Complex Faraday and Kerr Rotations in Right and Left Handed
Films and Layered Structures
J. Lofy (1), V. Gasparian (1), Z. Gevorkian (2), E. Jódar (3)
(1) Department of Physics. California State University. Bakersfield. CA 93311 (USA).
Phone Number: 001-661-654-6004, e-mail: [email protected](2) Yerevan Physics and Institute of Radiophysics and Electronics. Ashtarak-2. 0203 (Armenia).
(3) Dpto. Física Aplicada. Campus Muralla del Mar. UPCT. 30202 Cartagena (Spain).
1. Introduction – Negative refractive index magneto optical metamaterials, also called left handed
materials (LHM), are a new type of artificial material characterized by having a permittivity and
permeability µ both negative [1]. They have multiple uses that include: the ability to resolve images
beyond the diffraction limit [2], act as electromagnetic cloaks for particular frequencies of light [3],
enhance quantum interference, or yield to slow light propagation [4]. In this work we study the Faraday
and Kerr rotations of light with angular frequency passing through a right-handed and left-handed
materials film of arbitrary thickness taking into account multiple reflections from the boundaries without
absorption.
The descriptions of the real portions as the linear angle of rotation and imaginary portions as the
ellipticity of the rotation allow us to separate the two distinct phenomena and visualize their maximums
and effects within different kinds of mediums. To shed some light on the obstacles which have persisted
in the tunneling time problem, we analyze the real and imaginary portions of the complex Faraday
rotation angle () in forbidden bands of finite stack of alternating right and left-handed materials.
2. Results and Discussion
Image 1. We calculate (a) the transmission coefficient and (b) real
and imaginary parts of the Faraday Rotation angle as a function of
for an alternating structure described in the introduction. In Fig.
(a), one observes that practically the entire transmission spectrum is
formed by forbidden gaps. Further increase of cells will be
narrowed by the allowed bands and for an ideal infinite crystal one
gets a set of periodically distributed Lorentzian resonances. (b)The
maximums of Re() are centered in the allowed bands. At these
resonance peaks we deal with the pure Faraday rotation of linearly
polarized wave. Within any forbidden bands Re() is an almost flat
function with very small value. However, the situation is
completely different for Im() (proportional to the degree of
ellipticity). Where the value of Re() is almost zero, one notes that
Im() changes drastically in both value and sign.
3. Conclusions - We found that the rotation and ellipticity of the transmitted or reflected light of the
Faraday and Kerr effects are odd and even functions with respect to the refractive index n. In the limit of
an ultra-thin left-handed materials film under specific circumstances, a large resonant enhancement of the
reflected Kerr rotational angle experimentally can be obtained. In forbidden bands of finite stack of
alternating right and left-handed materials it has been shown that in spite of the fact that Re() in the
forbidden gap is almost zero, Im() changes drastically in both value and sign.
4. References
[1] W. J. Padilla, D. N. Basov, and D. R. Smith, Materials Today 9 ,28 (2006).
[2] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[3] S. Yang, P. Liu, M. Yang, Q. Wang, J. Song, and L. Dong, Scientific Reports 6, 21921 (2016).
[4] N. Papasimakis and N. I. Zheludev, Opt. Photon. News 20, 22 (2009).
M&Ns-19, Paris, 17-19 Pag. 13M&Ns-19, Paris, 17-19 July 2019
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