Birefringent filters

Birefringent filter is a commonly used filter element that tunes and compresses spectral line width, which is widely used in dye lasers and solid-state lasers.

When a beam of linear polarized light enters a birefringent crystal, it will be divided into polarized light with vibration directions perpendicular to each other, namely ordinary light (O light) and unusual light (E light). If the angle between the incident light and the optical axis of the crystal is α, the phase difference generated after passing through a crystal with a thickness of d ∆ Ø is

$∆\Phi =\frac{2\pi }{\lambda }(n_0-n_e)d\cos \alpha =\frac{2\pi }{\lambda }∆nd\cos \alpha$

where n subscript o and n subscript e e are the refractive indices of o light and e light respectively, and d is the thickness of the crystal.

When ∆Ø=2kπ, the same linear polarized light as the polarization direction of the incident light is obtained, that is, the polarization state of the incident polarized light is not changed, and the transmittance is the greatest at this time. When ∆Ø=(2k 1)π, a linearly polarized light perpendicular to the polarization direction of the incident light is obtained, and the transmittance is the smallest. The transmittance of a birefringent filter is T left bracket lambda ( lowercase ) right bracket equals cos square left bracket fraction lambda ( lowercase ) divided by normal pi ( lowercase ) increment nd end fraction right bracket

$T\left(\lambda \right)={\cos }^2\left(\frac{\mathrm{\pi }∆\mathrm{nd}}{\lambda }\right)$

where the increment T is the insertion loss.

The line width increment lambda (lowercase) is

$∆\lambda =\frac{{\lambda }^2}{\pi ∆nd}{(∆T)}^{\frac{1}{2}}$

The Free Spectral Range (FSR) is

$F=\frac{{\lambda }^2}{∆nd}$

When the angle between the incident light and the crystal optical axis changes α, the wavelength of the maximum transmittance changes, so as to realize the tuning of the laser.

The spectral transmittance curve of a single birefringent filter is relatively flat, and it is generally difficult to obtain a laser with a narrow line width, so in order to obtain a narrower line width, three birefringent filters of different thicknesses are usually combined (separated by air or glass), as shown in Figure 1.

Fig.1 Birefringent filter with three combinations (thickness ratio=d:2d:9d)

When tuning with several birefringent filters, the thick sheet determines the line width and the thin sheet determines the free spectral range (tuning range). To suppress the transmission subpeaks of the combined birefringent filter, the transmission peaks of the three crystals should coincide at the transmission peaks of the thinnest crystal, so the optical axes of the three crystals are required to be parallel to each other. In addition, in order to improve the polarization of the incident light and reduce the loss, the normal direction of the combined birefringent filter should be at a Brüster angle with the direction of the incident light.