光子的轨道角动量及应用-巩龙延
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A1. Pioneering work For a linearly polarized laser mode:
7
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work
8
Getting started on Orbital Angular Momentum of Light
(III)Pitch-Fork Hologram
Modulator: phase
Ref. PHD_2011 B.Jack
28
Making helical phasefronts B2. Hologram
(III)Pitch-Fork Hologram
Modulator: phase
29
Making helical phasefronts B2. Hologram
17
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase
18
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
Making helical phasefronts B2. Hologram
24
Making helical phasefronts B2. Hologram (I)Blazed diffraction grating:
Ref. PHD_2011 B.Jack
25
Making helical phasefronts B2. Pitch-Fork Hologram
(II)Spiral phase hologram:
Ref. PHD_2011 B.Jack
26
Making helical phasefronts B2. Hologram
(II)Spiral phase hologram:
Ref. PHD_2011 B.Jack
27
Making helical phasefronts B2. Hologram
(III)Pitch-Fork Hologram
Modulator: phase and intensity
Ref. PHD_2011 B.Jack
30
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 inhomogeneous. 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.[12][13]
A1. Pioneering work
The linear momentum density:
9
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work For arbitrary polarization:
The linear momentum density:
A1. Pioneering work
Professor Les Allen
5
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work Formalism:
6
Getting started on Orbital Angular Momentum of Light
[15]Phys. Rev. A 54 (2): 1593–1596 [17]Nature Physics 4 (4): 282
[16]Optics Express 12 (22): 5448–56 [18]Optics Letters 30 (24): 3308–10
34
Application
C2. Merits Qunits (sometimes qudits)
[14] Phys. Rev. A 45 (11): 8185–8189
32
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
15
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase Amplitude:
16
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase Phase:
20
Making helical phasefronts B1. Spiral Phase Plate (SPP)
Optics Communication 112 (5–6): 321
21
Making helical phasefronts B1. Spiral Phase Plate (SPP)
33
Application
C1. Introduction
1.Orientational manipulation of particles or particle aggregates in optical tweezers[15]
2.High-bandwidth information encoding in free-space optical communication [16]
Spin angular momentum
14
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
Orbital angular momentum
[7]JETP Letters 52 (8): 429. [8]Journal of Modern Optics 39 (5): 985 [9]Optical and Quantum Electronics 24 (9): S951 [10]Phys. Rev. A 56 (5): 4064
23
[11]Optics Letters 17 (3): 221
19
Making helical phasefronts B1. Spiral Phase Plate (SPP) A light beam can acquire OAM by crossing a spiral phase plate, with a inhomogeneous thickness
The Z component of total angular momentum density
10
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
[12] Phys. Rev. Lett. 96,163905 [13]Applied Physics Letters 94 (23): 231124 31
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 figure) in order to introduce a well-defined relative phase between horizontal and vertical Hermite-Gauss beams.[14]
A2.Orbital Angular Momentum from helical phase fronts Calculate AM from EM field
13
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
3
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
4
Getting started on Orbital Angular Momentum of Light
3.Higher-dimensional quantum information encoding, for possible future quantum cryptography or quantum computation applications[17] 4. Sensitive optical detection [18]
The most immediate advantage is given by the availability of a larger “alphabet,” consisting of the various 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. Maybe most intriguingly, there are tasks that can be solved more efficiently using higher-dimensional systems, e.g., the Byzantine agreement problem or quantum coin tossing.
11
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
Angular-momentum of light
12
Getting started on Orbital Angular Momentum of Light
Orbital Angular Momentum of Photons
ቤተ መጻሕፍቲ ባይዱ
1
2
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
The complex amplitude of incident beams The complex amplitude directly after the plate
22
Making helical phasefronts B2. Hologram
A more convenient approach for generating OAM is based on using diffraction on a fork-like or pitchfork hologram.[7][8][9][10] Holograms can be also generated dynamically under the control of a computer by using a spatial light modulator, or SLM [11].
7
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work
8
Getting started on Orbital Angular Momentum of Light
(III)Pitch-Fork Hologram
Modulator: phase
Ref. PHD_2011 B.Jack
28
Making helical phasefronts B2. Hologram
(III)Pitch-Fork Hologram
Modulator: phase
29
Making helical phasefronts B2. Hologram
17
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase
18
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
Making helical phasefronts B2. Hologram
24
Making helical phasefronts B2. Hologram (I)Blazed diffraction grating:
Ref. PHD_2011 B.Jack
25
Making helical phasefronts B2. Pitch-Fork Hologram
(II)Spiral phase hologram:
Ref. PHD_2011 B.Jack
26
Making helical phasefronts B2. Hologram
(II)Spiral phase hologram:
Ref. PHD_2011 B.Jack
27
Making helical phasefronts B2. Hologram
(III)Pitch-Fork Hologram
Modulator: phase and intensity
Ref. PHD_2011 B.Jack
30
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 inhomogeneous. 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.[12][13]
A1. Pioneering work
The linear momentum density:
9
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work For arbitrary polarization:
The linear momentum density:
A1. Pioneering work
Professor Les Allen
5
Getting started on Orbital Angular Momentum of Light
A1. Pioneering work Formalism:
6
Getting started on Orbital Angular Momentum of Light
[15]Phys. Rev. A 54 (2): 1593–1596 [17]Nature Physics 4 (4): 282
[16]Optics Express 12 (22): 5448–56 [18]Optics Letters 30 (24): 3308–10
34
Application
C2. Merits Qunits (sometimes qudits)
[14] Phys. Rev. A 45 (11): 8185–8189
32
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
15
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase Amplitude:
16
Getting started on Orbital Angular Momentum of Light
A3.Amplitude and phase Phase:
20
Making helical phasefronts B1. Spiral Phase Plate (SPP)
Optics Communication 112 (5–6): 321
21
Making helical phasefronts B1. Spiral Phase Plate (SPP)
33
Application
C1. Introduction
1.Orientational manipulation of particles or particle aggregates in optical tweezers[15]
2.High-bandwidth information encoding in free-space optical communication [16]
Spin angular momentum
14
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
Orbital angular momentum
[7]JETP Letters 52 (8): 429. [8]Journal of Modern Optics 39 (5): 985 [9]Optical and Quantum Electronics 24 (9): S951 [10]Phys. Rev. A 56 (5): 4064
23
[11]Optics Letters 17 (3): 221
19
Making helical phasefronts B1. Spiral Phase Plate (SPP) A light beam can acquire OAM by crossing a spiral phase plate, with a inhomogeneous thickness
The Z component of total angular momentum density
10
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
[12] Phys. Rev. Lett. 96,163905 [13]Applied Physics Letters 94 (23): 231124 31
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 figure) in order to introduce a well-defined relative phase between horizontal and vertical Hermite-Gauss beams.[14]
A2.Orbital Angular Momentum from helical phase fronts Calculate AM from EM field
13
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
3
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
4
Getting started on Orbital Angular Momentum of Light
3.Higher-dimensional quantum information encoding, for possible future quantum cryptography or quantum computation applications[17] 4. Sensitive optical detection [18]
The most immediate advantage is given by the availability of a larger “alphabet,” consisting of the various 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. Maybe most intriguingly, there are tasks that can be solved more efficiently using higher-dimensional systems, e.g., the Byzantine agreement problem or quantum coin tossing.
11
Getting started on Orbital Angular Momentum of Light
A2.Orbital Angular Momentum from helical phase fronts
Angular-momentum of light
12
Getting started on Orbital Angular Momentum of Light
Orbital Angular Momentum of Photons
ቤተ መጻሕፍቲ ባይዱ
1
2
Outline
Getting started on Orbital Angular Momentum of Light
Making helical phasefronts Application Conclusions
The complex amplitude of incident beams The complex amplitude directly after the plate
22
Making helical phasefronts B2. Hologram
A more convenient approach for generating OAM is based on using diffraction on a fork-like or pitchfork hologram.[7][8][9][10] Holograms can be also generated dynamically under the control of a computer by using a spatial light modulator, or SLM [11].