In contrast with planar waveguides which can be made quite birefringent, polarization mode coupling effects can be severe in circular optical fibers as the two linearly polarized components are degenerate. In practice this degeneracy may be broken by imperfections in manufacturing process or from mechanical stress. However the birefringence from this source is not large enough to prevent the polarization mode coupling. More birefringence is necessary to reduce such mode coupling and generally a rather short polarization beat length in the centimeter or millimeter range is required. This can only be obtained by reengineering the fiber to introduce significant birefringence. Typically, the polarization beat length is defined as [169]:
(4.1)
One of the most straightforward ways of creating birefringence in a step- index chalcogenide fiber is via form birefringence, i.e. make the fiber core asymmetric [170]. A rectangular fiber design was developed with the compositions being the same as the all-arsenic fiber discussed in Section 4.3.1 but with a ratio between the long and short axes being ~2:1. The fiber was made by extrusion and special care was taken not to twist the fiber during drawing. For a 5.86 µm by 2.78 µm fiber of this kind, the calculated dispersion profiles for the two orthogonal modes are shown in Fig. 4.18. The first ZDW at the fast axis condition was shifted to 3.8 μm and the ZDW at the slow axis was calculated to be 4.25 μm. The calculated polarization beat length for this fiber at 4 μm is ~0.7 mm, which means high birefringence is realized.
2 . B eff L n 2 3 4 5 6 7 8 9 10 -60 -40 -20 0 Wavelength (m) D is p e rs io n p a ra m e te r (p s /( k m *n m )) TE0 mode TM0 mode
Chapter 4 MIR SC Generation in Chalcogenide Optical Fibers 91
Fig. 4.18: Calculated dispersion parameter for the 5.86 µm by 2.78 µm Ge-As-Se/Ge-As-S fiber. TE0: fast axis, TM0: slow axis.
The SC spectra generated when pumping along the fast axis with 4 μm, 330 fs pulses are shown in Fig. 4.19. Obvious dispersive waves in the normal dispersion regimes clearly show the dominance of soliton-related dynamics. At an input average power of 100 mW, the output power of a 14 cm rectangular fiber after the NA=0.56 lens was around 6 mW. The measured average PER was around 9.1 dB which meant that this fiber reduced the polarization mode coupling effect to some extent although higher PER would be still an advantage.
Fig. 4.19: Experimental SC spectra as a function of coupled peak power from the 14 cm long 5.86 µm by 2.78 µm rectangular Ge-As-Se/Ge-As-S fiber when pumping at 4 μm. The curves are offset
by 10 dB relative to each other for clarity.
4.4 Summary
This Chapter focused on MIR SC generation in chalcogenide fibers. Benefitting from the longer integration lengths and lower spectral losses, the generated SC extends more than two octaves if the chalcogenide material is carefully chosen and the dispersion is well engineered in the case of custom fibers. For instance, the selenide core, sulphide cladding step-index fiber managed to deliver SC from 1.8 μm to 10 μm, with the long end extension limited by the cladding material absorption. Also, to solve this problem, two types of all-selenide-based step- index fibers have been designed to overcome the material absorption from the sulphide cladding. In the Ge-Sb-Se/Ge-As-Se2 case, the first ZDW was 5.4 µm for a fiber with a radius of 3.75 µm. By pumping in the normal dispersion regime at 4.586 µm with 330 fs, 21MHz pulses from the OPA system, a SC spectrum
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spanning from 3 µm to 12 µm within a dynamic range of ±15 dB with an average power of 9 mW after the NA=0.56 output lens was generated. In the Ge-Sb-Se/Ge- Se case, benefited from more index contrast between the core and the cladding, the first ZDW was shifted to around 4.2 µm. By pumping an 11 cm long fiber with a radius of 3 µm at 4.485 µm in the anomalous dispersion regime, a flat SC spectrum has been obtained from 2.2 µm to 12 µm with the ±5 dB spectrum spanning from 2.5 µm to 9.5 µm. The output average power for an input of 132 mW was 17 mW after the NA=0.56 output lens. Simulations showed good agreement with the experimental results.
This multi-octave spanning flat SC source promises to be a useful tool for MIR spectroscopy. However, due to the fact that the two polarization states in a circular fiber are degenerate, polarization mode coupling is almost inevitable thus the effective power coupled into one of the axis was low and the spectrum was not stable. To solve this problem, rectangular fibers with large axis ratio have been designed and tested and these showed a significant improvement in terms of the polarization.
A significant difficulty with all these dispersion engineered fibers is that they are multimode at shorter wavelengths due to the relative large index contrast between the core and cladding. As a consequence the power can couple into multiple transverse modes reducing the brightness of the source. To solve these issues a different approach is required. In the next Chapter we show that chalcogenide planar waveguides can support single mode operation of the full SC spectrum and also produce a single polarization state.