Modal dispersion

This spread in velocity is called modal dispersion and is the principle limit to the use of multimode fibres for long-distance transmissive applications. 

As described above for small a and NA, a fibre is single mode if U < 2.405. Here only one mode, with one group velocity, is possible. This lack of modal dispersion is why single-mode fibre dominates transport media in long-haul communication systems. 

Modal Dispersion—Pulse spreading due to multiple light rays traveling different distances and speeds through an optical fiber. 

Fig. 2. Typical guided wave modal dispersion in the effective index Neg versus film thickness for a slab waveguide with nc

Fig.4. Schematic representation of the different common phase-matching techniques in the k space representation. (ADM) anomalous dispersion (WBM) waveguide birefringence (MD) modal dispersion (QPM) quasi-phase-matching (C) Cerenkov and (CP) counter propagating Cerenkov...

Fig. 5. Effective index of the TMO and TM, modes at both the fundamental and harmonic frequencies versus film thickness for a slab waveguide. MD identifies modal dispersion wavevector matching for TM0(ft>)—>TM1(2ft)). The solid vertical arrow identifies QPM for TM0(a>)—>TM0(2a>). The region C—> identifies film thicknesses for which Cerenkov SHG...

Fig. 8. An approach to increasing the overlap integral via modal dispersion phase-matching. The sign of the nonlinearity d(y) is reversed at the same point as the TM1(2co) field. The solid lines show the nonlinearity for TM0(a>)— TM ft)).

Fig. 12. SHG figure of merit r reported in poled-polymer devices using quasi-phase matching (QPM) and modal dispersion phase matching (MDPM)...

Even with completely monochromatic light, pulse spreading can still occur, because the radiation can take various paths, or modes, through the fibre, as sketched in Figure 14.31. It is apparent that a ray that travels along the axis of a fibre will travel less than one that is continually reflected on its journey. [In fact, the dispersion that results cannot be properly understood in terms of the transmission of light rays, and the various modes are better described in terms of the allowed wave patterns that can travel down the fibre.] The resultant pulse broadening, due to the various modes present, is called modal (or intermodal) dispersion. In order to overcome modal dispersion a number of different fibre types have evolved. 

For best results, monomode fibres (Figure 14.32c) are now used. The number of possible modes is reduced by decreasing the diameter of the core. When the core diameter reaches 10 pm or less only one mode can propagate and, in principle, modal dispersion is zero for these fibres. Monomode fibres have a high performance but are harder to make and join. 

The optimum refractive-index distribution of the high bandwidth graded-index polymer optical fiber (GI POP) was clarified by consideration of both modal and material dispersions. The ultimate bandwidth achieved by the POP is investigated by a quantitative estimation of the material dispersion as well as the modal dispersion. 

Since all commercially available POF have been of the step-index (SI) type, the modal dispersion limits the possible bit rate of POF links to less than 100 megabit per second (Mb/s). Because of this, it has been thought that POF cannot be utilized for high speed transmission medium. Recently, however, we proposed a large core, low loss, and high bandwidth graded-index polymer optical fiber (GI POF) (7,2) for the first time and we confirmed that 2.5 Gb/s signal transmission for 100 m distance was possible in the GI POF (2,5). 

It is well known that the dispersion in the optical fibers is divided into three parts, modal dispersion, material dispersion, and waveguide dispersion. In the case of the SI POF, the modal dispersion is so large that the other two dispersions can be approximated to be almost zero. However, the quadratic refractive-index distribution in the GI POF can dramatically decrease the modal dispersion. We have succeeded in controlling the refractive-index profile of the GI POF to be almost a quadratic distribution by the interfacial-gel polymerization technique (2). Therefore, in order to analyze the ultimate bandwidth characteristics of the GI POF in this paper the optimum refractive index profile is investigated by taking into account not only the modal dispersion but also the material dispersion. 

Refractive-Index Profile. The refractive-index profile was approximated by the conventional power law. The output pulse width from the GI POF was calculated by the Wentzel-Kramers-Brillouin (WKB) method (10) in which both modal and material dispersions were taken into account as shown in Equations (3), (4), and (5). Here, aintemodai cTintramodai, and CTtotai signify the root mean square pulse width due to the modal dispersion, intramodal (material) dispersion, and both dispersions, respectively. 

Figure 4. Pulse width (ototai) versus index exponent of PHFIP 2-FA-base GI POF assuming equal power in all modes and light source having rms spectral width of 2 nm. (A) Only modal dispersion is considered at 780-nm wavelength.

Single-mode fibers are used to reduce the number of modes traveling down a fiber and therefore reduce modal dispersion. A single-mode fiber is basically a step index fiber with a very small core... 

---