to be less than 0.5 dB.

The unambiguous monitoring range is determined by the frequency of the monitoring tone. As one can see from (6), the DL product is inversely proportional to the square of the monitoring frequency, f_RF . For example, an absolute unambiguous monitoring range of 2700 ps/nm can be achieved by using a 6.8 GHz monitoring tone. However, the overall monitoring sensitivity would be reduced by a factor of two.

4. Performance analysis and discussion

For this technique, the dispersion is calculated from measurement of the RF monitoring tone modulation depth. Thus, any inaccuracy in the measurements will lead to errors in the residual dispersion. Many factors such as drifts in electrical driving signals at the transmitter, residual chirp of the modulator, noise in the transmission and measurement systems, and other fiber impairments, may all cause the modulation depth measurements to deviate from the theoretical values. Instead of investigating individual error effect, we analyze how the net-error in the modulation depth measurements affects the monitoring accuracy.

 

Fig. 4. Normalized monitoring error plotted as a function of the RF modulation depth measurement error.

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Figure 4 shows the normalized monitoring error plotted as a function of the error in the measured RF modulation depth, where the normalized monitoring error represents the maximum error as a percentage of the monitoring range. We compare the analysis result of the technique using a dispersion offset (DO) of -350 ps/nm (same dispersion offset value as the experimental demonstration) and -655 ps/nm (best performance case) with the conventional technique that uses a single RF monitoring tone (dashed curve). A dispersion offset of -655 ps/nm (equivalent to the unambiguous monitoring range of the conventional technique) provides the best accuracy, but gives no improvement in the monitoring range. In comparison, when a -350 ps/nm dispersion offset is used, the accuracy is still twice as good as the conventional technique and the unambiguous monitoring range is more than 1.8 times more with a moderate 0.5 to 1 dB error in the modulation depth measurements. For a monitoring error of 5% and 10% of the monitoring range, the level of tolerable error in the modulation depth measurements for the conventional technique is 0.02 dB and 0.1 dB. The tolerable error level is relaxed to 0.3 dB and 0.6 dB when a -350 ps/nm dispersion offset is used.

5. Conclusion

In conclusion, we have demonstrated a simple dispersion monitoring technique using the modulation depth measurements of a single added RF monitoring tone at a pair of detectors, one with a dispersion offset before it. The technique removes the ambiguity in the sign of the residual dispersion that exists in conventional monitoring techniques using a single RF monitoring tone, and doubles the unambiguous monitoring range without sacrificing the overall monitoring sensitivity. An absolute unambiguous monitoring range of 1300 ps/nm was achieved with a power penalty of less than 0.5 dB. The overall monitoring error is less than ±35 ps/nm. Compared with the conventional technique, our proposed technique showed significant improvement in tolerating the errors in the modulation depth measurements.