lasers, oscillation of light
In conventional sources of light, such as a light bulb, the emission of photons
, occurs spontaneously. In this case, the photons emitted from different atoms of the source, do not know anything about each other. Photons from different atoms are emitted randomly in different directions, resulting in light with poorly-defined “wave” properties. However, photon emission can also be stimulated by another photon. In the latter case the newly-emitted photon has exactly the same properties as the incident photon, which stimulated its emission. The newly-born photon is sent out in the same direction and vibrates in exactly the same way, i.e. its crests and troughs are all in lockstep with the stimulating photon. In essence, the photon clones itself, creating its perfect copy. In such a case physicists say that the emission is coherent. If this occurs repeatedly in an ensemble of atomic antennas, i.e. excited atoms, the result is the “merger” of the emitted photons to an intense, coherent light wave. In spite of their wave-like nature, such a merger of electrons to a macroscopic electron wave is not possible, see box.
, occurs spontaneously. In this case, the photons emitted from different atoms of the source, do not know anything about each other. Photons from different atoms are emitted randomly in different directions, resulting in light with poorly-defined “wave” properties. However, photon emission can also be stimulated by another photon. In the latter case the newly-emitted photon has exactly the same properties as the incident photon, which stimulated its emission. The newly-born photon is sent out in the same direction and vibrates in exactly the same way, i.e. its crests and troughs are all in lockstep with the stimulating photon. In essence, the photon clones itself, creating its perfect copy. In such a case physicists say that the emission is coherent. If this occurs repeatedly in an ensemble of atomic antennas, i.e. excited atoms, the result is the “merger” of the emitted photons to an intense, coherent light wave. In spite of their wave-like nature, such a merger of electrons to a macroscopic electron wave is not possible, see box.
Fig. 1. Relation between wave length, periodic time and energy for electromagnetic waves from infrared light (IR) via visible light (VIS), vacuum ultraviolet (VUV), extreme ultraviolet (XUV), soft X-Rays up to X-Rays. (© ch)
The process can, in principle, be initiated by a single incident photon. Upon propagation through the medium of suitably prepared atomic antennas more and more photons can join the wave by repeated stimulated emission. This leads to a light wave of ever increasing intensity, via Light Amplification by Stimulated Emission of Radiation: LASER. It consists of a large number of coherently emitted photons and can be described in terms of well-defined, periodically varying, i.e. oscillating, electric and magnetic fields. In red light, one wave period lasts about 2 femtoseconds, equal to 2000 attoseconds. In infrared light, the period stretches to several femtoseconds whereas in ultraviolet and X-ray light it becomes successively shorter, from about 1000 towards 1 attosecond, see scale. Hence the unit of time for clocking light oscillations and their origin, electron motion inside atoms, is attosecond.
. In red light, one wave period lasts about 2 femtoseconds, equal to 2000 attoseconds. In infrared light, the period stretches to several femtoseconds whereas in ultraviolet and X-ray light it becomes successively shorter, from about 1000 towards 1 attosecond, see scale. Hence the unit of time for clocking light oscillations and their origin, electron motion inside atoms, is attosecond.
The period of light field oscillations, T_0, is connected to the energy of the emitted photons, W_{ph}, by
, just as expected.
T_0=1/f=h/W_{ph},
which – through W_{ph}=\Delta W, – is equal to the oscillation period, T_{\rm osc}=h/\Delta W, of the electron cloud in the atomic antennas, just as expected.
Can the wave-like nature of electrons result in a macroscopic electron wave, just as the wave-like nature of photons result in a light wave? The answer is no. This is, because, unlike photons, electrons can’t occupy the same quantum state, i.e. they can’t clone each other, as the photons do in the process of stimulated emission. This fact is expressed in Pauli’s exclusion principle, which is the origin of the existence of the great variety of atoms with different chemical properties, and hence the existence of life.
As a matter of fact, if electrons were able to occupy the same quantum state like photons can do, they would – regardless of the atomic number, which determines the number of protons in the nucleus and hence the number of electrons in the atom – be residing in their lowest-energy atomic quantum state. Hence, all atoms would have the same chemical properties, only their mass would be different. Thanks to the exclusion principle, this is not the case and hence different atoms can form different molecules with different biological functions, the basis of living creatures. The price we have to pay is the lack of macroscopic electron waves.