# A very special light

The word LASER is the acronym for Light Amplification by Stimulated Emission of Radiation.

A laser is a very coherent light source. The high degree of spatial coherence allows the beam to be highly collimated and also very good focusable.

Further more the spectral longitudinal coherence is very high. All photons do have very similar energies and are therefore monochromatic.

These properties make laser light very suitable to form the standing light wave where the molecules are diffracted.

Laserlight can be highly polarized. In the KDTLI we use polarization optics to adjust the light power reaching the molecules and to separate the departing and returning laser beams.

Extra: Polarisation optics

Our laser is linearly polarized – the electrical light field oscillates in one plane. This property can be used to guide and modulate the light field.

Polarizing beam splitters direct light of a predefined polarization (e.g. horizontal orientation of the electric field) out of the beam and allow the perpendicular polarized light (vertical orientation of the electrical field) pass.

By rotating the polarization axis of the incoming laser beam we can use the polarizing beam splitter as a precision attenuator. The intensity can be continuously divided between the two exits. To rotate the polarization we use half-wave-plates, where the phase between two orthogonal components of the light field is shifted by $$\pi$$. We could also change the laser power with the current. But this usually affects also other beam parameters (profile, wavelength,…). Therefore it is advantageous to use polarization optics.

A quarter-wave-plate transforms linearly polarized light to circular polarized light and vice-versa. If a beam passes this element twice (forwards and after reflection at the mirror backwards) can rotate the polarization of a laser beam by 90 degrees. We use that in the KDTLI to protect the laser head from damage caused by back reflecting light.

Many lasers have a cross sectional intensity profile that can be described by a Gaussian function. In the interferometer we need a beam focussed to only $$20 \times 1000 \, \mathrm{\mu m}^2$$. Accordingly, we use a cylindrical lens to obtain a homogeneous field distribution over the whole molecular beam.

Extra: Gaussian beams

A Gaussian intensity profile has this form:

$$I=I_0 \cdot \exp(- 2r^2/w_0^2)$$,

where the distance $$r$$ from the optical axis and the waist $$w_0$$ define the distance where the intensity dropped to $$1/e^2$$.

This particular beam profile has some optical properties we want to memorize:

1. Its wave nature (diffraction) inhibits to focus light to an arbitrarily small point. The smallest focus with an extended light wave (wavelength $$\lambda$$, beam diameter $$D$$) behind a lens with focal lenght $$f$$ can be:
$$w_1= \frac{f \lambda}{\pi D}$$.
2. A laser beam can not be kept small over arbitrarily long distances. Immediately after the waist the beam diverges.
$$w (z)= w_0 \sqrt{1+(z/z_R)^2}$$,  with the Rayleigh length  $$z_R = \pi w_0^2/\lambda$$

## Experimental challenge: Lightgrating height

Go to the laboratory and follow the instructions. Once you have accomplished your task, continue here.