Giant photonic Hall effect in magnetophotonic crystals
A. M. Merzlikin,
1
A. P. Vinogradov,
1
M. Inoue,
2
and A. B. Granovsky
3
1
Institute of Theoretical and Applied Electromagnetism, OIVT, Russian Academy of Sciences, 125412, Moscow, Izhorskay 13/19, Russia
2
Department of Electrical and Electronic Engineering, Toyohashi University of Technology, 1-1, Hibari-Ga-Oka, Tempaku,
Toyohashi 441-8580, Japan
3
Faculty of Physics, Lomonosov Moscow State University, Leninski Gory, Moscow 119992, Russia
Received 16 November 2004; revised manuscript received 29 March 2005; published 7 October 2005
We have considered a simple, square, two-dimensional 2D PC built of a magneto-optic matrix with square
holes. It is shown that using such a magnetophotonic crystal it is possible to deflect a light beam at very large
angles by applying a nonzero external magnetic field. The effect is called the giant photonic Hall effect
GPHE or the magnetic superprism effect. The GPHE is based on magneto-optical properties, as is the
photonic Hall effect B. A. van Tiggelen and G. L. J. A. Rikken, in Optical Properties of Nanostructured
Random Media, edited by V. M. Shalaev Springer-Verlag, Berlin, 2002, p. 275; however GPHE is not caused
by asymmetrical light scattering but rather by the influence of an external magnetic field on the photonic band
structure.
DOI: 10.1103/PhysRevE.72.046603 PACS numbers: 42.70.Qs
Recently, significant attention has been attracted to pho-
tonic crystals PC. The main reason for this interest is the
incredible speed with which the results of the investigations
are brought into practical use, such as low threshold lasers,
guiding and sharp bending of light in photonic crystals, etc.
The application of magneto-optical materials in PC intro-
duces new possibilities of light manipulation with a magnetic
field. Photons do not possess electric charge and therefore
cannot couple to a magnetic field directly. However, a static
magnetic field changes the optical properties of a medium,
inducing asymmetrical light scattering and light beam bend-
ing 1–4. This effect was called the photonic Hall effect
PHE1. In some sense the photonic Hall effect is caused
by a spin-orbit interaction 2–4; since spin-orbit interactions
are small, the photonic Hall effect is small, too.
In the paper, we consider light propagation in magneto-
photonic crystals MPC5. It is shown that the unique
properties of photonic crystals make it possible to deflect a
light beam at a very large angle by applying magnetic field.
The effect is called the giant photonic Hall effect GPHE.
The GPHE is based on magneto-optical properties as is the
photonic Hall effect, but the GPHE is not caused by asym-
metrical light scattering. Its main mechanism is the influence
of the external magnetic field on the photonic band structure
of MPC. Although the changes in band structure are small,
they may considerably alter the direction of light propagation
for some specific conditions. The GPHE is itself similar to a
“superprism,” in which a small of the order of a degree or
less variation of the angle of incidence of an electromag-
netic wave may result in significant more than hundreds of
degrees deviation of a refracted wave 6–9.
The GPHE may be observed at a fixed angle of incidence
due to the application of the external magnetic field that
causes a deviation of the refracted wave at a large angle.
Actually, the GPHE and superprism effect are caused not by
diffraction but by refraction. The superprism effect in a PC
6–9 can be described briefly as follows. Consider the PC as
a diffraction grating representing the surface of the PC that
lies on a homogeneous medium imitating the PC. This grat-
ing splits the incident wave into several lobes the Floquet
waves. Under proper conditions frequency, angle of inci-
dence, etc. it is possible to obtain two nonevanescent lobes:
the central lobe and the side lobe. The inhomogeneous nature
of the PC results in the appearance of band gaps at fixed
direction of wave propagation or in the appearance of certain
directions along which the propagation of the Bloch waves is
forbidden at a fixed frequency. Matching the inclusion shape
and the lattice symmetry, it is possible to achieve the situa-
tion where the sidelobe cannot propagate because it points
into a forbidden direction. Thus, we have only one wave
propagating through the PC, like ordinary refraction. A small
variation of the angle of incidence leads to a small change in
the direction of propagation of the lobes. The superprism
effect is observed if the sidelobe initially directed into the
forbidden angle is redirected into an allowed one and the
central lobe initially directing the allowed direction is redi-
rected into forbidden one. Thus, the role of the “refracted”
wave is now played by the sidelobe and the angle of such a
“refraction” changes considerably more than the angle of in-
cidence.
By applying the magnetic field to MPCs, it is possible to
switch from one lobe to another by varying the band struc-
ture at the fixed angle of incidence. The influence of the
external magnetic field on the band structure of the PC with
permeable inclusions has been studied previously 10–13.
To the best of our knowledge, the bending of light in MPCs
has not been considered in the literature. In the present com-
munication we consider the strong deflection of light that
may occur directly in magnetophotonic crystals by applying
a magnetic field. By definition this phenomenon is the
GPHE.
In optics, the permeability is equal to unity and to control
the MPC band structure with magnetic field we deal with
magneto-optical materials. The application of magneto-
optical materials does not permit a pronounced modification
of the band structure due to smallness of the control param-
eter off-diagonal entry of the permittivity tensor. Never-
theless, it is shown that a strong deflection of light more
PHYSICAL REVIEW E 72, 046603 2005
1539-3755/2005/724/0466034/$23.00 ©2005 The American Physical Society 046603-1