Theory
The lasing threshold is reached when the optical gain of the laser medium is exactly balanced by the sum of all the losses experienced by light in one round trip of the laser's optical cavity. This can be expressed, assuming steady-state operation, as
- .
Here and are the mirror (power) reflectivities, is the length of the gain medium, is the round-trip threshold power gain, and is the round trip power loss. Note that . This equation separates the losses in a laser into localised losses due to the mirrors, over which the experimenter has control, and distributed losses such as absorption and scattering. The experimenter typically has little control over the distributed losses.
The optical loss is nearly constant for any particular laser, especially close to threshold. Under this assumption the threshold condition can be rearranged as
- .
Since, both terms on the right side are positive, hence both terms increase the required threshold gain parameter. This means that minimising the gain parameter requires low distributed losses and high reflectivity mirrors. The appearance of in the denominator suggests that the required threshold gain would be decreased by lengthening the gain medium, but this is not generally the case. The dependence on is more complicated because generally increases with due to diffraction losses.
Read more about this topic: Lasing Threshold
Famous quotes containing the word theory:
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (1803–1882)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)