### 0.1 Ramen Scattering


**Definition 0.1.1 **  A **two photon absorption** process is is any process where two photons are absorbed simultaneously to accesses an otherwise inaccessible energy state. These processes typically require extremely high intensity for there to be enough photons overlapping for the effect to be significant. 

**Definition 0.1.2 **  A **stimulated Ramen scattering** experiment is where a narrow band pump is sent into a sample and the resulting emission spectra is measured. This can be used to reveal the energy levels of the state available for excitation.

**Definition 0.1.3 **  A **Stokes scattering** process refers to scattered light produced with a lower energy than the pump. This occurs when a phonon is emitted into the material after the initial excitation.

**Definition 0.1.4 **  An **anti-Stokes scattering** process refers to scattered light produced with a higher energy than the pump. This occurs when a phonon is absorbed from the material after the initial excitation.

**Image 0.1.5 Types of Ramen Scattering **&nbsp; <a href="https://commons.wikimedia.org/wiki/File:Ramanscattering.svg"><img src="https://kaedon.net/l/1ker" alt="Types of Ramen Scattering" style="filter:invert(var(--invert-images));display:block;margin-left:auto;margin-right:auto;width:600px;height:auto;"></a>


**File 0.1.5 **&nbsp; Ramanscattering.svg

**Definition 0.1.6 **&nbsp; A **saturable absorber** is a material that will become "saturated" at high intensity and won't be able to absorb as much light. The relationship between the absorption rate $\alpha$ and intensity $I$ is described by the following equations.
\[\alpha = \frac{\alpha_0}{1 + I/I_0},\quad I(z) = I_0e^{-\alpha z}\]
where $\alpha_0$ is the linear absorption at low intensity, $I_0$ is the saturation intensity and $z$ is the distance through the crystal.

**Definition 0.1.7 **&nbsp; The **Kerr effect** is a process where non-zero $\chi_e^{(3)}$ leads to an index of refraction that changes with intensity.

**Definition 0.1.8 **&nbsp; The **self focusing** process is a [Kerr effect](https://kaedon.net/l/^h407) driven process where a positive $\chi_e^{(3)}$ causes a high intensity light pulse to be focused by it's own induced refractive index in a material.

**Definition 0.1.9 **&nbsp; A **Kerr lens** is a apparent lens produced by a [self focusing](https://kaedon.net/l/^60n0#0w2j) at high intensity.