The two fundamental elements of a laser are the amplifier and a cavity which produces a positive feedback between the light and the amplifying medium. First we will have a look on the amplifier and the physics on which it is based |

traversing a two level system can either be absorbed or induce a de-excitation which generates another photon with the same properties. This is called stimulated emission. Another fundamental de-excitation is the spontaneous emission which is not dependent on the intensity of the incoming photons. The probability for the absorption of a light quanta is given by B

Due to time-reversal symmetry the transtion probability for absorption equals the probability for spontaneous emission (B

Thus we get a spectral intensity of

which is equivalent to Planck's Law. What condition must be given to get amplification by stimulated emission? Looking on a system which is traversed by n photons per second the deviation with respect to the position z is

The constants a

Therefore a gain can just be obtained when there are more electrons in the excited state than in the ground state what is called

whereas m is an integer, c the speed of light and the period of the light. As gain is just possible for a certain bandwidth in the frequency domain, the number of active modes is finite.

So far we have a laser which emits continuously light. But how do we get short laser pulses? This can be explained by a process which is called **mode locking**. We will now have a closer look on this phenomenon.

The detector measures the intensity I of the field and because its response time is much greater than the period of optical oscillations the mean of the intensity is detected:

The mode now depends on whether there is a relationship between and .

If these phase factors are random and independent, the integral term (beating term) averages to zero. Therefore the detector records a constant signal and the laser operates in a multimode regime. In case of totally correlated phases, we get a sinusodial modulation with the frequency

.

In case of N modes we have multiple phase beating terms and the peaks become much narrower. If the laser works in the free mode, the different modes will compete for the gain due to stimulated emission. This causes fluctuations in the phase.

But there is a way to regulate this competition:
If a nonlinear medium is inserted in the cavity, the fluctuation with the largest maximum is enhanced at the cost of the weaker ones while the light is propagating. At the optimum all the energy is concentrated in one maximum in the cavity. This corresponds to constant phase relation between the modes in the frequency domain (passive mode locking).
One can also give an explanation in the frequency domain. By an additional modulation close to the intermode frequency c/2L (L= cavity length) sidebands to each frequency mode are created which lie close to the neighboring frequency band and therefore compete with them for gain (active mode locking).
In a Ti:Sapphire laser the modes can lock without inserting a saturable absorber or any external modulation. This **self locking** is based on the **Kerr Lens Effect**. The Kerr effect states that the refractive index is a function of intensity

If n_{2}is positiv a beam propagating through this medium, is more focused near the optical beam axis where its intensity is stronger. This is called self focusing.
The Ti:Sapphire crystal has this nonlinear property. The low intensity part of the beam can be removed by a pinhole. Thus high intensity maxima are much better amplified and the laser reaches the condition to give short pulses. A possible setup for such a laser is shown in the figure below