A vector wave analysis is presented of a multimode optical fiber with an <i>a</i>-power law index profile that includes an additional fourth-order term. By optimizing <i>a</i> and the coefficient of the fourth-order term, the ultimate limit of the width of the impulse response is derived. The effect of the second-order material dispersion of the refractive index is completely compensated by the fourth-order term in the index distribution. As a result, the rms width of the impulse response is reduced to 20 ps/km, one-fifth of the value achievable with the ordinary <i>a</i>-power distribution, even if all modes carry equal power and there is no mode coupling. For a fiber whose normalized frequency is less than 40, the ultimate width of the impulse response is determined by the term with the gradient of the square of the index or ▽<i>n</i><sup>2</sup> in the wave equation.
© 1978 Optical Society of America
Shigeta Ishikawa, Kazuhito Furuya, and Yasuharu Suematsu, "Vector wave analysis of broadband multimode optical fibers with optimum refractive index distribution," J. Opt. Soc. Am. 68, 577-583 (1978)