[align=left]Laser threshold condition:
When the excitation mechanism of a laser is activated, energy flows into the active medium, causing atoms to move from the ground state to certain excited states. In this way, population inversion is created. Some of the atoms in the upper lasing level drop to the lower lasing level spontaneously, emitting incoherent photons at the laser wavelength and in random directions. Most of these photons escape from the active medium, but those that travel along the axis of the active medium produce stimulated emission, as indicated in Figure 1. The beam produced is reflected back through the active medium by the mirrors. A portion of the light that strikes the output coupler leaves the laser as the output beam.
Then in order to get lasing action, a threshold condition must be satisfied. Oscillation begins only when the gain in the active material must compensate the loss in the laser cavity which can be summarized in the followings:
Loss due to non- perfect reflection.
Losses due to absorption and scattering in the A.M.
Losses due to diffraction in the mirror.
[align=center]][/align][/align]
[align=center]Fig.1 Lasing begins.[/align]
Then the gain in each pass through the active material ( or the ratio between the output to the incident photon fluxes ) is:
[align=left][/align]
Or:
[align=left][/align]Where:
l: is the length of the active material.
If the losses in the laser cavity is only due to the transmission through the mirrors, so the threshold satisfied when:
[align=left][/align]Where:
R1, R2: is the reflectivities of the first and second mirrors.
From equation (2) we see that the threshold condition will be satisfied when the population inversion reaches a value called " critical population inversion " when which the oscillation start from the spontaneous emission. The photons which emitted spontaneously along the cavity axis, in face start the amplification process which is the begin of lasing.
If one keeps track of the number of photons in the beam during one round trip, say from HR to OC and back to HR, and the number of photons in the beam increases, the laser beam power increases. If the number is the same, the beam power is steady. If the number is less, the laser power decreases and eventually lasing stops. As we shall see later in more detail, the round-trip gain of the laser comes from the degree of population inversion in the active laser medium and the probability for a stimulated emission process to occur. The round-trip overall loss comes from imperfect reflection at the HR mirror, scattering and diffraction losses as the beam passes through the active medium absorption losses, cavity mirror misalignment losses, and of course, "the programmed" loss through the output mirror. When the gain for a round-trip exceeds the losses, laser power grows. When the round-trip gain is less than the losses, laser power dies out. And, when round-trip gain and loss are just equal, the laser operates in what we call a "steady-state" condition.
In pulsed lasers, the excitation mechanism supplies energy in short bursts. Both gain and output power rise quickly to a high level and drop off, producing a burst of laser light. In continuous-wave (CW) lasers, the excitation mechanism supplies a constant power to the active medium. The system quickly reaches a "steady-state" condition, in which loss and gain are in balance. This condition thereby results in a constant output beam.
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