Optical Regenerators
An important application of optical signal processing is for regenerating optical signals degraded during transmission through fibers and amplifiers. An ideal optical regenerator transforms the degraded bitstream into its original form by performing three functions: reamplification, reshaping, and retiming. Such devices are referred to as 3R regenerators to emphasize that they perform all three functions. With this terminology, optical amplifiers can be classified as 1R regenerators because they only reamplify the bitstream. Devices that perform the first two functions are called 2R regenerators. Since 2R and 3R regenerators have to work at time scales shorter than the bit slot in order to carry out pulse reshaping and retiming, they must operate at time scales of 10 ps or less, depending on the bit rate of the optical signal. As nonlinear effects in optical fibers respond at femtosecond time scales, highly nonlinear fibers are often employed for such devices. However, the use of SOAs is also being pursued in view of their low-power requirements.
1. Fiber-Based 2R Regenerators
All three major nonlinear effects, SPM, XPM, and FWM, can be employed for optical regeneration. An SPM-based 2R regenerator, proposed in 1998 for regenerating RZ signals, has been studied extensively in recent years. The following figure shows the underlying idea behind this scheme. The distorted noisy signal is first amplified by an EDFA before it propagates through a highly nonlinear fiber, where its spectrum broadens considerably because of SPM-induced frequency chirp. It is subsequently passed through a bandpass filter (BPF), whose center wavelength is chosen judiciously, resulting in an output bitstream with much-reduced noise and much-improved pulse characteristics.
It may appear surprising at first sight that spectral filtering of a bitstream whose phase has been modified nonlinearly improves the signal in the time domain. However, it is easy to see why this scheme would remove noise from the 0 bits. If the passband of the optical filter is offset enough from the peak of the input spectrum, this noise would be blocked by the filter. In practice, this offset is chosen such that pulses representing 1 bits pass through the filter without much distortion. The noise level of 1 bits is also reduced because a small change in the peak power does not affect the pulse spectrum significantly, resulting in a much cleaner output bitstream.
To understand the operation of SPM-based regenerators, one may employ the analysis given in the basic concepts of optical receivers tutorial. If we neglect the dispersive effects within the highly nonlinear fiber, only the phase of the optical field is affected by SPM within the fiber such that
where Leff = (1 - e-αL)/α is the effective length for a fiber of length L with the loss parameter α, P0 is the peak power of pulses, and U(0, t) represents bit pattern of the input bitstream. As an optical filter acts in the spectral domain, the optical field after the filter can be written as
where F is the Fourier-transform operator and Hf(ω-ωf) is the transfer function of a filter offset from the carrier frequency of pulses by ωf.
The performance of an SPM-based regenerator depends on three parameters: the maximum nonlinear phase shift φNL ≡ γP0Leff, the filter-passband offset ωf, and the filter bandwidth δω, which must be large enough to accommodate the entire signal so that the width of optical pulses remains intact. This leaves only two design parameters whose optimum values were investigated in a 2005 study using Gaussian-shaped pulses and a Gaussian transfer function for the filter. In general, φNL should not be too large because, if the spectrum becomes too broad, filter-induced losses become too large. Its optimum value is close to 3π/2 because the SPM-broadened spectrum then exhibits two peaks with a sharp dip at eh original carrier frequency of the pulse. Noting that φNL = Leff/LNL , where LNL is the nonlinear length, the optimum length Leff is close to 5LNL. The optimum value of the filter offset in this case is found to be ωf = 3/T0, where T0 is the half-width of Gaussian pulses with the power profile P(t) = P0 exp(-t2/T02).
The following figure shows a numerical example of the noise reduction provided by SPM-based 2R regenerators in the case of φNL = 5 and 2-ps-wide Gaussian pulses (appropriate for a 160-Gb/s bitstream). Each input pulse could have up to 10% variations in its peak power (average value 1 mW) but its width was changed to keep the same pulse energy. At the output end, the noise power is reduced from 10% to 0.6% of the average peak power, and the amplitude of power variations is reduced from 10% to 4.6%. The reason behind a large reduction in noise power is related to almost complete blocking of noise pulses in 0-bit time slots. For example, a noise pulse with 0.1-mW peak power in figure (a) below is nearly blocked by the regenerator.
The preceding analysis holds as long as dispersive effects are negligible. At high bit rates, pulses become so short that such effects may not remain negligible. However, one must distinguish between the cases of normal and anomalous dispersion. The anomalous-GVD case was studied during the 1990s in the context of soliton-based systems. In this case, SPM and GVD occur inside the transmission fiber itself. Soliton regenerators with a design similar to that shown in the previous figure have also been considered but they operate differently because the optical filter is centered on the carrier frequency itself. In the case of normal GVD, the SPM-based regenerator is designed with a filter offset from the carrier frequency but it is important to include the dispersive effects. Considerable theoretical work has shown that the optimization of a 2R regenerator is quite sensitive to the magnitude of dispersion. Experiments performed at a bit rate of 40 Gb/s also show that the optimum power launched into the fiber depends on the fiber length and filter offset, and it must be optimized for such a regenerator to work well.
The required fiber length can be reduced considerably by employing non silica fibers with large values of n2. A 2.8-m-long piece of chalcogenide (As2Se3) fiber was employed in a 2005 experiment. This fiber exhibited a high normal dispersion near 1550 nm with β2 > 600 ps2/km. However, it turned out that this large value actually helped the device performance, rather than hindered it. The large value of the nonlinear parameter (γ ≈ 1200 W-1/km) reduced the required peak power to ~1 W, whereas large values of β2 reduced the dispersion length LD close to 18 m for 5.8-ps pulses employed in the experiment. The optimum fiber length under these conditions was close to 3 m. The following figure shows the impact of fiber dispersion on the SPM-broadened spectrum and the resulting changes in the transfer function of the regenerator for a fixed position of the optical filter. Improvements in the transfer function result from the reduced amplitude of spectral oscillations, resulting in a relatively smooth spectrum. Even the presence of two-photon absorption in chalcogenide fibers, a normally undesirable phenomenon, helps in improving the device performance.
In a 2006 experiment, a 1-m length of a bismuth-oxide fiber was employed in combination with a tunable 1-nm bandpass filter. The center wavelength of the filter was offset by 1.7 nm from the carrier wavelength of the incoming 10-Gb/s bitstream. Losses were negligible (about 0.8 dB) for such a short fiber that also exhibited a normal dispersion of 330 ps2/km at 1550 nm. The nonlinear parameter γ for this fiber was close to 1100 W-1/km. Because of a high nonlinearity and normal dispersion, such a fiber performed well as a 2R regenerator when the peak power of input pulses was large enough (about 8 W) to induce significant spectral broadening. The following figure compares the measured power-transfer function with the theoretical prediction. A negligible output at low input powers and a relatively broad peak ensure that power fluctuations will be reduced considerably for both 0 and 1 bits.
The nonlinear phenomenon of XPM is also useful for optical regeneration. Any nonlinear device in which a combination of the XPM and XPM effects produces nonlinear power transfer characteristics similar to that seen in the above figure can be used as a 2R regenerator. A NOLM is just such a nonlinear device, and its was used as early as 1992 for realizing optical regeneration. In this experiment, the XPM-induced phase shift was employed to modify the NOLM transmission and to regenerate the bitstream. Sonn after, such devices were analyzed and employed for optical regeneration of pulses in soliton-based systems. The use of a Kerr shutter where XPM is used to change the state of polarization provided regenerators at speeds of up to 40 Gb/s.
A highly asymmetric NOLM was employed in a 2003 experiment, and it reduced the signal noise by as much as 12 dB. The following figure shows the experimental setup schematically. The NOLM was built using a fiber coupler whose splitting ratio could be varied to ensure that power levels in the counterpropagating directions differed substantially inside the Sagnac loop made with a 250-m-long polarization-maintaining fiber. For a splitting ratio of 90:10, the combination of SPM and XPM produced a relative phase shift in the two directions such that the power-transfer function of the NOLM exhibited a nearly flat region around 5 mW of input power, and the noise level was reduced considerably in this region. The optical SNR of a 40-Gb/s system could be improved by 3.9 dB with this approach. In another system experiment, a 10-Gb/s signal could be propagated over 100,000 km using a NOLM as a 2R regenerator within a recirculating fiber loop. Three cascaded NOLMs were used in a 2004 experiment to realize regeneration fo 160-Gb/s signals.
FWM attracted attention for 2R regeneration starting in 2000, and several experiments have demonstrated its use in practice. As we have seen in the dispersion problem and its solutions tutorial, FWM converts a fiber into a parametric amplifier. Similar to any amplifier, the gain of a parametric amplifier also features when signal power becomes large enough to saturate the amplifier. Because of this gain saturation, fluctuations in the peak power of a pulse are reduced by a large factor. Figure (a) below shows the improvement realized in the case of a parametric amplifier made using a 2.5-km-long dispersion-shifted fiber and pumped close to the zero-dispersion wavelength with 500-ps pulses (peak power 1.26 W). The FOPA exhibited a gain of 45 dB at low signal powers, but the gain saturated when the output signal power approached 200 mW. Because of it, the noise power of the signal was reduced by more than a factor of 20. This is also evident from the temporal patterns seen in part (b).
The simple theory of the dispersion problem and its solutions tutorial cannot be used for describing gain saturation in parametric amplifiers because it assumes that the pump power remains nearly undepleted along the fiber. For a parametric amplifier to be useful as a 2R regenerator, the signal power must become large enough that the pump is depleted significantly. Moreover, large power levels of the signal and idler initiate a cascaded FWM process by acting as the pump and creating multiple other waves. All of these idlers act as a wavelength-shifted replica of the signal and exhibit much less noise compared with the signal. Experimental results for a single-pump parametric amplifier agree with a theoretical model that takes into account pump depletion. Au dual-pump parametric amplifier has also been used as a 2R regenerator. As seen in the dispersion problem and its solutions tutorial, multiple idlers at different wavelengths are generated in this case. The device performs better if one of the idlers is used as the regenerated signal.
The performance of FWM-based regenerators can be improved further by cascading two parametric amplifiers in series. In a 2006 experiment, the output of the first parametric amplifier was filtered with an optical filter to select a higher-order idler that acted as the pump for the second-stage parametric amplifier. A CW seed acted as the signal and created its corresponding idler. This idler had the same bit pattern as the signal launched at the input end of the first parametric amplifier but with a much-reduced noise level. The following figure shows the measured transfer functions after the first and second stages. A nearly step-function-like shape after the second stage indicates the extent of improvement possible with such a scheme.
2. SOA-Based 2R Regenerators
SOA-based wavelength converters can be used as 2R regenerators because they transfer the bit pattern of a degraded signal to a CW optical beam at the new wavelength. After this transfer process, the SNR of the new signal is much better than the original signal. Since SOAs also provide amplification and pulse shaping, the new bitstream has all the features provided by a 2R regenerator except that the signal wavelength has also changed. In a 2000 experiment, the optical SNR of a 40-Gb/s degraded signal was improved by 20 dB when an MZ interferometer with two SOAs in its arms was employed as a wavelength converter. Four additional SOAs were added near the input and output ports to ensure that the converted signal was amplified as well.
Several schemes exist that can provide 2R regeneration without a wavelength shift, and two of them are shown in the figure below. A 2 x 2 MMI coupler was employed in a 2002 experiment. Such an SOA acts as a directional coupler that transfers a low-power signal to its cross port. In contrast, high-power signals not only saturate the SOA gain but they also exit through the bar port. As a result, the noise level is reduced for both the 0 and 1 bits as they pass through the SOA. The second scheme in the following figure combines a saturable absorber (deposited on a mirror) with an SOA through an optical circulator. Such a device acts as a 2R regenerator because low-power 0 bits are absorbed while high-power 1 bits are reflected and amplified by the SOA. The intensity noise of 1 bits is reduced considerably by the saturable absorber. The holding beam in the following figure helps to shorten the gain-recovery time of the SOA so that it can be operated at a bit rate of 10 Gb/s or more. It is possible to integrate saturable absorbers and SOAs on the same chip if we make use of the electroabsorption properties of InGaAsP quantum wells (the same material used for making SOAs) under reverse bias. In this design, a saturable absorber follows the SOA, and this cascading pattern is repeated if necessary. As before, 0 bits are absorbed while 1 bits pass through the absorbers.
Another scheme makes use of cross-gain saturation inside an SOA occurring when two optical fields are amplified simultaneously. The new feature of this scheme is that the degraded bitstream is launched inside the SOA together with a bit-inverted copy of it at a different wavelength. This inverted copy is generated from the original signal using another SOA acting as a wavelength converter, as shown in the figure below. The wavelength converter employs a bandpass filter with a wavelength offset chosen to create an inverted bit pattern similar to that shown in the third trace of the previous figure. The two signals with inverted bit patterns are launched into the SOA2 such that the total power is nearly constant. Owing to cross-gain saturation, noise levels of both the 0 and 1 bits are reduced considerably for the output at the original-signal wavelength, resulting in a regenerated signal. This scheme works for any signal polarization and can be used at bit rates of 40 Gb/s or more.
3. Fiber-Based 3R Regenerators
As mentioned earlier, a 3R regenerator performs the retiming function, in addition to reamplification and reshaping, to reduce the timing jitter of the incoming bitstream. An optical modulator was used during the 1990s for this purpose in the context of soliton systems, and its use is often necessary for 3R regenerators. An electrical clock signal, extracted from the input data itself, drives the modulator and provides the timing information related to the duration of each bit slot. An SPM-based 3R regenerator can be built by adding a modulator. A schematic of such a device is shown in the figure below. Numerical simulations for a fiber link containing such 3R regenerators at periodic intervals indeed show a considerable reduction in timing jitter. As early as 2002, this approach was used to realize transmission of a 40-Gb/s over 1000,000 km using a 400-km-long recirculating fiber loop. The 40-GHz electric clock used to drive the modulator was recovered fro the incoming bitstream itself. Another 2002 experiment used an SOA-based wavelength converter after a fiber-based regenerator to transmit a 40-Gb/s over 1000,000 km.
Several fiber-based schemes have been proposed for reducing the timing jitter of ba bitstream. In one scheme, a single-phase modulator in combination with a dispersive fiber is found to be effective in reducing timing jitter. In another, an optical AND gate is used to correlate data pulses with clock pulses that have been chirped and broadened inside a dispersive fiber. The combination of a dispersion-compensating fiber and a fiber grating is also found to be effective in suppressing timing jitter induced by the intrachannel XPM effects. In an interesting scheme, a sampled fiber grating is used first to broaden and reshape data pulses into a nearly rectangular shape. These pulses are then launched into a NOLM acting as an optical switch and driven by narrow clock pulses. Clock pulses shift the phase of each data pulse through XPM and direct only its central part to the output port, resulting in regenerated data with much-reduced timing jitter. In the absence of a fiber grating, such an optical switch does not reduce timing jitter much.
A simple design of a 3R regenerator makes use of XPM inside a highly nonlinear fiber, followed by an optical filter. The following figure shows the configuration adopted in a 2005 experiment together with its principle of operation. The clock pulses at the wavelength λ2 are narrower than signal pulses and are delayed such that each of them continues overlapping with a signal pulse over the entire fiber length in spite of their different speeds. The optical filter is set at λ2 with a bandwidth narrower than the clock spectrum. As the signal power increases in parts (b) to (d), the XPM-induced wavelength shift of clock pulses reduces their transmission, resulting in a power-transfer function, shown in figure (e). The output of such a device is a wavelength-converted signal with a reversal of 1 and 0 bits. In the experiment, the 10-Gb/s signal at a wavelength of 1534 nm was launched inside a 750-m-long highly nonlinear fiber together with 2.9-ps clock pulses at 1552 nm at a 10-GHz repetition rate. The regeneration 10-Gb/s signal improved the BER significantly because of reduced noise level and timing jitter.
The XPM-based scheme shown in the figure above has been analyzed in detail theoretically. It turns out that the improvement in BER after the regenerator occurs only if the power-transfer function of the regenerator is different for 0 and 1 bits. The scheme of this figure exhibits this feature because the wavelength shift of the clock depends on the derivative of the signal power as δω = -2γLeff(dP/dt). Data bits representing a logical 1 shift the clock spectrum through XPM, and the filter blocks these clock bits. On the other hand, 0 bits containing only noise produce little spectral shift of clock pulses, which pass through the filter unchanged. Timing jitter is eliminated because clock pulses now represent the data with reversed polarity.
An electro-absorption modulator acting as a saturable absorber can also eliminate timing jitter through the process of cross-absorption modulation. In this scheme, a 2R regenerator is used first to reduce the noise level. The intense data pulses are then passed through a saturable absorber together with low-power clock pulses. Clock pulses are absorbed when a logical 1 appears in the data stream but are transmitted otherwise. The resulting output is an inverted replica of the original bitstream with virtually no timing jitter.
4. SOA-Based 3R Regenerators
Similar to the case of optical fibers, one can combine any SOA-based 2R regenerator with a modulator driven by an electrical clock at the bit rate. In one 2009 experiment, the regenerator shown in the figure below was combined with an electroabsorption modulator to provide retiming of an incoming 43-Gb/s bitstream. The electrical clock needed for the modulator was extracted from the incoming signal itself using a clock recovery circuit consisting of a 40-GHz photodiode and a phase-locked loop. The cascadability of such a 3R regenerator was investigated by placing it inside a recirculating fiber loop whose length was varied from 100 to 300 km. A 43-Gb/s signal could be transmitted over 10,000 km when the loop length or regenerating spacing was 200 km or less.
One may ask if an optical clock can be used in place of the electrical one. As early as 2001, such an approach was used to realize a 3R regenerator with the setup shown in figure (a) below.
The device is essentially a wavelength converter designed with a single SOA followed by an unbalanced MZ interferometer providing a relative delay of one bit period between its two arms. The optical signal at the wavelength λ1 is launched into the SOA together with an optical clock at the bit rate of the signal but at a different wavelength λ2. The clock pulses are passed through the device in the absence of the signal (during 0 bits) but are blocked when the signal is on (during 1 bits). As a result, the bit pattern of the incoming signal is transferred to this clock with bit inversion, and the clock pulses now serve the role of the regenerated signal at a new wavelength.
Another scheme shown in the figure (b) above uses the same idea but employs a balanced MZ interferometer with one SOA in its every arm. This device is also a wavelength converter with the only change that an optical clock at the bit rate of the signal is used in place of a CW beam. An advantage of this scheme is that regeneration occurs without inversion of the incoming bit pattern. The following figure shows how such a 3R regenerator works. In essence, data pulses open an optical switch for a duration shorter than a bit slot but longer than their widths. Clock pulses are synchronized such that they appear within this switching window. The timing jitter is eliminated at the output end because regularly spaced clock pulses are used as a regenerated signal at a new wavelength associated with them. In the 2002 experiment, such a device was operated successfully at a bit rate of 84 Gb/s.
The use of an optical clock requires a mode-locked laser, capable of operating at the bit rate of the incoming signal, but its pulse train should be synchronized with data pulses in the signal, a difficult task in practice. The alternative is to extract the optical clock from the signal itself. Considerable progress has been made in recent years to realize 3R regenerators that extract an optical clock from the incoming signal. A simple idea is based on the concept of spectral filtering. If an optical signal l is passed through a multipeak optical filter, such as an FP filter, whose relatively narrow transmission peaks are spaced by exactly the bit rate of the signal, the filtered spectrum would consist of a frequency comb that corresponds to a periodic train of optical pulses, or an optical clock with a repetition rate equal fo the signal's bit rate. In a 2004 experiment, a tunable FP filter was used in combination with an SOA to extract a 40-Gb/s optical clock; the SOA acted as an amplitude equalizer. The optical clock exhibited low amplitude noise (<0.5%) and low timing jitter (<0.5 ps). Several other schemes have been used for extracting optical clocks, including those based on electroabsorption modulators, self-pulsing DFB or quantum-dot lasers, mode-locked ring or semiconductor lasers, and FP-type SOAs.
In some cases, the recovered optical clock is converted to an electrical clock that is used to drive a modulator. The following figure shows an example of such a 3R regenerator. It makes use of three SOA-based 2R regenerators based on an MZ configuration with six SOAs. One of them (upper branch) is followed by a Fabry-Perot filter for recovering the optical clock, which is converted into an electrical clock. The other two 2R regeneration (lower branch) are combined in series to improve the optical SNR and cancel the wavelength shift occurring after the first regenerator. Four patterns at the bottom show the eye diagram for the incoming 10-Gb/s signal, the signal before clock recovery, the recovered clock, and the regenerated signal. Such a 3R regenerator was used in a recirculating fiber loop to realize the transmission of a 10-Gb/s signal over 125,000 km without dispersion compensation. This experiment clearly shows the ultimate potential of SOAs for optical signal processing.
5. Regeneration of Phase-Encoded Signals
So far we have considered all-optical regeneration of NRZ or RZ bitstreams. Most of the schemes discussed earlier do not work for the regeneration of phase-encoded signals because their operation is based on different power levels associated with the 0 and 1 bits. As we saw in previous tutorials, it is common to employ a pulse in every bit slot whose phase takes two or more values depending on the format chosen. Recently, several techniques have been developed for regenerating RZ-DPSK signals.
In a 2005 study, a NOLM similar to that sown in the following figure was employed with one crucial difference: an attenuator with different losses in the counterpropagating Directions was inserted near one end of the fiber loop. This device works similar to an optical isolator and can be fabricated using polarizers and a Faraday rotator. Although much higher input powers are required, the power-transfer function exhibits a flat region around which the phase shift produced by the NOLM is also constant and relatively small. The experimental results were in agreement with the theoretical predictions.
A bidirectional EDFA (in place of a directional attenuator) at one end of the NOLM was used in a 2007 experiment to realize the regeneration of RZ-DPSK signals. The input signal was split asymmetrically at the fiber coupler such that each weaker sub pulse was first amplified by the EDFA, while the stronger sub pulse passed through it after traversing the Sagnac loop. As a result, the SPM-induced phase shift was much larger for the weaker sub-pulses. As the phase of output pulse is set by stronger sub-pulses, the NOLM does not distort the phase of outgoing pulses much. The following figure shows the measured power and phase characteristics for a 3-km-long fiber loop (γ = 2.5 W-1/km) for several splitting ratios of the fiber coupler when the amplifier was pumped to provide a small-signal gain of 23 dB. As expected, the output power becomes nearly constant in a specific range of input powers, a feature that reduces the noise of 1 bits. Since the phase is nearly constant in the region, the amplitude noise of the signal can be suppressed without transferring it into phase jitter. At the same time, the relative phase shift between the 0 and 1 bit s is so small (< 0.07 π) that it does not affect the decoding of the DPSk bitstream. Indeed, measured BERs for a 10-Gb/s RZ-DPSK bitstream were improved considerably with such a regenerator. The amplification can also be provided through the Raman gain by injecting pump light into the loop such that it propagates in one direction only.
The SPM-based 2R regenerator can also be adopted for the RZ-DPSK format with suitable modifications. For example, the signal phase can be almost preserved over long distances if the nonlinear fiber provides anomalous dispersion and a saturable absorber is inserted before it. In this case, the combination of soliton effects and narrowband filtering reduces amplitude noise and reshapes RZ pulses without affecting the signal phase significantly. A FWM-based approach can also be used by pumping the fiber near the zero-dispersion wavelength and increasing the signal power so that the parametric gain is saturated and multiple idlers are generated through cascaded FWM. However, one should set the optical filter such that it selects the signal and rejects all idlers to minimize degradation of the information contained in signal phase. An XPM-based scheme has also been proposed for regenerating DPSK signals.
The preceding schemes regenerate RZ pulses by reducing amplitude noise (while preserving their phases) but they do not reduce the phase noise. A FWM-based approach accomplishes this task by making use of phase-sensitive amplification inside a Mazh-Zehnder or Sagnac interferometer. A 6-km-long Sagnac loop (or NOLM) was employed in a 2005 experiment to realize >13 dB of phase-sensitive gain at a pump power of 100 mW. Phase noise was reduced enough to improve the BER of the regenerated DPSk signal by a factor of 100. In a later experiment, the same loop was used to reduce both the amplitude and phase noises by a relatively large factor.
The following figure shows the experimental setup employed for phase-sensitive amplification inside a Sagnac interferometer. The DPSK signal is first split into two parts using a 90:10 fiber coupler. The branch with 90% average power acts as a pump, while the low-power branch acts as the signal; a delay line in the pump branch ensures decorrelation between the two. Phase and amplitude noises are added to the signal before it enters the 6-km-long fiber loop, where a degenerate FWM process transfers power from the pump to the signal. The extent of power transfer depends on the relative phase difference between the pump and signal. It is this feature that reduces phase noise at the NOLM output. The second figure below shows the extent of improvement realized with this scheme using constellation diagrams. Both the amplitude and phase noises are reduced significantly after phase-sensitive amplification. A dual-pump parametric amplifier can also be employed for this purpose provided the signal frequency is located exactly in the middle of the two pumps so that it coincides with the idler frequency.
The design of a fiber-based 3R regenerator for DPSk signals is shown in the following figure. It adds a 1-bit delay interferometer in front of a 2R regenerator whose output is fed to a fiber-based phase modulator driven by an optical clock recovered from the signal itself (or obtained from a pulsed optical source). The role of a delay interferometer is to convert the incoming DPSK signal into an RZ-ASK signal whose noise is reduced by the 2R amplitude regenerator. The regenerated data stream is finally used to modulate the phase of clock pulses through XPM inside an optical fiber. In a 2008 experiment, a 2.4-km-long highly nonlinear fiber was used as a phase modulator together with a fiber-based 2R regenerator. Such a device reduces both the amplitude and phase noises of the incoming DPSK bitstream. A 2009 experiment showed that it was capable of reducing the impact of nonlinear phase noise that affects a DPSK signal considerably.
The optical regeneration of RZ-DQPSK signals is also of considerable practical interest. A 2-km-long NOLM was used for this purpose in a 2007 experiment to regenerate an 80-Gb/s signal. Numerical simulations show that phase-sensitive amplification can also be used with success. Even the scheme shown in the figure above can be generalized to the case of DQPSK signals, but it requires two delay interferometers, two 2R regenerators, and two phase modulators to deal with four possible phases of a single symbol.