laser dynamics (original) (raw)

Definition: the temporal evolution of quantities such as the optical power and gain in a laser

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What is Laser Dynamics?

The dynamic behavior of a laser is determined by the interaction of the intracavity light field with the gain medium. Essentially, the intracavity laser power can grow or decay exponentially according to the difference between gain and resonator losses, whereas the rate of change in the gain is determined by stimulated and spontaneous emission (and possibly by other effects such as quenching and energy transfer).

With certain approximations, including a not too high laser gain, the dynamics of the intracavity optical power ($P$) and the gain coefficient ($g$) in a continuous-wave laser can be described with the following coupled differential equations: \frac{\textrm{d} P}{\textrm{d} t} = \frac{g - l}{T_\textrm{rt}}P$$ \frac{{\textrm{d} g}}{{\textrm{d} t}} = - \frac{{g - {g_{{\textrm{ss}}}}}}{{{\tau _{\textrm{g}}}}} - \frac{{g\;P}}{{{E_{{\textrm{sat}}}}}}$$

where ($T_\textrm{rt}$) is the cavity round-trip time, ($l$) the cavity loss per resonator round trip (including both the output coupler transmission and parasitic losses), ($g_\textrm{ss}$) the small-signal gain (for a given pump power), ($\tau_\textrm{g}$) the gain relaxation time (often close to the upper-state lifetime), and ($E_\textrm{sat}$) the saturation energy of the gain medium. The equations can be generalized in various ways, for example allowing for high gain and loss and for a time-dependent pump power, or separately describing the optical powers in individual resonator modes, which involves mode competition phenomena. A wide range of phenomena can be simulated in such ways.

Typical Phenomena of Laser Dynamics

Dynamic aspects of special interest in the case of a continuous-wave laser are the following:

When the pump source of a laser is switched on, the laser undergoes some dynamics until steady-state operation is reached. This often includes spiking of the output power.
One can study how a laser reacts to disturbances during operation, e.g. sudden changes in pump power. Usually, such disturbances lead to relaxation oscillations.

In these respects, different types of lasers exhibit very different behaviors. For example, doped-insulator lasers (exhibiting low transition cross-sections and a long upper-state lifetime) exhibit a strong tendency for spiking and relaxation oscillations, whereas for laser diodes this is not the case.

Dynamic aspects are particularly important in Q-switched lasers, where the energy stored in the gain medium undergoes a large change during pulse emission. Q-switched fiber lasers, typically having a high laser gain, can exhibit additional dynamical phenomena. This can lead to a temporal sub-structure of the pulses, which cannot be explained with equations such as those given above.

Similar equations can be used for passively mode-locked lasers [1]; an additional term appears in the first equation, which describes the losses of the saturable absorber. The effect of this is typically that the damping of the relaxation oscillations is reduced. The relaxation oscillations may even become undamped, so that the steady-state solution becomes unstable, and the laser exhibits Q-switched mode locking or other kinds of Q-switching instabilities.

In optical amplifiers based on laser amplification, there can be a similar interplay of signal power and gain. In the case of a regenerative amplifier, the similarity is strongest.

Case Studies

Pulse generation in an actively Q-switched Nd:YAG laser (with power propagation)
We simulate pulse generation in an actively Q-switched Nd:YAG laser with simple power propagation. This is useful for investigating the laser dynamics.
Pulse generation in an actively Q-switched Nd:YAG laser (with beam propagation)
We simulate pulse generation in an actively Q-switched Nd:YAG laser with numerical beam propagation. There, we see the evolution of the beam profile over the resonator round trips. Close to a mode frequency degeneracy, the changes in beam diameter become substantial.
Pulse generation in a passively Q-switched Nd:YAG laser (with power propagation)
We simulate pulse generation in a passively Q-switched Nd:YAG laser with simple power propagation.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is meant by laser dynamics?

Laser dynamics refers to the time-dependent behavior of a laser, resulting from the interaction between the light inside the laser cavity and the gain medium. It explains phenomena like power fluctuations when a laser is turned on or disturbed.

What are relaxation oscillations in a laser?

Relaxation oscillations are damped oscillations of the laser's output power that typically occur after a disturbance, such as a change in pump power. They arise from the dynamic interplay between the stored energy in the gain medium and the optical power in the resonator.

Why are relaxation oscillations more pronounced in some lasers than in others?

Lasers with a long upper-state lifetime and low transition cross-sections, like many doped-insulator lasers, exhibit strong spiking and relaxation oscillations. In contrast, laser diodes have a very short upper-state lifetime, leading to strongly damped oscillations and more stable output.

How can laser dynamics be modeled?

A common method is to use a set of coupled differential equations, known as rate equations. These describe the evolution of the intracavity optical power and the laser gain based on key parameters like cavity losses, gain relaxation time, and the saturation energy of the gain medium.

What is the role of laser dynamics in pulsed lasers?

Bibliography

[1]	A. Schlatter et al., “Pulse-energy dynamics of passively mode-locked solid-state lasers above the Q-switching threshold”, J. Opt. Soc. Am. B 21 (8), 1469 (2004); doi:10.1364/JOSAB.21.001469
[2]	O. Svelto, Principles of Lasers, Plenum Press, New York (1998)
[3]	A. E. Siegman, Lasers, University Science Books, Mill Valley, CA (1986)

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