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Beat length

Light in the fast and slow axes travels at slightly different speeds, and so when a laser source is interfered together in the fiber it will fall in and out of phase at regular intervals, the beat length, along the fiber. This gives visible bright and dark fringes that can be seen when illuminating a HiBi fiber with visible light, using for example a HeNe source.

Beat length is important because it is a fundamental measure of the polarization-preserving performance of an optical fiber. A fiber with a short beat length will preserve polarization more strongly than a fiber with a longer beat length. Beat-length is particularly useful because, unlike h-parameter (another commonly-used measure of polarization performance), it is independent of either length or the way in which the fiber has been deployed.  H-parameter will be reduced by high winding-tensions, small coil-diameters and multi-layered winds whereas beat length will remain constant. This independence means that beat length enables you to compare the performance of polarization-preserving fibers - the shorter the beat-length, the better it is.

 What is ‘Beat length’?

When light is launched into HiBi fiber with a linear component along each of the two birefringent axes, the slight difference in index between the fast and slow axes leads to different propagation velocities for the two components. Birefringence, B is simply the difference between these two indices.

This means the light on the two axes falls in and out of phase along the optical path and causes the resultant polarization to vary along the length of the fiber. The beat length (Lp) is the length over which a 2π phase retardation is introduced between the two components. Beat length is wavelength dependant and is related to birefringence, B, by the following equation:

This can lead to visible fringes along the fiber length where light on fast and slow axes interferes, and the beat length is the spacing of maxima in the interference pattern seen through the fiber – often a convenient technique for assessment of beat-length and birefringence. A greater birefringence in the fiber leads to a greater difference between the two velocities, and a shorter beat length.

How is beat length measured?

The beat-length of HiBi fiber can be measured at 633nm using a helium-neon laser.  Light is launched into the fiber with its polarization oriented at 45° to the birefringent axes; so that equal optical power is coupled into both axes. The birefringence changes the relative wavelength of the light slightly, and causes light on the fast and slow axis to beat together, falling in and out of phase along the fiber length. Rayleigh scattering (see ‘Attenuation’) within the fiber causes fringes or ‘beats’ to appear as alternating regions of light and dark - the bright regions occurring each time the fast and slow fall into phase.

 Typical beat lengths measured for HiBi fiber are 1mm - 2mm when assessed at 633nm. By comparison standard telecom fibers can have a beat length from a few meters to around a kilometer, though their fast and slow axes are the result of random perturbations in the waveguide and not well defined.

Another technique to measure beat length is shown schematically below. The key feature is that the principal birefringent axes of the fiber under test are spliced at 45° to the polarizers, so that light from a broadband source (BBS) is launched with equal intensity onto both axes. The spectral intensity is assessed with an optical spectrum analyser (OSA) to reveal a fringe pattern related to the birefringence

 Using a polarized source, formed from the back ASE of a long length of erbium doped fiber pumped at 980nm, the following spectrum is obtained. This shows the broadband interference pattern between fast and slow axes across the spectrum, with fringes as a function of wavelength superimposed on the source spectrum.

This technique requires careful selection of sources. The source must be broadband, over a wavelength range at which the fiber is single-mode. The in-line fiber polarizers must polarize at the operating wavelength band and the optical spectrum analyzer must also have reasonable dynamic range at the operating wavelength. The limitation caused by the availability of in-line polarizers outside the telecoms window and increased difficulty of obtaining super-fluorescent broadband sources in the visible region generally limit the use of this method to all but fibers with 1550nm operation.

 

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