4. Experimental setup

In Figure 6, the experimental setup is showed. For the source of signal, a continuous wave distributed feedback semiconductor laser with a wavelength of 1550 nm was used. The continuous wave signal was gated and amplified by the erbium doped fiber amplifier (EDFA) from which you can get pulses with 1–10 ns duration and a maximum peak power of about 150 W. To assure the stable polarization state, the pulses from the EDFA pass through a polarization controller (PC) and a polarizer. With the rotation of quarter wave retarder (QWR1), we can change the polarization ellipticity to be able to control the input polarization on the fiber. The output of the fiber under the test (twisted fiber) is connected to a quarter wave retarder (QWR2) and polarization beam splitter (PBS). The QWR2 and PSB convert the right and left circularly polarized component at the output fiber to orthogonally polarized linear components at the output PBS. The output of PSB (linearly polarized component) is separated in time by a delay line (10 m of SMF-28 fiber), and they come together using a 50/50 coupler to launch the same monochromator input. The output pulses are detected and monitored by an oscilloscope. A typical

Figure 6. Experimental setup.

average polarization ellipticity of solitons is 0.02. The maximum ellipticity found

The number of solitons with different ellipticity generated by modulation instability at polarization of the input

0.82 is showed in Figure 4. From Figure 4, it can be observed that the average soliton polarization moves toward circular polarization. For the case when the polarization of the input pulse is close to the circular polarization, the dispersion of the polarization ellipticity of solitons becomes much less, see Figure 5. For Figure 5, the polarization ellipticity of the input pulse used was equal to 0.906 and 0.906. It

The number of solitons with different ellipticity generated by the effect of modulation instability at linear

Nonlinear Optics ‐ Novel Results in Theory and Applications

The distribution of polarization of solitons when the input pulse has ellipticity of

in this set of calculations was 0.3.

Figure 3.

Figure 4.

78

pulse of 0.82 and 0.82.

polarization of the input pulse.

Figure 7. A typical oscilloscope trace.

oscilloscope trace is shown in Figure 7. The first pulse is that traveling from a port 1 of the polarization beam splitter, and second pulse travels from a port 2 of the polarization beam splitter through the delay line (10 m of SMF-28 fiber). With this experimental setup, we can measure the amplitudes of left and right circularly polarized component at any wavelength using one single shot in the oscilloscope [17]. The ellipticity is calculated using the next equation:

$$\rho = \tan^{-1} \left( \frac{\sqrt{P\_+} - \sqrt{P\_-}}{\sqrt{P\_+} + \sqrt{P\_-}} \right) \tag{11}$$

the 65-m SMF-28 fiber. It can be observed that the dependence is the same as the

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber…

Next step was the measurements of the ellipticity at the fiber output at low power. These measurements show the effect of residual linear birefringence in the fiber. In Figure 9, we show the ellipticity at the output of the 218-m fiber without twist. As another example, Figure 10 shows the ellipticity at the output of the 218 m twisted fiber wounded on the cylinder with a diameter of 25 cm (squares); Figure 10 shows the ellipticity at the output of the same fiber however wounded on the cylinder with a diameter of 50 cm (circles). Figure 10 (for fiber wounded on the

dependence of the ellipticity on the QWR1 angle at the fiber input.

The ellipticity at the output of the 218-m fiber without twist.

Figure 8.

Figure 9.

81

Ellipticity at the QWR1 output measured by our setup.

DOI: http://dx.doi.org/10.5772/intechopen.81574

where P<sup>+</sup> and P� are the pulse amplitudes at the monochromator output. A disadvantage of this method is that we measure the average ellipticity of the bundle of solitons.

We used span of SMF-28 fiber with different lengths, twisted, and without twist. To calibrate the ellipticity measurement system, the ellipticity was measured at the polarizer output. The results of measurements are presented in Figure 8. The angle 0 on the position of the QWR1 corresponds to linearly polarized signal at the QWR1 output. Taken into account that the ellipticity of the signal at the QWR1 output is equal to the angle of the rotation of QWR1 in the range �45° + 45° [18]. The maximum ellipticity measured was 35°. At this ellipticity, 97% of the power is in one circularly polarized component and only 3% is in orthogonal component. In our setup, the measurement of the higher ellipticity is restricted by the possibility of the measurement of low power pulse. In the experiment, it was used 1-ns pump pulse with a maximum power of 150 W and a wavelength of 1550 nm. Linearly polarized pump pulses passed through QWR1. The angle of QWR1 defined the polarization state of the input pulse that is launched to the fiber. In the experiment, the span of SMF-28 fibers was used with lengths of 65 and 218 m. The fibers under the test were twisted with a twist of 6 turn/m and they were put on the cylinder with diameters of 25 and 50 cm. From the experimental results, it can be observed that both fibers conserved the polarization ellipticity along the fiber at low powers. Figure 8 shows the ellipticity of the low power continuous wave (CW) radiation at the output of

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber… DOI: http://dx.doi.org/10.5772/intechopen.81574

Figure 8. Ellipticity at the QWR1 output measured by our setup.

## Figure 9.

oscilloscope trace is shown in Figure 7. The first pulse is that traveling from a port 1 of the polarization beam splitter, and second pulse travels from a port 2 of the polarization beam splitter through the delay line (10 m of SMF-28 fiber). With this experimental setup, we can measure the amplitudes of left and right circularly polarized component at any wavelength using one single shot in the oscilloscope

> ffiffiffiffiffiffi Pþ <sup>p</sup> � ffiffiffiffiffiffi P� p

ffiffiffiffiffiffi Pþ <sup>p</sup> <sup>þ</sup> ffiffiffiffiffiffi P� p � �

We used span of SMF-28 fiber with different lengths, twisted, and without twist. To calibrate the ellipticity measurement system, the ellipticity was measured at the polarizer output. The results of measurements are presented in Figure 8. The angle 0 on the position of the QWR1 corresponds to linearly polarized signal at the QWR1 output. Taken into account that the ellipticity of the signal at the QWR1 output is equal to the angle of the rotation of QWR1 in the range �45° + 45° [18]. The maximum ellipticity measured was 35°. At this ellipticity, 97% of the power is in one circularly polarized component and only 3% is in orthogonal component. In our setup, the measurement of the higher ellipticity is restricted by the possibility of the measurement of low power pulse. In the experiment, it was used 1-ns pump pulse with a maximum power of 150 W and a wavelength of 1550 nm. Linearly polarized pump pulses passed through QWR1. The angle of QWR1 defined the polarization state of the input pulse that is launched to the fiber. In the experiment, the span of SMF-28 fibers was used with lengths of 65 and 218 m. The fibers under the test were twisted with a twist of 6 turn/m and they were put on the cylinder with diameters of 25 and 50 cm. From the experimental results, it can be observed that both fibers conserved the polarization ellipticity along the fiber at low powers. Figure 8 shows the ellipticity of the low power continuous wave (CW) radiation at the output of

where P<sup>+</sup> and P� are the pulse amplitudes at the monochromator output. A disadvantage of this method is that we measure the average ellipticity of the bundle

(11)

[17]. The ellipticity is calculated using the next equation:

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of solitons.

80

Figure 7.

A typical oscilloscope trace.

<sup>ρ</sup> <sup>¼</sup> tan �<sup>1</sup>

The ellipticity at the output of the 218-m fiber without twist.

the 65-m SMF-28 fiber. It can be observed that the dependence is the same as the dependence of the ellipticity on the QWR1 angle at the fiber input.

Next step was the measurements of the ellipticity at the fiber output at low power. These measurements show the effect of residual linear birefringence in the fiber. In Figure 9, we show the ellipticity at the output of the 218-m fiber without twist. As another example, Figure 10 shows the ellipticity at the output of the 218 m twisted fiber wounded on the cylinder with a diameter of 25 cm (squares); Figure 10 shows the ellipticity at the output of the same fiber however wounded on the cylinder with a diameter of 50 cm (circles). Figure 10 (for fiber wounded on the

Figure 10. The ellipticity at the output of the 218-m fiber: squares—on 25-cm cylinder and circles—on the 50-cm cylinder.

cylinder with a diameter of 50 cm) shows the ellipticity at the fiber output is the same as at the fiber input. It means that there is no effect of linear birefringence. However, for the 25-cm diameter cylinder, the effect of the linear birefringence can be clearly seen.

Figure 11.

Figure 12.

83

without twist on the 50 cm cylinder.

The ellipticity at the output of the 218-m fiber for 1560 nm: squares for the twisted fiber and circles for the fiber

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber…

DOI: http://dx.doi.org/10.5772/intechopen.81574

The process of the pulse breakup.

When the pulses with the power of 150 W were launched to the input fiber, the pulse breakup occurred followed by the soliton formation and soliton selffrequency shift; see Figure 11. The polarization ellipticity was measured at the output of the 218-m twisted fiber on the 50-cm cylinder and also at the output fiber with the same length but without twist. The measurements were done for high power wavelengths of 1560, 1570, and 1580 nm. The results for these wavelengths are presented in Figures 12–14, for 1560, 1570, and 1580 nm, respectively. For these results, it can be seen that solitons at the output of twisted fiber present a high grade of polarization at least when the input polarization has circular polarization, for the angle of QWR1 of about 50°. We can use Eq. (11) to calculate that about 90% of output power is in the same circular polarization as in the output and only about 10% in the orthogonal polarization. With this technique used, we can measure the averaged polarization, and so if measured ellipticity is close to 0, it does not imply that solitons have linear polarization, it just means that powers of all solitons in the selected spectral range in both circularly polarized components are equal. For the case of the fibers without twist, the polarization is chaotic. It can be seen that for the wavelengths of 1570 and 1580 nm, where the measured ellipticity is very close to 0 [17]. There are no physical reasons for the linear polarization at any input polarization; so we can think that the polarization ellipticity of solitons most probably is random.

The slope of the dependencies of the output ellipticity on the input at the input ellipticity equal to 0 is equal to 1.9 for wavelengths 1570 and 1580 nm and 0.9 for 1560 nm. The fact that the slope is higher than in 1570 and 1580 nm can show that the output ellipticity tends to be higher than the input ellipticity. The ellipticity of the highest soliton generated in the process of pulse breakup at different noise imposed on the pulse was also calculated. The equations and the procedure described before were used [7]. The equations are taken into account the difference of group velocity of orthogonal circularly polarized components and vectorial nature of the Raman

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber… DOI: http://dx.doi.org/10.5772/intechopen.81574

Figure 11. The process of the pulse breakup.

cylinder with a diameter of 50 cm) shows the ellipticity at the fiber output is the same as at the fiber input. It means that there is no effect of linear birefringence. However, for the 25-cm diameter cylinder, the effect of the linear birefringence can

The ellipticity at the output of the 218-m fiber: squares—on 25-cm cylinder and circles—on the 50-cm cylinder.

pulse breakup occurred followed by the soliton formation and soliton selffrequency shift; see Figure 11. The polarization ellipticity was measured at the output of the 218-m twisted fiber on the 50-cm cylinder and also at the output fiber with the same length but without twist. The measurements were done for high power wavelengths of 1560, 1570, and 1580 nm. The results for these wavelengths are presented in Figures 12–14, for 1560, 1570, and 1580 nm, respectively. For these results, it can be seen that solitons at the output of twisted fiber present a high grade of polarization at least when the input polarization has circular polarization, for the angle of QWR1 of about 50°. We can use Eq. (11) to calculate that about 90% of output power is in the same circular polarization as in the output and only about 10% in the orthogonal polarization. With this technique used, we can measure the averaged polarization, and so if measured ellipticity is close to 0, it does not imply that solitons have linear polarization, it just means that powers of all solitons in the selected spectral range in both circularly polarized components are equal. For the case of the fibers without twist, the polarization is chaotic. It can be seen that for the wavelengths of 1570 and 1580 nm, where the measured ellipticity is very close to 0 [17]. There are no physical reasons for the linear polarization at any input polarization; so we can think that the polarization ellipticity of solitons most probably is

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When the pulses with the power of 150 W were launched to the input fiber, the

The slope of the dependencies of the output ellipticity on the input at the input ellipticity equal to 0 is equal to 1.9 for wavelengths 1570 and 1580 nm and 0.9 for 1560 nm. The fact that the slope is higher than in 1570 and 1580 nm can show that the output ellipticity tends to be higher than the input ellipticity. The ellipticity of the highest soliton generated in the process of pulse breakup at different noise imposed on the pulse was also calculated. The equations and the procedure described before were used [7]. The equations are taken into account the difference of group velocity of orthogonal circularly polarized components and vectorial nature of the Raman

be clearly seen.

Figure 10.

random.

82

Figure 12.

The ellipticity at the output of the 218-m fiber for 1560 nm: squares for the twisted fiber and circles for the fiber without twist on the 50 cm cylinder.

Figure 13.

The ellipticity at the output of the 218-m fiber for 1570 nm: squares for the twisted fiber and circles for the fiber without twist on the 50 cm cylinder.

Figure 14.

The ellipticity at the output of the 218-m fiber for 1580 nm: squares for the twisted fiber and circles for the fiber without twist on the 50-cm cylinder.

average output ellipticity is equal to 0.54, and the case for input ellipticity is equal to

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber…

Numerical calculations were done for different input polarizations. The dependence of the average output soliton ellipticity on the input ellipticity is showed in Figure 16. The simulations corroborate the measured tendency of soliton to have the higher ellipticity than the input pulse. Simulations show that the fluctuations of the soliton polarization get to be smaller when the input polarization approaches to the circular. We also made calculations for β<sup>1</sup> = 0, that is, for ideal fiber without any

0.9, the average output ellipticity is equal to 0.95, see Figure 15 [18].

Figure 15.

Figure 16.

85

Statistics of the ellipticity of the highest soliton.

DOI: http://dx.doi.org/10.5772/intechopen.81574

Average output polarization vs. input polarization.

birefringence and found similar statistic for the polarization of solitons.

effect in the optical fiber. Like in Figure 15, we have examples of the 50 calculations with 30 ps input pulse with 40 W of power. For the numerical calculation, the following parameters were used: β<sup>1</sup> = 0.2 ps/km and β<sup>2</sup> = 25 ps2 /km. The input polarizations were equal to 0.4 (equal to 21.8°) and 0.9 (equal to 42°). As we can see in most of the realizations, the output ellipticity of the solitons was greater than the ellipticity of the input pulse. For the case when input ellipticity is equal to 0.4, the

Polarization Properties of the Solitons Generated in the Process of Pulse Breakup in Twisted Fiber… DOI: http://dx.doi.org/10.5772/intechopen.81574

Figure 15. Statistics of the ellipticity of the highest soliton.

Figure 16. Average output polarization vs. input polarization.

average output ellipticity is equal to 0.54, and the case for input ellipticity is equal to 0.9, the average output ellipticity is equal to 0.95, see Figure 15 [18].

Numerical calculations were done for different input polarizations. The dependence of the average output soliton ellipticity on the input ellipticity is showed in Figure 16. The simulations corroborate the measured tendency of soliton to have the higher ellipticity than the input pulse. Simulations show that the fluctuations of the soliton polarization get to be smaller when the input polarization approaches to the circular. We also made calculations for β<sup>1</sup> = 0, that is, for ideal fiber without any birefringence and found similar statistic for the polarization of solitons.

effect in the optical fiber. Like in Figure 15, we have examples of the 50 calculations with 30 ps input pulse with 40 W of power. For the numerical calculation, the

The ellipticity at the output of the 218-m fiber for 1580 nm: squares for the twisted fiber and circles for the fiber

The ellipticity at the output of the 218-m fiber for 1570 nm: squares for the twisted fiber and circles for the fiber

polarizations were equal to 0.4 (equal to 21.8°) and 0.9 (equal to 42°). As we can see in most of the realizations, the output ellipticity of the solitons was greater than the ellipticity of the input pulse. For the case when input ellipticity is equal to 0.4, the

/km. The input

following parameters were used: β<sup>1</sup> = 0.2 ps/km and β<sup>2</sup> = 25 ps2

Figure 13.

Figure 14.

84

without twist on the 50-cm cylinder.

without twist on the 50 cm cylinder.

Nonlinear Optics ‐ Novel Results in Theory and Applications
