Cavity and Its Bearing on the Operation of Lasers

Abstract

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This chapter begins with a series of simple but revealing illustrations to justify why there would not be a laser without a cavity. A few thought experiments, cleverly planned with equally thoughtful illustrations, have been used here to decode the rich physics that a cavity holds. As an example, we reproduce below an excerpt from such a thought experiment that would make a cavity reveal its deepest secret.

The Cavity: A Deeper Insight A cavity not only has made possible the realization of a laser, as we just saw in the preceding section, but also has gifted it all its prized attributes. It would be beneficial at this point to gain a qualitative, but nevertheless deeper, insight on certain unique features of a cavity that have strong bearing in the operation of a laser. Let us begin by considering a typical Fabry-Perot cavity comprising of two parallel mirrors each of reflectivity ~99% and separated by a distance l as shown in the first figure. Let a beam of light of power 1 W shine upon it. The front mirror, being 99% reflective, will allow only 1% of this input, i.e., 10 mW to get inside the cavity. Of this 10 mW, the rear mirror reflects 99% back transmitting therefore just about 100 μW out. Thus, it is obvious that the cavity transmits merely an insignificant fraction of the light incident on it. Fortunately, this is not always true; else, the cavity would have lost all its importance in the context of a laser. A simple experiment can be performed to make the cavity reveal its deepest secrets, and the same is depicted in the trace of Fig. 6.9. For this we derive the input beam of light from a tunable source that is capable of giving out light of continuously changing wavelength. The transmission of the cavity is monitored as a function of the wavelength of the incident light by placing a detector on its other side and the same is recorded in Fig. 6.9a. As expected, for most of the wavelengths, the cavity hardly transmits any light. Intriguingly, however, at certain discrete wavelengths, the cavity is seen to transmit almost whatever is incident on it. For these wavelengths, the cavity is said to be on a resonance, and the corresponding wavelengths are called resonant wavelengths. Thus, a resonant cavity is one that transmits the entire light that shines upon it, while a nonresonant cavity reflects it back almost entirely. On closer examination, it would be seen that only those wavelengths, the half of which times an integer fits exactly inside the cavity, are actually resonant to the cavity. This fact is schematically illustrated here for two different wavelengths. The resonant equation can be mathematically expressed as

$$ n\times {\${\lambda}_n\$}\!\left/ \!{\$2\$}\right.=l $$

(6.1)

where n is an integer, l is the length of the cavity, and λ_n is the wavelength corresponding to the n^th integer. In terms of frequency ν_n, this equation can be rewritten as

$$ {\upnu}_n=\frac{nc}{2l} $$

(6.2)

where “c” is the velocity of light.

These discrete frequencies that can oscillate back and forth inside a cavity without decay are called cavity modes. . An obvious analogy is Bohr’s orbits of electrons. It is well known that electrons can revolve only in those orbits without decaying into which its de Broglie wavelength fits an integer number of times as is shown here.

Graphical Abstract