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For numerical simulations, an Nd3+-doped aluminosilicate fibre is assumed. The Nd3+ ion concentration is assumed to be 1.654×1019 ions/cm3, which is similar to the fibre F432-LF197. The fibre design in section 6.1.1 is used with a 2 µm inner radius of the doped ring. The cladding size is assumed to be 125 µm and the fibre length is 15 m. The launched pump power is assumed to be up to 20 W at 808 nm. The emission and absorption cross-sections and wavelength-dependent propagation loss of the F432- LF197 Nd3+-doped aluminosilicate fibre, detailed in the previous section, are used. The details of the numerical simulator are described in appendix A. In order to consider the effect of ESA, a wavelength dependent gain will be used. For the effect of the OH– ion absorption, a comparison between the cases with and without considering the OH– ion absorption will be presented. The effect of the amplified spontaneous emission at 1.06 µm is investigated by varying the inner radius of the

Figure 6.13. Configuration assumed for the numerical simulation of an NDFA operating at 1.38 µm. Tunable laser @ 1.38 µm Isolator Dichroic Pump @ 808 nm Nd-doped fibre OSA Power meter Signal Lens Tunable laser @ 1.38 µm Isolator Dichroic Pump @ 808 nm Nd-doped fibre OSA Power meter Signal Lens

Advanced waveguides for high power optical fibre sources D. B. S. Soh

Nd3+-doped ring.

The configuration adopted for the simulations is shown in figure 6.13. The Nd3+- doped fibre is cladding-pumped by a diode laser at 808 nm from one end of the fibre. The seed signal is launched from the other end. A dichroic mirror at the pump launch end transmits the pump wavelength and reflects the signal from 850 nm to 1500 nm. A tuneable single-mode laser is assumed for the seed source. The amplified signal is reflected from the dichroic mirror. The fibre end at the pump launching end is assumed to be angle-cleaved in order to prevent back-reflection of the signal.

Figure 6.14 shows a typical spectrum of the output signal from the amplifier. Thanks to the fibre waveguide design, the competing emissions at 0.92 µm and 1.06 µm are well suppressed. For this simulation, a fibre length of 15 m was used, coiled with a sufficiently large coiling diameter so that the wavelength dependent bending loss was negligible (especially compared to the OH- ion loss). The launched pump power is 10 W of which 6.7 W is absorbed. The seed signal is assumed to be monochromatic at 1380 nm with a power of 100 mW launched into the core. For a realistic simulation, a white noise is inserted to the seed signal with the power level of

Figure 6.14. A typical spectrum of the output signal (blue solid) from the amplifier. For comparison, the spectrum of the input signal is also shown (red solid). Results of simulations.

Advanced waveguides for high power optical fibre sources D. B. S. Soh

–75 dBm. The output signal power becomes 2.6 W according to the simulations, for a net gain of 14.1 dB. This is difficult to obtain from a step-index conventional neodymium-doped fibre amplifier.

Figure 6.15 shows the amplifier gain for different wavelengths. The circled data points indicate the amplifier gain when a monochromatic seed signal is launched at the specific wavelength. For this simulation, the pump launched power is assumed to be 20 W. The seed signal power is 10 mW for all wavelengths. As is expected from figure 6.10 (the cross-sections), the amplifier shows positive net gain from ~ 1340 nm. In the case of (excess) absorption caused by the presence of OH–-ions, the maximum gain is 26.9 dB at 1410 nm, resulting in the output signal power of 4.86 W. When the OH–-absorption is neglected, the maximum gain is 28.2 dB at 1385 nm, resulting in an output signal power of 6.4 W. The total background loss at 1385 nm is 4.5 dB induced by the OH- ion absorption. The difference of the amplifier gain at 1385 nm between the case with and without the OH–-absorption is only 2.2 dB, due to the

Figure 6.15. The amplifier gain vs. wavelength for a 1.3 – 1.4 µm NDFA. Blue square-marked (red circle-marked) line represents the amplifier gain for 10 mW input signal without (with) OH- ion absorption, respectively. Results of simulations.

Advanced waveguides for high power optical fibre sources D. B. S. Soh

amplifier gain saturation by the signal power. However, in the small signal regime, the difference approaches 4.5 dB.

Figure 6.16 shows the output power of the signal and amplifier gain with different pump powers. For this calculation, a seed signal with 100 mW power at 1385 nm is assumed. When fully pumped (20 W), the amplifier gain is 16.8 dB. Since there seems to be no sign of roll over in the signal output power, the figure implies that a still higher signal output power may be obtainable if more pump power is launched. The lack of roll-over is indeed what is expected with the used model.

Figure 6.17 shows the effect of the inner radius of the doped ring, i.e., d₁. For this calculation, a 10 mW input signal power was used for 1360 nm and 1385 nm seed signals. The pump power is 20 W. The variation of gain with d₁ depends on the wavelength of the signal. For short wavelengths ( ~ 1360 nm) where the effective emission cross-section at short wavelengths is small and, hence the gain is small, d₁

plays a significant role. If d₁ becomes small, the overlap factor of the shorter Figure 6.16. Signal output power vs. pump power. The blue line with squares (red line with circles) represents the signal output power (the amplifier gain). The wavelength of the seed signal is 1385 nm with 100 mW input power. Results of simulations.

Advanced waveguides for high power optical fibre sources D. B. S. Soh

wavelength increases and, as a consequence, a large amount of amplified spontaneous emission at 1.06 µm may build up. This strong amplified spontaneous emission at 1.06 µm saturates the amplifier so that the gain at longer wavelengths reduces. However, when the signal power at longer wavelength is high due to either large gain of the amplifier or large seed power, the amplified spontaneous emission build-up at 1.06 µm is less efficient since the number of excited Nd3+-ions can be smaller. But, still if d₁ becomes less than 0.7 µm, even strong signal power at longer wavelength does not prevent the build-up of the amplified spontaneous emission at 1.06 µm, and hence, the gain becomes significantly reduced. The maximum gain depends on the signal wavelength (and the seed signal power) as well. For instance, the maximum gain for 1360 nm can be achieved when d₁ is 1.8 µm while that for 1385 nm requires

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d to be 1.2 µm, both for 10 mW seed signal. It is noteworthy here that going to longer wavelengths with lower cross-sections will clearly degrade performance

Figure 6.17. The effect of the inner radius of doped ring. The upper and the lower curves represent the gain of a NDFA for the input signal at 1385 nm and 1360 nm, respectively with OH- ion absorption. Results of simulations.

Advanced waveguides for high power optical fibre sources D. B. S. Soh

requiring higher Nd3+ ion excitation. Therefore, for longer wavelength operation, the fibre design becomes more critical.