Optical lattice – All about the topic

The diffraction of waves can happen at three different obstacles. There are single column, double column and multiple column. Multiple slits are optical gratings. We will cover these in this article. For a better understanding of the topic, read the articles on single-slit diffraction and double-slit interference.

Like the optical lattice, these topics are sub-areas of wave theory and belong to the subject of physics.

What is an optical lattice?

An optical grating can also be referred to as a multiple slit or a diffraction grating. In general, optical gratings are periodic structures used to diffract light. What the diffraction of light is is explained to you in the article on diffraction at a single slit.

From the articles on single-slit diffraction and double-slit interference, we already know that there are single-slits, double-slits and multiple-slits. It is best to read the two articles first to better understand the optical lattice.

An optical grating is a multiple slit, i.e. a series of slits with the same slit width and the same distance from one another. As with single and double slits, light is diffracted in an optical grating. Interference occurs and the resulting interference pattern can be displayed on an observation screen. The interference pattern in an optical grating is the same as that of the double slit with the same slit width. However, the maxima are brighter and sharper. The increased brightness is due to the fact that several columns are illuminated. This allows more light to reach the screen.

Light, which consists of a mixture of different colors, is fanned out into its individual colors like in a prism. An example of such a light is white light. A well-known example from everyday life are CDs. The incident light interferes on its surface. This makes the interference colors visible.

• An optical grating can also be referred to as a multiple slit or a diffraction grating.
• An optical grating is a series of slits with the same slit width and the same distance from one another.
• Because several slits are illuminated with the multiple slit, the interference pattern is brighter and sharper than with the double slit.
• For example, white light is fanned out into its individual colors as with a prism.

How does the optical lattice work?

As with the single slit and the double slit, Huygens’ principle plays a role in the multiple slit. According to Huygens’ principle, when a wave meets a slit, every point on the wave front is a starting point for a new elementary wave. These elementary waves are superimposed and form an interference pattern when they hit the screen.

Gratings work by diffraction of coherent light. The light from the individual columns interferes and forms an interference pattern. Monochromatic light, i.e. single-colored, visible light, is deflected in a few different directions. The deflection angles depend on the grating constant and the wavelength.

The lattice constant

The spacing between the individual columns is called the lattice constant. In the figure above, the lattice constant is marked with b. The smaller the distance between the columns, i.e. the smaller the lattice constant, the greater the distance between the maxima. Optical gratings with several hundred lines per millimeter can be produced. This is a great advantage of the optical grating.

With a double slit, such small slit distances do not work. Since there are only two slits in the double slit, so little light would get through that the diffraction pattern would not be visible. In the case of optical gratings, it is therefore possible to produce small gap distances, so that there are large distances between the maxima.

main maxima

Main maxima occur in optical gratings. These are the spots on the screen where light arrives. Here the waves of the slits interfere constructively. This is the case when the path difference Δs between the individual rays is equal to a multiple of the wavelength. Therefore, for the main maxima:

Δs=k⋅λ

There are also smaller minima and maxima between the main maxima, as can be seen in the following figure.

• Monochrome, visible light is deflected in a few different directions. The deflection angles depend on the grating constant and the wavelength.
• The lattice constant describes the distances between the individual columns.
• The smaller the lattice constant, the greater the distance between the maxima.
• Main maxima are the points on the screen where light arrives and the waves interfere constructively. The following applies: Δs=k⋅λ

What types of optical gratings are there?

Different types of grids can be distinguished. The two most important are the transmission grating and the reflection grating.

The transmission grating

Transmission gratings are those gratings that allow light to pass through. They are also called amplitude grids and consist of a sequence of permeable and impermeable areas. Curtains, for example, act like transmission gratings.

The reflection grid

Reflection gratings are also called phase gratings. They are optical gratings that reflect light. Therefore, they are generally more efficient than transmission gratings because all radiated power contributes to the diffracted power. Mobile phone displays or CDs, for example, act like reflection gratings. This happens with a column spacing below 1.25 µm

• There are, among other things, transmission gratings and reflection gratings.
• Transmission gratings consist of a sequence of transparent and opaque areas.
• Reflective gratings reflect light and are more efficient than transmission gratings.

How are optical gratings used?

Optical gratings are used in optical measuring devices. They are used to monochromatize radiation or to analyze spectra. In addition, laser frequencies are stabilized with optical grids, short high-power laser pulses are amplified and dot patterns are generated in laser shows.

CD as an optical grating

As already mentioned in the article above, CDs can be cited as an example of optical gratings. If you look at a CD in the light, you can see that it shimmers with colour. The reason for this is that CDs act like optical lattices. Interference maxima arise, the position of which depends on the wavelength of the light. The surface appears in different colors depending on the viewing angle.

The digital information on a CD is stored in a spiral track with indentations of different lengths. The distance between the tracks is very small and constant. The surface thus has a regular structure. On the other side of the CD is the reflective layer, so the CD represents a reflective grating.

• CDs act like optical gratings, more precisely like reflection gratings.
• Interference maxima arise, the position of which depends on the wavelength of the light. The surface appears in different colors depending on the viewing angle.

Optical lattice – everything important at a glance:

• An optical grating can also be referred to as a multiple slit or a diffraction grating.
• An optical grating is a series of slits with the same slit width and the same distance from one another.
• The lattice constant describes the distances between the individual columns.
• The smaller the lattice constant, the greater the distance between the maxima.
• Main maxima are the points on the screen where light arrives and the waves interfere constructively. The following applies: Δs=k⋅λ
• Transmission gratings consist of a sequence of transparent and opaque areas.
• Reflective gratings reflect light and are more efficient than transmission gratings.
• CDs act like optical gratings, more precisely like reflection gratings.