ANEXO C: Tabla valoración controles SGSI (carga MS Power BI)

With the experimental configuration set up to look at the fibre output on the OSA, the coupling and polarisation of the pump beam were optimised to ob- tain the largest Raman gain at1.62µm. We found that, at the time of the mea- surements, this corresponded to an input pump power of 210 mWand a cou- pling efficiency of ∼ 8 %so that the peak power of the pump in the fibre was

∼25 mW.

The measured autocorrelation trace of a Raman amplified pulse is shown in Fig. 6.18(a). This was taken for an AOM window size of 4µs and with only

10 mW of average signal power before the fibre, we estimate an average cou- pled power of ∼ 1 mW, corresponding to a peak signal power of ∼ 2 W. Clearly there is a very large noise component to this pulse which makes it difficult to distinguish any defining features. This is due to the extremely low average power of the signal beam and, in fact, for this window size it was not possible to measure an autocorrelation trace of the signal pulses through the fibre without gain (i.e., with the pump turned off). Nevertheless, the steepness of the edges of this trace suggests that the pulse has departed from its input hyperbolic secant profile.

The output spectrum from the microstructured fibre showing both the pump at1.536µmand the amplified spectrum at1.62µmis plotted in Fig. 6.18(b). To estimate the Raman pulse gain we then closed the AOM window down even

Chapter 6 Parabolic Evolution in Microstructured Fibre Raman Amplifiers −120 −6 0 6 12 0.5 1.0 Delay (ps) Autocorrelation (arb.) (a) 1540 1560 1580 1600 1620 1640 −40 −30 −20 −10 0 Wavelength (nm) Spectrum (arb.) (b)

Figure 6.18: (a) Measured autocorrelation trace and (b) spectrum of a Raman amplified pulse.

further to60 ns, so that there were approximately4significant signal pulses in each train, and measured the spectrum of the signal pulses with and without the copropagating pump. The resulting pulse spectra can be seen in Fig. 6.19 and from these we calculated the Raman gain to be ∼ 16 dB. Importantly we note that due to the reduction in the peak power, caused by the reduction of the AOM window, we can expect that this calculation will actually underestimate the true Raman pulse gain and this is facilitated by the suppression of the pulse shaping effects seen from Fig. 6.18(b) to Fig. 6.19(b). However, as it was not possible to measure the Raman gain directly from the temporal pulses, this was the best estimate that we could obtain.

To investigate these results in more detail, the system has been simulated based on the input pump and signal pulse properties, as estimated above, and with

1610 1615 1620 1625 1630 −10 −5 0 Wavelength (nm) Power (arb.) 1610 1615 1620 1625 1630 −30 −20 −10 0 Wavelength (nm) (a) (b)

Figure 6.19: Signal pulse spectra corresponding to (a) no gain (pump off) and (b) gain (pump on) to estimate the total Raman gain.

Chapter 6 Parabolic Evolution in Microstructured Fibre Raman Amplifiers

the fibre parameters given in Table 6.2. Fig. 6.20(a) shows the intensity profile and chirp of the output pulse from the simulation (solid curves). The total output pulse gain was 15.9 dB, consistent with the estimated measured gain. Clearly, not only is this pulse starting to look visually parabolic, it is also in good agreement with the parabolic fit to its intensity profile and the linear fit to its chirp (circles).4 _{In addition, the corresponding spectrum of Fig. 6.20(b)}

appears to be developing the oscillations on its edges typically associated with the entrance to the parabolic regime [Section 4.4].

−60 −4 −2 0 2 4 6 10 20 30 40 50 Time (ps) Power (W) −1 0 1 Chirp (THz) (a) 1600 1610 1620 1630 1640 −12 −8 −4 0 Wavelength (nm) Spectrum (arb.) (b)

Figure 6.20: (a) Intensity profile (left axis) and chirp (right axis) of the simulated Ra- man amplified pulse together with parabolic and linear fits (circles). (b) Correspond- ing spectrum.

To compare our measured pulse with the simulation results, Fig. 6.21(a) shows the autocorrelation trace of the pulse from Fig. 6.18(a) (solid curve) together with the calculated autocorrelation of the pulse from Fig. 6.20(a) (dashes). De- spite the noise induced asymmetry in the peak of the measured trace, there is still good agreement between the autocorrelations and specifically between their half maximum widths which are7.2 ps(measured) and7.3 ps(simulated). Furthermore, not only is there good agreement between the spectral widths (8.3 nmand8.4 nmfor the measured and simulated spectra, respectively), there is also excellent qualitative agreement between the shape of the spectral pro- files as seen in Fig. 6.21(b). Consequently, we can expect that the simulated pulse of Fig. 6.20 is a reasonable representation of the measured amplified pulse in Fig. 6.18 which indicates that parabolic pulses are indeed being gen-

4_{As in Section 6.3.2, the fits are obtained via a minimisation scheme based on the Nelder-}

Chapter 6 Parabolic Evolution in Microstructured Fibre Raman Amplifiers −12 −6 0 6 12 0 0.5 1 Delay (ps) Autocorrelation (arb.) (a) 1600 1610 1620 1630 1640 −12 −8 −4 0 Wavelength (nm) Spectra (arb.) (b)

Figure 6.21: (a) Autocorrelation traces and (b) Raman amplified spectra of the mea- sured pulse (solid curves) compared with the simulated parabolic pulse (dashed curves).

erated in our system.

Finally, to emphasise the parabolic nature of the output pulse, Fig. 6.22 com- pares the measured autocorrelation trace (solid line) with calculated autocor- relations for parabolic (dashes), Gaussian (dot-dashed) and hyperbolic secant (dotted) fits to the simulated pulse of Fig. 6.20, on a logarithmic scale. Clearly, the parabola offers the best fit to the experimental pulse, especially in the wings. Thus these results offer the first confirmation of a parabolic pulse gen- erated via Raman amplification in a microstructured fibre.

−9 −6 −3 0 3 6 9 10−2 10−1 100 Delay (ps) Autocorrelation (arb.)

Figure 6.22: Autocorrelation trace of the experimentally measured pulse (solid curve) compared with calculated autocorrelations of parabolic (dashes), Gaussian (dot- dashes) and hyperbolic secant (dots) fits to the simulated pulse of Fig. 6.20.

Chapter 6 Parabolic Evolution in Microstructured Fibre Raman Amplifiers

6.4.4 Future Directions

The results presented in this section have indicated that the main limiting fea- ture of this experiment is the very low coupling efficiency of the microstruc- tured fibre, which is due to the extremely small core size. Unfortunately, to date, investigations of the dispersion properties of various microstructured fi- bres have shown that in the wavelength range1.5µm−1.7µmnormal disper- sion is typically associated with small core structures [61]. In the interest of establishing the structural features that give rise to the dispersion, and also the nonlinearity, of a microstructured fibre, members of Dr T. Monro’s microstruc- tured fibre group are currently working to solve the inverse problem of calcu- lating possible fibre structures given a fixed dispersion profile. Thus it is hoped that in the near future we could exploit this technique to design fibres with dis- persion and nonlinear properties that are optimised to our specific needs. As well as the small coupling efficiencies, we also faced the additional problem that the signal source was passively mode locked so that this could not be synchronised exactly with the pump source. Thus in order to improve the efficiency of the measurements it would also be beneficial to design a signal source that could be triggered directly off our pump source, such as a Raman fibre laser [62], enabling single pulse measurements.

Finally, to make more rigorous comparisons between the experimental mea- surements and the parabolic theory it is important that our pulse diagnostic techniques are improved. Thus, to this end, we will need to develop a FROG setup (such as that described in Section 5.3.4) that operates at ∼ 1.62µm so that we can obtain a complete retrieval of both the intensity and phase of the field. Furthermore, it is hoped that a better understanding of the output pulse characteristics, and hence the precise effects of the dispersion and nonlinearity, will aid in the design process of the microstructured fibres.

Chapter 7

Self-Similar Solutions of the NLSE

with Distributed Coefficients

7.1 Introduction

The self-similar solutions discussed in the previous two chapters exist under the conditions of normal dispersion and gain. In this chapter a new class of solutions which exist for a much wider parameter range that extends to both signs of the dispersion parameter, and either gain or loss is investigated. These solutions have been found for a generalised form of the nonlinear Schr ¨odinger equation (NLSE) with distributed coefficients which vary longitudinally down the length of the fibre or fibre amplifier. It will be shown that this system permits a broad class of exact self-similar solutions and that these include a set of solitary wave solutions. In order to establish the robustness of these solutions to realistic experimental conditions, a numerical investigation into their stability is also presented.