Parametric Gain Peak Optimization

Finally the parametric gain peak is investigated as a function of both the total fiber length LT and the ratio RL= L1/L2, with Li as in the previous Subsection. The two

configurations are studied calculating the parametric gain for each set (LT, RL) with

an input pump power of 30 dBm and a signal power of -50 dBm.

The results of our simulations are shown in Figure 7.14.

Total Length [m] Length Al−HNLF [%] 0 0.2 0.4 0.6 0.8 1 100 200 300 400 500 600 700 800 900 1000 1100 −12 −10 −8 −6 −4 −2 0 2

(a) “Al first”

Total Length [m] Length Al−HNLF [%] 0 0.2 0.4 0.6 0.8 1 100 200 300 400 500 600 700 800 900 1000 1100 −12 −10 −8 −6 −4 −2 0 2 (b) “Ge first”

Figure 7.14: Peak parametric gain as a function of total length and ratio between the Al and Ge-doped length for the “Al first” (a) and “Ge first” (b) configurations. The input power is set to 30 dBm

Both the maps show the presence of maxima for specific values of LT and RL. To

understand at least the general trend shown in the Figures we can compare with similar maps showing output pump power both at the first and the second stage, again for both configuration (Figure 7.15).

Total Length [m] Length Al−HNLF [%] 0.2 0.4 0.6 0.8 200 400 600 800 1000 10 15 20 25 30

(a) “Al first” 1st stage

Total Length [m] Length Al−HNLF [%] 0.2 0.4 0.6 0.8 100 200 300 400 500 600 700 800 900 1000 1100 10 15 20 25 30

(b) “Ge first” 1st stage

Total Length [m] Length Al−HNLF [%] 0.2 0.4 0.6 0.8 100 200 300 400 500 600 700 800 900 1000 1100 10 15 20 25 30

(c) “Al first” 2nd stage

Total Length [m] Length Al−HNLF [%] 0.2 0.4 0.6 0.8 100 200 300 400 500 600 700 800 900 1000 1100 10 15 20 25 30

(d) “Ge first” 2nd stage

Figure 7.15: Pump power at the output of the first (a)-(b) and second (c)-(d) fiber span as a function of LT and RL for the “Al first” (a)-(c) and “Ge first” (b)-(d)

configurations. The input power is set to 30 dBm

Comparing Figure 7.14(a) with Figure 7.15(a) we can justify the decrease of parametric gain along the direction of increase of both LT and RT (diagonal of the Figure) with a

decrease of the pump power. Concerning the second stage (Figure 7.15(c)) instead, a simple relation between the pump power and the parametric gain cannot be highlighted.

Similar comments can be made for the second configuration. Also in this case the first stage seems to have most of the influence on the general trend followed by the parametric gain peak. Nevertheless no straightforward relation can be defined overall.

Conclusions and Future Work

The scope of this thesis was the analysis of all-optical signal regeneration for QPSK

modulations through the use ofPSAinFOPA.

In particular we have focused on twoDP FOPAschemes in a respectively non-degenerate and degenerate configuration. The latter method has actually been proposed in this study and it has been developed starting from some conclusions drawn investigating the saturation regime of FOPAs. Both the regenerators have been discussed semi- analytically and optimized models have been implemented in MATLAB®

in order to analyze their individual performances other than providing a comparison between the two.

The regenerators have been tested propagatingNRZ,CSRZand RZ33% QPSKsignals at 28 and 40 Gbaud and the reduction in the signal phasestd and the improvement in theBERperformances at the output have been investigated.

As illustrated in Chapter 6 the regeneration has been demonstrated by the signifi- cant increase in the performances. Phase stds improvements up to 80% and R-OSNR

decreases up to 10 dB have been calculated for both the regeneration schemes. Fur- thermore error-free detection1 has been shown for phase noise stds which would not have permitted it without regeneration.

The BER analysis has reported a good baudrate transparency for both the schemes. The baudrate dependence characterizing the output phasestdwhen the non-degenerate

1

scheme is used requires to investigate further the impact of phase squeezing and am- plitude un-squeezing on the receiver.

Concerning the complexity of the schemes, the non-degenerate scheme requires two

FOPA stages for the idler generation unlike the comb generator needed by degenerate case. The use of the idler-free configuration discussed in Section 4.4 has however the potential to ease the implementation.

TheMZI of the proposed scheme, on the other hand, requires careful optimization and two identical HNLFs since the alignment of the responses in the two arms is critical. Nonetheless, mapping the MZI into a SIremoves the need for two HNLFs and is thus expected to lower the tuning requirements.

Further studies are desirable to refine the results. First of all a reliable model for the phase noise generated through the propagation in optical fibers is required. As shown in [40] the measured performances are highly impacted by the chosen phase noise rep- resentation.

Furthermore, in this study we have analyzed regeneration performed at the receiver end. The regeneration performed within the optical link is indeed interesting for fur- ther research. The spacing of regenerators within an optical link needs to be evaluated according to the trade-off between minimizing their number and the abrupt increase in power penalty when the amount of phase noise in input to the regenerator reaches a certain threshold σi≈ 12○ according to our results.

Finally, in the main part of our investigation SBShas been neglected in order to keep low the computational requirements. Nonetheless its detrimental effects have been discussed through a MATLAB®

model simulating the dynamic behavior of SBS and a dual-fiber link made of an Al-doped and a Ge-doped HNLF has been optimized in length according to the maximum parametric gain. The consequent step would thus be the analysis of the regenerator schemes taking the Brillouin effects into account in order to reproduce more precisely the behavior of a practical scheme.

Optical Fibers

In this Appendix we briefly introduce and discuss the main parameters affecting the wave propagations through an optical fiber: losses, dispersion and nonlinearities. The equations describing the propagation are then analyzed in Appendix B.

A.1

Losses

An optical wave propagating through a fiber is attenuated by several physical effects [15]. The overall losses are usually defined by the attenuation constant α commonly expressed in dB/km and are related to the power P(z) of a CW field through Beer’s Law:

dP(z)

dz = −αz . (A.1)

In general, the attenuation (or “losses”) is wavelength dependent as shown in Figure A.1 for a Corning LEAF©

fiber.

Figure A.1: Attenuation spectrum of a Corning LEAF©

The attenuation spectrum however, shows a slow variation of α around 1550 nm, i.e. the wavelength window we use in our simulations. Throughout this thesis then, α(λ) = α0.

Usual values of α for single mode fibers are on the order of 0.15÷ 0.2 dB/km around λ=1550 nm. In this study however we deal mainly with HNLFscharacterized by losses around 0.6÷ 1 dB/km for common Ge-doped fibers. Then, due to the need to suppress

SBS (Chapter 7), Al-doped fibers are also considered. The Al doping increase signifi- cantly the losses and values up to 15 dB/km are commonly reported [47, 64].

Finally losses determine the effective length of a fiber defined as: Lef f =

1− e−αL

α , (A.2)

where L is the physical length of the fiber. The effective length plays an important role in determining properties like the SBST (7.4). When αL ≫ 1 it is common to approximate Lef f ≈ 1/α.