[Paper Review] Role of Azimuthal Energy Flows in the Geometric Spin Hall Effect of Light

A. Ya. Bekshaev|arXiv (Cornell University)|Jun 6, 2011

Orbital Angular Momentum in Optics22 references3 citations

TL;DR

This paper investigates the geometric spin Hall effect of light by analyzing azimuthal energy flows in oblique sections of paraxial beams with angular momentum. It explains the transverse shift of the beam's center of gravity via internal energy redistribution, distinguishing between orbital flow in scalar beams and spin flow in elliptically polarized beams, with implications for detector placement and beam geometry.

ABSTRACT

In an oblique section of a paraxial beam with angular momentum, the beam center of gravity (CG) is shifted with respect to its position in the normal cross section. We relate this shift with the internal energy redistribution occurring on the passage between the normal and oblique sections. The transverse orbital flow explains the effect for scalar beams, similar incorporation of the spin flow enables explanation of the CG shift in oblique sections of the elliptically polarized beams. Role of the special properties of the position-sensitive detector placed in the oblique beam section is discussed.

Motivation & Objective

• To explain the transverse shift of the center of gravity (CG) in oblique sections of paraxial beams with angular momentum.
• To clarify the role of azimuthal energy flows—specifically orbital and spin flows—in inducing the CG shift.
• To address the influence of position-sensitive detectors on observing the geometric spin Hall effect.
• To provide a consistent framework for energy redistribution in beams with spin angular momentum, despite unresolved generalization of energy flow rules.

Proposed method

• Analyzes the beam's center of gravity (CG) shift in oblique cross sections relative to normal sections.
• Introduces the concept of transverse orbital energy flow to explain CG shift in scalar beams.
• Extends the analysis to elliptically polarized beams by incorporating spin flow into the energy redistribution model.
• Uses geometric optics and energy flow formalism to describe how internal energy redistribution causes transverse CG displacement.
• Discusses the impact of detector position and sensitivity on measuring the effect.
• Relies on theoretical analysis of energy flow in paraxial beams, focusing on azimuthal components.

Experimental results

Research questions

• RQ1 What causes the transverse shift of the center of gravity in oblique sections of a paraxial beam with angular momentum?
• RQ2 How do azimuthal energy flows—specifically orbital and spin flows—contribute to the geometric spin Hall effect?
• RQ3 Why does the position of a detector affect the observation of the geometric spin Hall effect in oblique beam sections?
• RQ4 Can the energy redistribution rules for orbital flow be generalized to include spin flow in the context of the geometric spin Hall effect?
• RQ5 What is the role of internal energy redistribution in producing the observed CG shift?

Key findings

• The center of gravity (CG) of a paraxial beam shifts transversely in oblique sections due to internal energy redistribution, not external forces.
• For scalar beams, the transverse orbital energy flow explains the CG shift in oblique sections.
• For elliptically polarized beams, the inclusion of spin flow is necessary to explain the CG shift, extending the orbital flow model.
• The shift arises from the geometric arrangement of the beam and the non-uniform energy distribution in oblique cross sections.
• The position-sensitive detector's placement significantly influences the observed magnitude of the effect due to spatial sensitivity to energy flow.
• The paper acknowledges unresolved issues in generalizing energy flow rules to spin flow, though the conceptual framework remains valid and insightful.