Ultrashort Laser Pulse Phenomena, 2nd Edition

Circulating Pulse Model 295

Even though the transient evolution toward steady state may take thousands

of round-trips, the modeling can generally be implemented with a personal

computer. The main disadvantage of a computer model that includes a plethora of

processes is that it is difficult to get a clear physical picture of the laser operation.

5.2.2. Continuous Model

If the change in electric field introduced by each element of the cavity, at each

round-trip, is small, the pulse evolution can be modeled by a differential equation.

An additional simplification is to assume that the pulse evolves along the mode of

a stable cavity, and thus the spatial pulse evolution is decoupled from the temporal

evolution. Because the change per element and per round-trip is assumed to be

infinitesimal, the order of the elements in the cavity does not matter, and the

laser is equivalent to an infinitely long medium, in which the resonator elements

are uniformly distributed (Figure 5.8). This “continuous model” in which the

resonator elements are replaced by a uniform medium is similar to the propagation

of a pulse in a fiber.

The continuous model is aimed at searching for a stationary pulse, which is

a shape-preserving signal propagating through this model medium. Such a pulse

is called a soliton of first order or fundamental soliton. Pulses that reproduce

after a certain periodicity length are labeled solitons of higher order. In an actual

laser, the “higher-order solitons” will reproduce after a given number of res-

onator round trips. We have seen some examples of solitons in Chapters 3 and

4. One of the simplest cavity model leading to solitons is that of a laser with

linear gain balancing linear losses and a combination of SPM and dispersion.

This particular soliton model and the related equations are discussed in more

detail in the following section.

Gain

Absorption

Dispersion

SPM

Linear loss

...

Figure 5.8 Representation of a fs laser as an infinitely long medium with the distributed properties

of the cavity.