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 distancel as shown in the first figure. Let a beam of light of power1 W shine upon it. The front mirror, being99% reflective, will allow only1% of this input, i.e.,10 mW to get inside the cavity. Of this 10 mW, the rear mirror reflects99% back transmitting therefore just about100 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

wheren is an integer,l is the length of the cavity, andλ_n is the wavelength corresponding to then^th integer. In terms of frequency ν_n, this equation can be rewritten as

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

A typical cavity usually reflects back almost the entire light incident upon it

Transmission of a cavity as a function of the wavelength of the incident light (a) Typical experimental layout for such a measurement. Input to the cavity is derived from a tunable source. Transmission as a function of wavelength is monitored by placing a detector on the other side of the cavity (b) Recording of the cavity transmission as a function of wavelength

A resonant cavity transmits entire light, while a nonresonant cavity reflects the incident light wholly

Illustration of two examples of resonance occurring in a cavity for two different wavelengths. For the longer wavelengthλ_R, the resonance condition is satisfied for an integer value of 8 (top trace), while for the shorter wavelengthλ_B, the resonance condition is satisfied for an integer value of 16 (bottom). In reality, however, the value ofn is much higher. For visible light, this value ofn can run into several millions for a typical cavity of 1 m length

Schematic illustration of electrons orbiting around the nucleus at the center. An electron can only reside in those orbits into which its de Broglie wavelength fits an integer number of times

1. 1.

   We shall learn in a future chapter that the ability of such a cavity to store light in its entirety can be exploited to manufacture ultrashort pulses in the operation of a certain class of lasers.

2. 2.

   Exception to this statement is very high gain systems where amplified spontaneous emission may exhibit some of the characteristics of a laser like its monochromaticity; a case in point here is Maiman’s famed experiment.

3. 3.

   Steady state represents a state where the properties of the system do not change with time.

4. 4.

   While the front mirror reflects 99% of the power incident on it, for an equilibrium power of 100 W inside the cavity, it also transmits an equal amount that interferes destructively with the reflected component leading to a complete coupling of the incident power into the cavity under a resonant condition.

5. 5.

   An optical cavity that contains a population inverted medium between its parallel mirrors is termed as an active cavity in the common parlance.

6. 6.

   Reduction in pressure reduces the rate of collisions that, in turn, increases the time of residence of a species in the excited state, thereby reducing the broadening of the energy levels in accordance with the uncertainty principle.

7. 7.

   Chandra Kumar Patel, who invented CO₂ lasers in 1963 and served as an executive director of AT&T Bell Laboratories, Murray Hill, NJ, presented a theoretical estimate of laser linewidth to be less than even a hertz in his well-read review paper on gas lasers [22]. It may be of interest to note here that CO₂ laser finds wide applications in industry, medicine, military, skin resurfacing, and many more.

8. 8.

   The cavity length is basically the product of the geometrical separationl of the mirrors and the r.i. of the medium enclosed between them. For a gas laser, the r.i. of the medium is~1, and the cavity length can therefore be approximated asl.

9. 9.

   Wave front is the locus of all the points where waves starting simultaneously from the source arrive at a given instant of time. The wave front of a point source will therefore be a sphere, and the rays of light will be normal to the surface of the sphere.

10. 10.

    TEM stands for transverse electromagnetic, and the prefix00 basically means that the field of the Gaussian beam decays asymptotically to zero in the transverse directions to its motion. This will be better understood when we learn about higher order transverse modes.

Authors and Affiliations

1. Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Mumbai, India

   Dhruba J. Biswas

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