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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Angular diffraction

Sonja Franke‐Arnold, Barry Jack, Jonathan Leach, Miles J. Padgett

Published Dec 29, 2008• 7 citations

Abstract

The angular profile and the orbital angular momentum of a light mode are related by Fourier transform. Any modification of the angular distribution, e. g. via diffraction off a suitably programmed spatial light modulator, influences the orbital angular momentum spectrum of the light. This holds true even at the single photon level. We observe the influence of various angular masks on the orbital angular momentum spectrum, both in the near and the far field, and describe the resulting patterns in terms of angular diffraction. If photons are entangled in their orbital angular momentum, diffraction of one photon affects the orbital angular momentum spectrum of its partner photon, and angular ghost diffraction can be measured in the coincidence counts. We highlight the role of the angular Fourier relationship for these effects.

DOI: 10.1117/12.813564

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The angular profile and the orbital angular momentum of a light mode are related by Fourier transform. Any modification of the angular distribution, e. g. via diffraction off a suitably programmed spatial light modulator, influences the orbital angular momentum spectrum of the light. This holds true even at the single photon level. We observe the influence of various angular masks on the orbital angular momentum spectrum, both in the near and the far field, and describe the resulting patterns in terms of angular diffraction. If photons are entangled in their orbital angular momentum, diffraction of one photon affects the orbital angular momentum spectrum of its partner photon, and angular ghost diffraction can be measured in the coincidence counts. We highlight the role of the angular Fourier relationship for these effects.

Light contains both spin and orbital angular momentum. Despite contributing equally to the total photonic angular momentum, these components derive from quite different parts of the electromagnetic field profile, namely its polarization and spatial variation, respectively, and therefore do not always share equal influence in light–matter interactions. With the growing interest in utilizing light’s orbital angular momentum to practice added control in the study of atomic systems, it becomes increasingly important for students and researchers to understand the subtlety involved in these interactions. In this article, we present a review of the fundamental concepts and recent experiments related to the interaction of beams containing orbital angular momentum with atoms. An emphasis is placed on understanding light’s angular momentum from the perspective of both classical waves and individual photons. We then review the application of these beams in recent experiments, namely single- and few-photon transitions, strong-field ionization, and high-harmonic generation, highlighting the role of light’s orbital angular momentum and the atom’s location within the beam profile within each case.

Spatially incoherent light can result from nonlinear processes where a group of photons are emitted in entangled states of spatial modes, which results in an incoherent mixture of constituting spatial modes when the photons are assessed one by one. In this paper we explore a method which uses a tilted lens to probe the orbital angular momentum (OAM) spectrum of such a mixture. We examine the general case where the photons are in mixtures of both different OAM and radial modes, resulting in a 2-dimensional random distribution that creates a more difficult challenge compared to mixtures of OAM only.

The quantum Talbot effects with orbital angular momentum (OAM) photons have been investigated theoretically. Two schemes, holographic ghost-image and twin-photon configuration, have been considered. They exhibit unique properties, which are different from the cases of previous classical and quantum Talbot effects. The Talbot effects in the present schemes originate from lateral translation of the periodic object instead of transverse coherences of optical fields or photon wave functions. The Talbot pattern in the present case can be manipulated by the OAM number of the incident photons, which is equivalent to the Talbot effect of an effective periodic object illuminated by photons without the OAM. This means that complex diffraction patterns of an unusual periodic object can be obtained by designing the Talbot effect with OAM photons, which provides a promising idea in optical designs for the diffraction patterns.