Beam splitter

In its most common form, a cube, a beam splitter is made from two triangular glass prisms which are glued together at their base using polyester, epoxy, or urethane-based adhesives.

The thickness of the resin layer is adjusted such that (for a certain wavelength) half of the light incident through one "port" (i.e., face of the cube) is reflected and the other half is transmitted due to FTIR (frustrated total internal reflection).

This is composed of an optical substrate, which is often a sheet of glass or plastic, with a partially transparent thin coating of metal.

The thickness of the deposit is controlled so that part (typically half) of the light, which is incident at a 45-degree angle and not absorbed by the coating or substrate material, is transmitted and the remainder is reflected.

To reduce loss of light due to absorption by the reflective coating, so-called "Swiss-cheese" beam-splitter mirrors have been used.

Originally, these were sheets of highly polished metal perforated with holes to obtain the desired ratio of reflection to transmission.

Later, metal was sputtered onto glass so as to form a discontinuous coating, or small areas of a continuous coating were removed by chemical or mechanical action to produce a very literally "half-silvered" surface.

Depending on its characteristics (thin-film interference), the ratio of reflection to transmission will vary as a function of the wavelength of the incident light.

Dichroic mirrors are used in some ellipsoidal reflector spotlights to split off unwanted infrared (heat) radiation, and as output couplers in laser construction.

An optically similar system is used in reverse as a beam-combiner in three-LCD projectors, in which light from three separate monochrome LCD displays is combined into a single full-color image for projection.

Arrangements of mirrors or prisms used as camera attachments to photograph stereoscopic image pairs with one lens and one exposure are sometimes called "beam splitters", but that is a misnomer, as they are effectively a pair of periscopes redirecting rays of light which are already non-coincident.

In some very uncommon attachments for stereoscopic photography, mirrors or prism blocks similar to beam splitters perform the opposite function, superimposing views of the subject from two different perspectives through color filters to allow the direct production of an anaglyph 3D image, or through rapidly alternating shutters to record sequential field 3D video.

In order for energy to be conserved (see next section), there must be a phase shift in at least one of the outgoing beams.

In any case, the details of the phase shifts depend on the type and geometry of the beam splitter.

Having determined the constraints describing a lossless beam splitter, the initial expression can be rewritten as Applying different values for the amplitudes and phases can account for many different forms of the beam splitter that can be seen widely used.

These include: In quantum mechanics, the electric fields are operators as explained by second quantization and Fock states.

In this theory, the four ports of the beam splitter are represented by a photon number state

produced by the beam splitter is translated into the same relation of the corresponding quantum creation (or annihilation) operators

The transmission/reflection coefficient factor in the last equation may be written in terms of the reduced parameters that ensure unitarity: where it can be seen that if the beam splitter is 50:50 then

Note that this is true for all types of 50:50 beam splitter irrespective of the details of the phases, and the photons need only be indistinguishable.

From the correspondence principle we might expect the quantum results to tend to the classical one in the limits of large n, but the appearance of large numbers of indistinguishable photons at the input is a non-classical state that does not correspond to a classical field pattern, which instead produces a statistical mixture of different

Rigorous derivation is given in the Fearn–Loudon 1987 paper[4] and extended in Ref [3] to include statistical mixtures with the density matrix.

In 2000 Knill, Laflamme and Milburn (KLM protocol) proved that it is possible to create a universal quantum computer solely with beam splitters, phase shifters, photodetectors and single photon sources.

The beam splitter is an essential component in this scheme since it is the only one that creates entanglement between the Fock states.

In fact, it is possible to simulate arbitrary Gaussian (Bogoliubov) transformations of a quantum state of light by means of beam splitters, phase shifters and photodetectors, given two-mode squeezed vacuum states are available as a prior resource only (this setting hence shares certain similarities with a Gaussian counterpart of the KLM protocol).

[5] The building block of this simulation procedure is the fact that a beam splitter is equivalent to a squeezing transformation under partial time reversal.

Typically, reflection beam splitters are made of metal and have a broadband spectral characteristic.

Due to their compact design, beam splitters of this type are particularly easy to install in infrared detectors.

[9] At this application, the radiation enters through the aperture opening of the detector and is split into several beams of equal intensity but different directions by internal highly reflective microstructures.

Each beam hits a sensor element with an upstream optical filter.