light waves
Fig. 1. A varying magnetic field causes an electric field. The image shows a rising magnetic field and the corresponding electric field. (© chh)
Charges at rest produce an electric field constant in time just as a stationary current produces a static magnetic field
. In both cases the spatial distribution of charge is constant in time. If the charge distribution varies, it induces temporally-varying fields. But can these dynamic fields carry away energy and propagate as waves? They can, thanks to the fact that not only charge can produce fields, but also temporally-varying fields. Electric field changing in time generates a magnetic field and vice versa, hence the two types of fields can build up each other and carry energy away from the temporally-varying charge distribution that is often localized to a small volume in space in form of an electromagnetic wave.
. In both cases the spatial distribution of charge is constant in time. If the charge distribution varies, it induces temporally-varying fields. But can these dynamic fields carry away energy and propagate as waves? They can, thanks to the fact that not only charge can produce fields, but also temporally-varying fields. Electric field changing in time generates a magnetic field and vice versa, hence the two types of fields can build up each other and carry energy away from the temporally-varying charge distribution that is often localized to a small volume in space in form of an electromagnetic wave.
Fig. 2. A varying electric field produces a magnetic field. In this picture the electric field is about to rise. (© chh)
Just as the oscillating macroscopic current in the antenna of a mobile phone network induces electric and magnetic fields, which continue producing each other and propagate away as electromagnetic waves at microwave frequencies, the much faster oscillating electron “cloud” in an atomic “antenna”, produces fields carrying away energy as electromagnetic waves at light frequencies. It is apparent that the emitted photon carries signatures of these field oscillations, otherwise their “cloning” via stimulated emission weren’t possible. Nevertheless, the fields of a single photon can’t be measured. Only when many coherently-emitted photons merge to a strong light wave, do the light fields become, in principle, measurable, by measuring the forces that the electric and magnetic field of the wave exert on a charged particle. To resolve the hyperfast variation of the fields, this probe charge must be put in place within a fraction of one half wave oscillation period, i.e. within less than one femtosecond.
Such a probe remained out of reach for more than hundred years after the discovery of the electromagnetic nature of light. Attosecond metrology has put an end to this unsatisfactory state of affairs.
, produces fields carrying away energy as electromagnetic waves at light frequencies. It is apparent that the emitted photon carries signatures of these field oscillations, otherwise their “cloning” via stimulated emission weren’t possible. Nevertheless, the fields of a single photon can’t be measured. Only when many coherently-emitted photons merge to a strong light wave, do the light fields become, in principle, measurable, by measuring the forces that the electric and magnetic field of the wave exert on a charged particle. To resolve the hyperfast variation of the fields, this probe charge must be put in place within a fraction of one half wave oscillation period, i.e. within less than one femtosecond.
Such a probe remained out of reach for more than hundred years after the discovery of the electromagnetic nature of light. Attosecond metrology has put an end to this unsatisfactory state of affairs.further reading
- Michael Faraday established the basis for the electromagnetic field concept in physics. He discovered electromagnetic induction, diamagnetism, and laws of electrolysis.
- James Clerk Maxwell was a Scottish theoretical physicist and mathematician. His most significant achievement was the development of the classical electromagnetic theory.
- The German physicist Heinrich Rudolf Hertz clarified and expanded the electromagnetic theory of light.
The experiments of Michael Faraday (1791-1867) revealed that a temporally-varying magnetic field induces an electric field around it, see Fig. 1. In a similar way, a temporally-varying electric field induces a magnetic field around itself, see Fig. 2. This latter finding arose theoretically: James Clerk Maxwell (1831-1879) recognized the inconsistency of the laws of electromagnetism without this latter effect and summarized the laws of electromagnetism in his famous equations. Faraday’s and Maxwell’s discoveries have revealed the existence of electromagnetic waves, which was experimentally verified by Heinrich Hertz (1857-1894). Hertz’s famous experiment in 1886 also revealed that light is nothing else but an electromagnetic wave.
For the generation and propagation of light waves, Maxwell’s equations can be written in the form
\nabla \times \vec{B} -\frac{1}{c^2}\,\frac{\partial \vec{E}}{\partial t} = \mu_0\,\frac{\partial\vec{P}}{\partial t}
and
\nabla \times \vec{E} + \frac{\partial \vec{B}}{\partial t} = 0
Here \vec{P} is the density of dipole moments and called polarization. It is represented by an arrow, just as the fields, whose direction is parallel to that of the atomic dipole antennas, see Fig. 3, and whose length is proportional to the number of dipole moment per unit volume. The dipole moment is equal to separated charge times distance of separation.
Fig. 3. In a sending antenna a charge seperation occurs by a varying current. This current produces a varying magnetic field which in turn produces an electric field and that again a magnetic field. This way the antenna can establish a propagating electromagnetic wave. (© chh)
The polarization \vec{P} is connected to the electric field \vec{E} and responsible for all light phenomena in matter. In a LASER, this connection is such that it leads to the amplification of the electric (and hence magnetic) field, i.e. it serves as a source of coherent light. In a metal, such as aluminum it makes the incident light get reflected, that’s why we see ourselves in a mirror. In glass, it refracts light, that’s why eyeglasses help us see better.