Laser Oscillator
In Chap. 1 we studied the processes which lead to optical amplification in substances. The regenerative laser oscillator is essentially a combination of two basic components: an optical amplifier, and an optical resonator. The optical resonator, comprised
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In Chap. 1 we studied the processes which lead to optical amplification in substances. The regenerative laser oscillator is essentially a combination of two basic components: an optical amplifier, and an optical resonator. The optical resonator, comprised of two opposing plane-parallel or curved mirrors at right angles to the axis of the active material, performs the function of a highly selective feedback element by coupling back in phase a portion of the signal emerging from the amplifying medium. Figure 3.1 shows the basic elements of a laser oscillator. The pump lamp inverts the electron population in the laser material, leading to energy storage in the upper laser level. If this energy is released to the optical beam by stimulated emission, amplification takes place. Having been triggered by some spontaneous radiation emitted along the axis of the laser, the system starts to oscillate if the feedback is sufficiently large to compensate for the internal losses of the system. The amount of feedback is determined by the reflectivity of the mirrors. Lowering the reflectivity of the mirrors is equivalent to decreasing the feedback factor. The mirror at the output end of the laser must be partially transparent for a fraction of the radiation to "leak out" or emerge from the oscillator. An optical structure composed of two plane-parallel mirrors is called a Fabry-Perot resonator. In Chap. 5 we will discuss the temporal and spatial mode structures which can exist in such a resonator. For the purpose of this discussion it is sufficient to know that the role of the resonator is to maintain an electromagnetic field configuration whose losses are replenished by the amplifying medium through induced emission. Thus, the resonator defines the Pump lamp Mirror
Fig. 3.1. Major components of an optically pumped solid-state laser oscillator
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W. Koechner, Solid-State Laser Engineering © Springer-Verlag Berlin Heidelberg 1988
spectral, directional, and spatial characteristics of the laser radiation, and the amplifying medium serves as the energy source. In this chapter we will develop an analytical model of a laser oscillator that is based mainly on laser systems parameters.
3.1. Operation at Threshold We will calculate the threshold condition of a laser oscillator composed of two mirrors having the reflectivities R1 and R2, and an active material of length l. We assume a gain per unit length of g in the inverted laser material. In each passage through the material the intensity gains by a factor of exp(gl). At each reflection a fraction 1 - R1 or 1 - R2 of the energy is lost. Starting at one point, the radiation will suffer two reflections before it can pass the same point in the original direction. The threshold condition is established by requiring that the photon density - after the radiation has traversed the laser material, been reflected by mirror with R1, and returned through the material to be reflected by mirror with R2 - be equal to the initial photon density. Then on every complete two-way passage of the light
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