Orbital Angular Momentum and other newly recongnised EM degrees of freedom

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EISCAT
-
3D Workshop, Uppsala, 19


21 May 2010


Orbital Angular
Momentum and
other newly
recongnised

EM degrees of freedom

Bo Thidé

Swedish Institute of Space Physics, IRF, Uppsala, Sweden



With contributions from the LOIS OAM/radio topology collaboration


EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

2

Phase singularities (dislocations) are to be expected

in radio beams propagating through space

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

EM angular momentum is a conserved
physical observable. Just like the linear
momentum (
Poytning

vector),
it that can
carry information over huge distances

Bo Thid
é

3

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Mechanical effects of photon spin angular momentum (1936)

and of photon orbital angular momentum (1992)

Bo Thid
é

4

Beth’s experiment, 1936

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

EM beam with circular polarisation (SAM)
S

but

no

orbital angular momentum (OAM)
L

Bo Thid
é

5

M. J. Padgett, J. Leach
et al
., U. Glasgow, UK; Royal Society

Phase fronts (loci of constant phase)

Sjöholm and Palmer, 2007

Optics (LG)

Radio

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Different OAM states correspond to different
topological charges (vortex winding numbers)

Bo Thid
é

6

M. J. Padgett, J. Leach
et al
., U. Glasgow, UK; Royal Society

l
=+1

l
=+3

l
=
-
4

Spiraling Poynting/OAM
vectors carry a lot of
information! The Jones
matrix goes from 2
×
2 to
2(
j
+1)
×
2(
j
+1),

j=s+l .

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Difference

between

polarisation (SAM) and
orbital

angular

momentum

(OAM)

7

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Micromechanical

action of laser light
carrying

SAM and OAM

8

Spin angular momentum
s
= 1

Orbital angular momentum
l
= 8

Particles of sizes 1

3
μ
m irradiated by SAM/OAM laser beams

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Imparting vorticity/OAM onto an EM beam (laser,
mm wave) with the help of a spiral plate or hologram

Bo Thid
é

9

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

10

Very readable pioneering

paper on
photon
OAM in
astrophysics

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

11

POAM in light around a Kerr black hole (Sgr A*)

Tamburini

et al
., (Submitted)

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

12

Bo

Thidé.
Stimulated Electromagnetic Emission and nonlinear wave
-
wave interactions in
ionospheric

heating experiments
. In M.

Q. Tran and M.

L.
Sawley
, editors,
Proceedings,
Contributed Papers, International Conference on Plasma Physics
, volume

I, page 131,
Lausanne, Switzerland, 27 June
-
3 July 1984. Centre de
Recherche

en Physique des
Plasmas,
Ecole

Polytechnique

Federal de Lausanne, CRPP
-
EPFL
.

O mode SEE

X mode SEE

Circular
, (
nearly
) O
-
mode
pumping

1983 experiment: p
olarisation

(SAM) of the secondary radio
emissions exhibit
polarimetry

anomalies


OAM?

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

13

Polarimetry

(SAM) studies of SEE exhibit
anomalies

Experiments in
Vasil’sursk
, Russia, 1998

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Linear transfer of OAM radio ↔ plasma

Bo Thid
é

14

EPL, in press

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Nonlinear transfer of OAM radio ↔ plasma

Bo Thid
é

15

Brillouin = ion line

Raman = plasma line

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Plasmons (Langmuir waves) can carry OAM but not SAM

Bo Thid
é

16

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Fundamental question: What are the complete

physical characteristics of EM radiation?

Bo Thid
é

17

Symmetric under inhomogeneous Lorentz transformations. The
concomitant Lie group is the 10
-
dimensional Poincaré group
P(10).
According to Noether’s theorem there therefore exist 10 conserved
EM quantities. In fact there exist 23 exact continuous
symmetries/conserved quantities (in vacuo), plus an as yet unknown
number of approximate, conservation laws [Ibragimov, 2008].

Start from the beginning: the microscopic Maxwell
-
Lorentz equations

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Conserved quantities in a closed electromechanical
system (matter + EM fields) [
Boyer
, 2005] (1)

Homogeneity in time => conservation of system energy
(
cf
.
Poynting’s

theorem):




Homogeneity in space => conservation of system linear
momentum (gives rise to translational Doppler shift):



Foundation of conventional ‘linear momentum’ radio.


Bo Thid
é

18

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Conserved quantities in a closed electromechanical
system (matter + EM fields) [
Boyer
, 2005] (2)

Invariance under proper Lorentz transformations =>
conservation of system centre of energy:



Isotropy in space => conservation of system angular
momentum (gives rise to azimuthal Doppler shift):



The first part is the mechanical angular momentum
J
mech

.
The second part is the EM angular momentum

J
field

.

Foundation of ‘angular momentum’ radio or ‘dual radio’.

Bo Thid
é

19

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

EM field angular momentum. Directly

from the Maxwell
-
Lorentz equations

Bo Thid
é

20

EM field angular momentum around the origin:

, where

, where

where

For each (temporal) Fourier component:

(SAM operator)

(OAM operator)

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Radio OAM can be observed by phased arrays
Optimal results with
vector
sensing antennas

Bo Thid
é

21

Thidé
et al.
, Phys. Rev. Lett.,
99
, 087701, 2007

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Field
vector
sensing means
total

configurability

Bo Thid
é

22

The ultimate radio coronagraph!

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Radio beam carrying both SAM and OAM

Linear momentum (Poynting) flux and
E
(t,
x
)

vs. OAM flux

Bo Thid
é

23

Mohammadi
et al
., IEEE Trans. Ant. Propag., Vol.
58
,2009

Distribution of linear momentum
(Poynting ) flux and E
-
field vectors

Distribution of orbital angular
momentum flux

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Observations at 94 GHz of angular momentum
induced azimuthal (rotational ) Doppler shift

Bo Thid
é

24

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Rotational Doppler shift spectrum

Bo Thid
é

25

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

OAM spectrum probing (spiral imaging)


a
new scatter radar diagnostic

Bo Thid
é

26

Recent digital spiral imaging experiments (Ll. Torner
et al
., Opt. Express,
13,
873

881, 2005;
Molina
-
Terriza
et al.,
J. Eur. Opt. Soc., Rapid Publ.,
2
, 07014, 2007) have demonstrated that
probing with OAM gives a wealth of new information about the object under study.

The stimulus…

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Spiral (OAM) spectrum imaging results

Bo Thid
é

27

…and its response

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

28

EM equivalent of fluid vorticity

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

29

The OAM topological degree of freedom has
revolutionised wireless communications

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Hyperentangled SAM and OAM photon states break
the linear
-
optics channel capacity threshold

Bo Thid
é

30

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

31

The conventional Shannon dimensionality of 2 can be
exceeded by using OAM degrees of freedom

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

32

Recent call for funding of practical “on
-
the
-
scene”
information
-
rich applications using OAM
etc.

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Thank you for your attention

Bo Thid
é

33

....there may be more things in heaven and earth than even Maxwell had dreamt of …

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Conserved quantities in EM fields and matter (1)

Bo Thid
é

34

Homogeneity in time => conservation of system energy
(Poynting’s theorem):

Homogeneity in space => conservation of system linear
momentum (gives, e.g., rise to EM Doppler shift):

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Conserved quantities in EM fields an matter (2)

Bo Thid
é

35

Invariance under proper Lorentz transformations =>
conservation of system centre of energy:

Isotropy in space => conservation of system angular
momentum (gives rise to azimuthal Doppler shift):

Foundation of ‘angular momentum radio’ and vorticity

probing radio and radar methods.

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Total radiated EM field angular momentum

Bo Thid
é

36

For radiation beams in free space, EM field angular momentum
J
em

can
be separated into two parts [
Jackson
, 1998;

Thidé
,
2010]:



For each single Fourier mode in real
-
valued representation [
van
Enk

&
Nienhuis
, 1992]:



The first part is the EM

spin angular momentum (SAM)
S
em

,
a.k.a.
wave
polarisation
,

and the second part is the EM
orbital angular
momentum (OAM)

L
em

.

NB: In general, both EM linear momentum
p
em
,
and

EM angular
momentum
J
em

=
L
em

+
S
em

are radiated all the way out to the far zone!

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

LOIS prototype station under construction in Ronneby

To be augmented by two outer, concentric rings, with 16 and 24 radio units,
respectively, for a total of 48 units with three dipoles each (funding permitting)

Bo Thid
é

37

EISCAT_3D Workshop, Uppsala, 19


21 May 2010

Bo Thid
é

38

LOIS has measured the photon spin current
V

in ionospheric radio signals since 2003