### Optical Magnus Effect: Topological Monopole Deflects Spinning Light

**Konstantin Y. Bliokh**

[This is an invited article based on recent work of the authors -- 2Physics.com]

**Authors: Konstantin Y. Bliokh, Avi Niv, Vladimir Kleiner, and Erez Hasman**

**Affiliation: Micro and Nanooptics Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel**

>> Link to the Group Homepage

In an article published in the December 2008 issue of Nature Photonics a team from Micro- and Nanooptical Laboratory of Technion-Israel Institute of Technology has reported the first direct observation of the topological spin transport of photons, also known as the spin Hall effect of light or the optical Magnus effect [1]. The effect represents a polarization-dependent transverse deflection of the light beam upon a bending of its trajectory, and it can be attributed to a Coriolis effect or a spin-orbit coupling of light. Remarkably, the spin-orbit interaction of light has an inherent topological origin which is described by the Berry-phase monopole in the momentum space.

**Vladimir Kleiner, Erez Hasman, and Avi Niv (left to right)**

Two decades ago, the Berry phase brought a geometrical beauty to the description of quantum adiabatic evolution [2,3]. Afterwards, physicists realized that seemingly ‘passive’ geometrical concepts, such as Berry curvature, also manifest themselves dynamically, producing a real action on physical objects. As a result, the geometry-induced forces appear which affect the dynamics of quantum particles with some internal properties [4]. In particular, they describe the Magnus effect of quantum vortices [5] and spin Hall effect of spinning particles [6-8]. This offers a novel type of quantum transport which is robust against the details of the system and is determined solely by the geometry and intrinsic properties of the particles.

The spin-Hall effect was invented in the context of semiconductor spintronics, where it is expected to have promising applications [6]. The same effect also occurs within the fundamental equations of high-energy physics involving such intriguing mathematical objects as topological monopoles and space non-commutativity [8]. It seems that optics provides an ideal field for exploring this striking phenomenon. First, trajectory of light propagation can be directly observed in relatively clean and simple systems, and the accuracy of modern optics allows sub-wavelength resolution at nano-scales. Second, classical light captures all basic features of relativistic spinning particles, which enables one to extrapolate results to a diversity of physical systems, where such observations are impossible.

**Fig. 1. The trajectories of left- and right-handed circularly polarized light beams propagating along the reflecting surface of a glass cylinder. The spin-orbit coupling between the intrinsic angular momentum of light and the curved propagation trajectory produces opposite deflections for the two beams. This is the spin Hall effect of light described by a Lorentz-force-type term from a topological monopole in momentum space**[This figure is reprinted from "The dynamics of spinning light" by Franco Nori, Nature Photonics 2, 717 (2008). Our thanks to 'Nature Photonics']

The experiment of Ref. 1 was realized by launching a laser beam at a grazing angle to the internal surface of a glass cylinder, so that the light propagated along a smooth helical trajectory due to total internal reflection, Fig. 1. Such a helical path induces a spin-orbit interaction between the geometry of the trajectory and the intrinsic spin angular momentum carried by the polarized light. The theory and experiment of Ref. 1 provide a fairly complete picture of the geometrodynamical evolution of polarized light. On the one hand, the geometry of the trajectory determines the variations of the polarization of light. On the other hand, a spin-dependent perturbation of the trajectory occurs which deflects the right- and left-handed circularly polarized beams in opposite directions tangent to the cylinder surface (see Fig. 1).

In addition to fundamental interest, the spin Hall effect of light may have promising applications in photonics. Utilizing this effect in optical devices may lead to the development of a promising new area of research – spinoptics. The hope is that we will be able to control light in all-optical nanometer scale devices in ways that were impossible before [9,10]. While tiny wavelength-scale effects were negligible a decade ago, nowadays they can be crucial for numerous nano-optical applications.

**References:**

**[1]**“Geometrodynamics of Spinning Light”, K.Y. Bliokh, A. Niv, V. Kleiner, E. Hasman, Nature Photonics, 2, 748 (2008). Abstract.

**[2]**“Quantal Phase Factors Accompanying Adiabatic Changes”, M.V. Berry, Proc. R. Soc. A 392, 45 (1984). Abstract.

**[3]**“Geometric Phases in Physics”, A. Shapere, F. Wilczek (eds) (World Scientific, Singapore, 1989).

**[4]**“Origin of the Geometric Forces Accompanying Berry’s Geometric Potentials”, Y. Aharonov, A. Stern, Phys. Rev. Lett. 69, 3593 (1992). Abstract.

**[5]**“Transverse Force on a Quantized Vortex in a Superfluid”, D.J. Thouless, P. Ao, Q. Niu, Phys. Rev. Lett. 76, 3758 (1996). Abstract.

**[6]**“Dissipationless Quantum Spin Current at Room Temperature”, S. Murakami, N. Nagaosa, S.C. Zhang, Science 301, 1348 (2003). Abstract.

**[7]**“Topological Spin Transport of Photons: The Optical Magnus Effect and Berry phase”, K.Y. Bliokh, Y.P. Bliokh, Phys. Lett. A 333, 181 (2004). Abstract.

**[8]**“Spin Hall Effect and Berry Phase of Spinning Particles”, A. Bérard, H. Mohrbach, Phys. Lett. A 352, 190 (2006). Abstract.

**[9]**“Observation of the Spin Hall Effect of Light via Weak Measurements”, O. Hosten, P. Kwiat, Science 319, 787 (2008). Abstract. Related article in 2Physics.

**[10]**“Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect”, K.Y. Bliokh, Y. Gorodetski, V. Kleiner, E. Hasman, Phys. Rev. Lett. 101, 030404 (2008). Abstract.

Labels: Condensed Matter 2, Laser 2, Nanotechnology

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