Light orbital angular momentum and laser beam characterization

Transcription

1 Light orbital angular momentum and laser beam characterization Julio Serna INDLAS May 013 Bran, Romania Mini Symposium/Workshop on Laser Induced Damage and Laser Beam Characterization 1

2 Outline Why angular momentum? 1 Laser beam characterization Angular momentum (paraxial) 3 Measurements 4

3 Why angular momentum? 3

4 Why angular momentum? Light transports energy Metal cutting Optical communications 4

5 Why angular momentum? Light transports linear momentum Solar sail Optical tweezers 5

6 Why angular momentum? Light transports angular momentum Trivial case Orbital angular momentum Circular polarization Spin angular momentum 6

7 Why angular momentum? You can really rotate things with light Changes in path length in an interferometer OAM of a Bessel beam 7

8 Why angular momentum? Examples Polarization Ray hyperboloid 8

9 Laser beam characterization What could we say about angular momentum? 9

10 Why laser beam characterization? Beam Propagation Beam Irradiance Irradiance information: Too much? Not enough? 10

11 Why laser beam characterization? Sometimes irradiance + free space propagation are not enough Shukhov Tower, Moscow 11

12 Why laser beam characterization? Beam characterization approach Parameters Valid for arbitrary beams Analytical and numerical approach Measurable parameters Adequate propagation ISO (Full info Wigner distribution) 1

13 Why laser beam characterization? D (beam width): Beam divergence Waist size Waist position M parameter P x xu xu u Easy? 13

14 Why laser beam characterization? 3D: ( Polarization) Beam matrix Two invariant quantities W M P t M U M 4 eff, a x xy xu xv xy y yu yv xu yu u uv xv yv uv v Angular momentum Stokes s 3 antisymmetric M 14

15 Angular momentum (paraxial) What do we want to calculate? Poynting vector S c ε 0 E B Linear momentum density P ε 0 E B Angular momentum density M ε 0 r (E B) 15

16 Angular momentum (paraxial) We have to accept some non transversality in our beams M r P Solution: A, vector potential (x,y,z) (not E, not B) amplitude 16

17 Angular momentum (paraxial) Propagation in z with a slowly varying amplitude in transversal direction: Vector potential: A A o (x,y,z) e -i(ω t-k z) e polarization: e (α ^x + β y); ^ α α * + β β * 1 e ^x linear polarization e ( ^x + i y)/ circular pol. (left) ^ Scalar potential: φ φ o (x,y,z) e-i(ω t-k z) 17

18 Angular momentum (paraxial) B A E φ 1 A + c φ t A t 0 Lorentz gauge 18

19 19 Angular momentum (paraxial) ) ( 4 ˆ ˆ ) Im( ˆ ) ( 4 0 * 0 * * * * 0 A A A A c i x A y A c A k c c ω ε β α ω ε ω ε ε y x z B E B E S Time average (harmonic field)

20 0 Angular momentum (paraxial) ) ( ˆ ˆ ) Im( 1 ˆ * * * β α + + k i x y k y x z S In terms of the amplitude ),, ( ),, ( irradiance 0 0 z y x c i z y x A ε ω

21 1 [ ] + φ φ β α * * * ) Im( 1 1 kc i r r kc c z z S r M z component of the angular momentum density (cylindrical coordinates): Angular momentum (paraxial)

22 Angular momentum (paraxial) (x, y) contribution. Example: Laguerre Gauss beam LG p l r p p 0; l 1 s 3 0 s 3 1 s 3-1

23 Angular momentum (paraxial) LG beams in free space propagation r p p 0; l 1; s 3 1 3

24 Angular momentum (paraxial) Angular momentum flux through the xy plane: J c M dx dy 4

25 5 Angular momentum (paraxial) Definitions from the beam matrix P formalism: dx dy x x y ki i yu dx dy y y x ki i xv dx dy x x ki i u dx dy x I x dx dy dx dy I z * * * * * * 1 S

26 6 Angular momentum (paraxial) Angular momentum flux components: ) Im( ; 1 ) ( ) ( ) ( * 3 3 β α ω I s s yu xv c I u z x c I v z y c I z y x + + J J J (Stokes parameter)

27 Angular momentum (paraxial) Orbital angular momentum flux Beam matrix formalism J z L I c ( xv yu ) P W M t M U M : waist position/radius of curvature & orbital angular momentum flux 7

28 Angular momentum (paraxial) Laguerre Gauss beams: J z I l ω l per photon + polarization p 0; l 1 s 3 0 s 3 1 s 3-1 8

29 Measurements Two different approaches: Mechanical effects Beam characterization approach 9

30 Measurements. Mechanical effect Polarization, macroscopic effects: R. A. Beth 30

31 Measurements. Mechanical effect Polarization, macroscopic effects: R. A. Beth No lasers! 31

32 Measurements. Mechanical effect Orbital angular momentum, macroscopic effects: Beijersbergen et al. Modern times. No result! 3

33 Measurements. Mechanical effect Orbital angular momentum, small particles He, Friese, Heckenberg, Rubinsztein Dunlop LG 03 and they change polarization. Expected ratio: :3:4. Exp.: 1.8:.8:3.8 Simpson, Dholakia, Allen, Padgett 33

34 Measurements. Beam characterization approach: Polarization linear circular elliptical 34

35 Measurements. Beam characterization approach: Orbital angular momentum complete spatial characterization 35

36 Measurements. Beam characterization approach: Orbital angular momentum irradiance doughnut + cyl amplitude doughnut no angular momentum + i cyl angular momentum 36

37 Measurements. Beam characterization approach: Orbital angular momentum 0.5x telescope electrooptical chopper cyl R1 half symmetric TEA CO laser R L1 L L3 0 pyroelectric camera ruler Setup 37

38 Measurements. Beam characterization approach: Orbital angular momentum Cylindrical lens fx184 mm Cylindrical lens fx184 mm 38

39 Measurements. Beam characterization approach: Orbital angular momentum Cylindrical lens fx184 mm Cylindrical lens fx184 mm 39

40 Measurements. Beam characterization approach: Orbital angular momentum 3.0 before after <x>, <y>, <xy> <x> <xy> <y> angle π/ angle (after the lens) π/4 angle z (mm) 0 40

41 Measurements. Beam characterization approach: Orbital angular momentum Results: M 4 eff lz (1 ± To be compared with LG 0 1 : M a 4 eff a l z 3 ± ± ) orbital angular momentum per photon 41

42 Acknowlegments This work has been supported by the Ministerio de Ciencia e Innovación of Spain, under project FIS

43 Optics & Applications Group University of Glasgow Profs. Courtial & Padgett 43

44 015 44