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1、1,Orbital Angular Momentum of Photons,2,3,Outline,Getting started on Orbital Angular Momentum of LightMaking helical phasefrontsApplicationConclusions,4,Outline,Getting started on Orbital Angular Momentum of LightMaking helical phasefronts ApplicationConclusions,5,Getting started on Orbital Angular
2、Momentum of Light,Professor Les Allen,A1. Pioneering work,6,Getting started on Orbital Angular Momentum of Light,Formalism:,A1. Pioneering work,7,Getting started on Orbital Angular Momentum of Light,For a linearly polarized laser mode:,A1. Pioneering work,8,Getting started on Orbital Angular Momentu
3、m of Light,A1. Pioneering work,9,Getting started on Orbital Angular Momentum of Light,The linear momentum density:,A1. Pioneering work,10,Getting started on Orbital Angular Momentum of Light,The linear momentum density:,For arbitrary polarization:,The Z component of total angular momentum density,A1
4、. Pioneering work,11,Getting started on Orbital Angular Momentum of Light,A2.Orbital Angular Momentum from helical phase fronts,12,Getting started on Orbital Angular Momentum of Light,Angular-momentum of light,A2.Orbital Angular Momentum from helical phase fronts,13,Getting started on Orbital Angula
5、r Momentum of Light,Calculate AM from EM field,A2.Orbital Angular Momentum from helical phase fronts,14,Getting started on Orbital Angular Momentum of Light,Spin angular momentum,A2.Orbital Angular Momentum from helical phase fronts,15,Getting started on Orbital Angular Momentum of Light,Orbital ang
6、ular momentum,A2.Orbital Angular Momentum from helical phase fronts,16,A3.Amplitude and phase,Getting started on Orbital Angular Momentum of Light,Amplitude:,17,A3.Amplitude and phase,Getting started on Orbital Angular Momentum of Light,Phase:,18,A3.Amplitude and phase,Getting started on Orbital Ang
7、ular Momentum of Light,19,Outline,Getting started on Orbital Angular Momentum of LightMaking helical phasefrontsApplicationConclusions,20,Making helical phasefronts,B1. Spiral Phase Plate (SPP),A light beam can acquire OAM by crossing a spiral phase plate, with a inhomogeneous thickness,21,Making he
8、lical phasefronts,B1. Spiral Phase Plate (SPP),Optics Communication 112 (56): 321,22,Making helical phasefronts,B1. Spiral Phase Plate (SPP),The complex amplitude of incident beams,The complex amplitude directly after the plate,23,Making helical phasefronts,B2. Hologram,A more convenient approach fo
9、r generating OAM is based on using diffraction on a fork-like or pitchfork hologram.78910 Holograms can be also generated dynamically under the control of a computer by using a spatial light modulator, or SLM 11.,7JETP Letters 52 (8): 429.,8Journal of Modern Optics 39 (5): 985,9Optical and Quantum E
10、lectronics 24 (9): S951,10Phys. Rev. A 56 (5): 4064,11Optics Letters 17 (3): 221,24,Making helical phasefronts,B2. Hologram,25,(I)Blazed diffraction grating:,Ref. PHD_2011 B.Jack,Making helical phasefronts,B2. Hologram,26,(II)Spiral phase hologram:,Ref. PHD_2011 B.Jack,Making helical phasefronts,B2.
11、 Pitch-Fork Hologram,27,(II)Spiral phase hologram:,Ref. PHD_2011 B.Jack,Making helical phasefronts,B2. Hologram,28,(III)Pitch-Fork Hologram,Ref. PHD_2011 B.Jack,Making helical phasefronts,B2. Hologram,Modulator: phase,29,(III)Pitch-Fork Hologram,Making helical phasefronts,B2. Hologram,Modulator: pha
12、se,30,(III)Pitch-Fork Hologram,Ref. PHD_2011 B.Jack,Making helical phasefronts,B2. Hologram,Modulator: phase and intensity,31,Making helical phasefronts,B3. Q-Plate,Another method for generating OAM is based on the SAM-OAM coupling that may occur in a medium which is both anisotropic and inhomogeneo
13、us. In particular, the so-called q-plate is a device, currently realized using liquid crystals, polymers or sub-wavelength gratings, which can generate OAM by exploiting a SAM sign-change. In this case, the OAM sign is controlled by the input polarization.1213,12 Phys. Rev. Lett. 96,163905,13Applied
14、 Physics Letters 94 (23): 231124,32,Making helical phasefronts,B4. Cylindrical Mode Converters,OAM can also be generated by converting Hermite-Gaussian beams into the Laguerre-Gaussian ones by using an astigmatic system with two well-aligned cylindrical lenses placed at a specific distance (see figu
15、re) in order to introduce a well-defined relative phase between horizontal and vertical Hermite-Gauss beams.14,14 Phys. Rev. A 45 (11): 81858189,33,Outline,Getting started on Orbital Angular Momentum of LightMaking helical phasefrontsApplicationConclusions,34,Application,1.Orientational manipulation
16、 of particles or particle aggregates in optical tweezers15 2.High-bandwidth information encoding in free-space optical communication 16 3.Higher-dimensional quantum information encoding, for possible future quantum cryptography or quantum computation applications17 4. Sensitive optical detection 18,
17、15Phys. Rev. A 54 (2): 15931596,16Optics Express 12 (22): 544856,17Nature Physics 4 (4): 282,18Optics Letters 30 (24): 330810,C1. Introduction,35,Application,C2. Merits,Qunits (sometimes qudits),The most immediate advantage is given by the availability of a larger “alphabet,” consisting of the vario
18、us OAM states.,Higher-dimensional quantum systems are also known to improve the level of security in quantum cryptography under the presence of noise , and are required by some quantum protocols and quantum computation Schemes.,Ref: Structured Light and Its Applications (BOOK),Maybe most intriguingl
19、y, there are tasks that can be solved more efficiently using higher-dimensional systems, e.g., the Byzantine agreement problem or quantum coin tossing.,36,Application,C3. Holographic ghost imaging,Professor M.J. Padgett,37,Application,C3. Holographic ghost imaging,The predicted coincidence count is proportional to,38,Application,C3. Holographic ghost imaging,39,Application,C3. Holographic ghost imaging,Note: Edge Enhanced images,40,Application,C4. Quantum key distribution,41,Thank you!,
