Structured light from helical undulators · 2018. 3. 5. · LG01 LG02 LG11 • Optical vortex...
Transcript of Structured light from helical undulators · 2018. 3. 5. · LG01 LG02 LG11 • Optical vortex...
Structured light from helical undulators
Shunya Matsuba
Hiroshima synchrotron radiation center Hiroshima University
The 9th Asian Forum for Accelerators and Detectors
2018/0131
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Introduction
• Structured light means light which have spatially controlled intensity, polarization and (or) phase distribution.
• Spatially uniform polarization state with left-handed or right-handed spiral phase front called optical vortex.
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Optical vortex
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equiphasic surface equiphasic surfacePhase condition on a vertical plane
Normal beam Optical Vortex
Phase condition on a vertical plane
Laguerre-Gauss mode
L𝐺𝑝𝑙 𝑟, 𝜙 =2𝑝!
𝜋 𝑝+ 𝑙 !
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𝑤 𝑧
𝑟 2
𝑤 𝑧
𝑙
exp−𝑟2
𝑤2 𝑧𝐿𝑝𝑙 2𝑟2
𝑤2 𝑧exp 𝑖𝑙𝜙
exp𝑖𝑘0𝑟
2𝑧
2(𝑧2+𝑧𝑅2)
exp −𝑖 2𝑝 + 𝑙 + 1 tan−1𝑧
𝑧𝑅
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Magnitude
Phase
LG01 LG02 LG11 • Optical vortex carries 𝑙ℏ of orbital angular momentum per photon other than spin angular moment which originate from right or left circular polarization.
L. Allen, et. al. PRA 45 8185-8189 (1992).
Higher harmonics from helical undulators
𝐴 𝛾𝜃, 𝜙 = Τ𝐴𝑥 − 𝑖𝐴𝑦 2
= 2 exp 𝑖 𝑛 − 1 𝜙 𝛾𝜃 −𝑛𝐾
𝑋𝐽𝑛 𝑋 − 𝐾𝐽𝑛
′ (𝑋)
Shigemi Sasaki and Ian McNulty
PRL 100, 124801 (2008)
• Higher harmonics from helical undulators become optical vortex.
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𝑑2𝐼
𝑑𝜔𝑑Ω=𝑒2𝛾2𝑛2𝜉2
4𝜋𝜖0𝑐𝐴𝑥
2 + 𝐴𝑦2𝐿
𝑁Δ𝜔
𝜔
Intensity distribution equation for APPLE undulator
First Experimental Demonstration
J.Bahrdt, et. al. PRL 111, 034801 (2013).
Interference pattern from tandem undulator at photon energies of 99 eVBESSY II Storage ring E = 917 MeV
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Experiment at UVSOR-III storage-ring
E : 500 MeVε : 8 nmrad
Diffraction limited Wavelength ~100 nm
Experiment at UVSOR-III
Circular polarizationFundamental 710 nm2nd 355 nm
CCD camera
Bandpass filter355 nm ±2.2 nm FWHM
Linear polarizationFundamental 355 nm
Interference pattern of linear and helical
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Linear + Left Cir Linear + Right Cir
Simulation results by SRW
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https://github.com/ochubar/SRW
Experiment at UVSOR-III
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Phase shifter
Wire gridPolarizer
CCD camera
Bandpass filter355 nm ±2.2 nm FWHM
Right Circular polarizationFundamental 710 nm2nd 355 nm
Left circular polarizationFundamental 355 nm
1st right circular and 2nd harmonics left circular mode
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Without polarizer With polarizer
1st right circular and 2nd harmonics left circular mode
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0 °
1st right circular and 2nd harmonics left circular mode
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Experiment at UVSOR-III
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Wire gridPolarizer
Bandpass filter355 nm ±2.2 nm FWHM
Right Circular polarizationFundamental 710 nm2nd 355 nm
Left circular polarizationFundamental 355 nm
Phase shifter
CCD camera
Phase shifter rotates the spiral pattern
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• Bump orbit was made in between undulators by phase shifter.The orbit lengthening converted the relative phase retardation.
25.8°of relative phase retardation
Phase shifter simulation
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000 degree 090 degree90 degree
Experiment at UVSOR-III
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Phase shifter
Wire gridPolarizer
CCD camera
Bandpass filter248 nm± 1 nm FWHM
Right Circular polarizationFundamental 496 nm2nd 248 nm
Left circular polarizationFundamental 496 nm 2nd 248 nm
2nd harmonics right circular and 2nd harmonics left circular mode with polarizer
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Conclusion
• Experiment on optical vortex was performed in UVSOR-III
• We measured the interference patterns of following• Fundamental from the linear undulator and second harmonics of
right and left circularly polarized from the helical undulator.
• Fundamental from the right circularly polarized undulator and second harmonics from the left circularly polarized helical undulator.
• Second harmonics from the left circularly polarized and right
circularly polarized helical undulators.
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