This chapter is devoted to the study of dispersive effects that affect short pulses inside a graded-index fiber. An equation governing the evolution of optical pulses inside a GRIN medium is found in Section 4.1. The dispersion parameters appearing in this equation change, depending on which mode is being considered. Section 4.2 focuses on the distortion of optical pulses resulting from differential group delay and group velocity dispersion. Section 4.3 deals with the effects of linear coupling among the modes, occurring because of random variations in the core’s shape and size along a fiber’s length. A non-modal approach is developed in Section 4.4 for the propagation of short optical pulses inside a GRIN medium. The focus of Section 4.5 is on the applications where optical pulses are sent through a GRIN rod or fiber

The geomagnetic field supports a wide range of magnitudes, spatial scales and temporal variations. Outlined here are particular recent advances in temporal variability, stretching from geomagnetic field polarity reversals over millions of years, through secular field variations and ultra-low frequency (ULF) waves (1mHz – 5Hz), to very low frequency(VLF) emissions with frequencies in the kHz range. Long-term variations are discussed with respect to paleomagnetic, geological and archaeological records. Both external and internal fields contribute to temporal variations on decadal to daily time scales. More rapid oscillations at ULF wave frequencies associated with Sun-Earth connection contribute to weather in space. These involve the magnetosphere, ionosphere and atmosphere system, and may affect charged/neutral particle populations. Waves are generated external and internal to the magnetosphere and through integration of global magneto-hydrodynamic or local magneto-ionic modelling with satellite and ground observations, progress has been made in understanding the dynamics of waves and energy transfer within the coupled system. Equally important to space weather is the understanding of ULF and VLF waves on energetic charged particles in the Van Allen radiation belts during geomagnetic storms.