Orbitalt impulsmoment (bølge)

For alternative betydninger, se orbitalt impulsmoment. (Se også artikler, som begynder med orbitalt impulsmoment)

For alternative betydninger, se OAM. (Se også artikler, som begynder med OAM)

Orbitalt impulsmoment (OAM) er en egenskab ved både tværbølger og længdebølger, som specificerer den geometriske orientering af bølgefronten. Bølger som besidder orbitalt impulsmoment kaldes også snoede bølger.

Elektromagnetiske bølgers (EM) (f.eks. lys eller radiobølger) er tværbølger. Elektromagnetiske bølger med OAM kaldes snoede elektromagnetiske bølger, snoede radiobølger^[3], snoet lys) er elektromagnetiske bølgers impulsmoments komponent, som er afhængig af det rumlige EM-felts fordeling - og ikke polariseringen. En anden måde at forklare det på er, at OAM alene er en spiralerende amplitudemodulation af bølgefronten.

OAM kan yderligere inddeles i intern OAM og ekstern OAM. Den interne OAM er en oprindelsesuafhængige EM-impulsmoment og kan forbindes med en skruelinjeformet eller vreden bølgefront. Den eksterne OAM er den oprindelsesafhængige EM-impulsmoment som kan bestemmes som krydsproduktet af EM-stråle positionen (strålens centrum) og dens totale lineære impuls.

Selv én enkelt foton kan få en OAM baseret bølgefront.^[4]

Akustiske bølger, i fx luft og vand, er longitudinale bølger, men kan også anvendes til OAM.^[5]

Introduktion

En EM-stråle bærer en lineær impuls $\mathbf {P}$ , og kan herved også have en ekstern angulær moment $\mathbf {L} _{e}=\mathbf {r} \times \mathbf {P}$ . Denne eksterne angulær moment afhænger af koordinatsystemets origos valg. Hvis origo vælges til at være på stråleaksen og strålen er cylindrisk symmetrisk (i hvert fald i dens impulsfordeling), vil den eksterne impulsmoment forsvinde. Den eksterne impulsmoment er en form for OAM, fordi den er urelateret til polariseringen og afhænger af den rumlige fordeling af EM-feltet.

En mere interessant eksempel af OAM er den interne OAM som dukker op når en paraksial EM-stråle er i en såkaldt “skruelinje mode/tilstand”. EM-skruelinje modes er karakteriseret ved en bølgefront som er formet som en skruelinje med en optisk hvirvel i centrum, ved EM-strålens akse (se figuren). Skruelinje modes er karakteriseret ved et heltalsnummer $m$ , positiv eller negativ. Hvis $m=0$ , er moden ikke med skruelinje og bølgefronterne er flere uforbundne flader/planer, for eksempel, en sekvens af parallelle planer (fra hvilken navnet “planbølge” stammer). Hvis $m=\pm 1$ , bestemmer håndetheden fortegnet af $m$ , bølgefronten er formet som en enkelt skruelinje, hvor en hel skrues længde er lig bølgelængden $\lambda$ . Hvis $|m|\geqslant 2$ består bølgefronten af $|m|$ distinkte men sammenskruede skruelinjer. Heltallet $m$ kaldes også for den såkaldte “topologiske ladning” af den optiske hvirvel.

Snoede radiobølger

En snoet radiobølge kan laves med fx flere radioantenner.^[6] Det kan vælges om alle antenner skal anvendes linear polarisering (fx vandret, lodret i forhold til jorden) eller cirkulær polarisering (venstre- eller højre-drejet).

Med fx fire antenner kan OAM +1, 0 og -1 dannes.

De fire antenner kan placeres i en firkantnet, så antennernes signalfase i strålingsretningen er 0, 90, 180 og 270 grader forskudt (OAM +1) - eller 0, -90, -180 og -270 grader forskudt (OAM -1). Har de alle fire 0 grader i strålingsretningen, sendes med OAM=0.

Hvis de fire antenner i stedet er placeret alene med 0 grader (samme fase i strålingsretningen), kan OAM +1, 0 og -1 dannes ved at man føder antennerne med RF-signalerne 0, 0, 0, 0 grader eller 0, 90, 180 og 270 grader eller 0, -90, -180 og -270 grader fx via forsinkelsestransmissionslinjer eller via fire separate sendere med de ønskede faser.

Radiomodtager antennen fases på samme måde.

De tre OAM +1, 0 og -1 er tre separate kanaler; fx kunne OAM=+1 anvendes til højre lydkanal, OAM=0 anvendes til en mono lydkanal - og OAM=+1 anvendes til venstre lydkanal. OAM +1, 0 og -1 kan alle sendes via de samme fire antenner.

En OAM kan også dannes ved at klippe i en (offset) parabolformet reflektor og forskyde dens forskellige reflektor "cirkeludsnit", så de passer med den ønskede reflekterede signalfase i strålingsretningen - rundt på reflektoren fx fra -180...+180 grader ved OAM= +1 eller -1.^[7] Ulempen er at reflektoren kun kan sende/modtage den enkelte OAM, den er designet til. Dér hvor fasen springer mellem -180 og +180 grader vil der være en tilsigtet diskontinuitet i reflektor ved OAM= -1 og +1. For OAM= -2 og +2 kan der være to diskontinuiter, da reflektoren skal klippes to steder; rundt på reflektoren skal den reflekterede signal i strålingsretningen følge -180...+180 grader og igen -180...+180 grader (720 grader i alt). Man kan nøjes med én reflektordiskontinuit, hvis fasen rundt følger -360...+360 grader (720 grader i alt).

Kilder/referencer

^ Vieira, J. et al. Amplification and generation of ultra-intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 7:10371 doi: 10.1038/ncomms10371 (2016) Citat: "...Figure 1: Generation and amplification of OAM lasers via stimulated Raman backscattering...Figure 3: Simulation results showing the generation and amplification of a new OAM modes...We note that our seed laser pulse final intensity, on the order of 10^17 W cm^−2, and seed laser spot size, on the order of 1 mm, indicate the production and amplification of Petawatt class twisted lasers with OAM..."
^ ist.utl.pt: Prof. Jorge Vieira: Structured light. Structured light and lasers with orbital angular momentum. A new twist for plasma physics?, backup Citat: "...Structured lasers have non-trivial phase structures and polarisations. A well known example of structured light is the orbital angular momentum. Lasers with orbital angular momentum are characterized by helical wavefronts, with a phase singularity at the center of the laser, and have doughnut shaped intensity profiles. They are interesting from a fundamental point of view because they possess quantized amounts of angular momentum. Unlike circularly polarized light, which is featured by spin-angular momentum, twisted lasers contain angular momentum even if they are linearly polarized...Together with Dr. Raoul Trines from Rutherford Appleton Laboratory, I have recently shown that Raman backscattering can efficiently generate and amplify twisted lasers with orbital angular momentum...A laser with orbital angular momentum in a special configuration of stimulated Raman backscattering in plasmas..."
^ 25. feb 2011, ing.dk: Snoede radiobølger skal skaffe båndbredde til hungrende mobilbrugere Citat: "...Udover at skelne mellem radiobølger med forskellig frekvens, skal man også skelne mellem radiobølger med forskellig snoning af de elektromagnetiske bølgefronter..."
^ Nov 1, 2012, physicsworld.com: Spooky action with twisted beams. Citat: "...Using this technique, Zeilinger and co-workers found they could obtain differences in quantum number as high as 600 (in other words l = +300 on one photon and l = –300 on the other). Lapkiewicz points out that there is, in theory, no upper limit to a photon's l value, which suggests that a photon – a quantum object – could acquire as much OAM as a macroscopic object, leading to what he calls a "tension between the quantum and classical worlds"..."
^ 28. jun 2017, ing.dk: Snoede lydbølger øger båndbredden ved undervandskommunikation Citat: "...Men også akustiske bølger kan have OAM. Tre forskere fra University of California, Berkeley anført af Xiang Zhang beretter i Procesdings of the National Academy of Sciences PNAS, at de har opnået en spektral effektivitet på 8 bit/s pr. hertz båndbredde ved overførsel af et signal på en akustisk bølge ved 16 kHz...", Chengzhi Shi, Marc Dubois, Yuan Wang, and Xiang Zhang. High-speed acoustic communication by multiplexing orbital angular momentum. PNAS 2017; published ahead of print June 26, 2017 Arkiveret 13. juli 2017 hos Wayback Machine
^ Experimental near field OAM-based communication with circular patch array, pdf Citat: "...In fact, OAM waves do not interact during propagation in a homogeneous medium, i.e., they form an orthogonal set of propagating modes [8]...Circular arrays composed by elementary dipoles [6], patches [23], [24] or Vivaldi antennas [25], have been simulated for OAM generation...Fig. 15. Maps of reception zones for multi-channels OAM based communication system (A), (C) and for single channel traditional ones (B), (D). Vertical axis reports the distance between Tx and Rx arrays. Horizontal axis indicates lateral shift (A), (B) or angular tilt (C), (D) between Rx and Tx array. Red areas indicates physical space where the Rx array receives three channels. In yellow and green areas at most two channels can be correctly received...We designed two circular arrays, composed by patch antennas, in order to generate and detect OAM modes with l=−1,0,+1 value, at the frequency of 5.75GHz. A very good agreement with theoretical predictions is found..."
^ Fabrizio Tamburini et al 2012 New J. Phys. 14 033001, iopscience.iop.org: Encoding many channels on the same frequency through radio vorticity: first experimental test Citat: "...Moreover, our experimental findings demonstrate that the spatial phase signature was preserved even in the far-field region and for incoherent non-monochromatic wave beams. These results open up new perspectives not only for wireless communication but also for physics and astronomy, including the possible detection of Kerr black holes in the test general relativity [21]...A.4. Offset helicoidal parabolic antenna..."

Yderligere læsning

Allen, L.; Barnett, Stephen M. & Padgett, Miles J. (2003). Optical Angular Momentum. Bristol: Institute of Physics. ISBN 978-0-7503-0901-1 Skabelon:Inconsistent citations{{cite book}}: CS1-vedligeholdelse: postscript (link).
Torres, Juan P. & Torner, Lluis (2011). Twisted Photons: Applications of Light with Orbital Angular Momentum. Bristol: Wiley-VCH. ISBN 978-3-527-40907-5 Skabelon:Inconsistent citations{{cite book}}: CS1-vedligeholdelse: postscript (link).
Andrews, David L. & Babiker, Mohamed (2012). The Angular Momentum of Light. Cambridge: Cambridge University Press. s. 448. ISBN 9781107006348.

Eksterne henvisninger

Youtube: 2015, Miles J. Padgett: 14/44 Structured light concepts and theory, light twist OAM
25 June 2012, BBC News: 'Twisted light' carries 2.5 terabits of data per second Citat: "...Recent work suggests that the trick could vastly boost the data-carrying capacity in wi-fi and optical fibres...The idea is not to create light waves wiggling in different directions but rather with different amounts of twist, like screws with different numbers of threads..."
Oct 19, 2012, physicsworld.com: Chip puts a twist on light Citat: "...Indeed, he says that they aim to produce devices that can emit different OAM values at the same time. This, he claims, could enhance telecommunication bandwidth, by increasing the number of channels available, and boost the power of quantum computers – devices, still under development, that promise much faster data crunching by processing multiple quantum states simultaneously. "Currently, quantum computers rely on electron spin or photon spin, which only have two states, whereas OAM has many states," he explains..."
University of Southern California (2013, June 27). Breakthrough in Internet bandwidth: New fiber optic technology could ease Internet congestion, video streaming. ScienceDaily Citat: "...the technology centers on donut-shaped laser light beams called optical vortices, in which the light twists like a tornado as it moves along the beam path, rather than in a straight line...Unlike in conventional fibers, OAM modes in these specially designed fibers can carry data streams across an optical fiber while remaining separate at the receiving end..."

[1] Vieira, J. et al. Amplification and generation of ultra-intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 7:10371 doi: 10.1038/ncomms10371 (2016) Citat: "...Figure 1: Generation and amplification of OAM lasers via stimulated Raman backscattering...Figure 3: Simulation results showing the generation and amplification of a new OAM modes...We note that our seed laser pulse final intensity, on the order of 10^17 W cm^−2, and seed laser spot size, on the order of 1 mm, indicate the production and amplification of Petawatt class twisted lasers with OAM..."

[2] st.utl.pt: Prof. Jorge Vieira: Structured light. Structured light and lasers with orbital angular momentum. A new twist for plasma physics?, backup Citat: "...Structured lasers have non-trivial phase structures and polarisations. A well known example of structured light is the orbital angular momentum. Lasers with orbital angular momentum are characterized by helical wavefronts, with a phase singularity at the center of the laser, and have doughnut shaped intensity profiles. They are interesting from a fundamental point of view because they possess quantized amounts of angular momentum. Unlike circularly polarized light, which is featured by spin-angular momentum, twisted lasers contain angular momentum even if they are linearly polarized...Together with Dr. Raoul Trines from Rutherford Appleton Laboratory, I have recently shown that Raman backscattering can efficiently generate and amplify twisted lasers with orbital angular momentum...A laser with orbital angular momentum in a special configuration of stimulated Raman backscattering in plasmas..."

[3] 25. feb 2011, ing.dk: Snoede radiobølger skal skaffe båndbredde til hungrende mobilbrugere Citat: "...Udover at skelne mellem radiobølger med forskellig frekvens, skal man også skelne mellem radiobølger med forskellig snoning af de elektromagnetiske bølgefronter..."

[4] Nov 1, 2012, physicsworld.com: Spooky action with twisted beams. Citat: "...Using this technique, Zeilinger and co-workers found they could obtain differences in quantum number as high as 600 (in other words l = +300 on one photon and l = –300 on the other). Lapkiewicz points out that there is, in theory, no upper limit to a photon's l value, which suggests that a photon – a quantum object – could acquire as much OAM as a macroscopic object, leading to what he calls a "tension between the quantum and classical worlds"..."

[5] 28. jun 2017, ing.dk: Snoede lydbølger øger båndbredden ved undervandskommunikation Citat: "...Men også akustiske bølger kan have OAM. Tre forskere fra University of California, Berkeley anført af Xiang Zhang beretter i Procesdings of the National Academy of Sciences PNAS, at de har opnået en spektral effektivitet på 8 bit/s pr. hertz båndbredde ved overførsel af et signal på en akustisk bølge ved 16 kHz...", Chengzhi Shi, Marc Dubois, Yuan Wang, and Xiang Zhang. High-speed acoustic communication by multiplexing orbital angular momentum. PNAS 2017; published ahead of print June 26, 2017 Arkiveret 13. juli 2017 hos Wayback Machine

[6] Experimental near field OAM-based communication with circular patch array, pdf Citat: "...In fact, OAM waves do not interact during propagation in a homogeneous medium, i.e., they form an orthogonal set of propagating modes [8]...Circular arrays composed by elementary dipoles [6], patches [23], [24] or Vivaldi antennas [25], have been simulated for OAM generation...Fig. 15. Maps of reception zones for multi-channels OAM based communication system (A), (C) and for single channel traditional ones (B), (D). Vertical axis reports the distance between Tx and Rx arrays. Horizontal axis indicates lateral shift (A), (B) or angular tilt (C), (D) between Rx and Tx array. Red areas indicates physical space where the Rx array receives three channels. In yellow and green areas at most two channels can be correctly received...We designed two circular arrays, composed by patch antennas, in order to generate and detect OAM modes with l=−1,0,+1 value, at the frequency of 5.75GHz. A very good agreement with theoretical predictions is found..."

[7] Fabrizio Tamburini et al 2012 New J. Phys. 14 033001, iopscience.iop.org: Encoding many channels on the same frequency through radio vorticity: first experimental test Citat: "...Moreover, our experimental findings demonstrate that the spatial phase signature was preserved even in the far-field region and for incoherent non-monochromatic wave beams. These results open up new perspectives not only for wireless communication but also for physics and astronomy, including the possible detection of Kerr black holes in the test general relativity [21]...A.4. Offset helicoidal parabolic antenna..."

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