Amplitude splitting utilized in cube beamsplitters is done by dielectric interference coatings or half-silvered mirrors. The splitting ratio is simply provided by the used filter design. Two prisms with a 45° angle are cemented together with the coating in between. Polarizing beam splitters are a commonly used alternative, where one polarization is transmitted and the other (perpendicular one) reflected. In the latter case, the splitting ratio can be adjusted by a polarization rotator before the element. For more details see: https://en.wikipedia.org/wiki/Beam_splitter

A beam splitter (or beamsplitter, power splitter) is an optical device which can split an incident light beam (e.g. a laser beam) into two or more beams, which may or may not have the same optical power. Different types of beam splitters exist, as described in the following, and are used for very different purposes. For example, beam splitters are required for interferometers, autocorrelators, cameras, projectors and laser systems.

− Types of Beam Splitters

− Dielectric Mirrors

A partially reflecting mirror, used as a beam splitter.

Any partially reflecting mirror can be used for splitting light beams. In laser technology, dielectric mirrors are often used for such purposes. The angle of incidence, also determining the angular separation of the output beams, may be 45° (as in Figure 1), which is often convenient, but it can also have other values, and influences the characteristics of the beam splitter. A wide range of power splitting ratios can be achieved via different designs of the dielectric coating.

In general, the reflectivity of a dichroic mirror depends on the polarization state of the beam. Such a device can be optimized to function as a thin-film polarizer, where in some wavelength range a beam with a certain polarization can be nearly totally reflected, while a beam with different polarization is largely transmitted. On the other hand, it is also possible to optimize for a minimized polarization dependence to obtain a non-polarizing beam splitter. This is most easily achieved for near normal incidence.

Dielectric beam splitters can also have a strongly wavelength-dependent reflectivity. This can be used for dichroic beam splitters (→ dichroic mirrors), which can separate spectral components of a beam. For example, such a device may be used after a frequency doubler for separating the harmonic beam from residual pump light. The separation may occur based on the difference in wavelength or polarization.

A beam splitter cube, which may be polarizing or non-polarizing.

Many beam splitters have the form of a cube, where the beam separation occurs at an interface within the cube. Such a cube is often made of two triangular glass prisms which are glued together with some transparent resin or cement. The thickness of that layer can be used to adjust the power splitting ratio for a given wavelength.

Instead of glass, crystalline media can be used, which can be birefringent. This allows the construction of various types of polarizing beam splitter cubes such as Wollaston prisms and Nomarski prisms, where the two output beams emerge from the same face, and the angle between these beams is typically between 15° and 45°, i.e., much smaller than shown in Figure 2. Other types are the Glan–Thompson prism, and the Nicol prism, the latter having a rhombohedral form (i.e., not that of a cube).

It is also possible to use a multilayer coating within a cube. This further expands the possible device characteristics, e.g. in terms of operation bandwidth or polarizing properties.

Beam splitter cubes can be used not only for simple light beams, but also for beams carrying images, e.g. in various types of cameras and projectors.

Resources

https://www.rp-photonics.com/beam_splitters.html

It is better explained here.

http://olympusmicro.com/primer/java/prismsandbeamsplitters/beamsplitters/index.html

Let me recommend Article Quantum Physics of Simple Optical Instruments

Equation 3.19 is explicit enough, but 4.24 and the text which follow should also help.