## Polarisation and Propagation of Light

#1026

Theoretical and Experimental Study of Physical Effects Concerned with Interaction between Polarization and Propagation of Light

**Tech Area / Field**

- PHY-OPL/Optics and Lasers/Physics

**Status****8** Project completed

**Registration date****26.06.1997**

**Completion date****24.06.2005**

**Senior Project Manager**

Kirichenko V V

**Leading Institute**

Joint Nonlinear Optics Laboratory/Electrophysics Institute and Chelyabinsk State Technical University, Russia, Chelyabinsk reg., Chelyabinsk

**Supporting institutes**

- Vavilov State Optical Institute (GOI), Russia, St Petersburg\nVNIITF, Russia, Chelyabinsk reg., Snezhinsk

**Collaborators**

- University of Joensuu, Finland, Joensuu\nStanford University / SLAC / School of Engineering, USA, CA, Stanford\nUniversity of Central Florida / Center for Research and Education in Optics and Lasers, USA, FL, Orlando

**Project summary**

Now we intend to investigate theoretically and experimentally the influence of the external magnetic field on the propagation of the light through an optical fiber. We hope to find and observe inverse effect to the effect of influence of circular polarization s = ± 1 in a vacuum, namely, transverse shift D x » sl of the focal waist of a converging semi-spherical beam.

*Description of the Proposal*

If we consider propagation of a narrow light beam through a homogeneous medium, the solution of Maxwell equations can be approximately written in the form __E__ (x, y, z) » (a_{x}__x__+a_{y}__y__) f (x, y, z) exp [- i (wt - kz)]. Such factorization means that polarization and the process of propagation are mutually independent. But it is not correct for the case of inhomogeneous medium. It was shown theoretically by F.Bortoloti (1926), S.Rytov (1938), V.Vladimirsky (1941) that rotation of the plane of polarization of linear polarized light depends on helicity of its trajectory. It was demonstrated by propagating linear polarized light through helically coiled monomode fiber (A.Tomita and R.Chiao, 1986) and interpreted on the base of adiabatic theorem (geometric phase) of M.V.Berry (1984). This effect can be considered as a result of spin-orbit interaction of a photon and in that case the inverse effect - influence of polarization on propagation process can be expected. For the first time this idea was proposed by the head of the laboratory of nonlinear optics Prof. B.Ya.Zel'dovich and then Optical Magnus Effect was predicted and experimentally observed in the laboratory. Optical Magnus Effect manifests itself in rotation of speckle-pattern of circular polarized light transmitted through multimode rectilinear optical fiber under change of sign of circularity [1].

The experimental result was in a good agreement with numerically calculated result and theoretically predicted one [2]. The set of theoretical and experimental investigations of new interaction phenomena between polarization and propagation were performed later.

It was shown experimentally, that influence of the external magnetic field on the light propagation through optical fiber results in rotation of the speckle pattern of light passed through an optical fiber. The rotation angle corresponds in order of magnitude and also in sign to the angle of Faraday rotation of the polarization plane [3]. The fiber material (quartz) which was used has a very small Verdet constant. By using other materials one could intensify the effect at least two orders of magnitude.

The experimental investigations of interactions of polarization and spatial degrees of freedom in a vacuum were carried out. If upper half (y > 0) of a lens is illuminated by a plane wave propagating with s = ± 1 circular polarization in the direction of lens axis z*, *then the focal waist shows right-left shift D x** **» ls. In order to observe that effect scattered medium was placed in the focal waist. The observation was carried out in z -polarized scattered light [4]. The experimental results were in good coincidence with theoretical prediction. It should be stressed that the inverse effect - influence of the propagation on polarization must exist in vacuum too. The paper [5] shows that-observed effect of transverse shift of a focal spot upon a change in the sign of circular polarization can be explained on the base of spin-orbit interaction of a photon in inhomogeneous medium. In order to decide if spin-orbit interaction of a photon exists in a vacuum, the existence of the inverse effect should be demonstrated.

*So the problems to be solved are the following:*

1. To investigate theoretically the influence of the magnetic field on light propagation through multimode and a few mode optical fiber with step-like refractive index profile. To show how the angle of the speckle pattern rotation depends on the length of the fiber and the magnetic field magnitude. To show the influence of the state of light polarization on the angle of the speckle pattern rotation.

2. To prepare optical fiber using optical material with high magnitude of the Verdet constant and carry out experimental investigation of the influence of magnetic field on light propagation through optical fiber. To compare theoretical and experimental results.

3. To find out the experimental conditions when the influence of the propagation on the polarization manifests itself in a vacuum (or homogeneous medium).

4. To demonstrate experimentally the existence of the effect which is inverse to the effect of transverse shift of the focal waist.

*References*

1. Dooghin A.V., Zeldovich B.Ya., Kundikova N.D., Liberman V.S. Pismav ZhETP, 1991, 53, 186-188.

2. Dooghin A.V., Kundikova N.D. Liberman V.S.Zeldovich B.Ya. Physical Review A, 1992, 45,

**8204-8208.**

3. Darsht M.Ya., Zhirgalova I.V. Zel'dovich B.Ya., Kundikova N.D.

__JETP Lett., 1994, 59, 763-763.__

4. Zel'dovich B.Ya., Kundikova N.D. Rogacheva L.F. JETP Lett., 1994, 59, 766-769.

5. Sadykov N.R. Kvant. elektr. 1996, 23, 177-179.

The co-authors of the papers [1-5] are going to take part in that project.

*Potential role of foreign collaborators*

We invite Universities, Institutes, Commercial firms from USA, countries of European Community, Japan and Norway to take part in that project. The cooperation can be regarded as exchange of scientific information, carrying out joint experimental and theoretical work, checking of our results.

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