Dispersion (optics)

Introduction

Dispersion in optics refers to the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency. Media having this common property may be termed "dispersive media". Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion (GVD) to emphasize the role of the group velocity.

A prism under white light, showing the dispersion of light into its constituent colors.

Physical Explanation

Dispersion is caused by the variation of the speed of light with wavelength. Light moves slower in a denser medium, and the speed can vary with the wavelength of the light. This variation of speed with wavelength leads to the phenomenon of dispersion.

Mathematical Description

The mathematical description of dispersion involves the phase velocity v of the wave, which is related to the wave's wavelength λ and its frequency f by the equation v = λf. In a dispersive medium, the phase velocity itself varies with the wavelength, leading to a variation in the index of refraction n with wavelength. This variation is described by the dispersion relation, which can be written in the form n = c/v, where c is the speed of light in vacuum.

Types of Dispersion

There are several types of dispersion, including normal dispersion, anomalous dispersion, and zero-dispersion.

Normal Dispersion

In normal dispersion, the index of refraction increases with increasing wavelength. This is the usual type of dispersion encountered in optical materials.

Anomalous Dispersion

In anomalous dispersion, the index of refraction decreases with increasing wavelength. This type of dispersion is observed in certain circumstances, such as in the vicinity of an absorption line.

Zero-Dispersion

In zero-dispersion, the index of refraction is independent of the wavelength. This situation can occur at a particular wavelength known as the zero-dispersion wavelength.

Dispersion in Optical Fibers

Dispersion is a crucial factor in the operation of optical fibers, which are used for data transmission. The dispersion of the optical fiber can affect the quality of the data transmission, causing a broadening of the pulse as it travels along the fiber.

Dispersion Compensation

Various techniques can be used to compensate for the effects of dispersion, such as the use of dispersion-compensating fibers, the use of chirped gratings, and the use of electronic equalization techniques.