Lyot-Filter

Named after its inventor, French astronomers Bernard Lyot Ferdinand, named Lyot filter is an optical filter that uses birefringence, to generate a narrow pass band of the transmitted wavelengths. The scope of the Lyot filter are astronomy, laser physics to realize tunable lasers, and optical data transmission.

Construction

A Lyot filter is made of a birefringent crystal, usually quartz, and a subsequent polarization filter. In order to increase the free spectral range of a plurality of Lyot filter in series. The thickness of the crystal plates is halved with each subsequent filter.

Physical principle

Due to the birefringent properties of the plates, the ordinary and extraordinary components of a light beam subject to different refractive indices and therefore have different phase velocities. This leads to different wavelengths at different phase differences between the ordinary and extraordinary rays, after passing through the crystal. Considering linearly polarized light incident on the filter, the light is elliptically polarized by the disc in general. Only when the phase difference between the two sub-beams corresponding to the light behind the filter in the same way, polarized linearly ( being a natural number ). This is the case only at certain wavelengths.

The field strength is divided parallel to the optical axis ( an extraordinary ray ), and perpendicular to the optical axis ( ordinary ray ) in the components of

When the birefringent crystal is placed in the beam path, in that it starts and ends, and its optical axis coincides with the z- axis, the field strength behind the crystal is

Described. Here, the wave number, and the refractive index of the ordinary and the refractive index of extraordinary ray.

By comparison with the field strength before impinging on the crystal followed by the phase difference between the two partial beams:

So the subsequent polarization filter attenuates components of light that do not have this wavelength. The Lyot filter is thus a wavelength-dependent optical filter. Now let the angle of the polarization filter, set so that the linearly polarized light is optimally transmitted. Now, if the polarization filter is rotated, so the component is only allowed through or intensity

Now, it is also the intensity of light after the intensity and before the Lyot filter. The transmission results after a short calculation to

Or

The free spectral range is obtained from the distance between two maxima

Cascaded Lyot filter

The total transmission of cascaded filters arises from the individual transmissions:

The picture to four Lyot filters were connected in series. The thickness of the plates ( birefringent crystal ) was cut in half with each further filter.

Tunability of the Lyot filter

The transmitted wavelengths of a Lyot filter are through, the thickness of the crystal and respectively, the refractive indices of the ordinary and extraordinary ray of the birefringent material set. If these parameters are changed, then the passband of the filter changes.

The easiest way to the Lyot filter detuning by the crystal about the z -axis is rotated, resulting in a change of. , Is, for example, a cubic crystal, it is minimal when the light is perpendicularly incident on a side surface. The crystal is rotated around the z- axis, so the light must pass through a greater distance in the crystal, resulting in a change in the phase difference between the two partial beams and hence a change in the passband of the filter.

By rotating the crystal at the angle to the x-axis, the transmission maximum of the Lyot filter is changed, since, independently but is dependent on ( refractive index ellipsoid ).

The use of electrically variable birefringence elements (e.g. liquid crystal ) produces a "Electrically tunable Lyot filter ". By varying the field strength of an external electric field, the refractive index of special crystals such as KDP ( potassium dihydrogen phosphate ) by the electro-optical effect is changed. This in turn leads to a tunable Lyot filter, the tunable range is small.