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Differential Mode Delay

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

The group velocities of different modes in a multimode fiber are generally different, resulting in mode-dependent group delays for a given length of fiber. This phenomenon of intermodal dispersion is generally a limiting factor for the achievable transmission bandwidth (data rate) in optical fiber communications as far as multimode fibers are used.

For quantifying intermodal dispersion in telecom fibers, one usually specifies the differential mode delay (sometimes also called differential modal delay or differential group delay). This is often essentially understood as the difference between the maximum and minimum time delay (group delay) of a short signal pulse within a certain length of the fiber under test. It must be measured under carefully standardized conditions, e.g. using bandwidth-limited ultrashort pulses with a certain pulse duration well below the DMD result. The pulses should be in a diffraction-limited beam at a certain optical center wavelength, and the time delay should be measured for a range of radial positions of the input beam across the fiber core. Special DMD analyzer tools have been developed for such measurements.

In some cases, the difference in mode delays between two particular modes is considered. In such cases, positive and negative results are possible; indeed, one can design fibers where e.g. the LP₁₁ mode is a higher or lower group velocity than the LP₀₁ mode, or that difference may even change sign due to uncontrolled variations of fiber parameters in the fiber fabrication.

For constant fiber properties along the whole length, the total difference in group delays is proportional to the fiber length. Therefore, the differential mode delay is often specified in picoseconds per kilometer (ps/km), for example. Its value can substantially depend on the optical wavelength.

Graded-index fibers can be optimized for a small differential mode delay, which however is usually achieved only within a quite limited wavelength range. This limits the application of wavelength division multiplexing. There are special wideband multimode fibers, however, where a low differential mode delay is achieved over a larger wavelength range with the width of e.g. 100 nm.

Case Studies

Case Study: Telecom Fiber With Parabolic Index Profile

We investigate how intermodal dispersion of a multimode fiber can be minimized with a parabolic doping profile.

Typical differential group delays of few-mode fibers with step-index profile are of the order of several picoseconds per meter (ps/m), while graded-index fibers can be made with differential group delays far below 1 ps/m, in some cases even well below 0.1 ps/m = 100 ps/km.

A minimized differential mode delay is not ideal for all applications. For example, intermodal nonlinear effects such as cross-phase modulation can be more strongly disturbing in fiber-optic telecom systems based on fibers with low differential mode delay. In some cases, one uses sequences of fibers having opposite signs of differential mode delay, so that the local DMD is relatively large, and nevertheless the total difference in group delay is over long transmission line are relatively small.

More to Learn

Case studies:

• Case Study: Telecom Fiber With Parabolic Index Profile

Encyclopedia articles:

• intermodal dispersion
• group velocity
• group delay
• multimode fibers
• few-mode fibers

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