7/22/2016
Optical vortex laser measurement
Yoshitaka Taira
National Institute of Advanced Industrial Science and Technology (AIST)
1 Laser and CCD camera Laser: World Star Tech Wavelength: 532 nm Power: < 5 mW Beam size: 0.54 mm (H), 0.59 mm(V) at FWHM Camera: COHU, Model 4812 Pixel size: 0.0135 mm/px Pixel: 512 (H), 480 (V)
5000 f(x)
4000
3000 σ = 0.230 mm 2000 +/-0.1%
1000
0 0 1 2 3 4 5 6 X (mm) 2 Coordinate system Detector plane X
Y
Z X Y Laser
Coordinate system of the calculated result should be reversed to compare with the measurement results.
3 Diffraction pattern
Grating CCD Laser
140 mm 25 mm OAM value = m×n (m is the charge of grating, n is the diffraction order )
5000 l = 1, 26A
Scat. 4000
angle Diff. angle 3000
2000
1000 n = -1 n = 0 n = 1 0 0 1 2 3 4 5 6 X (mm) 4 List of gratings
Grating # Charge, m Lines Diff. angle Scat. angle /mm (mrad) (mrad) 27A 1 30 ± 2 13.9 ± 0.4 1.8 ± 0.3 26A 1 30 ± 2 14.7 ± 0.1 2.1 ± 0.2 24A 2 30 ± 2 14.8 ± 0.1 2.2 ± 0.3 2A 2 22 ± 2 10.6 ± 0.1 2.3 ± 0.2 34A 3 30 ± 2 9A 3 22 ± 2 35A 4 30 ± 2 Charge, m = 2 10A 4 22 ± 2 33A 5 30 ± 2 11A 5 22 ± 2 29A 10 30 ± 2 Lines per mm was measured with a optical microscope and microscale.
5 Power measurement Pin = 4.59 mW Power of diffracted beam (n = 0 and n = 1) was measured. 17 2 22 lpm 22 lpm 30 lpm 30 lpm 16 1.5 15 (%) (%) in 14 in 1 /P /P n=0 n=1
P 13 P 0.5 12
11 0 1 2 3 4 5 1 2 3 4 5 OAM value of grating OAM value of grating Power of non diffracted beam increases as the lpm is large. Power of n=1 beam increases as the lpm in small (except OAM = 4) and differs even if same OAM value (OAM =1). 6 Interference pattern measurement
1. OAM + reference (R = 215 mm) 2. OAM + reference (R = ∞) 3. OAM (double gratings) + reference (R = 215 mm) 4. OAM + OAM
7 Interference pattern with lens
Reference light Iris Lens f100 ND filter Beam splitter CCD Laser Optical glass Grating
OAM light Mirror Iris
8 Interference pattern
OAM Reference light OAM light Interference value
-1
-2
9 Calculation of interference pattern Interference between two different electric fields
1 exp()iE φ1 2 exp()iE φ2
2 2 2 = 1 exp()()φ + 21 exp φ2 1 2 ++= EEEEiEiEI cos2 ()−φφ 2121
10 Gaussian beam (reference light)
ω r 2 r 2 = 0 − −+− ψ EE 0 exp 2 exp kkzi ()z ω()z ω ()z 2 ()zR
2 z ωω += ()z 0 1 Beam radius zR
2 z () zzR 1+= R Rradius of curvature of the beam's wavefront z
πω 2 z = 0 Rayleigh range R λ
−1 z ψ ()z = tan Gouy phase zR
ω0 = mm053.0 Waist size when the laser is focused by a f100 lens
11 Laguerre Gaussian beam (OAM light)
m C r 22 r 2 r 2 = m − E Lp 2 exp 2 2 ω()z ω ()z ω ()z 1+ ()zz R 2 zkr −1 z exp −× i 22 exp()()− φ mpiim ++ tan12exp 2()+ zz R zR
m p ()xL Laguerre polynominal, m is OAM value
m 0 ()xL =1
12 Interference pattern: OAM = -1
Reference light OAM light Interference
Left hand
2000 2000 4000 -1.5 3.5 Meas. Meas. Meas. Calc. Clac. R = 215 mm Calc. 3 ω = 0.70 mm 3500 -1 Right hand ω = 0.88 mm 2.5 1500 1500 3000 -0.5 2 2500 0 1.5 1000 1000 2000 Y (mm) 0.5 1 1500 1 0.5 500 500 1000 1.5 0 500 1.5 1 0.5 0 -0.5 -1 -1.5 0 0 0 X (mm) 2 2.5 3 3.5 4 4.5 5 5.5 2 2.5 3 3.5 4 4.5 5 5.5 2 2.5 3 3.5 4 4.5 5 5.5 X (mm) X (mm) X (mm)
13 Interference pattern: OAM = -2 OAM light Interference OAM value is inverted. Why?
Left hand But, we can explain the spiral interference pattern. This is due to a finite curvature of the wave front.
2000 4000 -1.5 3 Meas. Meas. Clac. 3500 R = 215 mm Calc. -1 Right hand 2.5 ω = 0.70 mm 1500 3000 -0.5 2
2500 0 1.5 Y (mm) 1000 2000 0.5 1
1500 1 0.5 500 1000 1.5 0 500 1.5 1 0.5 0 -0.5 -1 -1.5 X (mm) 0 0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 X (mm) X (mm)
14 Interference pattern without lens
CCD Laser
CCD Laser
15 Interference pattern w/o lens
OAM Reference light OAM light Interference value
-1
-2
I cannot understand why the interference pattern become fork, but.. 16 Interference pattern w/o lens If the beam intersects another beam at angle, alpha, Gaussian beam can be expressed as
ω r 2 r 2 = 0 − − αα −++ ψ EE 0 exp 2 exp kzi cos sin kkx ()z ω()z ω ()z 2 ()zR
The term kxsin(alpha) induce fork interference pattern, and the pattern will change by the value of alpha.
17 Changing crossing angle: OAM = -1
alpha = 0
18 Chaning crossing angle: OAM = -2
alpha = 0
19 What will happen if OAM laser injects Grating non OAM Laser OAM = m × n m: the charge of grating n: the diffraction order n=0, ±1, ±2, ...
OAM Laser OAM = ??
20 Interference pattern using double gratings
Reference light Iris Lens f100 ND filter Beam splitter CCD Laser Optical glass Grating 1
Iris OAM light Grating 2
Mirror Iris
21 Interference pattern
OAM G1 = -1 OAM G1 = -1 OAM G1 = -1 OAM G2 = -1 OAM G2 =0 OAM G2 =+1
OAM = -2 OAM = -1 OAM = 0 Profile of the beam from G2 L = 920 mm L = 290 mm
OAM = 0 OAM = 0 22 Interference pattern
OAM G1 = -1 OAM G1 = -1 OAM G1 = -1 OAM G2 = -2 OAM G2 = 0 OAM G2 = +2
OAM = -3 OAM = -1 OAM = +1
23 Interference pattern
OAM G1 = -2 OAM G1 = -2 OAM G1 = -2 OAM G2 = -1 OAM G2 =0 OAM G2 =+1
OAM = -3 OAM = -2 OAM = -1
24 Interference pattern
OAM G1 = +2 OAM G1 = +2 OAM G1 = +2 OAM G2 = -1 OAM G2 = 0 OAM G2 = +1
OAM = +1 OAM = +2 OAM = +3
25 Interference pattern
Grating non OAM Laser OAM = m × n m: the charge of grating n: the diffraction order n=0, ±1, ±2, ...
OAM, m1 Laser OAM = m1+m2 × n m2: the charge of grating n: the diffraction order n=0, ±1, ±2, ... OAM value is preserved.
26 Interference pattern between OAM laser
Grating 1 BS Laser OAM light ND Grating 2 Iris Iris CCD
OAM light
27 Interference pattern with reference laser OAM value = -1: Right hand spiral interference is produced OAM laser from G1 and reference laser (without G2)
OAM laser from G2 and reference laser (without G1)
OAM value from G2 is inverted.
28 Interference pattern
OAM value (value of G2 is inverted from the actual value)
-1.5 4 3.5 -1 3 -0.5 2.5 G1 = -1 0 2
Y (mm) 1.5 G2 = +1 0.5 1 1 0.5 1.5 0 -1.5 -1 -0.5 0 0.5 1 1.5 X (mm)
-1.5 4 3.5 -1 3 -0.5 2.5 G1 = -1 0 2
Y (mm) 1.5 G2 = -1 0.5 1 1 0.5 1.5 0 -1.5 -1 -0.5 0 0.5 1 1.5 X (mm) 29 Interference pattern
-1.5 3.5
-1 3 2.5 -0.5 2 G1 = -1 0
Y (mm) 1.5 0.5 G2 = -2 1 1 0.5 1.5 0 1.5 1 0.5 0 -0.5 -1 -1.5 X (mm)
-1.5 3.5
-1 3 2.5 -0.5 2 G1 = -1 0
Y (mm) 1.5 0.5 G2 = +2 1 1 0.5 1.5 0 1.5 1 0.5 0 -0.5 -1 -1.5 X (mm) 30 Interference pattern
-1.5 4 3.5 -1 3 -0.5 2.5 G1 = -2 0 2
Y (mm) 1.5 G2 = +2 0.5 1 1 0.5 1.5 0 -1.5 -1 -0.5 0 0.5 1 1.5 X (mm)
-1.5 4 3.5 -1 3 -0.5 2.5 G1 = -2 0 2
Y (mm) 1.5 G2 = -2 0.5 1 1 0.5 1.5 0 -1.5 -1 -0.5 0 0.5 1 1.5 X (mm) 31 Fabry Perot cavity with OAM laser
Self-mode-locked Laguerre-Gaussian beam with staged topological charge by thermal-optical field coupling
Y. Zhang et al., Opt. Exp., 24 5514 (2016). 32 Hall A, C or Hall D? Hall A, C Merit: Low cost (polarimeter exists). Demerit: Many restriction?
Beam line to Hall D Merit: Free access. Laser inj. Demerit: 90 deg. High cost? (Laser injection sysytem should be constructed.) Det. 33 Schedule
End of 2016 2017 2018 Fellowship Jul Oct Jan Apr Jul Oct Jan Apr
Learn theory and basic High power Install a grating to a Exp?? experiment to store a test using a Fabry Perot cavity at Gamma ray OAM laser to an real Fabry Hall A or C? vortex from optical cavity. Perot cavity ICS using at optical Calculation of laboratory? Constraction of a Exp?? vortex laser characteristics of Fabry Perot cavity at X-rays and how to CEBAF beam line to measure OAM of Prepare Hall D? emitted X-rays. proposal
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