Higher-order Dispersion Over Broad Bandwidths
When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate the dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading.
In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion. These terms are simply a Taylor series expansion of the dispersion relation of the medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations, by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation.
Read more about this topic: Dispersion (optics)
Famous quotes containing the words dispersion and/or broad:
“The slogan offers a counterweight to the general dispersion of thought by holding it fast to a single, utterly succinct and unforgettable expression, one which usually inspires men to immediate action. It abolishes reflection: the slogan does not argue, it asserts and commands.”
—Johan Huizinga (1872–1945)
“I hardly know an intellectual man, even, who is so broad and truly liberal that you can think aloud in his society. Most with whom you endeavor to talk soon come to a stand against some institution in which they appear to hold stock,—that is, some particular, not universal, way of viewing things. They will continually thrust their own low roof, with its narrow skylight, between you and the sky, when it is the unobstructed heavens you would view.”
—Henry David Thoreau (1817–1862)