7/22/2016

Optical vortex 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 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 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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