Orbital Angular Momentum of Light Melvin Eloy Irizarry Stony Brook University

Outline • • • •

Light and angular momentum Transverse modes - LG Generation of beams with OAM Mechanical effects – Tweezers, wrenches and other machines

• Photon entanglement and beyond Melvin Eloy Irizarry

Orbital Angular Momentum of Light

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Light’s Angular Momentum • In 1936 R. Beth measured light induced torque • Birefringent plate changes polarization of light beam

Melvin Eloy Irizarry

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Photon’s spin number • Assigning an ±ħ to each photon produced the same result • Light polarization related to angular momentum - Spin

Melvin Eloy Irizarry

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OK, Spin… What about L? • Transverse modes of laser light can be described by Gaussian modes • In 1992 L. Allen et al recognized that the amplitude of LG modes had an azimuthal phase dependence • Analogy with quantum mechanics leads to well-defined orbital angular momentum Melvin Eloy Irizarry

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What to do? • Set up and experiment similar to Beth’s • More convenient is to convert a beam with zero OAM

Melvin Eloy Irizarry

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Getting Laguerre-Gaussian • Spiral phase plates • Computer-generated holographic converters • Cylindrical-lens mode converters

Melvin Eloy Irizarry

http://antwrp.gsfc.nasa.gov/apod/ap03111 9.html

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Spiral phase plates and holographic converters

• Introduce the azimuthal phase term to a HG00 mode to produce an LGpl mode with p = 0 and specific l • A screw phase dislocation, produced on axis, causes destructive interference, leading to the characteristic ring intensity pattern in the far field Melvin Eloy Irizarry

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Cylindrical-lens converters • Converts higher-order HG_mn modes to LG modes with 100% efficiency

• l = |m-n| and p = min(m,n)

Melvin Eloy Irizarry

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LG Mode Generation

Physics Today May ’04

Melvin Eloy Irizarry

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Light beams with OAM Physics Today May ’04

Melvin Eloy Irizarry

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Mechanical applications

Optical Tweezers • Strong intensity gradient at tight focus of a laser beam • Small, lightweight dielectric particle experiences a gradient force towards the beam axis

http://www.stanford.edu/group/blocklab/Op tical%20Tweezers%20Introduction.htm Melvin Eloy Irizarry

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Melvin Eloy Irizarry

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Optical Wrenches • Optical tweezers are used to held particles in a 3-D trap with out mechanical suspension • Light with angular momentum induces rotation on objects

Melvin Eloy Irizarry

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“…with respect to absorption and resulting mechanical rotation of a particle, the spin and the orbital angular momenta of light are equivalent.”

Melvin Eloy Irizarry

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Experimental configuration of the optical spanner

Melvin Eloy Irizarry

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Successive frames of the video image showing the stop–start behavior of a 2-µm-diameter Teflon particle held with the optical spanner.

Melvin Eloy Irizarry

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“Unlike the spin angular momentum of a light beam which is always intrinsic, the z component of the orbital angular momentum can be described as intrinsic only if the z direction can be stipulated such that the transverse momentum integrated over the whole beam is zero. If an interaction is with only a fraction of the beam cross section, then the orbital angular as measured about the original axis is extrinsic.”

Melvin Eloy Irizarry

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Spinning and Orbiting, I • “…sufficiently small to be subject to a well-defined scattering force, allowing them to interact with the orbital angular momentum of the beam.” • “…orbiting the beam axis at a frequency around 1 Hz”

http://www.physics.gla.ac.uk/Optics/projects/spinningAndOrbiting/orbit.mpg Melvin Eloy Irizarry

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Spinning and Orbiting, II • Calcite fragment “…large enough not to interact detectably with the beam’s orbital angular momentum.” • “due to its birefringence it interacts with the spin angular momentum of the beam and is set spinning about its own axis” http://www.physics.gla.ac.uk/Optics/projects/spinningAndOrbiting/spin.mpg Melvin Eloy Irizarry

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“We outline a photolithographic method for producing transparent ‘‘machine elements’’ with features on the order of 1 mm, which are then trapped on an optical ‘‘axle’’ and caused to rotate about this axle by a nearby spinning particle driven by optical torque”

Melvin Eloy Irizarry

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Melvin Eloy Irizarry

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Melvin Eloy Irizarry

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Entanglement • Two-state quantum system – Spin • LG modes can be used to define an infinite-dimensional discrete Hilbert space • Possibility of entanglement involving many orthogonal quantum states • New approaches to encryption and data storage Melvin Eloy Irizarry

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And maybe… “And we could search for signals from extraterrestrials who might be availing themselves of the high information density made possible by orbital angular momentum.” Physics Today May 2004

Melvin Eloy Irizarry

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Things I won’t mention • Motion of atoms in light beams with orbital angular momentum – Azimuthal Doppler Shift. • Astronomical techniques employing orbital angular momentum of light • Optical vortices • Spin-orbit coupling, entanglement, etc • Bell-type test of non-locality Melvin Eloy Irizarry

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References • • • • • • Melvin Eloy Irizarry

Animation – ♥ Merideth Frey ♥ Allen, L, Introduction to the atoms and angular momentum of light special issue J. Opt. B: Quantum Semiclass. Opt. 4 S1-S6 2002 Allen, L et al., Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45, 8185 (1992) Padgett M et al, Light’s Orbital Angular Momentum Physics Today May ’04 Mair, A et al, Entanglement of the orbital angular momentum states of photons Nature 412, 313-316 (19 July 2001) Other sources cited in previous slides Orbital Angular Momentum of Light

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Question or Comments Thank you for your attention

Orbital Angular Momentum of Light

18. Successive frames of the video image showing the stop–start behavior of a 2-µm-diameter. Teflon particle held with the optical spanner.
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