### 6.2.2 Laser Modes

| This module is not finished but you can get a rough idea of what it's all about.
| The Fabry Perot resonator introduced in chapter 6.1.3 is an oversimplification of the situation in a real semiconductor Laser.
|  | Without mentioning it, we have assumed an infinitely extended system in the illustrations, i.e. a one-dimensional situation.
|  | The active region in a real Laser, however, is finite. Often, it consists of a particular material embedded in an other material with a different index of refraction; in any case it ends somewhere. In a most simple approximation we may consider it to be a box of length l, thickness d and width w.
| This simply means that many standing waves - with different wavelengths and different wave vector directions - satisfy the resonance condition.
|  | In other words - and that is the common lingo - the Laser cavity may contain many internal modes and thus does not automatically emit monochromatic light in one direction only.
|  | We may distinguish between axial or longitudinal modes, and transverse modes. The figures below illustrates this
|  | Longitudinal Modes |  |  | Transverse Modes
|  | Many wavelengths fit in the longitudinal direction which we define to be the direction where we want emission We have l = m ·l/2nr and m = 1,2,3,... |  |  | Many transverse modes are possible as shown. They are undesirable and should be avoided.
|  | Only wavelengths compatible with the band gap energy, i.e. l = c/nr·n » c · h/nr · Eg » µm will become amplified, i.e. m is large since l is typically many µm.
|  | The distance between allowed frequencies is D n = c/2l · n » 80 GHz for l = 500 µm. The emission lines of the longitudinal, modes are thus very close together.
| Laser modes, what to do with them, and how to make a Laser working in only one mode - this is what we naively expect a Laser to be - is clearly a science in itself.
|  | We will not go into details, suffice it to say that monomode Lasers are possible by optimizing the resonating properties of the cavity to the local gain inside it.

© H. Föll (Semiconductors - Script)