A. Linewidth

Laser light is highly monochromatic, that is, it has a very narrow spectral width. The spectral width is greater than zero, but typically it is much less than that of conventional light sources. The narrow spectral linewidth is one of the most important features of lasers. Early calculations [1] indicated that the linewidth could be a small fraction of 1 Hz. Of course, most practical lasers have much greater linewidth.

In discussing linewidth, we must distinguish between the width of one mode of the resonant cavity and the width of the total spectrum of the laser output. As Chapter 1 described, many lasers operate simultaneously in more than one longitudinal mode, so that the total linewidth may approach the fluorescent linewidth of the laser material. Figure 2-1 illustrates the situation. The evenly spaced cavity modes are illustrated in part (a). The frequency spacing is c/2nD, with D the distance between the two mirrors and n the index of refraction of the material. For a gas, the index of refraction is close to unity, and the spacing becomes c/2D. This spacing is equivalent to a wavelength spacing of λ2/2D, where λ is the wavelength. Figure 2-1b shows the gain and the loss as functions of frequency. The gain curve has the same shape as the fluorescent line, and the loss is essentially independent of frequency, at least over a reasonably small range. All modes for which the gain is greater than loss can be present in the laser output. Thus, the spectral form of the output can be as shown in Figure 2-1c.

Some typical values are shown in Table 2-1 for representative lasers. The fluorescent linewidth varies considerably for different laser materials. The table presents the operating wavelength and frequency of the laser, the fluorescent linewidth of the laser material, and the typical number of longitudinal modes present in the output of the laser. The number of modes is calculated as the fluorescent linewidth divided by the quantity c/2D, the spacing between longitudinal modes. In most cases this will be an overestimate, because near the edges of the fluorescent line, the gain will not be high enough to sustain laser operation. Thus, for typical commercial helium–neon lasers, perhaps three or four modes will be present, rather than ten as the calculation indicates. CO2 lasers present an interesting case, because at low gas pressure the fluorescent linewidth is narrow, of the order of 60 MHz. As the pressure increases to near atmospheric, the fluorescent linewidth broadens. Atmospheric pressure CO2 lasers may operate in several modes. Neodymium:glass has an unusually wide fluorescent linewidth, and an Nd:glass laser can have hundreds or even thousands of longitudinal modes present in its output. In particular, in mode-locked operation (to be described later) the emission spectrum can fill the fluorescent linewidth.

In summary, the total spectral width covered by many practical lasers will be almost as wide as the fluorescent linewidth, often around 109 Hz. We note that this is still much smaller than the operating frequency, around 1015 Hz. Even a laser with many longitudinal modes present in its output is still almost monochromatic.

Individual longitudinal modes have much narrower spectral width. To provide better monochromaticity, lasers are sometimes constructed so as to operate in only one longitudinal mode.

One method for providing single-mode operation involves construction of short laser cavities, so that the spacing between modes (c/2D) becomes large and gain can be sustained on only one longitudinal mode. Other longitudinal modes will fall outside the fluorescent line. This is illustrated in Figure 2-2. This approach is most commonly applied in helium–neon lasers. Commercial single-mode helium–neon lasers have spectral widths of the order of 107 Hz, much reduced from the 109 Hz range of multimode lasers. But this reduction is achieved at a sacrifice in output power. The short cavity limits the power that can be extracted.

A second method for obtaining single-mode operation involves use of multiple mirrors, as illustrated in Figure 2-3a. This defines cavities of two different lengths, D1 and D2. The length of the short cavity D1 is chosen so that only one mode lies within the fluorescent linewidth. The laser must operate in a mode that is simultaneously resonant in both cavities. This is illustrated in Figure 2-3b. The lengths of the two cavities must be adjusted carefully, so that there is an overlap of two resonant modes. This places stringent requirements on mirror position and stability. However, this arrangement allows operation of single-longitudinal-mode lasers with higher power. It is used most often with solid state lasers.

Another method for providing a long cavity and a short cavity involves insertion of a device called an etalon into the laser cavity. The etalon is a short resonant cavity, which may be formed from a piece of glass with its two faces polished to a high degree of parallelism. Figure 2-4 shows how an etalon may be inserted into a laser cavity. The etalon generally is tilted with respect to the axis of the cavity in order to provide tuning, as we will discuss. The surfaces of the etalon form a short cavity. The etalon produces loss at wavelengths that are not modes of its cavity. The longitudinal modes in the laser output must be simultaneously modes of the etalon and of the cavity that defines the laser. Generally, only one mode of the laser will satisfy this condition. This forces the laser to operate in only one of its longitudinal modes. The use of an intracavity etalon is perhaps the most common method for producing single-mode operation.

Usually the etalon is mounted so that its surfaces are tilted with respect to the axis of the laser. As the etalon is rotated, its effective length along the axis changes. The allowed wavelength then changes slightly, so that it is possible to tune the wavelength of the laser by a small amount within the gain curve of the laser material.

Another method for forcing the output of a pulsed laser into a single longitudinal mode is injection seeding. One directs the output of a small, stable, single-frequency laser, called the seed laser, into the laser cavity of the larger laser, which provides the output pulse. The seed laser is usually a continuous laser. The frequency of the seed laser must lie within the linewidth of the larger laser. When the pulse of the larger laser develops, it occurs at the longitudinal mode that is closest to the frequency of the seed laser. This longitudinal mode builds up rapidly by stimulated emission and saturates the gain of the laser before the other longitudinal modes have a chance to develop from noise. Thus, the output of the pulsed laser will be at a single frequency, rather than in a number of longitudinal modes at different frequencies.

Even when operating in a single longitudinal mode, a laser still has a finite spectral linewidth. Because the width of a single mode is much less than the intermode spacing, it will be much smaller than for multimode operation.

Further, the...