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47-496: Morris developed the Interrotron to improve the interview process in documentary filmmaking. The name "Interrotron" was coined by Morris's wife, Julia Sheehan, combining the concepts of "interview" and "terror," aiming to reduce the interviewee's discomfort. This setup allows for a more intimate and engaging interview, where subjects often reveal more about themselves or their stories. Morris's invention has significantly impacted

94-434: A ^ a † , a ^ b † , a ^ c † {\displaystyle {\hat {a}}_{a}^{\dagger },{\hat {a}}_{b}^{\dagger },{\hat {a}}_{c}^{\dagger }} , and a ^ d † {\displaystyle {\hat {a}}_{d}^{\dagger }} , so that where

141-669: A ^ d † {\displaystyle {\hat {a}}_{c}^{\dagger }{\hat {a}}_{d}^{\dagger }} term has cancelled. Therefore the output states always have even numbers of photons in each arm. A famous example of this is the Hong–Ou–Mandel effect , in which the input has n = m = 1 {\displaystyle n=m=1} , the output is always | 20 ⟩ c d {\displaystyle |20\rangle _{cd}} or | 02 ⟩ c d {\displaystyle |02\rangle _{cd}} , i.e.

188-561: A b {\displaystyle |00\rangle _{ab}} and add a photon in port a to produce then the beam splitter creates a superposition on the outputs of The probabilities for the photon to exit at ports c and d are therefore | r a c | 2 {\displaystyle |r_{ac}|^{2}} and | t a d | 2 {\displaystyle |t_{ad}|^{2}} , as might be expected. Likewise, for any input state | n m ⟩

235-401: A b {\displaystyle |nm\rangle _{ab}} and the output is Using the multi-binomial theorem , this can be written where M = n + m − N {\displaystyle M=n+m-N} and the ( n j ) {\displaystyle {\tbinom {n}{j}}} is a binomial coefficient and it is to be understood that

282-514: A c = ϕ 0 + ϕ R {\displaystyle \phi _{ad}=\phi _{0}+\phi _{T},\phi _{bc}=\phi _{0}-\phi _{T},\phi _{ac}=\phi _{0}+\phi _{R}} (and from the constraint ϕ b d = ϕ 0 − ϕ R − π {\displaystyle \phi _{bd}=\phi _{0}-\phi _{R}-\pi } ), so that where 2 ϕ T {\displaystyle 2\phi _{T}}

329-561: A c = | r a c | e i ϕ a c {\displaystyle r_{ac}=|r_{ac}|e^{i\phi _{ac}}} . The phase factor accounts for possible shifts in phase of a beam as it reflects or transmits at that surface. Then we obtain Further simplifying, the relationship becomes which is true when ϕ a d − ϕ b d + ϕ b c − ϕ

376-469: A c = π {\displaystyle \phi _{ad}-\phi _{bd}+\phi _{bc}-\phi _{ac}=\pi } and the exponential term reduces to -1. Applying this new condition and squaring both sides, it becomes where substitutions of the form | r a c | 2 = 1 − | t a d | 2 {\displaystyle |r_{ac}|^{2}=1-|t_{ad}|^{2}} were made. This leads to

423-542: A d − ϕ b d + ϕ b c − ϕ a c = π {\displaystyle \phi _{ad}-\phi _{bd}+\phi _{bc}-\phi _{ac}=\pi } . To include the constraints and simplify to 4 independent parameters, we may write ϕ a d = ϕ 0 + ϕ T , ϕ b c = ϕ 0 − ϕ T , ϕ

470-608: A dielectric surface such as glass, and the electric field of the light wave is in the plane of the surface, then the reflected wave will have a phase shift of π, while the transmitted wave will not have a phase shift; the blue arrow does not pick up a phase-shift, because it is reflected from a medium with a lower refractive index. The behavior is dictated by the Fresnel equations . This does not apply to partial reflection by conductive (metallic) coatings, where other phase shifts occur in all paths (reflected and transmitted). In any case,

517-440: A device was used in three-pickup-tube color television cameras and the three-strip Technicolor movie camera. It is currently used in modern three-CCD cameras. 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. Beam splitters with single-mode fiber for PON networks use

SECTION 10

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564-456: A prior resource only (this setting hence shares certain similarities with a Gaussian counterpart of the KLM protocol ). The building block of this simulation procedure is the fact that a beam splitter is equivalent to a squeezing transformation under partial time reversal . Reflection beam splitters reflect parts of the incident radiation in different directions. These partial beams show exactly

611-494: A symmetric beam splitter ϕ 0 = ϕ T = 0 , ϕ R = π / 2 {\displaystyle \phi _{0}=\phi _{T}=0,\phi _{R}=\pi /2} ), and for other phases where the output goes to one arm (e.g. the dielectric beam splitter ϕ 0 = ϕ T = ϕ R = 0 {\displaystyle \phi _{0}=\phi _{T}=\phi _{R}=0} )

658-430: Is a simplified version of Ref. The relation between the classical field amplitudes E a , E b , E c {\displaystyle {E}_{a},{E}_{b},{E}_{c}} , and E d {\displaystyle {E}_{d}} produced by the beam splitter is translated into the same relation of the corresponding quantum creation (or annihilation) operators

705-556: Is an optical device that splits a beam of light into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as interferometers , also finding widespread application in fibre optic telecommunications . 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. (Before these synthetic resins , natural ones were used, e.g. Canada balsam .) The thickness of

752-487: Is an essential component in this scheme since it is the only one that creates entanglement between the Fock states . Similar settings exist for continuous-variable quantum information processing . 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

799-852: Is given in the Fearn–Loudon 1987 paper and extended in Ref to include statistical mixtures with the density matrix . In general, for a non-symmetric beam-splitter, namely a beam-splitter for which the transmission and reflection coefficients are not equal, one can define an angle θ {\displaystyle \theta } such that { | R | = sin ⁡ ( θ ) | T | = cos ⁡ ( θ ) {\displaystyle {\begin{cases}|R|=\sin(\theta )\\|T|=\cos(\theta )\end{cases}}} where R {\displaystyle R} and T {\displaystyle T} are

846-446: Is possible to create a universal quantum computer solely with beam splitters, phase shifters, photodetectors and single photon sources. The states that form a qubit in this protocol are the one-photon states of two modes, i.e. the states |01⟩ and |10⟩ in the occupation number representation ( Fock state ) of two modes. Using these resources it is possible to implement any single qubit gate and 2-qubit probabilistic gates. The beam splitter

893-765: Is produced when θ = π / 4 {\displaystyle \theta =\pi /4} . The dielectric beam splitter above, for example, has i.e. ϕ T = ϕ R = ϕ 0 = 0 {\displaystyle \phi _{T}=\phi _{R}=\phi _{0}=0} , while the "symmetric" beam splitter of Loudon has i.e. ϕ T = 0 , ϕ R = − π / 2 , ϕ 0 = π / 2 {\displaystyle \phi _{T}=0,\phi _{R}=-\pi /2,\phi _{0}=\pi /2} . Beam splitters have been used in both thought experiments and real-world experiments in

940-412: Is the beam-splitter transfer matrix and r and t are the reflectance and transmittance along a particular path through the beam splitter, that path being indicated by the subscripts. (The values depend on the polarization of the light.) If the beam splitter removes no energy from the light beams, the total output energy can be equated with the total input energy, reading Inserting the results from

987-734: Is the phase difference between the transmitted beams and similarly for 2 ϕ R {\displaystyle 2\phi _{R}} , and ϕ 0 {\displaystyle \phi _{0}} is a global phase. Lastly using the other constraint that R 2 + T 2 = 1 {\displaystyle R^{2}+T^{2}=1} we define θ = arctan ⁡ ( R / T ) {\displaystyle \theta =\arctan(R/T)} so that T = cos ⁡ θ , R = sin ⁡ θ {\displaystyle T=\cos \theta ,R=\sin \theta } , hence A 50:50 beam splitter

SECTION 20

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1034-434: Is the use of a half-silvered mirror. 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 thin coating can be aluminium deposited from aluminium vapor using a physical vapor deposition method. 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

1081-419: 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 . A third version of the beam splitter is a dichroic mirrored prism assembly which uses dichroic optical coatings to divide an incoming light beam into a number of spectrally distinct output beams. Such

1128-413: The amplitudes of the two outgoing beams are the sums of the (complex) amplitudes calculated from each of the incoming beams, and it may result that one of the two outgoing beams has amplitude zero. In order for energy to be conserved (see next section), there must be a phase shift in at least one of the outgoing beams. For example (see red arrows in picture on the right), if a polarized light wave in air hits

1175-455: The area of quantum theory and relativity theory and other fields of physics . These include: In quantum mechanics, the electric fields are operators as explained by second quantization and Fock states . Each electrical field operator can further be expressed in terms of modes representing the wave behavior and amplitude operators, which are typically represented by the dimensionless creation and annihilation operators . In this theory,

1222-456: The coating or substrate material, is transmitted and the remainder is reflected. A very thin half-silvered mirror used in photography is often called a pellicle mirror . 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

1269-437: The coefficient is zero if j ∉ { 0 , n } {\displaystyle j\notin \{0,n\}} etc. 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 tan ⁡ θ = 1 {\displaystyle \tan \theta =1} and

1316-454: The complex conjugate. It is now easy to show that τ † τ = I {\displaystyle \tau ^{\dagger }\tau =\mathbf {I} } where I {\displaystyle \mathbf {I} } is the identity, i.e. the beam-splitter transfer matrix is a unitary matrix . Each r and t can be written as a complex number having an amplitude and phase factor; for instance, r

1363-415: The details of the phase shifts depend on the type and geometry of the beam splitter. For beam splitters with two incoming beams, using a classical, lossless beam splitter with electric fields E a and E b each incident at one of the inputs, the two output fields E c and E d are linearly related to the inputs through where the 2×2 element τ {\displaystyle \tau }

1410-413: The device is shown in the diagram. A light beam enters the first prism (A), and the blue component of the beam is reflected from a low-pass filter coating (F 1 ) that reflects blue light (high-frequency), but transmits longer wavelengths (lower frequencies). The blue beam undergoes total internal reflection from the front of prism A and exits it through a side face. The remainder of the beam enters

1457-412: The device to be used as a teleprompter by displaying text instead of the interviewer's face. The Interrotron has been praised for its ability to create a more personal and engaging interview experience, though some argue it can lead to an overly stylized portrayal of the subject. Its use has influenced documentary filmmaking beyond Morris's work. Beam splitter A beam splitter or beamsplitter

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1504-450: The four ports of the beam splitter are represented by a photon number state | n ⟩ {\displaystyle |n\rangle } and the action of a creation operation is a ^ † | n ⟩ = n + 1 | n + 1 ⟩ {\displaystyle {\hat {a}}^{\dagger }|n\rangle ={\sqrt {n+1}}|n+1\rangle } . The following

1551-536: The light's wavelength. That is, certain surfaces within the prism act as dichroic filters . These are used as beam splitters in many optical instruments . (See: Dichroism , for the etymology of the term.) One common application of dichroic prisms is in some camcorders and high-quality digital cameras . A trichroic prism assembly is a combination of two dichroic prisms which are used to split an image into red, green, and blue components, which can be separately detected on three CCD arrays . A possible layout for

1598-383: The only factor that depends on j is the ( − 1 ) j {\displaystyle (-1)^{j}} term. This factor causes interesting interference cancellations. For example, if n = m {\displaystyle n=m} and the beam splitter is 50:50, then where the a ^ c †

1645-435: 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. Beam splitters are sometimes used to recombine beams of light, as in a Mach–Zehnder interferometer . In this case there are two incoming beams, and potentially two outgoing beams. But

1692-570: The output is always in the same arm, not random in either arm as is the case here. 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 | n , m ⟩ {\displaystyle |n,m\rangle } known as Poissonian light . Rigorous derivation

1739-405: The probability of output with a photon in each mode (a coincidence event) is zero. 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. This contrasts with the classical result, in which equal output in both arms for equal inputs on a 50:50 beam splitter does appear for specific beam splitter phases (e.g.

1786-642: The reflection and transmission coefficients. Then the unitary operation associated with the beam-splitter is then U ^ = e i θ ( a ^ a † a ^ b + a ^ a a ^ b † ) . {\displaystyle {\hat {U}}=e^{i\theta \left({\hat {a}}_{a}^{\dagger }{\hat {a}}_{b}+{\hat {a}}_{a}{\hat {a}}_{b}^{\dagger }\right)}.} In 2000 Knill, Laflamme and Milburn ( KLM protocol ) proved that it

1833-469: 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) . Polarizing beam splitters , such as the Wollaston prism , use birefringent materials to split light into two beams of orthogonal polarization states. Another design

1880-646: The result and similarly, It follows that R 2 + T 2 = 1 {\displaystyle R^{2}+T^{2}=1} . 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. The transfer matrix appears to have 6 amplitude and phase parameters, but it also has 2 constraints: R 2 + T 2 = 1 {\displaystyle R^{2}+T^{2}=1} and ϕ

1927-597: The same intensity. Typically, reflection beam splitters are made of metal and have a broadband spectral characteristic. Dichroic prism A dichroic prism is a prism that splits light into two beams of differing wavelengths (colour). A trichroic prism assembly combines two dichroic prisms to split an image into 3 colours, typically as red, green and blue of the RGB colour model . They are usually constructed of one or more glass prisms with dichroic optical coatings that selectively reflect or transmit light depending on

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1974-399: The second prism (B) and is split by a second filter coating (F 2 ) which reflects red light but transmits shorter wavelengths. The red beam is also totally internally reflected due to a small air-gap between prisms A and B. The remaining green component of the beam travels through prism C. The trichroic prism assembly can be used in reverse to combine red, green and blue beams into

2021-546: The single-mode behavior to split the beam. The splitter is done by physically splicing two fibers "together" as an X. 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

2068-407: The style and approach of documentary interviews. Critics and filmmakers alike have noted the device's effectiveness in establishing a unique connection between the subject and the viewer. The Interrotron utilizes beam splitter glass and a monitor setup, allowing direct eye contact and reducing the interviewee's anxiety. This technique is not only beneficial for the production quality but also allows

2115-506: The transfer equation above with E b = 0 {\displaystyle E_{b}=0} produces and similarly for then E a = 0 {\displaystyle E_{a}=0} When both E a {\displaystyle E_{a}} and E b {\displaystyle E_{b}} are non-zero, and using these two results we obtain where " ∗ {\displaystyle ^{\ast }} " indicates

2162-418: The transfer matrix is given in classical lossless beam splitter section above: Since τ {\displaystyle \tau } is unitary, τ − 1 = τ † {\displaystyle \tau ^{-1}=\tau ^{\dagger }} , i.e. This is equivalent to saying that if we start from the vacuum state | 00 ⟩

2209-408: 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. Instead of a metallic coating, a dichroic optical coating may be used. Depending on its characteristics ( thin-film interference ), the ratio of reflection to transmission will vary as a function of

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