Optical fibres pulse dispersion

A short pulse of light launched into a fibre will tend to spread out, as a result of dispersion. In optical fibres, the dispersion is defined as the delay between the arrival time of the start of a light pulse and its finish time relative to that of the initial pulse. It is measured at half peak amplitude. If the initial pulse has a spread of fj seconds at 50 % amplitude and the final pulse a spread of tf seconds at 50 % amplitode after having travelled d kilometres, the dispersion is given by ... 

A cracial part of optical tomography instruments are the fibres or fibre bundles used to transmit the light to the sample and back to the detectors. The problem of the fibres is mainly pulse dispersion. The pulse dispersion in multimode fibres increases with the numerical aperture (NA) at which they are used. In particular, the detection fibre bundles, which have to be used at high NA, can introduce an amount of pulse dispersion larger than the transit time spread of the detectors [326, 443]. If the length of the bundles exceeds 1 or 2 meters, a tradeoff between time resolution and NA must often be made. 

In practice, the only feasible solution is often to transfer the light to the poly-chromator slit plane by an optical fibre. The slit is removed, and the numerical aperture at the input of the fibre is reduced to match the numerical aperture of the polyehromator. Because only moderate wavelength resolution is required, a relatively thick fibre (up to 1 mm) can be used. Therefore a reasonably high coupling efficiency with a single fibre can be obtained, even for nondescanned detection systems. The fibre should be not longer than 50 cm to avoid broadening of the IRF by pulse dispersion. 

Due to their high throughput eapability, multimode fibres are frequently used to transmit light in optical systems for TCSPC. Figure 7.22 shows how NA and pulse dispersion can be traded against fibre diameter. 

Another point to be considered is the pulse width of the light source and the pulse dispersion in the optical system. Multimode fibres or fibre bundles used at high NA can easily add a few hundred ps to the IRF widths. It is, of course, not necessary to use a detector that has an IRF width shorter than 30-50% of the pulse dispersion of the optical system. 

Barrel , K. F and Pask, C. (1980) Pulse dispersion in optical fibres of arbitrary refractive-index profile. Appl. Opt., 19, 1298-1305. 

An important characteristic of solitons is their non-dispersive (shape-conserving) motion. Conventional wave packets will lose their shape because the Fourier components of the packet propagate at different velocities. In a non-linear medium the velocity depends not only on the frequency of a wave but also on its amplitude. In favourable circumstances the effect of the amplitude dependence can compensate that of the frequency dependence, resulting in a stable solitary wave. A technical application of this idea is the propagation of soliton-like pulses in fibre optics, which considerably increases the bit rate in data transmission. 

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