Fig. 1. Typical laser tube. A laser consists of three subsystems: (1) a laser tube containing the lasing medium, or lasant (see Fig. 1); (2) a system for “pumping” the lasant, i.e., for raising the lasant atoms or molecules to the upper energy level of the lasing transition; and (3) a system for removing waste heat. Figure 2 shows how a laser works. In the first drawing, most of the molecules have been pumped to the excited state, i.e., the upper energy level of the lasing transition. When a molecule drops from the excited state to the lower energy level of the lasing transition, it emits a photon of frequency v = (e2 - e^/h, where e2 is the energy of the excited state, Ci is the energy of the lower energy level of the lasing transition, and h is Planck's constant. In a two-level system, the lower level of the lasing transition coincides with the ground state. A photon can be emitted by spontaneous emission or by stimulated emission. Initially the photons are emitted spontaneously. Those not traveling parallel to the tube axis leave the tube through the transparent walls. The first spontaneously emitted photon that is emitted parallel to the tube axis stimulates the emission of a second photon. By stimulated emission, more and more photons join the first two as the photons are reflected back and forth between the mirrors (see the second and third drawings in Fig. 2). Each stimulated photon will have the same frequency, direction, and phase as the stimulating photon(s). Assuming a continuous wave (cw) laser, a steady state is finally established where the loss of photons through the partially reflecting mirror on the right is balanced by the stimulated emission of new photons within the laser tube. (In addition to cw lasers, there are pulsed lasers that send out intense, intermittent bursts of photons.) The amplification process is more complicated than indicated in Fig. 2 because photons are lost by molecular absorption, and amplification occurs only if stimulated emission exceeds absorption. A mathematical statement of this condition is derived as follows. Consider a slab of infinitesimal thickness dr as shown in Fig. 3, and let I„ denote the intensity (energy passing per second through a unit area) at the left side of the slab for photons with frequency p moving to the right. The increase in due to stimulated emission in dr is (2) and the decrease in Iv due to absorption in d.r is (2)
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