Photo Orbital Angular Momentum in Astrophysics

(By Martin Harwit

ApJ, 2003, Vol. 597, 1266)

周建锋清华大学天体物理中心

Contents1. Introduction2. Multipole Fields3. Astronomical Instrumentation to Measure POA

M

4. Astrophysical Applications

5. Conclusion

• Dove-PrismMach-Zehnder Interferometers• Astronomical Limitations

• Masers as Probes of Inhomogeneities• Luminous Point Sources• SETI• Transfer of OAM by Kerr Black Holes• Blackbody Radiation and the CMB

1. Spin Angular Momentum

Photons are endowed with inherent spin angular momentum .

This is demonstrated by the selection laws in atomic physics,where

. 1,0 ,1 jl

Photons all carrying the same spin are circularly polarized.

1. Spin Angular Momentum

Plane waves are the superposition of circularly polarized photons.They actually don’t exist physically, just as that white light photons don’texist either.

Plane waves carry no angular momentum.

K (r)

E

H 0)( HErSr

1. Detection of Spin Angular Momentum

Beth Experiment in 1936 (Phys. Rev.)

Left circularly polarized light

Right circularly polarized light

/2 birefringent plate

1. Photon Orbital Angular Momentum

m

Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. (Allen, 1992, PRA)

Usually, a photon just has its spin angular momentum . It is also possible to possess a larger angular momentum of .

Beams of photons each with OAM as high as m =200 have been produced in lab. (Curtis et al., 2002, Opt. Commun.)

2. Multipole Fields (Classical Electrodynamics)

0 HE

kH

Spherical electromagnetic waves in free space, where

can be completely described by superpositions of electric and magnetic multipole fields.

For electric multipole (TM model),

For magnetic multipole (TE model), kE

2. Multipole Fields (Classical Electrodynamics)

For electric multipole radiation,

Each photon, with energy , here carries off angular momentum m

2. Multipole Fields (Quantum Electrodynamics)

In quantum electrodynamics, angular momentum J becomes an operator.

Spin and orbital angular momentum may notalways be clearly separable.

2. Comparison between Spin and Orbital AM

3. Astronomical Instrumentation to Measure POAM

Dove-Prism Mach-Zehnder Interferometer

3. Astronomical Instrumentation to Measure POAM

Rotation of phase profile

3. Astronomical Instrumentation to Measure POAM

Sort photons with odd and even OAM

Phases are controlled by rotation and path.

3. Astronomical Instrumentation to Measure POAM

Photon orbital angular momentum (POAM) produced by a spiral phase plate

3. Astronomical Instrumentation to Measure POAM

Photon orbital ang(POAM) produced by a spiral phase plate

3. Astronomical Instrumentation to Measure POAM

4. Astrophysical Applications

Masers as Probes of Inhomogeneities

4. Astrophysical Applications

SETI—Search Extra Terrestrial Intelligence

4. Astrophysical Applications

Detect Kerr Black Holes

Photons are more complex than we have known!