Abstract
In this chapter, we will consider a few cases where the pump rate and/or cavity losses are time dependent. We will also consider situations in which a nonlinear optical element, such as a saturable absorber, is inserted in the laser cavity, where the non-linearity leads to the laser departing from stable cw operation. For these various cases we are thus dealing with transient laser behavior. The transient cases to be considered can be separated into two categories: (i) Cases, such as relaxation oscillations, Q-switching, gain switching and cavity dumping, where, ideally, a single mode laser is involved and which can be described by a rate equation treatment. (ii) Cases where many modes are involved, e.g. mode-locking, and for which a different treatment needs to be considered. This requires a description in terms of either the fields of all oscillating modes (frequency domain description) or in terms of a self-consistent circulating pulse within the cavity (time domain description).
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- 1.
When (2πλL ′) ≪ nλ a 2, the acoustic grating behaves like a thin phase-grating and the cell is said to be operating in the Raman-Nath regime. This regime is seldom used for acousto-optic Q-switching owing to the higher requirement for rf power per unit volume of the cell.
- 2.
It should be noted, however, that one can operate an active Q-switch in an analogous fashion to the saturable absorber by setting the low Q (high loss) condition to a value that permits lasing to start (known as “prelasing”) before gradually switching to high Q after a long prelase has allowed mode selection to occur (38).
- 3.
In a mode-locked linear cavity, it proves to be simpler to talk in terms of round-trip loss and round trip gain, rather than in terms of the corresponding single-pass values.
- 4.
In a mode-locked linear cavity it is preferable to think in terms of round-trip loss and gain rather than in terms of the corresponding single-pass values
- 5.
According to (2.8.12) and for I ≪ I s , the absorbance, γ a , of an absorber of length l a can be written as \({\gamma }_{a} = \alpha {l}_{a} = {\alpha }_{0}\ {l}_{a}[1 - (I/{I}_{s})]\) and the intensity independent term α0 l a can be included in the total unsaturable loss γ.
- 6.
One may observe that the pulse spectrum must remain unchanged while the pulse propagates through a passive medium such as the dipersive medium considered here. In such a medium, however, the pulse broadens upon propagation [see (8.6.32)] and the spectral contribution arising from the finite pulse duration decreases. It then follows that the pulse must also acquire an appropriate frequency modulation to keep the spectrum unchanged.
- 7.
It must be noted that we have been using the terms “fast” and “slow” in regard to recovery time in different ways for the cases of absorber and gain medium. The recovery time of a saturable absorber is considered to be slow when its value (typically a few nanoseconds) is comparable to a typical cavity round trip time. This lifetime is typical for absorbers whose decay is determined by spontaneous emission via an electric-dipole-allowed transition. The recovery time is considered to be fast (a few picoseconds or shorter) when it is comparable to a typical duration of a mode-locked pulse. By contrast, the lifetime of a gain medium is considered to be fast when comparable to the cavity round trip time. This occurs for an electric-dipole-allowed laser transition. The lifetime of a gain medium is considered to be slow when it corresponds to an electric-dipole-forbidden transition.
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Svelto, O. (2010). Transient Laser Behavior. In: Principles of Lasers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1302-9_8
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