Abstract
Under conditions of heat equilibrium, the number of particles with higher energy is always smaller than the number with lower energy. Therefore, n12 > 0, σ > 0, Pabs > 0 and a wave propagating in a medium is damped. Nevertheless, the equilibrium condition can be disturbed by use of an additional energy source (a pumping source). Under definite conditions the number of particles on the upper level becomes greater than in the power level. As a result, n12 > 0, σ > 0, Pabs < 0 and instead of absorption we may observe electromagnetic wave amplification. Such a state is called population inversion or a state with a negative temperature. A medium with inversion is often called an active medium.
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Notes
- 1.
Nicolaas Bloembergen (1920–2017) was a Dutch–American physicist. He is known for his findings on nuclear magnetic resonance and electron paramagnetic resonance, quantum electronics, and nonlinear optics. He shared the 1981 Nobel Prize in Physics with Arthur Schawlow and Kai Siegbahn for work on spectroscopy. He was awarded prizes by the American Physical Society and the Institute of Radio Engineers, the US President’s National Medal of Science, and the Frederic Ives Medal from the Optical Society of America. He was a member of the US National Academy of Sciences and the Dutch Royal Academy of Sciences.
- 2.
In 1955, Nikolay Basov and Alexander Prokhorov offered a three-level pumping method in conformity with a molecule gas. However, it was not practically realized, apparently because of the absence of suitable generators to use as the pumping source. Generalization to a solid body was also not realized. In 1962 a gas laser was created, using cesium vapor, in which a three-level scheme with optical pumping from a helium gas discharge lamp was used. Generation was obtained at wavelengths of about 7 and 3 μm.
- 3.
Do not confuse these equations with equations for level populations, which are often also called balance equations. Equation (5.9) is purely classical, and the equations for populations are quantum ones.
- 4.
We should pay attention to the fact that that this method has much more in common with matrix description in quantum mechanics, as well as with signal expansion on an orthogonal basis in the theory of signals.
- 5.
Nonuniformity of volume filling can be taken into consideration by use of well-known mathematical formulas for integral estimation and introduction of a filling coefficient with an active medium.
- 6.
It should be taken into account that, besides pure mathematical simplifications, our equations may contain a variety of simplifications of physical aspects that are not mentioned in the text. For instance, we privately assume that the medium is homogeneous in the space, but the saturation effect changes the concentration difference; hence, n21 is a function of the coordinates. Details can be found in the specialist literature.
- 7.
The idea of mode synchronization has found applications in multimode generators with a delay line on the surface acoustic waves. A detector and a modulator are included in the circuit. As a result, the device generates a periodic sequence of radio pulses. The pulse shape depends upon the apodization law of interdigital transducers (the frequency response of the filter). Generation of periodic pulses with an infill frequency of 100 MHz, duration of 50 ns, and period of 1.8 μs has been reported (H. Gilden, J.M. Reeder, M.F. Lewis, in Proc. IEEE US Symp. (1975), p. 251).
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Shtykov, V.V., Smolskiy, S.M. (2020). Quantum Amplifiers and Generators. In: Introduction to Quantum Electronics and Nonlinear Optics. Springer, Cham. https://doi.org/10.1007/978-3-030-37614-7_5
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