7433:
6337:
7428:{\displaystyle {\begin{aligned}|\psi _{\text{out}}\rangle &={\frac {1}{\sqrt {n!m!}}}\sum _{j=0}^{n}\sum _{k=0}^{m}{\binom {n}{j}}\left(r_{ac}^{\ast }{\hat {a}}_{c}^{\dagger }\right)^{j}\left(t_{ad}^{\ast }{\hat {a}}_{d}^{\dagger }\right)^{(n-j)}{\binom {m}{k}}\left(t_{bc}^{\ast }{\hat {a}}_{c}^{\dagger }\right)^{k}\left(r_{bd}^{\ast }{\hat {a}}_{d}^{\dagger }\right)^{(m-k)}|00\rangle _{cd}\\&={\frac {1}{\sqrt {n!m!}}}\sum _{N=0}^{n+m}\sum _{j=0}^{N}{\binom {n}{j}}r_{ac}^{\ast j}t_{ad}^{\ast (n-j)}{\binom {m}{N-j}}t_{bc}^{\ast (N-j)}r_{bd}^{\ast (m-N+j)}\left({\hat {a}}_{c}^{\dagger }\right)^{N}\left({\hat {a}}_{d}^{\dagger }\right)^{M}|00\rangle _{cd},\\&={\frac {1}{\sqrt {n!m!}}}\sum _{N=0}^{n+m}\sum _{j=0}^{N}{\binom {n}{j}}{\binom {m}{N-j}}r_{ac}^{\ast j}t_{ad}^{\ast (n-j)}t_{bc}^{\ast (N-j)}r_{bd}^{\ast (m-N+j)}{\sqrt {N!M!}}\quad |N,M\rangle _{cd},\end{aligned}}}
248:
9779:
9711:
395:. In this case there are two incoming beams, and potentially two outgoing beams. But 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 a
5263:
6322:
9131:, i.e. 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. a symmetric beam splitter
36:
133:
4939:
3233:
158:
8949:
5013:
6027:
656:
5670:
4655:
2649:
6016:
4670:
3663:
2995:
8041:
5258:{\displaystyle \left({\begin{matrix}{\hat {a}}_{a}^{\dagger }\\{\hat {a}}_{b}^{\dagger }\end{matrix}}\right)=\left({\begin{matrix}r_{ac}^{\ast }&t_{ad}^{\ast }\\t_{bc}^{\ast }&r_{bd}^{\ast }\end{matrix}}\right)\left({\begin{matrix}{\hat {a}}_{c}^{\dagger }\\{\hat {a}}_{d}^{\dagger }\end{matrix}}\right).}
7932:
6317:{\displaystyle |\psi _{\text{out}}\rangle ={\frac {1}{\sqrt {n!}}}\left(r_{ac}^{\ast }{\hat {a}}_{c}^{\dagger }+t_{ad}^{\ast }{\hat {a}}_{d}^{\dagger }\right)^{n}{\frac {1}{\sqrt {m!}}}\left(t_{bc}^{\ast }{\hat {a}}_{c}^{\dagger }+r_{bd}^{\ast }{\hat {a}}_{d}^{\dagger }\right)^{m}|00\rangle _{cd}.}
399:
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
366:
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
449:
5432:
4501:
2423:
268:
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 the coating or substrate material, is transmitted and the remainder is reflected. A very thin half-silvered mirror used in
5827:
9633:
4934:{\displaystyle \tau =\left({\begin{matrix}r_{ac}&t_{bc}\\t_{ad}&r_{bd}\end{matrix}}\right)=e^{i\phi _{0}}\left({\begin{matrix}\sin \theta e^{i\phi _{R}}&\cos \theta e^{-i\phi _{T}}\\\cos \theta e^{i\phi _{T}}&-\sin \theta e^{-i\phi _{R}}\end{matrix}}\right).}
1854:
3473:
2925:
1640:
404:. 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, the details of the phase shifts depend on the type and geometry of the beam splitter.
3228:{\displaystyle {\begin{aligned}\phi _{T}&={\tfrac {1}{2}}\left(\phi _{ad}-\phi _{bc}\right)\\\phi _{R}&={\tfrac {1}{2}}\left(\phi _{ac}-\phi _{bd}+\pi \right)\\\phi _{0}&={\tfrac {1}{2}}\left(\phi _{ad}+\phi _{bc}\right)\end{aligned}}}
9786:
Reflection beam splitters reflect parts of the incident radiation in different directions. These partial beams show exactly the same intensity. Typically, reflection beam splitters are made of metal and have a broadband spectral characteristic.
5421:
8944:{\displaystyle {\begin{aligned}\left({\hat {a}}_{a}^{\dagger }\right)^{n}\left({\hat {a}}_{b}^{\dagger }\right)^{m}&\to \left^{n}\\&=\left^{n}\\&=\left^{2n}\left^{n}\\&={\frac {e^{-2in\phi _{0}}}{2^{n}}}\left^{n}\end{aligned}}}
9650:
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 |01âź© and |10âź© in the occupation number representation
7564:
2115:
4452:
3784:
3923:
9798:
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. Particularly in
651:{\displaystyle \mathbf {E} _{\text{out}}={\begin{bmatrix}E_{c}\\E_{d}\end{bmatrix}}={\begin{bmatrix}r_{ac}&t_{bc}\\t_{ad}&r_{bd}\end{bmatrix}}{\begin{bmatrix}E_{a}\\E_{b}\end{bmatrix}}=\tau \mathbf {E} _{\text{in}},}
9442:
9655:) of two modes. Using these resources it is possible to implement any single qubit gate and 2-qubit probabilistic gates. The beam splitter is an essential component in this scheme since it is the only one that creates
9271:, 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
4269:
5665:{\displaystyle |\psi _{\text{out}}\rangle =\left(r_{ac}^{\ast }{\hat {a}}_{c}^{\dagger }+t_{ad}^{\ast }{\hat {a}}_{d}^{\dagger }\right)|00\rangle _{cd}=r_{ac}^{\ast }|10\rangle _{cd}+t_{ad}^{\ast }|01\rangle _{cd}.}
255:
Another design 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
9017:
4650:{\displaystyle \left({\begin{matrix}{\hat {a}}_{c}^{\dagger }\\{\hat {a}}_{d}^{\dagger }\end{matrix}}\right)=\tau \left({\begin{matrix}{\hat {a}}_{a}^{\dagger }\\{\hat {a}}_{b}^{\dagger }\end{matrix}}\right)}
2644:{\displaystyle {\begin{bmatrix}E_{c}\\E_{d}\end{bmatrix}}={\begin{bmatrix}Re^{i\phi _{ac}}&Te^{i\phi _{bc}}\\Te^{i\phi _{ad}}&Re^{i\phi _{bd}}\end{bmatrix}}{\begin{bmatrix}E_{a}\\E_{b}\end{bmatrix}}.}
2785:
1941:
838:
6011:{\displaystyle |\psi _{\text{in}}\rangle =|nm\rangle _{ab}={\frac {1}{\sqrt {n!}}}\left({\hat {a}}_{a}^{\dagger }\right)^{n}{\frac {1}{\sqrt {m!}}}\left({\hat {a}}_{b}^{\dagger }\right)^{m}|00\rangle _{ab}}
4016:
1241:
9491:
9202:
8046:
6342:
3000:
2987:
1651:
1308:
281:" 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
9261:
3846:
1429:
3465:
285:
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.
1090:
966:
5005:
3658:{\displaystyle \tau =e^{i\phi _{0}}{\begin{bmatrix}\sin \theta e^{i\phi _{R}}&\cos \theta e^{-i\phi _{T}}\\\cos \theta e^{i\phi _{T}}&-\sin \theta e^{-i\phi _{R}}\end{bmatrix}}.}
2204:
2363:
2282:
4493:
4328:
3415:
384:
2790:
1437:
9129:
9091:
7515:
5820:
5304:
7553:
7967:
3700:
5316:
3369:
2701:
2412:
9303:
5775:
5728:
1330:
4189:
3296:
3266:
7927:{\displaystyle r_{ac}^{\ast j}t_{ad}^{\ast (n-j)}t_{bc}^{\ast (N-j)}r_{bd}^{\ast (m-N+j)}=(-1)^{j}\tan ^{2j}\theta (-\tan \theta )^{m-N}\cos ^{n+m}\theta \exp -i\left.}
3323:
8007:
1270:
9342:
7474:
4357:
1002:
874:
9803:, this design enables measurement with only one beam with a minimal beam cross-section, which significantly increases the interference immunity of the measurement.
9324:
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
9053:
4962:
1949:
1147:
1120:
679:
4362:
8033:
3712:
3854:
9484:
9464:
4106:
697:
along a particular path through the beam splitter, that path being indicated by the subscripts. (The values depend on the polarization of the light.)
9349:
2654:
Applying different values for the amplitudes and phases can account for many different forms of the beam splitter that can be seen widely used.
225:
9965:
9875:
Campos, Richard; Bahaa, Saleh; Malvin, Teich (Aug 1, 1989). "Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics".
4194:
7558:
The transmission/reflection coefficient factor in the last equation may be written in terms of the reduced parameters that ensure unitarity:
9976:
362:
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
9977:
Digital diffractive optics: an introduction to planar diffractive optics and related technology, Bernard C. Kress, Patrick
Meyrueis , 2005.
341:
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-
700:
If the beam splitter removes no energy from the light beams, the total output energy can be equated with the total input energy, reading
8957:
333:
to divide an incoming light beam into a number of spectrally distinct output beams. Such a device was used in three-pickup-tube color
2706:
1862:
706:
4359:
produced by the beam splitter is translated into the same relation of the corresponding quantum creation (or annihilation) operators
9628:{\displaystyle {\hat {U}}=e^{i\theta \left({\hat {a}}_{a}^{\dagger }{\hat {a}}_{b}+{\hat {a}}_{a}{\hat {a}}_{b}^{\dagger }\right)}.}
3931:
9833:
9754:
1155:
9812:
9667:
9019:
term has cancelled. Therefore the output states always have even numbers of photons in each arm. A famous example of this is the
1431:. The phase factor accounts for possible shifts in phase of a beam as it reflects or transmits at that surface. Then is obtained
4099:
9134:
1849:{\displaystyle {\frac {|r_{ac}|}{|t_{ad}|}}=-{\frac {|r_{bd}|}{|t_{bc}|}}e^{i(\phi _{ad}-\phi _{bd}+\phi _{bc}-\phi _{ac})}}
181:
into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as
100:
355:
use the single-mode behavior to split the beam. The splitter is done by physically splicing two fibers "together" as an X.
9678:
are available as a prior resource only (this setting hence shares certain similarities with a
Gaussian counterpart of the
9312:
Rigorous derivation is given in the Fearn–Loudon 1987 paper and extended in Ref to include statistical mixtures with the
72:
9987:
9683:
4160:
2930:
1275:
348:, in which light from three separate monochrome LCD displays is combined into a single full-color image for projection.
9486:
are the reflection and transmission coefficients. Then the unitary operation associated with the beam-splitter is then
9207:
3792:
119:
79:
1355:
4080:
3420:
9998:
2417:
Having determined the constraints describing a lossless beam splitter, the initial expression can be rewritten as
1009:
882:
4967:
4128:
4124:
4058:
2123:
392:
304:
2293:
2212:
4457:
86:
57:
53:
9800:
9020:
4274:
4159:
representing the wave behavior and amplitude operators, which are typically represented by the dimensionless
413:
2920:{\displaystyle \phi _{ad}=\phi _{0}+\phi _{T},\phi _{bc}=\phi _{0}-\phi _{T},\phi _{ac}=\phi _{0}+\phi _{R}}
1635:{\displaystyle |r_{ac}||t_{bc}|e^{i(\phi _{ac}-\phi _{bc})}+|t_{ad}||r_{bd}|e^{i(\phi _{ad}-\phi _{bd})}=0.}
9741:. A diffractive beam splitter can generate either a 1-dimensional beam array (1xN) or a 2-dimensional beam
4132:
4094:
278:
17:
9929:
Chakhmakhchyan, Levon; Cerf, Nicolas (2018). "Simulating arbitrary
Gaussian circuits with linear optics".
6328:
3374:
68:
10024:
1943:
and the exponential term reduces to -1. Applying this new condition and squaring both sides, it becomes
9682:). The building block of this simulation procedure is the fact that a beam splitter is equivalent to a
9306:
9096:
9058:
7479:
5784:
5416:{\displaystyle |\psi _{\text{in}}\rangle ={\hat {a}}_{a}^{\dagger }|00\rangle _{ab}=|10\rangle _{ab},}
5271:
9718:
9703:
9671:
7520:
2657:
The transfer matrix appears to have 6 amplitude and phase parameters, but it also has 2 constraints:
265:
9966:
Diffraction
Gratings and Applications, Loewen, Erwin C. and Popov, Evgeny. Marcel Dekker, Inc. 1997.
9358:
7940:
4271:. The following is a simplified version of Ref. The relation between the classical field amplitudes
3671:
9988:
Diffractive Optics – Design, Fabrication and Test, O'Shea, Suleski, Kathman and
Prather, 2004. p.83
9860:
R. Loudon, The quantum theory of light, third edition, Oxford
University Press, New York, NY, 2000.
9264:
3328:
2660:
2371:
372:
9274:
5733:
5686:
4102:
of 1978, 1984 etc., to test what makes a photon behave as a wave or a particle and when it happens
4083:
of 1932 to test the independence of the speed of light and the velocity of the measuring apparatus
1313:
9675:
9674:
of a quantum state of light by means of beam splitters, phase shifters and photodetectors, given
4156:
352:
46:
9782:
Principle drawing of a reflection beam splitter in a pyroelectric sensor (four optical channels)
9263:) the output is always in the same arm, not random in either arm as is the case here. From the
4166:
3271:
3241:
4163:. In this theory, the four ports of the beam splitter are represented by a photon number state
4110:
3301:
296:
7976:
2110:{\displaystyle {\frac {1-|t_{ad}|^{2}}{|t_{ad}|^{2}}}={\frac {1-|t_{bc}|^{2}}{|t_{bc}|^{2}}},}
1249:
9790:
Due to their compact design, beam splitters of this type are particularly easy to install in
9327:
7441:
4447:{\displaystyle {\hat {a}}_{a}^{\dagger },{\hat {a}}_{b}^{\dagger },{\hat {a}}_{c}^{\dagger }}
4333:
4114:
4086:
974:
846:
9204:), and for other phases where the output goes to one arm (e.g. the dielectric beam splitter
3779:{\displaystyle \tau ={\frac {1}{\sqrt {2}}}{\begin{bmatrix}1&1\\1&-1\end{bmatrix}},}
9734:
9656:
9026:
4947:
4090:
4031:
3918:{\displaystyle \tau ={\frac {1}{\sqrt {2}}}{\begin{bmatrix}1&i\\i&1\end{bmatrix}},}
1125:
1098:
664:
412:
For beam splitters with two incoming beams, using a classical, lossless beam splitter with
241:
221:
93:
8:
10029:
9267:
we might expect the quantum results to tend to the classical one in the limits of large
8012:
4148:
4136:
4118:
4062:
9938:
9469:
9449:
4027:
316:
189:
174:
9915:
9791:
7517:
is a binomial coefficient and it is to be understood that the coefficient is zero if
4069:
4051:
4039:
4035:
401:
334:
2787:. To include the constraints and simplify to 4 independent parameters, we may write
10019:
9948:
9911:
9884:
9766:
9647:
200:
In its most common form, a cube, a beam splitter is made from two triangular glass
9746:
277:. To reduce loss of light due to absorption by the reflective coating, so-called "
8009:
term. This factor causes interesting interference cancellations. For example, if
4076:'s claim of a positive result from repetitions of the Michelson-Morley experiment
345:
330:
292:
274:
247:
233:
9778:
9952:
9710:
9313:
1349:
1333:
323:
312:
201:
182:
9902:
Fearn, H.; Loudon, R. (1987). "Quantum theory of the lossless beam splitter".
9437:{\displaystyle {\begin{cases}|R|=\sin(\theta )\\|T|=\cos(\theta )\end{cases}}}
10013:
9888:
9750:
9738:
9722:
9721:(also known as multispot beam generator or array beam generator) is a single
4073:
694:
213:
220:) half of the light incident through one "port" (i.e., face of the cube) is
9679:
9643:
358:
Arrangements of mirrors or prisms used as camera attachments to photograph
237:
9733:
retains the same optical characteristics as the input beam, such as size,
299:), the ratio of reflection to transmission will vary as a function of the
9981:
9660:
4264:{\displaystyle {\hat {a}}^{\dagger }|n\rangle ={\sqrt {n+1}}|n+1\rangle }
690:
368:
359:
338:
270:
216:.) The thickness of the resin layer is adjusted such that (for a certain
186:
9970:
9742:
4147:
In quantum mechanics, the electric fields are operators as explained by
3268:
is the phase difference between the transmitted beams and similarly for
9959:
9762:
9758:
9730:
9726:
9690:
9652:
4155:. Each electrical field operator can further be expressed in terms of
4152:
396:
391:
Beam splitters are sometimes used to recombine beams of light, as in a
300:
282:
217:
363:
327:
257:
229:
5268:
This is equivalent to saying that if we start from the vacuum state
35:
9943:
9795:
308:
289:
9012:{\displaystyle {\hat {a}}_{c}^{\dagger }{\hat {a}}_{d}^{\dagger }}
5426:
then the beam splitter creates a superposition on the outputs of
4043:
157:
2780:{\displaystyle \phi _{ad}-\phi _{bd}+\phi _{bc}-\phi _{ac}=\pi }
1936:{\displaystyle \phi _{ad}-\phi _{bd}+\phi _{bc}-\phi _{ac}=\pi }
833:{\displaystyle |E_{c}|^{2}+|E_{d}|^{2}=|E_{a}|^{2}+|E_{b}|^{2}.}
383:
132:
1272:" indicates the complex conjugate. It is now easy to show that
4011:{\displaystyle \phi _{T}=0,\phi _{R}=-\pi /2,\phi _{0}=\pi /2}
387:
Phase shift through a beam splitter with a dielectric coating.
9831:
7937:
where it can be seen that if the beam splitter is 50:50 then
1332:
is the identity, i.e. the beam-splitter transfer matrix is a
261:
209:
205:
178:
1236:{\displaystyle r_{ac}t_{bc}^{\ast }+t_{ad}r_{bd}^{\ast }=0,}
843:
Inserting the results from the transfer equation above with
9714:
7x7 matrix using green laser and diffractive beam splitter.
9430:
3325:
is a global phase. Lastly using the other constraint that
429:
each incident at one of the inputs, the two output fields
371:
image, or through rapidly alternating shutters to record
342:
303:
of the incident light. Dichroic mirrors are used in some
9794:. At this application, the radiation enters through the
400:
lower refractive index. The behavior is dictated by the
204:
which are glued together at their base using polyester,
208:, or urethane-based adhesives. (Before these synthetic
9197:{\displaystyle \phi _{0}=\phi _{T}=0,\phi _{R}=\pi /2}
7484:
5189:
5093:
5022:
4784:
4685:
4584:
4510:
3881:
3848:, while the "symmetric" beam splitter of Loudon has
3739:
3508:
3171:
3093:
3021:
2603:
2475:
2432:
592:
516:
473:
240:
materials to split light into two beams of orthogonal
9494:
9472:
9452:
9352:
9330:
9277:
9210:
9137:
9099:
9061:
9029:
8960:
8044:
8015:
7979:
7943:
7567:
7523:
7482:
7444:
6340:
6030:
5830:
5787:
5736:
5689:
5435:
5319:
5274:
5016:
4970:
4950:
4673:
4661:
4504:
4460:
4365:
4336:
4277:
4197:
4169:
3934:
3857:
3795:
3715:
3674:
3476:
3423:
3377:
3331:
3304:
3274:
3244:
2998:
2933:
2793:
2709:
2663:
2426:
2374:
2296:
2215:
2126:
1952:
1865:
1654:
1440:
1358:
1316:
1278:
1252:
1158:
1149:
are non-zero, and using these two results we obtain
1128:
1101:
1012:
977:
885:
849:
709:
667:
452:
153:
In practice, the reflective layer absorbs some light.
9637:
4061:
of 1887 to measure the effect of the (hypothetical)
1352:
having an amplitude and phase factor; for instance,
9646:) proved that it is possible to create a universal
2982:{\displaystyle \phi _{bd}=\phi _{0}-\phi _{R}-\pi }
407:
60:. Unsourced material may be challenged and removed.
9928:
9668:continuous-variable quantum information processing
9627:
9478:
9458:
9436:
9336:
9297:
9255:
9196:
9123:
9085:
9047:
9011:
8943:
8027:
8001:
7961:
7926:
7547:
7509:
7468:
7427:
6316:
6010:
5814:
5769:
5722:
5675:The probabilities for the photon to exit at ports
5664:
5415:
5298:
5257:
4999:
4956:
4933:
4649:
4487:
4446:
4351:
4322:
4263:
4183:
4010:
3917:
3840:
3778:
3694:
3657:
3459:
3409:
3363:
3317:
3290:
3260:
3227:
2981:
2919:
2779:
2695:
2643:
2406:
2357:
2276:
2198:
2109:
1935:
1848:
1634:
1423:
1324:
1303:{\displaystyle \tau ^{\dagger }\tau =\mathbf {I} }
1302:
1264:
1235:
1141:
1114:
1084:
996:
960:
868:
832:
673:
650:
27:Optical device which splits a beam of light in two
9874:
7242:
7221:
7212:
7199:
6937:
6916:
6853:
6840:
6601:
6588:
6449:
6436:
4142:
10011:
9670:. In fact, it is possible to simulate arbitrary
9256:{\displaystyle \phi _{0}=\phi _{T}=\phi _{R}=0}
4089:(from ca. 1972) to demonstrate consequences of
4054:of 1851 to measure the speeds of light in water
3841:{\displaystyle \phi _{T}=\phi _{R}=\phi _{0}=0}
295:may be used. Depending on its characteristics (
136:Schematic illustration of a beam splitter cube.
9319:
1645:Further simplifying, the relationship becomes
1424:{\displaystyle r_{ac}=|r_{ac}|e^{i\phi _{ac}}}
9753:. The diffractive beam splitter is used with
7500:
7487:
4127:, used in various experiments, including the
3460:{\displaystyle T=\cos \theta ,R=\sin \theta }
9835:How does a Mach–Zehnder interferometer work?
9773:
9696:
9292:
9109:
9071:
7542:
7530:
7406:
7102:
6746:
6360:
6299:
6046:
5996:
5864:
5846:
5800:
5647:
5605:
5563:
5451:
5398:
5374:
5335:
5284:
4258:
4225:
4178:
1085:{\displaystyle |r_{bd}|^{2}+|t_{bc}|^{2}=1.}
961:{\displaystyle |r_{ac}|^{2}+|t_{ad}|^{2}=1,}
9901:
5000:{\displaystyle \tau ^{-1}=\tau ^{\dagger }}
2199:{\displaystyle |r_{ac}|^{2}=1-|t_{ad}|^{2}}
443:are linearly related to the inputs through
226:FTIR (frustrated total internal reflection)
4191:and the action of a creation operation is
4109:experiment (proposed in 2000) to test the
2358:{\displaystyle |r_{ac}|=|r_{bd}|\equiv R.}
2277:{\displaystyle |t_{ad}|=|t_{bc}|\equiv T,}
351:Beam splitters with single-mode fiber for
322:A third version of the beam splitter is a
9942:
4488:{\displaystyle {\hat {a}}_{d}^{\dagger }}
681:is the beam-splitter transfer matrix and
224:and the other half is transmitted due to
185:, also finding widespread application in
120:Learn how and when to remove this message
9856:
9854:
9777:
9729:into multiple output beams. Each output
9709:
382:
246:
156:
131:
9870:
9868:
9866:
9832:Zetie, K P; Adams, S F; Tocknell, R M,
9813:Power dividers and directional couplers
4660:where the transfer matrix is given in
4323:{\displaystyle {E}_{a},{E}_{b},{E}_{c}}
3668:A 50:50 beam splitter is produced when
14:
10012:
4026:Beam splitters have been used in both
9851:
9672:Gaussian (Bogoliubov) transformations
9642:In 2000 Knill, Laflamme and Milburn (
8035:and the beam splitter is 50:50, then
4021:
9863:
7969:and the only factor that depends on
3410:{\displaystyle \theta =\arctan(R/T)}
2206:were made. This leads to the result
58:adding citations to reliable sources
29:
4161:creation and annihilation operators
4100:Wheeler's delayed choice experiment
24:
7491:
7225:
7203:
6920:
6844:
6592:
6440:
1340:Expanding, it can be written each
367:allow the direct production of an
25:
10041:
9761:, and is designed for a specific
9638:Application for quantum computing
288:Instead of a metallic coating, a
9702:This section is an excerpt from
9124:{\displaystyle |02\rangle _{cd}}
9086:{\displaystyle |20\rangle _{cd}}
7510:{\displaystyle {\tbinom {n}{j}}}
5815:{\displaystyle |nm\rangle _{ab}}
5299:{\displaystyle |00\rangle _{ab}}
4662:classical lossless beam splitter
3703:
2120:where substitutions of the form
1318:
1296:
635:
455:
408:Classical lossless beam splitter
305:ellipsoidal reflector spotlights
34:
9676:two-mode squeezed vacuum states
7548:{\displaystyle j\notin \{0,n\}}
7390:
4135:; and in others in the area of
251:Aluminium-coated beam splitter.
212:, natural ones were used, e.g.
45:needs additional citations for
9992:
9922:
9895:
9825:
9598:
9579:
9557:
9533:
9501:
9424:
9418:
9405:
9397:
9389:
9383:
9370:
9362:
9279:
9101:
9063:
8992:
8968:
8899:
8882:
8856:
8815:
8798:
8772:
8672:
8625:
8571:
8521:
8387:
8342:
8290:
8245:
8171:
8147:
8131:
8100:
8061:
7990:
7980:
7962:{\displaystyle \tan \theta =1}
7913:
7887:
7878:
7852:
7843:
7817:
7814:
7802:
7751:
7735:
7707:
7697:
7689:
7671:
7650:
7638:
7617:
7605:
7392:
7369:
7351:
7330:
7318:
7297:
7285:
7094:
7066:
7027:
7010:
6992:
6971:
6959:
6908:
6896:
6738:
6732:
6720:
6697:
6638:
6580:
6568:
6545:
6486:
6346:
6291:
6262:
6217:
6143:
6098:
6032:
5988:
5960:
5906:
5853:
5832:
5789:
5781:Likewise, for any input state
5757:
5738:
5710:
5691:
5639:
5597:
5555:
5532:
5487:
5437:
5390:
5366:
5348:
5321:
5276:
5227:
5199:
5060:
5032:
4622:
4594:
4548:
4520:
4468:
4427:
4400:
4373:
4245:
4218:
4205:
4171:
4143:Quantum mechanical description
4095:local hidden-variable theories
3695:{\displaystyle \theta =\pi /4}
3404:
3390:
2342:
2324:
2316:
2298:
2261:
2243:
2235:
2217:
2186:
2167:
2147:
2128:
2091:
2072:
2059:
2040:
2014:
1995:
1982:
1963:
1841:
1777:
1762:
1744:
1737:
1719:
1702:
1684:
1677:
1659:
1621:
1589:
1577:
1559:
1554:
1536:
1527:
1495:
1483:
1465:
1460:
1442:
1394:
1376:
1066:
1047:
1033:
1014:
939:
920:
906:
887:
817:
801:
787:
771:
757:
741:
727:
711:
378:
13:
1:
9818:
3364:{\displaystyle R^{2}+T^{2}=1}
2696:{\displaystyle R^{2}+T^{2}=1}
2407:{\displaystyle R^{2}+T^{2}=1}
9916:10.1016/0030-4018(87)90275-6
9298:{\displaystyle |n,m\rangle }
5770:{\displaystyle |t_{ad}|^{2}}
5723:{\displaystyle |r_{ac}|^{2}}
4133:interaction-free measurement
4081:Kennedy–Thorndike experiment
1325:{\displaystyle \mathbf {I} }
7:
9806:
9666:Similar settings exist for
9320:Non-symmetric beam-splitter
4129:Elitzur–Vaidman bomb tester
4125:Mach–Zehnder interferometer
4059:Michelson–Morley experiment
393:Mach–Zehnder interferometer
10:
10046:
9953:10.1103/PhysRevA.98.062314
9701:
4184:{\displaystyle |n\rangle }
3291:{\displaystyle 2\phi _{R}}
3261:{\displaystyle 2\phi _{T}}
195:
9774:Reflection beam splitters
9719:diffractive beam splitter
9704:Diffractive beam splitter
9697:Diffractive beam splitter
9023:, in which the input has
5306:and add a photon in port
3706:above, for example, has
3318:{\displaystyle \phi _{0}}
2927:(and from the constraint
311:(heat) radiation, and as
266:physical vapor deposition
260:deposited from aluminium
230:Polarizing beam splitters
9889:10.1103/PhysRevA.40.1371
9745:(MxN), depending on the
9684:squeezing transformation
9265:correspondence principle
9055:, the output is always
8002:{\displaystyle (-1)^{j}}
5777:, as might be expected.
3704:dielectric beam splitter
1265:{\displaystyle ^{\ast }}
9337:{\displaystyle \theta }
7469:{\displaystyle M=n+m-N}
4352:{\displaystyle {E}_{d}}
997:{\displaystyle E_{a}=0}
971:and similarly for then
869:{\displaystyle E_{b}=0}
324:dichroic mirrored prism
146:- 50% transmitted light
9783:
9725:that divides an input
9715:
9629:
9480:
9460:
9438:
9338:
9299:
9257:
9198:
9125:
9087:
9049:
9013:
8945:
8029:
8003:
7963:
7928:
7549:
7511:
7470:
7429:
7195:
7174:
6836:
6815:
6432:
6411:
6331:, this can be written
6329:multi-binomial theorem
6318:
6012:
5816:
5771:
5724:
5666:
5417:
5300:
5259:
5001:
4958:
4935:
4651:
4489:
4448:
4353:
4324:
4265:
4185:
4111:Penrose interpretation
4032:real-world experiments
4012:
3919:
3842:
3780:
3696:
3659:
3461:
3411:
3365:
3319:
3292:
3262:
3229:
2983:
2921:
2781:
2697:
2645:
2408:
2359:
2278:
2200:
2111:
1937:
1850:
1636:
1425:
1326:
1304:
1266:
1237:
1143:
1116:
1086:
998:
962:
870:
834:
675:
661:where the 2Ă—2 element
652:
388:
307:to split off unwanted
297:thin-film interference
252:
177:that splits a beam of
162:
154:
9904:Optics Communications
9781:
9769:between output beams.
9713:
9630:
9481:
9461:
9439:
9339:
9300:
9258:
9199:
9126:
9088:
9050:
9048:{\displaystyle n=m=1}
9021:Hong–Ou–Mandel effect
9014:
8946:
8030:
8004:
7964:
7929:
7550:
7512:
7471:
7430:
7175:
7148:
6816:
6789:
6412:
6391:
6319:
6013:
5817:
5772:
5725:
5667:
5418:
5301:
5260:
5002:
4959:
4957:{\displaystyle \tau }
4936:
4652:
4490:
4449:
4354:
4325:
4266:
4186:
4115:quantum superposition
4087:Bell test experiments
4065:on the speed of light
4013:
3920:
3843:
3781:
3697:
3660:
3462:
3412:
3366:
3320:
3293:
3263:
3230:
2984:
2922:
2782:
2698:
2646:
2409:
2360:
2279:
2201:
2112:
1938:
1851:
1637:
1426:
1327:
1305:
1267:
1238:
1144:
1142:{\displaystyle E_{b}}
1117:
1115:{\displaystyle E_{a}}
1087:
999:
963:
871:
835:
676:
674:{\displaystyle \tau }
653:
386:
250:
160:
151:- 50% reflected light
135:
9492:
9470:
9450:
9350:
9328:
9275:
9208:
9135:
9097:
9059:
9027:
8958:
8042:
8013:
7977:
7941:
7565:
7521:
7480:
7442:
6338:
6028:
5828:
5785:
5734:
5687:
5433:
5317:
5272:
5014:
4968:
4948:
4671:
4502:
4458:
4363:
4334:
4275:
4195:
4167:
4091:quantum entanglement
4042:and other fields of
3932:
3855:
3793:
3713:
3672:
3474:
3421:
3375:
3329:
3302:
3272:
3242:
2996:
2931:
2791:
2707:
2661:
2424:
2372:
2294:
2213:
2124:
1950:
1863:
1652:
1438:
1356:
1314:
1276:
1250:
1156:
1126:
1099:
1010:
975:
883:
847:
707:
665:
450:
337:and the three-strip
326:assembly which uses
54:improve this article
9767:angle of separation
9755:monochromatic light
9747:diffractive pattern
9614:
9549:
9008:
8984:
8915:
8831:
8688:
8641:
8587:
8537:
8403:
8379:
8358:
8334:
8306:
8282:
8261:
8237:
8187:
8163:
8116:
8077:
8028:{\displaystyle n=m}
7693:
7654:
7621:
7588:
7373:
7334:
7301:
7268:
7082:
7043:
7014:
6975:
6912:
6879:
6713:
6689:
6654:
6630:
6561:
6537:
6502:
6478:
6278:
6254:
6233:
6209:
6159:
6135:
6114:
6090:
5976:
5922:
5637:
5595:
5548:
5524:
5503:
5479:
5364:
5243:
5215:
5175:
5155:
5133:
5113:
5076:
5048:
4638:
4610:
4564:
4536:
4484:
4443:
4416:
4389:
4149:second quantization
4137:quantum computation
4119:spacetime curvature
4063:luminiferous aether
4028:thought experiments
1859:which is true when
1223:
1189:
373:sequential field 3D
10025:Optical components
10003:on www.infratec.eu
9792:infrared detectors
9784:
9716:
9625:
9591:
9526:
9476:
9456:
9434:
9429:
9334:
9295:
9253:
9194:
9121:
9083:
9045:
9009:
8985:
8961:
8941:
8939:
8892:
8808:
8665:
8618:
8564:
8514:
8380:
8362:
8335:
8317:
8283:
8265:
8238:
8220:
8164:
8140:
8093:
8054:
8025:
7999:
7959:
7924:
7655:
7622:
7589:
7568:
7545:
7507:
7505:
7466:
7425:
7423:
7335:
7302:
7269:
7248:
7059:
7020:
6976:
6943:
6880:
6859:
6690:
6672:
6631:
6613:
6538:
6520:
6479:
6461:
6314:
6255:
6237:
6210:
6192:
6136:
6118:
6091:
6073:
6021:and the output is
6008:
5953:
5899:
5812:
5767:
5720:
5662:
5620:
5578:
5525:
5507:
5480:
5462:
5413:
5341:
5296:
5255:
5246:
5220:
5192:
5178:
5158:
5138:
5116:
5096:
5079:
5053:
5025:
4997:
4954:
4931:
4922:
4750:
4647:
4641:
4615:
4587:
4567:
4541:
4513:
4485:
4461:
4444:
4420:
4393:
4366:
4349:
4320:
4261:
4181:
4072:of 1935 to refute
4046:. These include:
4022:Use in experiments
4008:
3915:
3906:
3838:
3776:
3767:
3692:
3655:
3646:
3457:
3407:
3361:
3315:
3288:
3258:
3225:
3223:
3180:
3102:
3030:
2979:
2917:
2777:
2693:
2641:
2632:
2592:
2461:
2404:
2355:
2274:
2196:
2107:
1933:
1846:
1632:
1421:
1322:
1300:
1262:
1233:
1206:
1172:
1139:
1112:
1082:
994:
958:
866:
830:
671:
648:
621:
581:
502:
389:
335:television cameras
317:laser construction
273:is often called a
253:
190:telecommunications
163:
155:
9931:Physical Review A
9877:Physical Review A
9801:NDIR gas analysis
9601:
9582:
9560:
9536:
9504:
9479:{\displaystyle T}
9459:{\displaystyle R}
8995:
8971:
8902:
8818:
8756:
8675:
8628:
8574:
8524:
8465:
8464:
8390:
8345:
8293:
8248:
8174:
8150:
8103:
8064:
7498:
7388:
7240:
7210:
7146:
7145:
7069:
7030:
6935:
6851:
6787:
6786:
6700:
6641:
6599:
6548:
6489:
6447:
6389:
6388:
6357:
6265:
6220:
6184:
6183:
6146:
6101:
6065:
6064:
6043:
5963:
5946:
5945:
5909:
5892:
5891:
5843:
5535:
5490:
5448:
5351:
5332:
5230:
5202:
5063:
5035:
4625:
4597:
4551:
4523:
4471:
4430:
4403:
4376:
4242:
4208:
4070:Hammar experiment
4052:Fizeau experiment
4040:relativity theory
3874:
3873:
3732:
3731:
3179:
3101:
3029:
2102:
2025:
1767:
1707:
642:
462:
402:Fresnel equations
130:
129:
122:
104:
16:(Redirected from
10037:
10004:
9996:
9990:
9985:
9979:
9974:
9968:
9963:
9957:
9956:
9946:
9926:
9920:
9919:
9899:
9893:
9892:
9872:
9861:
9858:
9849:
9848:
9847:
9845:
9840:
9829:
9648:quantum computer
9634:
9632:
9631:
9626:
9621:
9620:
9619:
9615:
9613:
9608:
9603:
9602:
9594:
9590:
9589:
9584:
9583:
9575:
9568:
9567:
9562:
9561:
9553:
9548:
9543:
9538:
9537:
9529:
9506:
9505:
9497:
9485:
9483:
9482:
9477:
9465:
9463:
9462:
9457:
9443:
9441:
9440:
9435:
9433:
9432:
9408:
9400:
9373:
9365:
9343:
9341:
9340:
9335:
9307:Poissonian light
9304:
9302:
9301:
9296:
9282:
9262:
9260:
9259:
9254:
9246:
9245:
9233:
9232:
9220:
9219:
9203:
9201:
9200:
9195:
9190:
9179:
9178:
9160:
9159:
9147:
9146:
9130:
9128:
9127:
9122:
9120:
9119:
9104:
9092:
9090:
9089:
9084:
9082:
9081:
9066:
9054:
9052:
9051:
9046:
9018:
9016:
9015:
9010:
9007:
9002:
8997:
8996:
8988:
8983:
8978:
8973:
8972:
8964:
8950:
8948:
8947:
8942:
8940:
8936:
8935:
8930:
8926:
8925:
8924:
8919:
8914:
8909:
8904:
8903:
8895:
8886:
8885:
8881:
8880:
8868:
8867:
8841:
8840:
8835:
8830:
8825:
8820:
8819:
8811:
8802:
8801:
8797:
8796:
8784:
8783:
8757:
8755:
8754:
8745:
8744:
8743:
8742:
8716:
8708:
8704:
8703:
8698:
8694:
8693:
8689:
8687:
8682:
8677:
8676:
8668:
8664:
8663:
8662:
8661:
8640:
8635:
8630:
8629:
8621:
8617:
8616:
8615:
8614:
8592:
8588:
8586:
8581:
8576:
8575:
8567:
8563:
8562:
8561:
8560:
8536:
8531:
8526:
8525:
8517:
8513:
8512:
8511:
8510:
8479:
8478:
8470:
8466:
8460:
8459:
8458:
8457:
8456:
8436:
8423:
8419:
8418:
8413:
8409:
8408:
8404:
8402:
8397:
8392:
8391:
8383:
8378:
8373:
8357:
8352:
8347:
8346:
8338:
8333:
8328:
8311:
8307:
8305:
8300:
8295:
8294:
8286:
8281:
8276:
8260:
8255:
8250:
8249:
8241:
8236:
8231:
8202:
8198:
8197:
8192:
8188:
8186:
8181:
8176:
8175:
8167:
8162:
8157:
8152:
8151:
8143:
8126:
8125:
8120:
8115:
8110:
8105:
8104:
8096:
8087:
8086:
8081:
8076:
8071:
8066:
8065:
8057:
8034:
8032:
8031:
8026:
8008:
8006:
8005:
8000:
7998:
7997:
7968:
7966:
7965:
7960:
7933:
7931:
7930:
7925:
7920:
7916:
7912:
7911:
7899:
7898:
7877:
7876:
7864:
7863:
7842:
7841:
7829:
7828:
7781:
7780:
7765:
7764:
7728:
7727:
7715:
7714:
7692:
7666:
7653:
7633:
7620:
7600:
7587:
7579:
7554:
7552:
7551:
7546:
7516:
7514:
7513:
7508:
7506:
7504:
7503:
7490:
7475:
7473:
7472:
7467:
7434:
7432:
7431:
7426:
7424:
7417:
7416:
7395:
7389:
7375:
7372:
7346:
7333:
7313:
7300:
7280:
7267:
7259:
7247:
7246:
7245:
7239:
7224:
7217:
7216:
7215:
7202:
7194:
7189:
7173:
7162:
7147:
7132:
7128:
7120:
7113:
7112:
7097:
7092:
7091:
7086:
7081:
7076:
7071:
7070:
7062:
7053:
7052:
7047:
7042:
7037:
7032:
7031:
7023:
7013:
6987:
6974:
6954:
6942:
6941:
6940:
6934:
6919:
6911:
6891:
6878:
6870:
6858:
6857:
6856:
6843:
6835:
6830:
6814:
6803:
6788:
6773:
6769:
6761:
6757:
6756:
6741:
6736:
6735:
6718:
6714:
6712:
6707:
6702:
6701:
6693:
6688:
6683:
6665:
6664:
6659:
6655:
6653:
6648:
6643:
6642:
6634:
6629:
6624:
6606:
6605:
6604:
6591:
6584:
6583:
6566:
6562:
6560:
6555:
6550:
6549:
6541:
6536:
6531:
6513:
6512:
6507:
6503:
6501:
6496:
6491:
6490:
6482:
6477:
6472:
6454:
6453:
6452:
6439:
6431:
6426:
6410:
6405:
6390:
6375:
6371:
6359:
6358:
6355:
6349:
6323:
6321:
6320:
6315:
6310:
6309:
6294:
6289:
6288:
6283:
6279:
6277:
6272:
6267:
6266:
6258:
6253:
6248:
6232:
6227:
6222:
6221:
6213:
6208:
6203:
6185:
6176:
6172:
6170:
6169:
6164:
6160:
6158:
6153:
6148:
6147:
6139:
6134:
6129:
6113:
6108:
6103:
6102:
6094:
6089:
6084:
6066:
6057:
6053:
6045:
6044:
6041:
6035:
6017:
6015:
6014:
6009:
6007:
6006:
5991:
5986:
5985:
5980:
5975:
5970:
5965:
5964:
5956:
5947:
5938:
5934:
5932:
5931:
5926:
5921:
5916:
5911:
5910:
5902:
5893:
5884:
5880:
5875:
5874:
5856:
5845:
5844:
5841:
5835:
5821:
5819:
5818:
5813:
5811:
5810:
5792:
5776:
5774:
5773:
5768:
5766:
5765:
5760:
5754:
5753:
5741:
5729:
5727:
5726:
5721:
5719:
5718:
5713:
5707:
5706:
5694:
5671:
5669:
5668:
5663:
5658:
5657:
5642:
5636:
5631:
5616:
5615:
5600:
5594:
5589:
5574:
5573:
5558:
5553:
5549:
5547:
5542:
5537:
5536:
5528:
5523:
5518:
5502:
5497:
5492:
5491:
5483:
5478:
5473:
5450:
5449:
5446:
5440:
5422:
5420:
5419:
5414:
5409:
5408:
5393:
5385:
5384:
5369:
5363:
5358:
5353:
5352:
5344:
5334:
5333:
5330:
5324:
5305:
5303:
5302:
5297:
5295:
5294:
5279:
5264:
5262:
5261:
5256:
5251:
5247:
5242:
5237:
5232:
5231:
5223:
5214:
5209:
5204:
5203:
5195:
5183:
5179:
5174:
5169:
5154:
5149:
5132:
5127:
5112:
5107:
5084:
5080:
5075:
5070:
5065:
5064:
5056:
5047:
5042:
5037:
5036:
5028:
5006:
5004:
5003:
4998:
4996:
4995:
4983:
4982:
4963:
4961:
4960:
4955:
4940:
4938:
4937:
4932:
4927:
4923:
4919:
4918:
4917:
4916:
4882:
4881:
4880:
4879:
4849:
4848:
4847:
4846:
4815:
4814:
4813:
4812:
4778:
4777:
4776:
4775:
4755:
4751:
4747:
4746:
4732:
4731:
4715:
4714:
4700:
4699:
4656:
4654:
4653:
4648:
4646:
4642:
4637:
4632:
4627:
4626:
4618:
4609:
4604:
4599:
4598:
4590:
4572:
4568:
4563:
4558:
4553:
4552:
4544:
4535:
4530:
4525:
4524:
4516:
4494:
4492:
4491:
4486:
4483:
4478:
4473:
4472:
4464:
4453:
4451:
4450:
4445:
4442:
4437:
4432:
4431:
4423:
4415:
4410:
4405:
4404:
4396:
4388:
4383:
4378:
4377:
4369:
4358:
4356:
4355:
4350:
4348:
4347:
4342:
4329:
4327:
4326:
4321:
4319:
4318:
4313:
4304:
4303:
4298:
4289:
4288:
4283:
4270:
4268:
4267:
4262:
4248:
4243:
4232:
4221:
4216:
4215:
4210:
4209:
4201:
4190:
4188:
4187:
4182:
4174:
4017:
4015:
4014:
4009:
4004:
3993:
3992:
3977:
3963:
3962:
3944:
3943:
3924:
3922:
3921:
3916:
3911:
3910:
3875:
3869:
3865:
3847:
3845:
3844:
3839:
3831:
3830:
3818:
3817:
3805:
3804:
3785:
3783:
3782:
3777:
3772:
3771:
3733:
3727:
3723:
3701:
3699:
3698:
3693:
3688:
3664:
3662:
3661:
3656:
3651:
3650:
3643:
3642:
3641:
3640:
3606:
3605:
3604:
3603:
3573:
3572:
3571:
3570:
3539:
3538:
3537:
3536:
3502:
3501:
3500:
3499:
3466:
3464:
3463:
3458:
3416:
3414:
3413:
3408:
3400:
3370:
3368:
3367:
3362:
3354:
3353:
3341:
3340:
3324:
3322:
3321:
3316:
3314:
3313:
3297:
3295:
3294:
3289:
3287:
3286:
3267:
3265:
3264:
3259:
3257:
3256:
3234:
3232:
3231:
3226:
3224:
3220:
3216:
3215:
3214:
3199:
3198:
3181:
3172:
3162:
3161:
3148:
3144:
3137:
3136:
3121:
3120:
3103:
3094:
3084:
3083:
3070:
3066:
3065:
3064:
3049:
3048:
3031:
3022:
3012:
3011:
2988:
2986:
2985:
2980:
2972:
2971:
2959:
2958:
2946:
2945:
2926:
2924:
2923:
2918:
2916:
2915:
2903:
2902:
2890:
2889:
2874:
2873:
2861:
2860:
2848:
2847:
2832:
2831:
2819:
2818:
2806:
2805:
2786:
2784:
2783:
2778:
2770:
2769:
2754:
2753:
2738:
2737:
2722:
2721:
2702:
2700:
2699:
2694:
2686:
2685:
2673:
2672:
2650:
2648:
2647:
2642:
2637:
2636:
2629:
2628:
2615:
2614:
2597:
2596:
2589:
2588:
2587:
2586:
2561:
2560:
2559:
2558:
2531:
2530:
2529:
2528:
2503:
2502:
2501:
2500:
2466:
2465:
2458:
2457:
2444:
2443:
2413:
2411:
2410:
2405:
2397:
2396:
2384:
2383:
2368:It follows that
2364:
2362:
2361:
2356:
2345:
2340:
2339:
2327:
2319:
2314:
2313:
2301:
2283:
2281:
2280:
2275:
2264:
2259:
2258:
2246:
2238:
2233:
2232:
2220:
2205:
2203:
2202:
2197:
2195:
2194:
2189:
2183:
2182:
2170:
2156:
2155:
2150:
2144:
2143:
2131:
2116:
2114:
2113:
2108:
2103:
2101:
2100:
2099:
2094:
2088:
2087:
2075:
2069:
2068:
2067:
2062:
2056:
2055:
2043:
2031:
2026:
2024:
2023:
2022:
2017:
2011:
2010:
1998:
1992:
1991:
1990:
1985:
1979:
1978:
1966:
1954:
1942:
1940:
1939:
1934:
1926:
1925:
1910:
1909:
1894:
1893:
1878:
1877:
1855:
1853:
1852:
1847:
1845:
1844:
1840:
1839:
1824:
1823:
1808:
1807:
1792:
1791:
1768:
1766:
1765:
1760:
1759:
1747:
1741:
1740:
1735:
1734:
1722:
1716:
1708:
1706:
1705:
1700:
1699:
1687:
1681:
1680:
1675:
1674:
1662:
1656:
1641:
1639:
1638:
1633:
1625:
1624:
1620:
1619:
1604:
1603:
1580:
1575:
1574:
1562:
1557:
1552:
1551:
1539:
1531:
1530:
1526:
1525:
1510:
1509:
1486:
1481:
1480:
1468:
1463:
1458:
1457:
1445:
1430:
1428:
1427:
1422:
1420:
1419:
1418:
1417:
1397:
1392:
1391:
1379:
1371:
1370:
1331:
1329:
1328:
1323:
1321:
1309:
1307:
1306:
1301:
1299:
1288:
1287:
1271:
1269:
1268:
1263:
1261:
1260:
1242:
1240:
1239:
1234:
1222:
1217:
1205:
1204:
1188:
1183:
1171:
1170:
1148:
1146:
1145:
1140:
1138:
1137:
1121:
1119:
1118:
1113:
1111:
1110:
1091:
1089:
1088:
1083:
1075:
1074:
1069:
1063:
1062:
1050:
1042:
1041:
1036:
1030:
1029:
1017:
1003:
1001:
1000:
995:
987:
986:
967:
965:
964:
959:
948:
947:
942:
936:
935:
923:
915:
914:
909:
903:
902:
890:
875:
873:
872:
867:
859:
858:
839:
837:
836:
831:
826:
825:
820:
814:
813:
804:
796:
795:
790:
784:
783:
774:
766:
765:
760:
754:
753:
744:
736:
735:
730:
724:
723:
714:
680:
678:
677:
672:
657:
655:
654:
649:
644:
643:
640:
638:
626:
625:
618:
617:
604:
603:
586:
585:
578:
577:
563:
562:
546:
545:
531:
530:
507:
506:
499:
498:
485:
484:
464:
463:
460:
458:
331:optical coatings
141:- Incident light
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
10045:
10044:
10040:
10039:
10038:
10036:
10035:
10034:
10010:
10009:
10008:
10007:
9997:
9993:
9986:
9982:
9975:
9971:
9964:
9960:
9927:
9923:
9900:
9896:
9873:
9864:
9859:
9852:
9843:
9841:
9838:
9830:
9826:
9821:
9809:
9776:
9771:
9770:
9723:optical element
9707:
9699:
9640:
9609:
9604:
9593:
9592:
9585:
9574:
9573:
9572:
9563:
9552:
9551:
9550:
9544:
9539:
9528:
9527:
9525:
9521:
9514:
9510:
9496:
9495:
9493:
9490:
9489:
9471:
9468:
9467:
9451:
9448:
9447:
9428:
9427:
9404:
9396:
9393:
9392:
9369:
9361:
9354:
9353:
9351:
9348:
9347:
9329:
9326:
9325:
9322:
9278:
9276:
9273:
9272:
9241:
9237:
9228:
9224:
9215:
9211:
9209:
9206:
9205:
9186:
9174:
9170:
9155:
9151:
9142:
9138:
9136:
9133:
9132:
9112:
9108:
9100:
9098:
9095:
9094:
9074:
9070:
9062:
9060:
9057:
9056:
9028:
9025:
9024:
9003:
8998:
8987:
8986:
8979:
8974:
8963:
8962:
8959:
8956:
8955:
8938:
8937:
8931:
8920:
8910:
8905:
8894:
8893:
8888:
8887:
8876:
8872:
8863:
8859:
8849:
8845:
8836:
8826:
8821:
8810:
8809:
8804:
8803:
8792:
8788:
8779:
8775:
8768:
8764:
8763:
8759:
8758:
8750:
8746:
8738:
8734:
8721:
8717:
8715:
8706:
8705:
8699:
8683:
8678:
8667:
8666:
8657:
8653:
8649:
8645:
8636:
8631:
8620:
8619:
8610:
8606:
8602:
8598:
8597:
8593:
8582:
8577:
8566:
8565:
8556:
8552:
8545:
8541:
8532:
8527:
8516:
8515:
8506:
8502:
8495:
8491:
8490:
8486:
8485:
8481:
8480:
8471:
8452:
8448:
8441:
8437:
8435:
8431:
8430:
8421:
8420:
8414:
8398:
8393:
8382:
8381:
8374:
8366:
8353:
8348:
8337:
8336:
8329:
8321:
8316:
8312:
8301:
8296:
8285:
8284:
8277:
8269:
8256:
8251:
8240:
8239:
8232:
8224:
8219:
8215:
8214:
8210:
8209:
8200:
8199:
8193:
8182:
8177:
8166:
8165:
8158:
8153:
8142:
8141:
8139:
8135:
8134:
8127:
8121:
8111:
8106:
8095:
8094:
8089:
8088:
8082:
8072:
8067:
8056:
8055:
8050:
8049:
8045:
8043:
8040:
8039:
8014:
8011:
8010:
7993:
7989:
7978:
7975:
7974:
7942:
7939:
7938:
7907:
7903:
7894:
7890:
7872:
7868:
7859:
7855:
7837:
7833:
7824:
7820:
7801:
7797:
7770:
7766:
7754:
7750:
7720:
7716:
7710:
7706:
7667:
7659:
7634:
7626:
7601:
7593:
7580:
7572:
7566:
7563:
7562:
7522:
7519:
7518:
7499:
7486:
7485:
7483:
7481:
7478:
7477:
7443:
7440:
7439:
7422:
7421:
7409:
7405:
7391:
7374:
7347:
7339:
7314:
7306:
7281:
7273:
7260:
7252:
7241:
7229:
7220:
7219:
7218:
7211:
7198:
7197:
7196:
7190:
7179:
7163:
7152:
7127:
7118:
7117:
7105:
7101:
7093:
7087:
7077:
7072:
7061:
7060:
7055:
7054:
7048:
7038:
7033:
7022:
7021:
7016:
7015:
6988:
6980:
6955:
6947:
6936:
6924:
6915:
6914:
6913:
6892:
6884:
6871:
6863:
6852:
6839:
6838:
6837:
6831:
6820:
6804:
6793:
6768:
6759:
6758:
6749:
6745:
6737:
6719:
6708:
6703:
6692:
6691:
6684:
6676:
6671:
6667:
6666:
6660:
6649:
6644:
6633:
6632:
6625:
6617:
6612:
6608:
6607:
6600:
6587:
6586:
6585:
6567:
6556:
6551:
6540:
6539:
6532:
6524:
6519:
6515:
6514:
6508:
6497:
6492:
6481:
6480:
6473:
6465:
6460:
6456:
6455:
6448:
6435:
6434:
6433:
6427:
6416:
6406:
6395:
6370:
6363:
6354:
6350:
6345:
6341:
6339:
6336:
6335:
6302:
6298:
6290:
6284:
6273:
6268:
6257:
6256:
6249:
6241:
6228:
6223:
6212:
6211:
6204:
6196:
6191:
6187:
6186:
6171:
6165:
6154:
6149:
6138:
6137:
6130:
6122:
6109:
6104:
6093:
6092:
6085:
6077:
6072:
6068:
6067:
6052:
6040:
6036:
6031:
6029:
6026:
6025:
5999:
5995:
5987:
5981:
5971:
5966:
5955:
5954:
5949:
5948:
5933:
5927:
5917:
5912:
5901:
5900:
5895:
5894:
5879:
5867:
5863:
5852:
5840:
5836:
5831:
5829:
5826:
5825:
5803:
5799:
5788:
5786:
5783:
5782:
5780:
5761:
5756:
5755:
5746:
5742:
5737:
5735:
5732:
5731:
5714:
5709:
5708:
5699:
5695:
5690:
5688:
5685:
5684:
5683:are therefore
5650:
5646:
5638:
5632:
5624:
5608:
5604:
5596:
5590:
5582:
5566:
5562:
5554:
5543:
5538:
5527:
5526:
5519:
5511:
5498:
5493:
5482:
5481:
5474:
5466:
5461:
5457:
5445:
5441:
5436:
5434:
5431:
5430:
5401:
5397:
5389:
5377:
5373:
5365:
5359:
5354:
5343:
5342:
5329:
5325:
5320:
5318:
5315:
5314:
5287:
5283:
5275:
5273:
5270:
5269:
5245:
5244:
5238:
5233:
5222:
5221:
5217:
5216:
5210:
5205:
5194:
5193:
5188:
5184:
5177:
5176:
5170:
5162:
5156:
5150:
5142:
5135:
5134:
5128:
5120:
5114:
5108:
5100:
5092:
5088:
5078:
5077:
5071:
5066:
5055:
5054:
5050:
5049:
5043:
5038:
5027:
5026:
5021:
5017:
5015:
5012:
5011:
4991:
4987:
4975:
4971:
4969:
4966:
4965:
4949:
4946:
4945:
4921:
4920:
4912:
4908:
4901:
4897:
4883:
4875:
4871:
4867:
4863:
4851:
4850:
4842:
4838:
4831:
4827:
4816:
4808:
4804:
4800:
4796:
4783:
4779:
4771:
4767:
4763:
4759:
4749:
4748:
4739:
4735:
4733:
4724:
4720:
4717:
4716:
4707:
4703:
4701:
4692:
4688:
4684:
4680:
4672:
4669:
4668:
4664:section above:
4640:
4639:
4633:
4628:
4617:
4616:
4612:
4611:
4605:
4600:
4589:
4588:
4583:
4579:
4566:
4565:
4559:
4554:
4543:
4542:
4538:
4537:
4531:
4526:
4515:
4514:
4509:
4505:
4503:
4500:
4499:
4479:
4474:
4463:
4462:
4459:
4456:
4455:
4438:
4433:
4422:
4421:
4411:
4406:
4395:
4394:
4384:
4379:
4368:
4367:
4364:
4361:
4360:
4343:
4338:
4337:
4335:
4332:
4331:
4314:
4309:
4308:
4299:
4294:
4293:
4284:
4279:
4278:
4276:
4273:
4272:
4244:
4231:
4217:
4211:
4200:
4199:
4198:
4196:
4193:
4192:
4170:
4168:
4165:
4164:
4145:
4034:in the area of
4024:
4000:
3988:
3984:
3973:
3958:
3954:
3939:
3935:
3933:
3930:
3929:
3905:
3904:
3899:
3893:
3892:
3887:
3877:
3876:
3864:
3856:
3853:
3852:
3826:
3822:
3813:
3809:
3800:
3796:
3794:
3791:
3790:
3766:
3765:
3757:
3751:
3750:
3745:
3735:
3734:
3722:
3714:
3711:
3710:
3684:
3673:
3670:
3669:
3645:
3644:
3636:
3632:
3625:
3621:
3607:
3599:
3595:
3591:
3587:
3575:
3574:
3566:
3562:
3555:
3551:
3540:
3532:
3528:
3524:
3520:
3504:
3503:
3495:
3491:
3487:
3483:
3475:
3472:
3471:
3422:
3419:
3418:
3396:
3376:
3373:
3372:
3349:
3345:
3336:
3332:
3330:
3327:
3326:
3309:
3305:
3303:
3300:
3299:
3282:
3278:
3273:
3270:
3269:
3252:
3248:
3243:
3240:
3239:
3222:
3221:
3207:
3203:
3191:
3187:
3186:
3182:
3170:
3163:
3157:
3153:
3150:
3149:
3129:
3125:
3113:
3109:
3108:
3104:
3092:
3085:
3079:
3075:
3072:
3071:
3057:
3053:
3041:
3037:
3036:
3032:
3020:
3013:
3007:
3003:
2999:
2997:
2994:
2993:
2967:
2963:
2954:
2950:
2938:
2934:
2932:
2929:
2928:
2911:
2907:
2898:
2894:
2882:
2878:
2869:
2865:
2856:
2852:
2840:
2836:
2827:
2823:
2814:
2810:
2798:
2794:
2792:
2789:
2788:
2762:
2758:
2746:
2742:
2730:
2726:
2714:
2710:
2708:
2705:
2704:
2681:
2677:
2668:
2664:
2662:
2659:
2658:
2631:
2630:
2624:
2620:
2617:
2616:
2610:
2606:
2599:
2598:
2591:
2590:
2579:
2575:
2571:
2567:
2562:
2551:
2547:
2543:
2539:
2533:
2532:
2521:
2517:
2513:
2509:
2504:
2493:
2489:
2485:
2481:
2471:
2470:
2460:
2459:
2453:
2449:
2446:
2445:
2439:
2435:
2428:
2427:
2425:
2422:
2421:
2392:
2388:
2379:
2375:
2373:
2370:
2369:
2341:
2332:
2328:
2323:
2315:
2306:
2302:
2297:
2295:
2292:
2291:
2287:and similarly,
2260:
2251:
2247:
2242:
2234:
2225:
2221:
2216:
2214:
2211:
2210:
2190:
2185:
2184:
2175:
2171:
2166:
2151:
2146:
2145:
2136:
2132:
2127:
2125:
2122:
2121:
2095:
2090:
2089:
2080:
2076:
2071:
2070:
2063:
2058:
2057:
2048:
2044:
2039:
2032:
2030:
2018:
2013:
2012:
2003:
1999:
1994:
1993:
1986:
1981:
1980:
1971:
1967:
1962:
1955:
1953:
1951:
1948:
1947:
1918:
1914:
1902:
1898:
1886:
1882:
1870:
1866:
1864:
1861:
1860:
1832:
1828:
1816:
1812:
1800:
1796:
1784:
1780:
1773:
1769:
1761:
1752:
1748:
1743:
1742:
1736:
1727:
1723:
1718:
1717:
1715:
1701:
1692:
1688:
1683:
1682:
1676:
1667:
1663:
1658:
1657:
1655:
1653:
1650:
1649:
1612:
1608:
1596:
1592:
1585:
1581:
1576:
1567:
1563:
1558:
1553:
1544:
1540:
1535:
1518:
1514:
1502:
1498:
1491:
1487:
1482:
1473:
1469:
1464:
1459:
1450:
1446:
1441:
1439:
1436:
1435:
1410:
1406:
1402:
1398:
1393:
1384:
1380:
1375:
1363:
1359:
1357:
1354:
1353:
1339:
1317:
1315:
1312:
1311:
1295:
1283:
1279:
1277:
1274:
1273:
1256:
1253:
1251:
1248:
1247:
1218:
1210:
1197:
1193:
1184:
1176:
1163:
1159:
1157:
1154:
1153:
1133:
1129:
1127:
1124:
1123:
1106:
1102:
1100:
1097:
1096:
1070:
1065:
1064:
1055:
1051:
1046:
1037:
1032:
1031:
1022:
1018:
1013:
1011:
1008:
1007:
982:
978:
976:
973:
972:
943:
938:
937:
928:
924:
919:
910:
905:
904:
895:
891:
886:
884:
881:
880:
854:
850:
848:
845:
844:
821:
816:
815:
809:
805:
800:
791:
786:
785:
779:
775:
770:
761:
756:
755:
749:
745:
740:
731:
726:
725:
719:
715:
710:
708:
705:
704:
666:
663:
662:
639:
634:
633:
620:
619:
613:
609:
606:
605:
599:
595:
588:
587:
580:
579:
570:
566:
564:
555:
551:
548:
547:
538:
534:
532:
523:
519:
512:
511:
501:
500:
494:
490:
487:
486:
480:
476:
469:
468:
459:
454:
453:
451:
448:
447:
441:
434:
427:
420:
414:electric fields
410:
381:
313:output couplers
293:optical coating
275:pellicle mirror
234:Wollaston prism
198:
183:interferometers
152:
147:
142:
137:
126:
115:
109:
106:
69:"Beam splitter"
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
10043:
10033:
10032:
10027:
10022:
10006:
10005:
10000:Beam Splitters
9991:
9980:
9969:
9958:
9921:
9910:(6): 485–490.
9894:
9862:
9850:
9823:
9822:
9820:
9817:
9816:
9815:
9808:
9805:
9775:
9772:
9708:
9700:
9698:
9695:
9639:
9636:
9624:
9618:
9612:
9607:
9600:
9597:
9588:
9581:
9578:
9571:
9566:
9559:
9556:
9547:
9542:
9535:
9532:
9524:
9520:
9517:
9513:
9509:
9503:
9500:
9475:
9455:
9431:
9426:
9423:
9420:
9417:
9414:
9411:
9407:
9403:
9399:
9395:
9394:
9391:
9388:
9385:
9382:
9379:
9376:
9372:
9368:
9364:
9360:
9359:
9357:
9333:
9321:
9318:
9314:density matrix
9294:
9291:
9288:
9285:
9281:
9252:
9249:
9244:
9240:
9236:
9231:
9227:
9223:
9218:
9214:
9193:
9189:
9185:
9182:
9177:
9173:
9169:
9166:
9163:
9158:
9154:
9150:
9145:
9141:
9118:
9115:
9111:
9107:
9103:
9080:
9077:
9073:
9069:
9065:
9044:
9041:
9038:
9035:
9032:
9006:
9001:
8994:
8991:
8982:
8977:
8970:
8967:
8952:
8951:
8934:
8929:
8923:
8918:
8913:
8908:
8901:
8898:
8891:
8884:
8879:
8875:
8871:
8866:
8862:
8858:
8855:
8852:
8848:
8844:
8839:
8834:
8829:
8824:
8817:
8814:
8807:
8800:
8795:
8791:
8787:
8782:
8778:
8774:
8771:
8767:
8762:
8753:
8749:
8741:
8737:
8733:
8730:
8727:
8724:
8720:
8714:
8711:
8709:
8707:
8702:
8697:
8692:
8686:
8681:
8674:
8671:
8660:
8656:
8652:
8648:
8644:
8639:
8634:
8627:
8624:
8613:
8609:
8605:
8601:
8596:
8591:
8585:
8580:
8573:
8570:
8559:
8555:
8551:
8548:
8544:
8540:
8535:
8530:
8523:
8520:
8509:
8505:
8501:
8498:
8494:
8489:
8484:
8477:
8474:
8469:
8463:
8455:
8451:
8447:
8444:
8440:
8434:
8429:
8426:
8424:
8422:
8417:
8412:
8407:
8401:
8396:
8389:
8386:
8377:
8372:
8369:
8365:
8361:
8356:
8351:
8344:
8341:
8332:
8327:
8324:
8320:
8315:
8310:
8304:
8299:
8292:
8289:
8280:
8275:
8272:
8268:
8264:
8259:
8254:
8247:
8244:
8235:
8230:
8227:
8223:
8218:
8213:
8208:
8205:
8203:
8201:
8196:
8191:
8185:
8180:
8173:
8170:
8161:
8156:
8149:
8146:
8138:
8133:
8130:
8128:
8124:
8119:
8114:
8109:
8102:
8099:
8092:
8085:
8080:
8075:
8070:
8063:
8060:
8053:
8048:
8047:
8024:
8021:
8018:
7996:
7992:
7988:
7985:
7982:
7958:
7955:
7952:
7949:
7946:
7935:
7934:
7923:
7919:
7915:
7910:
7906:
7902:
7897:
7893:
7889:
7886:
7883:
7880:
7875:
7871:
7867:
7862:
7858:
7854:
7851:
7848:
7845:
7840:
7836:
7832:
7827:
7823:
7819:
7816:
7813:
7810:
7807:
7804:
7800:
7796:
7793:
7790:
7787:
7784:
7779:
7776:
7773:
7769:
7763:
7760:
7757:
7753:
7749:
7746:
7743:
7740:
7737:
7734:
7731:
7726:
7723:
7719:
7713:
7709:
7705:
7702:
7699:
7696:
7691:
7688:
7685:
7682:
7679:
7676:
7673:
7670:
7665:
7662:
7658:
7652:
7649:
7646:
7643:
7640:
7637:
7632:
7629:
7625:
7619:
7616:
7613:
7610:
7607:
7604:
7599:
7596:
7592:
7586:
7583:
7578:
7575:
7571:
7544:
7541:
7538:
7535:
7532:
7529:
7526:
7502:
7497:
7494:
7489:
7465:
7462:
7459:
7456:
7453:
7450:
7447:
7436:
7435:
7420:
7415:
7412:
7408:
7404:
7401:
7398:
7394:
7387:
7384:
7381:
7378:
7371:
7368:
7365:
7362:
7359:
7356:
7353:
7350:
7345:
7342:
7338:
7332:
7329:
7326:
7323:
7320:
7317:
7312:
7309:
7305:
7299:
7296:
7293:
7290:
7287:
7284:
7279:
7276:
7272:
7266:
7263:
7258:
7255:
7251:
7244:
7238:
7235:
7232:
7228:
7223:
7214:
7209:
7206:
7201:
7193:
7188:
7185:
7182:
7178:
7172:
7169:
7166:
7161:
7158:
7155:
7151:
7144:
7141:
7138:
7135:
7131:
7126:
7123:
7121:
7119:
7116:
7111:
7108:
7104:
7100:
7096:
7090:
7085:
7080:
7075:
7068:
7065:
7058:
7051:
7046:
7041:
7036:
7029:
7026:
7019:
7012:
7009:
7006:
7003:
7000:
6997:
6994:
6991:
6986:
6983:
6979:
6973:
6970:
6967:
6964:
6961:
6958:
6953:
6950:
6946:
6939:
6933:
6930:
6927:
6923:
6918:
6910:
6907:
6904:
6901:
6898:
6895:
6890:
6887:
6883:
6877:
6874:
6869:
6866:
6862:
6855:
6850:
6847:
6842:
6834:
6829:
6826:
6823:
6819:
6813:
6810:
6807:
6802:
6799:
6796:
6792:
6785:
6782:
6779:
6776:
6772:
6767:
6764:
6762:
6760:
6755:
6752:
6748:
6744:
6740:
6734:
6731:
6728:
6725:
6722:
6717:
6711:
6706:
6699:
6696:
6687:
6682:
6679:
6675:
6670:
6663:
6658:
6652:
6647:
6640:
6637:
6628:
6623:
6620:
6616:
6611:
6603:
6598:
6595:
6590:
6582:
6579:
6576:
6573:
6570:
6565:
6559:
6554:
6547:
6544:
6535:
6530:
6527:
6523:
6518:
6511:
6506:
6500:
6495:
6488:
6485:
6476:
6471:
6468:
6464:
6459:
6451:
6446:
6443:
6438:
6430:
6425:
6422:
6419:
6415:
6409:
6404:
6401:
6398:
6394:
6387:
6384:
6381:
6378:
6374:
6369:
6366:
6364:
6362:
6353:
6348:
6344:
6343:
6325:
6324:
6313:
6308:
6305:
6301:
6297:
6293:
6287:
6282:
6276:
6271:
6264:
6261:
6252:
6247:
6244:
6240:
6236:
6231:
6226:
6219:
6216:
6207:
6202:
6199:
6195:
6190:
6182:
6179:
6175:
6168:
6163:
6157:
6152:
6145:
6142:
6133:
6128:
6125:
6121:
6117:
6112:
6107:
6100:
6097:
6088:
6083:
6080:
6076:
6071:
6063:
6060:
6056:
6051:
6048:
6039:
6034:
6019:
6018:
6005:
6002:
5998:
5994:
5990:
5984:
5979:
5974:
5969:
5962:
5959:
5952:
5944:
5941:
5937:
5930:
5925:
5920:
5915:
5908:
5905:
5898:
5890:
5887:
5883:
5878:
5873:
5870:
5866:
5862:
5859:
5855:
5851:
5848:
5839:
5834:
5809:
5806:
5802:
5798:
5795:
5791:
5764:
5759:
5752:
5749:
5745:
5740:
5717:
5712:
5705:
5702:
5698:
5693:
5673:
5672:
5661:
5656:
5653:
5649:
5645:
5641:
5635:
5630:
5627:
5623:
5619:
5614:
5611:
5607:
5603:
5599:
5593:
5588:
5585:
5581:
5577:
5572:
5569:
5565:
5561:
5557:
5552:
5546:
5541:
5534:
5531:
5522:
5517:
5514:
5510:
5506:
5501:
5496:
5489:
5486:
5477:
5472:
5469:
5465:
5460:
5456:
5453:
5444:
5439:
5424:
5423:
5412:
5407:
5404:
5400:
5396:
5392:
5388:
5383:
5380:
5376:
5372:
5368:
5362:
5357:
5350:
5347:
5340:
5337:
5328:
5323:
5293:
5290:
5286:
5282:
5278:
5266:
5265:
5254:
5250:
5241:
5236:
5229:
5226:
5219:
5218:
5213:
5208:
5201:
5198:
5191:
5190:
5187:
5182:
5173:
5168:
5165:
5161:
5157:
5153:
5148:
5145:
5141:
5137:
5136:
5131:
5126:
5123:
5119:
5115:
5111:
5106:
5103:
5099:
5095:
5094:
5091:
5087:
5083:
5074:
5069:
5062:
5059:
5052:
5051:
5046:
5041:
5034:
5031:
5024:
5023:
5020:
4994:
4990:
4986:
4981:
4978:
4974:
4953:
4942:
4941:
4930:
4926:
4915:
4911:
4907:
4904:
4900:
4896:
4893:
4890:
4887:
4884:
4878:
4874:
4870:
4866:
4862:
4859:
4856:
4853:
4852:
4845:
4841:
4837:
4834:
4830:
4826:
4823:
4820:
4817:
4811:
4807:
4803:
4799:
4795:
4792:
4789:
4786:
4785:
4782:
4774:
4770:
4766:
4762:
4758:
4754:
4745:
4742:
4738:
4734:
4730:
4727:
4723:
4719:
4718:
4713:
4710:
4706:
4702:
4698:
4695:
4691:
4687:
4686:
4683:
4679:
4676:
4658:
4657:
4645:
4636:
4631:
4624:
4621:
4614:
4613:
4608:
4603:
4596:
4593:
4586:
4585:
4582:
4578:
4575:
4571:
4562:
4557:
4550:
4547:
4540:
4539:
4534:
4529:
4522:
4519:
4512:
4511:
4508:
4482:
4477:
4470:
4467:
4441:
4436:
4429:
4426:
4419:
4414:
4409:
4402:
4399:
4392:
4387:
4382:
4375:
4372:
4346:
4341:
4317:
4312:
4307:
4302:
4297:
4292:
4287:
4282:
4260:
4257:
4254:
4251:
4247:
4241:
4238:
4235:
4230:
4227:
4224:
4220:
4214:
4207:
4204:
4180:
4177:
4173:
4144:
4141:
4140:
4139:
4121:
4103:
4097:
4084:
4077:
4066:
4055:
4036:quantum theory
4023:
4020:
4007:
4003:
3999:
3996:
3991:
3987:
3983:
3980:
3976:
3972:
3969:
3966:
3961:
3957:
3953:
3950:
3947:
3942:
3938:
3926:
3925:
3914:
3909:
3903:
3900:
3898:
3895:
3894:
3891:
3888:
3886:
3883:
3882:
3880:
3872:
3868:
3863:
3860:
3837:
3834:
3829:
3825:
3821:
3816:
3812:
3808:
3803:
3799:
3787:
3786:
3775:
3770:
3764:
3761:
3758:
3756:
3753:
3752:
3749:
3746:
3744:
3741:
3740:
3738:
3730:
3726:
3721:
3718:
3691:
3687:
3683:
3680:
3677:
3666:
3665:
3654:
3649:
3639:
3635:
3631:
3628:
3624:
3620:
3617:
3614:
3611:
3608:
3602:
3598:
3594:
3590:
3586:
3583:
3580:
3577:
3576:
3569:
3565:
3561:
3558:
3554:
3550:
3547:
3544:
3541:
3535:
3531:
3527:
3523:
3519:
3516:
3513:
3510:
3509:
3507:
3498:
3494:
3490:
3486:
3482:
3479:
3456:
3453:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3426:
3406:
3403:
3399:
3395:
3392:
3389:
3386:
3383:
3380:
3360:
3357:
3352:
3348:
3344:
3339:
3335:
3312:
3308:
3285:
3281:
3277:
3255:
3251:
3247:
3236:
3235:
3219:
3213:
3210:
3206:
3202:
3197:
3194:
3190:
3185:
3178:
3175:
3169:
3166:
3164:
3160:
3156:
3152:
3151:
3147:
3143:
3140:
3135:
3132:
3128:
3124:
3119:
3116:
3112:
3107:
3100:
3097:
3091:
3088:
3086:
3082:
3078:
3074:
3073:
3069:
3063:
3060:
3056:
3052:
3047:
3044:
3040:
3035:
3028:
3025:
3019:
3016:
3014:
3010:
3006:
3002:
3001:
2978:
2975:
2970:
2966:
2962:
2957:
2953:
2949:
2944:
2941:
2937:
2914:
2910:
2906:
2901:
2897:
2893:
2888:
2885:
2881:
2877:
2872:
2868:
2864:
2859:
2855:
2851:
2846:
2843:
2839:
2835:
2830:
2826:
2822:
2817:
2813:
2809:
2804:
2801:
2797:
2776:
2773:
2768:
2765:
2761:
2757:
2752:
2749:
2745:
2741:
2736:
2733:
2729:
2725:
2720:
2717:
2713:
2692:
2689:
2684:
2680:
2676:
2671:
2667:
2652:
2651:
2640:
2635:
2627:
2623:
2619:
2618:
2613:
2609:
2605:
2604:
2602:
2595:
2585:
2582:
2578:
2574:
2570:
2566:
2563:
2557:
2554:
2550:
2546:
2542:
2538:
2535:
2534:
2527:
2524:
2520:
2516:
2512:
2508:
2505:
2499:
2496:
2492:
2488:
2484:
2480:
2477:
2476:
2474:
2469:
2464:
2456:
2452:
2448:
2447:
2442:
2438:
2434:
2433:
2431:
2403:
2400:
2395:
2391:
2387:
2382:
2378:
2366:
2365:
2354:
2351:
2348:
2344:
2338:
2335:
2331:
2326:
2322:
2318:
2312:
2309:
2305:
2300:
2285:
2284:
2273:
2270:
2267:
2263:
2257:
2254:
2250:
2245:
2241:
2237:
2231:
2228:
2224:
2219:
2193:
2188:
2181:
2178:
2174:
2169:
2165:
2162:
2159:
2154:
2149:
2142:
2139:
2135:
2130:
2118:
2117:
2106:
2098:
2093:
2086:
2083:
2079:
2074:
2066:
2061:
2054:
2051:
2047:
2042:
2038:
2035:
2029:
2021:
2016:
2009:
2006:
2002:
1997:
1989:
1984:
1977:
1974:
1970:
1965:
1961:
1958:
1932:
1929:
1924:
1921:
1917:
1913:
1908:
1905:
1901:
1897:
1892:
1889:
1885:
1881:
1876:
1873:
1869:
1857:
1856:
1843:
1838:
1835:
1831:
1827:
1822:
1819:
1815:
1811:
1806:
1803:
1799:
1795:
1790:
1787:
1783:
1779:
1776:
1772:
1764:
1758:
1755:
1751:
1746:
1739:
1733:
1730:
1726:
1721:
1714:
1711:
1704:
1698:
1695:
1691:
1686:
1679:
1673:
1670:
1666:
1661:
1643:
1642:
1631:
1628:
1623:
1618:
1615:
1611:
1607:
1602:
1599:
1595:
1591:
1588:
1584:
1579:
1573:
1570:
1566:
1561:
1556:
1550:
1547:
1543:
1538:
1534:
1529:
1524:
1521:
1517:
1513:
1508:
1505:
1501:
1497:
1494:
1490:
1485:
1479:
1476:
1472:
1467:
1462:
1456:
1453:
1449:
1444:
1416:
1413:
1409:
1405:
1401:
1396:
1390:
1387:
1383:
1378:
1374:
1369:
1366:
1362:
1350:complex number
1334:unitary matrix
1320:
1298:
1294:
1291:
1286:
1282:
1259:
1255:
1244:
1243:
1232:
1229:
1226:
1221:
1216:
1213:
1209:
1203:
1200:
1196:
1192:
1187:
1182:
1179:
1175:
1169:
1166:
1162:
1136:
1132:
1109:
1105:
1093:
1092:
1081:
1078:
1073:
1068:
1061:
1058:
1054:
1049:
1045:
1040:
1035:
1028:
1025:
1021:
1016:
993:
990:
985:
981:
969:
968:
957:
954:
951:
946:
941:
934:
931:
927:
922:
918:
913:
908:
901:
898:
894:
889:
865:
862:
857:
853:
841:
840:
829:
824:
819:
812:
808:
803:
799:
794:
789:
782:
778:
773:
769:
764:
759:
752:
748:
743:
739:
734:
729:
722:
718:
713:
670:
659:
658:
647:
637:
632:
629:
624:
616:
612:
608:
607:
602:
598:
594:
593:
591:
584:
576:
573:
569:
565:
561:
558:
554:
550:
549:
544:
541:
537:
533:
529:
526:
522:
518:
517:
515:
510:
505:
497:
493:
489:
488:
483:
479:
475:
474:
472:
467:
457:
439:
432:
425:
418:
409:
406:
380:
377:
232:, such as the
197:
194:
175:optical device
161:Beam splitters
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
10042:
10031:
10028:
10026:
10023:
10021:
10018:
10017:
10015:
10002:
10001:
9995:
9989:
9984:
9978:
9973:
9967:
9962:
9954:
9950:
9945:
9940:
9936:
9932:
9925:
9917:
9913:
9909:
9905:
9898:
9890:
9886:
9882:
9878:
9871:
9869:
9867:
9857:
9855:
9837:
9836:
9828:
9824:
9814:
9811:
9810:
9804:
9802:
9797:
9793:
9788:
9780:
9768:
9764:
9760:
9756:
9752:
9748:
9744:
9740:
9736:
9732:
9728:
9724:
9720:
9712:
9705:
9694:
9692:
9691:time reversal
9689:
9685:
9681:
9677:
9673:
9669:
9664:
9662:
9658:
9654:
9649:
9645:
9635:
9622:
9616:
9610:
9605:
9595:
9586:
9576:
9569:
9564:
9554:
9545:
9540:
9530:
9522:
9518:
9515:
9511:
9507:
9498:
9487:
9473:
9453:
9444:
9421:
9415:
9412:
9409:
9401:
9386:
9380:
9377:
9374:
9366:
9355:
9345:
9331:
9317:
9315:
9310:
9308:
9289:
9286:
9283:
9270:
9266:
9250:
9247:
9242:
9238:
9234:
9229:
9225:
9221:
9216:
9212:
9191:
9187:
9183:
9180:
9175:
9171:
9167:
9164:
9161:
9156:
9152:
9148:
9143:
9139:
9116:
9113:
9105:
9078:
9075:
9067:
9042:
9039:
9036:
9033:
9030:
9022:
9004:
8999:
8989:
8980:
8975:
8965:
8932:
8927:
8921:
8916:
8911:
8906:
8896:
8889:
8877:
8873:
8869:
8864:
8860:
8853:
8850:
8846:
8842:
8837:
8832:
8827:
8822:
8812:
8805:
8793:
8789:
8785:
8780:
8776:
8769:
8765:
8760:
8751:
8747:
8739:
8735:
8731:
8728:
8725:
8722:
8718:
8712:
8710:
8700:
8695:
8690:
8684:
8679:
8669:
8658:
8654:
8650:
8646:
8642:
8637:
8632:
8622:
8611:
8607:
8603:
8599:
8594:
8589:
8583:
8578:
8568:
8557:
8553:
8549:
8546:
8542:
8538:
8533:
8528:
8518:
8507:
8503:
8499:
8496:
8492:
8487:
8482:
8475:
8472:
8467:
8461:
8453:
8449:
8445:
8442:
8438:
8432:
8427:
8425:
8415:
8410:
8405:
8399:
8394:
8384:
8375:
8370:
8367:
8363:
8359:
8354:
8349:
8339:
8330:
8325:
8322:
8318:
8313:
8308:
8302:
8297:
8287:
8278:
8273:
8270:
8266:
8262:
8257:
8252:
8242:
8233:
8228:
8225:
8221:
8216:
8211:
8206:
8204:
8194:
8189:
8183:
8178:
8168:
8159:
8154:
8144:
8136:
8129:
8122:
8117:
8112:
8107:
8097:
8090:
8083:
8078:
8073:
8068:
8058:
8051:
8038:
8037:
8036:
8022:
8019:
8016:
7994:
7986:
7983:
7972:
7956:
7953:
7950:
7947:
7944:
7921:
7917:
7908:
7904:
7900:
7895:
7891:
7884:
7881:
7873:
7869:
7865:
7860:
7856:
7849:
7846:
7838:
7834:
7830:
7825:
7821:
7811:
7808:
7805:
7798:
7794:
7791:
7788:
7785:
7782:
7777:
7774:
7771:
7767:
7761:
7758:
7755:
7747:
7744:
7741:
7738:
7732:
7729:
7724:
7721:
7717:
7711:
7703:
7700:
7694:
7686:
7683:
7680:
7677:
7674:
7668:
7663:
7660:
7656:
7647:
7644:
7641:
7635:
7630:
7627:
7623:
7614:
7611:
7608:
7602:
7597:
7594:
7590:
7584:
7581:
7576:
7573:
7569:
7561:
7560:
7559:
7556:
7539:
7536:
7533:
7527:
7524:
7495:
7492:
7463:
7460:
7457:
7454:
7451:
7448:
7445:
7418:
7413:
7410:
7402:
7399:
7396:
7385:
7382:
7379:
7376:
7366:
7363:
7360:
7357:
7354:
7348:
7343:
7340:
7336:
7327:
7324:
7321:
7315:
7310:
7307:
7303:
7294:
7291:
7288:
7282:
7277:
7274:
7270:
7264:
7261:
7256:
7253:
7249:
7236:
7233:
7230:
7226:
7207:
7204:
7191:
7186:
7183:
7180:
7176:
7170:
7167:
7164:
7159:
7156:
7153:
7149:
7142:
7139:
7136:
7133:
7129:
7124:
7122:
7114:
7109:
7106:
7098:
7088:
7083:
7078:
7073:
7063:
7056:
7049:
7044:
7039:
7034:
7024:
7017:
7007:
7004:
7001:
6998:
6995:
6989:
6984:
6981:
6977:
6968:
6965:
6962:
6956:
6951:
6948:
6944:
6931:
6928:
6925:
6921:
6905:
6902:
6899:
6893:
6888:
6885:
6881:
6875:
6872:
6867:
6864:
6860:
6848:
6845:
6832:
6827:
6824:
6821:
6817:
6811:
6808:
6805:
6800:
6797:
6794:
6790:
6783:
6780:
6777:
6774:
6770:
6765:
6763:
6753:
6750:
6742:
6729:
6726:
6723:
6715:
6709:
6704:
6694:
6685:
6680:
6677:
6673:
6668:
6661:
6656:
6650:
6645:
6635:
6626:
6621:
6618:
6614:
6609:
6596:
6593:
6577:
6574:
6571:
6563:
6557:
6552:
6542:
6533:
6528:
6525:
6521:
6516:
6509:
6504:
6498:
6493:
6483:
6474:
6469:
6466:
6462:
6457:
6444:
6441:
6428:
6423:
6420:
6417:
6413:
6407:
6402:
6399:
6396:
6392:
6385:
6382:
6379:
6376:
6372:
6367:
6365:
6351:
6334:
6333:
6332:
6330:
6311:
6306:
6303:
6295:
6285:
6280:
6274:
6269:
6259:
6250:
6245:
6242:
6238:
6234:
6229:
6224:
6214:
6205:
6200:
6197:
6193:
6188:
6180:
6177:
6173:
6166:
6161:
6155:
6150:
6140:
6131:
6126:
6123:
6119:
6115:
6110:
6105:
6095:
6086:
6081:
6078:
6074:
6069:
6061:
6058:
6054:
6049:
6037:
6024:
6023:
6022:
6003:
6000:
5992:
5982:
5977:
5972:
5967:
5957:
5950:
5942:
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5923:
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5888:
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5849:
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5807:
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5703:
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5355:
5345:
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5326:
5313:
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5311:
5309:
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5280:
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5196:
5185:
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5159:
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5129:
5124:
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4992:
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4928:
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4909:
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4902:
4898:
4894:
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4876:
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4857:
4854:
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4828:
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4772:
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4711:
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4580:
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4498:
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4480:
4475:
4465:
4439:
4434:
4424:
4417:
4412:
4407:
4397:
4390:
4385:
4380:
4370:
4344:
4339:
4315:
4310:
4305:
4300:
4295:
4290:
4285:
4280:
4255:
4252:
4249:
4239:
4236:
4233:
4228:
4222:
4212:
4202:
4175:
4162:
4158:
4154:
4150:
4138:
4134:
4130:
4126:
4122:
4120:
4116:
4112:
4108:
4104:
4101:
4098:
4096:
4092:
4088:
4085:
4082:
4078:
4075:
4074:Dayton Miller
4071:
4067:
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4049:
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4019:
4005:
4001:
3997:
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3989:
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3978:
3974:
3970:
3967:
3964:
3959:
3955:
3951:
3948:
3945:
3940:
3936:
3912:
3907:
3901:
3896:
3889:
3884:
3878:
3870:
3866:
3861:
3858:
3851:
3850:
3849:
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3832:
3827:
3823:
3819:
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3806:
3801:
3797:
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3754:
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3728:
3724:
3719:
3716:
3709:
3708:
3707:
3705:
3689:
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3647:
3637:
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3626:
3622:
3618:
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3612:
3609:
3600:
3596:
3592:
3588:
3584:
3581:
3578:
3567:
3563:
3559:
3556:
3552:
3548:
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3542:
3533:
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3525:
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3505:
3496:
3492:
3488:
3484:
3480:
3477:
3470:
3469:
3468:
3454:
3451:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3427:
3424:
3401:
3397:
3393:
3387:
3384:
3381:
3378:
3358:
3355:
3350:
3346:
3342:
3337:
3333:
3310:
3306:
3283:
3279:
3275:
3253:
3249:
3245:
3217:
3211:
3208:
3204:
3200:
3195:
3192:
3188:
3183:
3176:
3173:
3167:
3165:
3158:
3154:
3145:
3141:
3138:
3133:
3130:
3126:
3122:
3117:
3114:
3110:
3105:
3098:
3095:
3089:
3087:
3080:
3076:
3067:
3061:
3058:
3054:
3050:
3045:
3042:
3038:
3033:
3026:
3023:
3017:
3015:
3008:
3004:
2992:
2991:
2990:
2976:
2973:
2968:
2964:
2960:
2955:
2951:
2947:
2942:
2939:
2935:
2912:
2908:
2904:
2899:
2895:
2891:
2886:
2883:
2879:
2875:
2870:
2866:
2862:
2857:
2853:
2849:
2844:
2841:
2837:
2833:
2828:
2824:
2820:
2815:
2811:
2807:
2802:
2799:
2795:
2774:
2771:
2766:
2763:
2759:
2755:
2750:
2747:
2743:
2739:
2734:
2731:
2727:
2723:
2718:
2715:
2711:
2690:
2687:
2682:
2678:
2674:
2669:
2665:
2655:
2638:
2633:
2625:
2621:
2611:
2607:
2600:
2593:
2583:
2580:
2576:
2572:
2568:
2564:
2555:
2552:
2548:
2544:
2540:
2536:
2525:
2522:
2518:
2514:
2510:
2506:
2497:
2494:
2490:
2486:
2482:
2478:
2472:
2467:
2462:
2454:
2450:
2440:
2436:
2429:
2420:
2419:
2418:
2415:
2401:
2398:
2393:
2389:
2385:
2380:
2376:
2352:
2349:
2346:
2336:
2333:
2329:
2320:
2310:
2307:
2303:
2290:
2289:
2288:
2271:
2268:
2265:
2255:
2252:
2248:
2239:
2229:
2226:
2222:
2209:
2208:
2207:
2191:
2179:
2176:
2172:
2163:
2160:
2157:
2152:
2140:
2137:
2133:
2104:
2096:
2084:
2081:
2077:
2064:
2052:
2049:
2045:
2036:
2033:
2027:
2019:
2007:
2004:
2000:
1987:
1975:
1972:
1968:
1959:
1956:
1946:
1945:
1944:
1930:
1927:
1922:
1919:
1915:
1911:
1906:
1903:
1899:
1895:
1890:
1887:
1883:
1879:
1874:
1871:
1867:
1836:
1833:
1829:
1825:
1820:
1817:
1813:
1809:
1804:
1801:
1797:
1793:
1788:
1785:
1781:
1774:
1770:
1756:
1753:
1749:
1731:
1728:
1724:
1712:
1709:
1696:
1693:
1689:
1671:
1668:
1664:
1648:
1647:
1646:
1629:
1626:
1616:
1613:
1609:
1605:
1600:
1597:
1593:
1586:
1582:
1571:
1568:
1564:
1548:
1545:
1541:
1532:
1522:
1519:
1515:
1511:
1506:
1503:
1499:
1492:
1488:
1477:
1474:
1470:
1454:
1451:
1447:
1434:
1433:
1432:
1414:
1411:
1407:
1403:
1399:
1388:
1385:
1381:
1372:
1367:
1364:
1360:
1351:
1347:
1343:
1337:
1335:
1292:
1289:
1284:
1280:
1257:
1254:
1230:
1227:
1224:
1219:
1214:
1211:
1207:
1201:
1198:
1194:
1190:
1185:
1180:
1177:
1173:
1167:
1164:
1160:
1152:
1151:
1150:
1134:
1130:
1107:
1103:
1079:
1076:
1071:
1059:
1056:
1052:
1043:
1038:
1026:
1023:
1019:
1006:
1005:
1004:
991:
988:
983:
979:
955:
952:
949:
944:
932:
929:
925:
916:
911:
899:
896:
892:
879:
878:
877:
863:
860:
855:
851:
827:
822:
810:
806:
797:
792:
780:
776:
767:
762:
750:
746:
737:
732:
720:
716:
703:
702:
701:
698:
696:
695:transmittance
692:
688:
684:
668:
645:
630:
627:
622:
614:
610:
600:
596:
589:
582:
574:
571:
567:
559:
556:
552:
542:
539:
535:
527:
524:
520:
513:
508:
503:
495:
491:
481:
477:
470:
465:
446:
445:
444:
442:
435:
428:
421:
415:
405:
403:
398:
394:
385:
376:
374:
370:
365:
361:
356:
354:
349:
347:
344:
340:
336:
332:
329:
325:
320:
318:
314:
310:
306:
302:
298:
294:
291:
286:
284:
280:
276:
272:
267:
263:
259:
249:
245:
243:
239:
235:
231:
227:
223:
219:
215:
214:Canada balsam
211:
207:
203:
193:
191:
188:
184:
180:
176:
172:
168:
167:beam splitter
159:
150:
145:
140:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
9999:
9994:
9983:
9972:
9961:
9934:
9930:
9924:
9907:
9903:
9897:
9880:
9876:
9842:, retrieved
9834:
9827:
9789:
9785:
9735:polarization
9687:
9680:KLM protocol
9665:
9659:between the
9657:entanglement
9644:KLM protocol
9641:
9488:
9445:
9346:
9323:
9311:
9268:
8953:
7970:
7936:
7557:
7437:
6326:
6020:
5779:
5680:
5676:
5674:
5425:
5310:to produce
5307:
5267:
4964:is unitary,
4943:
4659:
4146:
4093:and exclude
4025:
3927:
3788:
3667:
3237:
2656:
2653:
2416:
2367:
2286:
2119:
1858:
1644:
1345:
1341:
1338:
1245:
1094:
970:
842:
699:
686:
682:
660:
437:
430:
423:
416:
411:
390:
360:stereoscopic
357:
353:PON networks
350:
321:
287:
279:Swiss-cheese
254:
242:polarization
238:birefringent
199:
171:beamsplitter
170:
166:
164:
148:
143:
138:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
18:Beamsplitter
9883:(3): 1371.
9844:13 February
9661:Fock states
4153:Fock states
4117:depends on
2989:), so that
691:reflectance
397:dielectric
379:Phase shift
369:anaglyph 3D
339:Technicolor
271:photography
187:fibre optic
10030:Microscopy
10014:Categories
9944:1803.11534
9937:: 062314.
9819:References
9763:wavelength
9759:laser beam
9757:such as a
9653:Fock state
9344:such that
8954:where the
6327:Using the
4495:, so that
4131:involving
3371:we define
1095:When both
876:produces
364:periscopes
346:projectors
301:wavelength
218:wavelength
80:newspapers
9611:†
9599:^
9580:^
9558:^
9546:†
9534:^
9519:θ
9502:^
9422:θ
9416:
9387:θ
9381:
9332:θ
9305:known as
9293:⟩
9239:ϕ
9226:ϕ
9213:ϕ
9184:π
9172:ϕ
9153:ϕ
9140:ϕ
9110:⟩
9072:⟩
9005:†
8993:^
8981:†
8969:^
8912:†
8900:^
8874:ϕ
8870:−
8861:ϕ
8851:−
8828:†
8816:^
8790:ϕ
8786:−
8777:ϕ
8736:ϕ
8723:−
8685:†
8673:^
8655:ϕ
8643:−
8638:†
8626:^
8608:ϕ
8584:†
8572:^
8554:ϕ
8547:−
8534:†
8522:^
8504:ϕ
8497:−
8450:ϕ
8443:−
8400:†
8388:^
8376:∗
8355:†
8343:^
8331:∗
8303:†
8291:^
8279:∗
8258:†
8246:^
8234:∗
8184:†
8172:^
8160:†
8148:^
8132:→
8113:†
8101:^
8074:†
8062:^
7984:−
7951:θ
7948:
7905:ϕ
7901:−
7892:ϕ
7870:ϕ
7857:ϕ
7847:−
7835:ϕ
7822:ϕ
7792:−
7786:θ
7783:
7759:−
7748:θ
7745:
7739:−
7733:θ
7730:
7701:−
7678:−
7669:∗
7645:−
7636:∗
7612:−
7603:∗
7582:∗
7528:∉
7461:−
7407:⟩
7358:−
7349:∗
7325:−
7316:∗
7292:−
7283:∗
7262:∗
7234:−
7177:∑
7150:∑
7103:⟩
7079:†
7067:^
7040:†
7028:^
6999:−
6990:∗
6966:−
6957:∗
6929:−
6903:−
6894:∗
6873:∗
6818:∑
6791:∑
6747:⟩
6727:−
6710:†
6698:^
6686:∗
6651:†
6639:^
6627:∗
6575:−
6558:†
6546:^
6534:∗
6499:†
6487:^
6475:∗
6414:∑
6393:∑
6361:⟩
6352:ψ
6300:⟩
6275:†
6263:^
6251:∗
6230:†
6218:^
6206:∗
6156:†
6144:^
6132:∗
6111:†
6099:^
6087:∗
6047:⟩
6038:ψ
5997:⟩
5973:†
5961:^
5919:†
5907:^
5865:⟩
5847:⟩
5838:ψ
5801:⟩
5648:⟩
5634:∗
5606:⟩
5592:∗
5564:⟩
5545:†
5533:^
5521:∗
5500:†
5488:^
5476:∗
5452:⟩
5443:ψ
5399:⟩
5375:⟩
5361:†
5349:^
5336:⟩
5327:ψ
5285:⟩
5240:†
5228:^
5212:†
5200:^
5172:∗
5152:∗
5130:∗
5110:∗
5073:†
5061:^
5045:†
5033:^
4993:†
4989:τ
4977:−
4973:τ
4952:τ
4910:ϕ
4903:−
4895:θ
4892:
4886:−
4873:ϕ
4861:θ
4858:
4840:ϕ
4833:−
4825:θ
4822:
4806:ϕ
4794:θ
4791:
4769:ϕ
4675:τ
4635:†
4623:^
4607:†
4595:^
4577:τ
4561:†
4549:^
4533:†
4521:^
4481:†
4469:^
4440:†
4428:^
4413:†
4401:^
4386:†
4374:^
4259:⟩
4226:⟩
4213:†
4206:^
4179:⟩
3998:π
3986:ϕ
3971:π
3968:−
3956:ϕ
3937:ϕ
3859:τ
3824:ϕ
3811:ϕ
3798:ϕ
3760:−
3717:τ
3682:π
3676:θ
3634:ϕ
3627:−
3619:θ
3616:
3610:−
3597:ϕ
3585:θ
3582:
3564:ϕ
3557:−
3549:θ
3546:
3530:ϕ
3518:θ
3515:
3493:ϕ
3478:τ
3467:, hence
3455:θ
3452:
3437:θ
3434:
3388:
3379:θ
3307:ϕ
3280:ϕ
3250:ϕ
3205:ϕ
3189:ϕ
3155:ϕ
3142:π
3127:ϕ
3123:−
3111:ϕ
3077:ϕ
3055:ϕ
3051:−
3039:ϕ
3005:ϕ
2977:π
2974:−
2965:ϕ
2961:−
2952:ϕ
2936:ϕ
2909:ϕ
2896:ϕ
2880:ϕ
2867:ϕ
2863:−
2854:ϕ
2838:ϕ
2825:ϕ
2812:ϕ
2796:ϕ
2775:π
2760:ϕ
2756:−
2744:ϕ
2728:ϕ
2724:−
2712:ϕ
2577:ϕ
2549:ϕ
2519:ϕ
2491:ϕ
2347:≡
2266:≡
2164:−
2037:−
1960:−
1931:π
1916:ϕ
1912:−
1900:ϕ
1884:ϕ
1880:−
1868:ϕ
1830:ϕ
1826:−
1814:ϕ
1798:ϕ
1794:−
1782:ϕ
1713:−
1610:ϕ
1606:−
1594:ϕ
1516:ϕ
1512:−
1500:ϕ
1408:ϕ
1290:τ
1285:†
1281:τ
1258:∗
1220:∗
1186:∗
669:τ
631:τ
283:sputtered
258:aluminium
222:reflected
9807:See also
9796:aperture
7476:and the
3417:so that
689:are the
328:dichroic
309:infrared
290:dichroic
264:using a
244:states.
110:May 2014
10020:Mirrors
9751:element
9749:on the
9688:partial
7973:is the
5007:, i.e.
4044:physics
1246:where "
375:video.
196:Designs
94:scholar
9743:matrix
9686:under
9446:where
7555:etc.
7438:where
4944:Since
4454:, and
4330:, and
3702:. The
3385:arctan
3298:, and
3238:where
1310:where
236:, use
210:resins
202:prisms
173:is an
96:
89:
82:
75:
67:
9939:arXiv
9839:(PDF)
9739:phase
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3928:i.e.
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461:out
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10016::
9947:.
9935:98
9933:.
9908:64
9906:.
9881:40
9879:.
9865:^
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9693:.
9663:.
9316:.
9309:.
9106:02
9068:20
7099:00
6743:00
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4018:.
2414:.
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1336:.
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641:in
319:.
228:.
192:.
165:A
9955:.
9951::
9941::
9918:.
9914::
9891:.
9887::
9706:.
9651:(
9623:.
9617:)
9606:b
9596:a
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9577:a
9570:+
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9555:a
9541:a
9531:a
9523:(
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9508:=
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9474:T
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9425:)
9419:(
9410:=
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9390:)
9384:(
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9079:d
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9064:|
9043:1
9040:=
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9034:=
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8976:c
8966:a
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8922:2
8917:)
8907:d
8897:a
8890:(
8883:)
8878:R
8865:T
8857:(
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8847:e
8843:+
8838:2
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8823:c
8813:a
8806:(
8799:)
8794:R
8781:T
8773:(
8770:i
8766:e
8761:[
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8748:2
8740:0
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8729:i
8726:2
8719:e
8713:=
8701:n
8696:]
8691:)
8680:d
8670:a
8659:R
8651:i
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8633:c
8623:a
8612:T
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8595:(
8590:)
8579:d
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8468:]
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8364:r
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8314:(
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8217:(
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7866:+
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7818:(
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7812:m
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7799:[
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7762:N
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7736:(
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7712:j
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7704:1
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7687:j
7684:+
7681:N
7675:m
7672:(
7664:d
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7657:r
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7648:j
7642:N
7639:(
7631:c
7628:b
7624:t
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7615:j
7609:n
7606:(
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7540:n
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7534:0
7531:{
7525:j
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7496:j
7493:n
7488:(
7464:N
7458:m
7455:+
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7419:,
7414:d
7411:c
7403:M
7400:,
7397:N
7393:|
7386:!
7383:M
7380:!
7377:N
7370:)
7367:j
7364:+
7361:N
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7352:(
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7337:r
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7328:j
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7319:(
7311:c
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7213:)
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7110:d
7107:c
7095:|
7089:M
7084:)
7074:d
7064:a
7057:(
7050:N
7045:)
7035:c
7025:a
7018:(
7011:)
7008:j
7005:+
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6996:m
6993:(
6985:d
6982:b
6978:r
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6969:j
6963:N
6960:(
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6945:t
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6932:j
6926:N
6922:m
6917:(
6909:)
6906:j
6900:n
6897:(
6889:d
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6876:j
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6865:a
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6854:)
6849:j
6846:n
6841:(
6833:N
6828:0
6825:=
6822:j
6812:m
6809:+
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6801:0
6798:=
6795:N
6784:!
6781:m
6778:!
6775:n
6771:1
6766:=
6754:d
6751:c
6739:|
6733:)
6730:k
6724:m
6721:(
6716:)
6705:d
6695:a
6681:d
6678:b
6674:r
6669:(
6662:k
6657:)
6646:c
6636:a
6622:c
6619:b
6615:t
6610:(
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6597:k
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6589:(
6581:)
6578:j
6572:n
6569:(
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6553:d
6543:a
6529:d
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6517:(
6510:j
6505:)
6494:c
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6463:r
6458:(
6450:)
6445:j
6442:n
6437:(
6429:m
6424:0
6421:=
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6400:=
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6386:!
6383:m
6380:!
6377:n
6373:1
6368:=
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6312:.
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6304:c
6292:|
6286:m
6281:)
6270:d
6260:a
6246:d
6243:b
6239:r
6235:+
6225:c
6215:a
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6151:d
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6082:c
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6070:(
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6059:n
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6050:=
6033:|
6004:b
6001:a
5989:|
5983:m
5978:)
5968:b
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5951:(
5943:!
5940:m
5936:1
5929:n
5924:)
5914:a
5904:a
5897:(
5889:!
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5877:=
5872:b
5869:a
5861:m
5858:n
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5850:=
5833:|
5808:b
5805:a
5797:m
5794:n
5790:|
5763:2
5758:|
5751:d
5748:a
5744:t
5739:|
5716:2
5711:|
5704:c
5701:a
5697:r
5692:|
5681:d
5677:c
5660:.
5655:d
5652:c
5640:|
5629:d
5626:a
5622:t
5618:+
5613:d
5610:c
5598:|
5587:c
5584:a
5580:r
5576:=
5571:d
5568:c
5556:|
5551:)
5540:d
5530:a
5516:d
5513:a
5509:t
5505:+
5495:c
5485:a
5471:c
5468:a
5464:r
5459:(
5455:=
5438:|
5411:,
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5387:=
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5356:a
5346:a
5339:=
5322:|
5308:a
5292:b
5289:a
5277:|
5253:.
5249:)
5235:d
5225:a
5207:c
5197:a
5186:(
5181:)
5167:d
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5147:c
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5140:t
5125:d
5122:a
5118:t
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5098:r
5090:(
5086:=
5082:)
5068:b
5058:a
5040:a
5030:a
5019:(
4985:=
4980:1
4929:.
4925:)
4914:R
4906:i
4899:e
4877:T
4869:i
4865:e
4844:T
4836:i
4829:e
4810:R
4802:i
4798:e
4781:(
4773:0
4765:i
4761:e
4757:=
4753:)
4744:d
4741:b
4737:r
4729:d
4726:a
4722:t
4712:c
4709:b
4705:t
4697:c
4694:a
4690:r
4682:(
4678:=
4644:)
4630:b
4620:a
4602:a
4592:a
4581:(
4574:=
4570:)
4556:d
4546:a
4528:c
4518:a
4507:(
4476:d
4466:a
4435:c
4425:a
4418:,
4408:b
4398:a
4391:,
4381:a
4371:a
4345:d
4340:E
4316:c
4311:E
4306:,
4301:b
4296:E
4291:,
4286:a
4281:E
4256:1
4253:+
4250:n
4246:|
4240:1
4237:+
4234:n
4229:=
4223:n
4219:|
4203:a
4176:n
4172:|
4006:2
4002:/
3995:=
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3982:,
3979:2
3975:/
3965:=
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3952:,
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3946:=
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3908:]
3902:1
3897:i
3890:i
3885:1
3879:[
3871:2
3867:1
3862:=
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3820:=
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3807:=
3802:T
3774:,
3769:]
3763:1
3755:1
3748:1
3743:1
3737:[
3729:2
3725:1
3720:=
3690:4
3686:/
3679:=
3653:.
3648:]
3638:R
3630:i
3623:e
3601:T
3593:i
3589:e
3568:T
3560:i
3553:e
3534:R
3526:i
3522:e
3506:[
3497:0
3489:i
3485:e
3481:=
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3443:R
3440:,
3428:=
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3405:)
3402:T
3398:/
3394:R
3391:(
3382:=
3359:1
3356:=
3351:2
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3343:+
3338:2
3334:R
3311:0
3284:R
3276:2
3254:T
3246:2
3218:)
3212:c
3209:b
3201:+
3196:d
3193:a
3184:(
3177:2
3174:1
3168:=
3159:0
3146:)
3139:+
3134:d
3131:b
3118:c
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3106:(
3099:2
3096:1
3090:=
3081:R
3068:)
3062:c
3059:b
3046:d
3043:a
3034:(
3027:2
3024:1
3018:=
3009:T
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2956:0
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2943:d
2940:b
2913:R
2905:+
2900:0
2892:=
2887:c
2884:a
2876:,
2871:T
2858:0
2850:=
2845:c
2842:b
2834:,
2829:T
2821:+
2816:0
2808:=
2803:d
2800:a
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2767:c
2764:a
2751:c
2748:b
2740:+
2735:d
2732:b
2719:d
2716:a
2691:1
2688:=
2683:2
2679:T
2675:+
2670:2
2666:R
2639:.
2634:]
2626:b
2622:E
2612:a
2608:E
2601:[
2594:]
2584:d
2581:b
2573:i
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2537:T
2526:c
2523:b
2515:i
2511:e
2507:T
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2495:a
2487:i
2483:e
2479:R
2473:[
2468:=
2463:]
2455:d
2451:E
2441:c
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2430:[
2402:1
2399:=
2394:2
2390:T
2386:+
2381:2
2377:R
2353:.
2350:R
2343:|
2337:d
2334:b
2330:r
2325:|
2321:=
2317:|
2311:c
2308:a
2304:r
2299:|
2272:,
2269:T
2262:|
2256:c
2253:b
2249:t
2244:|
2240:=
2236:|
2230:d
2227:a
2223:t
2218:|
2192:2
2187:|
2180:d
2177:a
2173:t
2168:|
2161:1
2158:=
2153:2
2148:|
2141:c
2138:a
2134:r
2129:|
2105:,
2097:2
2092:|
2085:c
2082:b
2078:t
2073:|
2065:2
2060:|
2053:c
2050:b
2046:t
2041:|
2034:1
2028:=
2020:2
2015:|
2008:d
2005:a
2001:t
1996:|
1988:2
1983:|
1976:d
1973:a
1969:t
1964:|
1957:1
1928:=
1923:c
1920:a
1907:c
1904:b
1896:+
1891:d
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1875:d
1872:a
1842:)
1837:c
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1821:c
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1810:+
1805:d
1802:b
1789:d
1786:a
1778:(
1775:i
1771:e
1763:|
1757:c
1754:b
1750:t
1745:|
1738:|
1732:d
1729:b
1725:r
1720:|
1710:=
1703:|
1697:d
1694:a
1690:t
1685:|
1678:|
1672:c
1669:a
1665:r
1660:|
1627:=
1622:)
1617:d
1614:b
1601:d
1598:a
1590:(
1587:i
1583:e
1578:|
1572:d
1569:b
1565:r
1560:|
1555:|
1549:d
1546:a
1542:t
1537:|
1533:+
1528:)
1523:c
1520:b
1507:c
1504:a
1496:(
1493:i
1489:e
1484:|
1478:c
1475:b
1471:t
1466:|
1461:|
1455:c
1452:a
1448:r
1443:|
1415:c
1412:a
1404:i
1400:e
1395:|
1389:c
1386:a
1382:r
1377:|
1373:=
1368:c
1365:a
1361:r
1346:t
1342:r
1319:I
1297:I
1293:=
1231:,
1228:0
1225:=
1215:d
1212:b
1208:r
1202:d
1199:a
1195:t
1191:+
1181:c
1178:b
1174:t
1168:c
1165:a
1161:r
1135:b
1131:E
1108:a
1104:E
1077:=
1072:2
1067:|
1060:c
1057:b
1053:t
1048:|
1044:+
1039:2
1034:|
1027:d
1024:b
1020:r
1015:|
992:0
989:=
984:a
980:E
956:,
953:1
950:=
945:2
940:|
933:d
930:a
926:t
921:|
917:+
912:2
907:|
900:c
897:a
893:r
888:|
864:0
861:=
856:b
852:E
828:.
823:2
818:|
811:b
807:E
802:|
798:+
793:2
788:|
781:a
777:E
772:|
768:=
763:2
758:|
751:d
747:E
742:|
738:+
733:2
728:|
721:c
717:E
712:|
687:t
683:r
646:,
636:E
628:=
623:]
615:b
611:E
601:a
597:E
590:[
583:]
575:d
572:b
568:r
560:d
557:a
553:t
543:c
540:b
536:t
528:c
525:a
521:r
514:[
509:=
504:]
496:d
492:E
482:c
478:E
471:[
466:=
456:E
440:d
438:E
433:c
431:E
426:b
424:E
419:a
417:E
149:3
144:2
139:1
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
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