# Electromagnetic Oscillation

## Electromagnetic Oscillation

a coupled oscillation of the electric field **E** and the magnetic field **H** that constitute a single electromagnetic field. Electromagnetic oscillations propagate as electromagnetic waves, whose velocity in a vacuum is equal to the speed of light *c;* the relation between wavelength λ and period *T* and frequency ω is given by the equation λ = *cT* = 2π*c*/ω. By nature, an electromagnetic oscillation is an ensemble of photons. Only when the number of photons is large may such oscillations be considered a continuous process.

A distinction is made between forced electromagnetic oscillations, which are maintained by external sources, and free oscillations, which exist in the absence of such sources. Free electromagnetic oscillations with a continuous frequency spectrum are possible either in free space or in lossy, or dissipative, systems. Spatially bounded conservative systems, which are lossless, have a discrete spectrum of natural frequencies; one or more independent oscillations, or modes, correspond to each natural frequency. For example, between two reflecting surfaces separated by a distance *I*, only sinusoidal electromagnetic oscillations with frequencies ω_{n} = *n*π*c*/*l*, where *n* is an integer, are possible. The normal modes have the form of sinusoidal standing waves in which the oscillations of the vectors **E** and **H** are out of phase by λ/4 and the spatial distributions of the oscillation amplitudes are out of phase by λ/4, so that the maximums, or antinodes, of E coincide with the zeros, or nodes, of **H** and vice versa. In such electromagnetic oscillations, energy is not, on the average, transported in space. However, within each quarter-wave length between field nodes, electric energy is periodically converted into magnetic energy and—independently—magnetic energy is periodically converted into electric energy.

Electromagnetic oscillations may be represented as a superposition of modes with a discrete or continuous spectrum for any integrated system of conductors and dielectrics (*see*WAVE GUIDE, CAVITY RESONATOR, and OPEN RESONATOR) if the fields, currents, and charges in the conductors and dielectrics are linearly related. In quasi-stationary systems, the dimensions of which are considerably smaller than the wavelength, regions where electric or magnetic fields predominate may be spatially separated and lumped in different elements; **E** is lumped in capacitances *C*, and **H** is lumped in inductances *L*. A typical example of such a system with lumped parameters is an oscillatory circuit, in which charges oscillate on capacitor plates and currents oscillate in self-induction coils. Electromagnetic oscillations in systems that have distributed parameters *L* and *C* and a discrete spectrum of natural frequencies may be represented as electromagnetic oscillations in coupled oscillators; the number of oscillators is equal to the number of modes.

In media, electromagnetic oscillations interact with free and bound charged particles—that is, with electrons or ions—to produce induced currents. Conduction currents result in energy losses and the damping of electromagnetic oscillations. Currents that are due to the polarization and magnetization of a medium determine the values of the medium’s dielectric constant and permeability, as well as the velocity of electromagnetic-wave propagation in the medium and the natural frequency spectrum of the electromagnetic oscillations. If the induced currents are nonlinearly dependent on **E** and **H**, the period, shape, and other characteristics of the electromagnetic oscillations depend on the amplitudes of the oscillations (*see*NONLINEAR SYSTEMS). In this case, the superposition principle is invalid, and the energy of the electromagnetic oscillations may be transferred from some frequencies to others. Such nonlinearity is the basis of the operating principles of most electromagnetic oscillators, amplifiers, and frequency converters (*see*GENERATION OF ELECTRICAL OSCILLATIONS and SELF-OSCILLATIONS).

As a rule, electromagnetic oscillations are generated in devices with lumped parameters by means of the direct connection oscillators to the devices. In high-frequency devices with distributed parameters, they are generated by using various coupling elements, such as dipoles, coupling loops, coils, or apertures. In optical devices, they are generated by using, for example, lenses, prisms, or semitransparent mirrors.

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Purcell, E.

*Elektrichestvo i magnetizm*, 2nd ed. (

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Crawford, F.

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M. A. MILLER and L. A. OSTROVSKII