Derivation of an Analytical Expression for the Power Coupling Coefficient for Offset Launch Into Multimode Fiber

The demand for higher bandwidth in local area networks (LANs) has fuelled considerable research in techniques for mitigating modal dispersion in multimode fiber (MMF). These techniques include selective mode excitation, offset launching, angular multiplexing and electronic dispersion compensation, all of which strive to optimize the channel impulse response of a MMF. To obtain the optimal bandwidth-enhancement results from these techniques, knowledge of the distribution of power coupling coefficients given an arbitrary offset launch in a MMF is important. In this paper, an analytical expression for the power coupling coefficient for an incident Gaussian beam launched with a radial offset into a MMF having an infinite parabolic refractive index profile is derived. This expression is useful in understanding the parameters which may affect the power coupling coefficient and how they may enhance the MMF bandwidth. The power coupling coefficients obtained from the derived analytical expression are compared with numerical results and are in excellent agreement. The analytical expression may be extended to manufactured MMF.