Dispersion intermodal

Modal dispersion is generally a dominant factor in pulse broadening in MMFs, and in particular in SI MMFs. As shown in [4] for an ideal SI MMF, the difference in the propagation delay between the fastest and slowest modes is given by 

and thus an estimated electrical-to-electrical available bandwidth of B S 0.44/At (,j 30 MHz under worst case conditions. The actual bandwidth depends on several other parameters, related mainly to the NA of the source, the level of mode mixing inside the POF, and the fact that higher order modes (which travel more slowly) usually see higher attenuation and thus contribute less to the overall transfer function (see again [4]) than lower order modes. As a result, the actual available bandwidths for SI POFs are higher than those given by the theoretical treatment above, but are still limited to less than approximately 100 MHz over 50 m. 

However, the modal dispersion can be dramatically reduced by forming a near-parabolic refractive index profile in the core region of the MMF, which allows a much higher bandwidth (i.e., higher-speed data transmission) [5]. A typical graded-index (GI) MMF has a cylindrically symmetric refractive index profile that gradually decreases from the core axis to the core-cladding interface. 

The optimum profile exponent p, which minimizes the modal dispersion and the difference in the delay of all the modes and maximizes the bandwidth, is expressed as follows on the basis of an analysis of scalar wave equation  

If the refractive index of the material is wavelength-independent. Equation 3.6 becomes the simple expression 

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Multimode optical fibers, 11 131, 132 intermodal dispersion in, 11 134 Multimode stepped index optical fiber, 11 131, 132... 

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. 

From Figure 3 one may observe that the many modes in a multimode fiber travel different paths along the fiber axis. Lower order modes travel closer to the center, while higher order modes are further from it. This results in a path length difference between modes, which creates a time lag between them. This time lag causes different modes to arrive at the end of the fiber at different times, and is known as intermodal dispersion. By varying the index of the core as a function of radius, the effective differences in path length may be reduced. Typically, the core index profile is fabricated as... 

Intermodal dispersion in multimode fibers causes each mode to travel at a different speed due to different group delays, caused by different path lengths between modes. For step index multimode fibers, the maximum spread in delay time between the fastest and slowest modes Is given by... 

FIGURE 7.4 Intermodal dispersion in a step index multimode fiber. 

FIGURE 7.5 Intermodal dispersion in an optimally graded index profile. 

Proper index profiling of the core significantly reduces the intermodal dispersion. Such profiles, termed graded-indexprofiles, as shown in Fig. 7.5, have been developed for this purpose. These graded-index profiles can be expressed as follows ... 

In Chapters 1 and 2 we introduced the notion of ray transit time. The main contribution to pulse spreading is due to the obvious fact that the ray transit time is different for different ray paths. This effect is known as ray dispersion, and is sometimes referred to as intermodal dispersion, since early investigation used electromagnetic analysis in terms of modes [1], rather than ray theory. In addition to ray dispersion, material dispersion also affects pulse spreading. This effect arises because the materials constituting the fiber have a refractive index which varies with the wavelength of light. 

Consider a pulse within which only the two fundamental modes are excited. Waveguide dispersion describes the spread in each mode, but because of elUpticity the spread for each polarization is different. In addition, the sUght difference dpj —SPy between corrected propagation constants implies the respective group velocities are unequal and consequently there will be intermodal dispersion between the two modes. Intermodal dispersion which relies on polarization difference is often referred to as a birefringence effect. 

Intermodal dispersion can be expressed in terms of the difference between the transit time t and ty of the two modes over length z of fiber. Substituting Eqs. (16-2) and (16-7) into Eq. (11-36) gives for slight eccentricity... 

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