ScIentIfIc REPORtS | 7: 16593 | DOI:10.1038/s41598-017-16847-8
Capsize of polarization in dilute
, Arsen Hakhoumian
, Vladimir Gasparian
& Emilio Cuevas
We investigate, experimentally and theoretically, polarization rotation eects in dilute photonic
crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of
waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed
in a one-dimensional photonic crystal in the frequency range 10 ÷ 140 GHz. To gain more insights
into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal,
based on Maxwell’s equations with a spatially dependent two dimensional inhomogeneous dielectric
permittivity. We show that the polarization’s rotation can be explained by an optical splitting
parameter appearing naturally in Maxwell’s equations for magnetic or electric elds components. This
parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum
waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the
dynamical phase shift between the waves propagating in the orthogonal directions and nally leads to
capsizing of the initial polarization. Excellent agreement between theory and experiment is found.
e problem of the polarization rotation (PR) of an incident electromagnetic wave is one of the most interesting
in photonic crystals (PC)
. e investigations in this eld are stimulated by the possibility of creation of polariza-
tion controlling devices, where the polarization of the propagating light could be precisely manipulated and con-
. One of the mechanism that can account for this PR can be associated with the geometrical anisotropy
of photonic crystal (PC)
. e anisotropy, imposing asymmetry into a periodic two dimensional (2d) structure
in xy–plane, leads to a dierent speed in the x–and y–axes resulting in a phase delay between H
) and H
components. Another mechanism that can lead to the PR of propagating light is due to dielectric permittivity
inhomogeneity of medium. is phenomenon known long ago
and accepted view of the physics behind the
eect is that the rotation is controlled by the parameter λ/Λ
(λ is the wave length and Λ
is the typical length
scale of the system’s inhomogeneity). In the geometrical optics approximation when wavelength is much smaller
than inhomogeneity characteristic scale, rotation angle is negligible
. However, in the opposite limit, the rotation
of polarization due to dielectric permittivity inhomogeneity, is quite signicant. Particularly, such eects are
observed both in dielectric (see ref.
and references therein) and metallic
In this paper we investigate, experimentally and theoretically, the PR eects in a dilute photonic crystals
(DPC) with transverse permittivity inhomogeneity perpendicular to the z–traveling direction of waves. Interest
to DPC is largely motivated by a peculiar behavior of the transmission coecient, recently studied in ref.
parabolic (forward) scattering approximation to investigate electromagnetic wave propagation in inhomogeneous
, in ref.
was found an independence of the transmission coecient of the central diracted wave from
the incident wavelength in a dilute perforated metal system. As we will see below, it turns out that the DPC along
with the interesting transport properties lead to unusual polarization eects as well.
Our direct measurements indicate that under certain conditions the initial polarization changes its direction
by π/4 in 1d DPCs in the frequency range of 10 ÷ 140 GHz (see below). e main experimental nding consists of
not typical shi of distribution’s minimum and maximum regions in the spectra of the transmitted intensity (see
below). To understand and explain the rotating mechanism of the DPC, we have developed a theoretical model,
based on Maxwell’s equations with a spatially dependent two dimensional dielectric permittivity ε(x, y). Using the
same parabolic approximation, mentioned above, we show that the polarization’s rotation in 1d and 2d DPCs can
be explained by an optical splitting parameter appearing naturally in Maxwell’s equations for magnetic or electric
elds components. is term is an optical analogous of Rashba type spin-orbit interaction parameter, introduces
a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shi between
Yerevan Physics Institute, Alikhanian Brothers St. 2, 0036, Yerevan, Armenia.
Institute of Radiophysics and
Electronics, Ashtarak-2, 0203, Armenia.
California State University, Bakersfield, California, 93311-1022, USA.
Departamento de Física, Universidad de Murcia, E-30071, Murcia, Spain. Correspondence and requests for materials
should be addressed to Z.G. (email: email@example.com)
Received: 7 September 2017
Accepted: 17 November 2017
Published: xx xx xxxx