GRADED INDEX PHOTONIC CRYSTALS
The developments of science in recent years have allowed photonic crystals (PCs) to take their place among
various applicable research areas rather than just being mentioned as an obscure topic in physics [1,2]. The
arrangements of the PC structure offer superior performance over their conventional dielectric
counterparts in optics. As a consequence, PC based devices have come to be fully appreciated due to their key
features on controlling the flow of electromagnetic
(EM) waves. Efforts have been initiated to search for
alternative methods that can compete and even replace the existing schemes. In that respect, the self collimation
abilities of the PC
s has received much attention [3
6]. The graded index (GRIN) version
of the PC is a
distinguished candidate in the literature for realizing the self focusing phenomena. A theoretical work was
devoted to understand the critical design stages of the
GRIN PCs [
7]. Following that article, the GRIN PCs were
integrated with PCWs
to yield high coupling factors
8]. In the present study, we consider index based
confinement using a graded index (GRIN) PC by modulating the lattice spacing of the crystal. The advances in
fabrication technology allow the fabrication in the optical
frequency regime. At the same time, the scalability
of the Maxwell’s equations makes it possible to scale the wavelength to any spectral region. Since targeting the
microwave frequencies lifts some of the technological and practical burdens, the experiment
al work is performed
at the microwave regime.
Fig. 1 Schematic of the GRIN PC
Fig. 2 The focusing power of the GRIN PC with respect to the number of
layers (N). (a) FWHM values of the focused beam for several N values, (b)
the distribution of the inten
sity at the exit side of the GRIN PC.
Figure 2 reveals
power of the GRIN PC
. The response of the structure to spatially wide incident
beams is investigated and
cusing behavior is observed. A
large spot size conversion ratio can be
attainable and is mainly limited by the finite size of the structure. The designed GRIN PC shows promise for use
in optical systems that require compact and powerful focusing elements compared to the traditional bulky lenses.
Figure 3 demonstrates bo
theoretically and experimentally the
focusing abilities of the GRIN
structure. Such a structure can be used
to further reduce the coupling losses of
the Photonic Crystal based waveguides
The beams diverge quickly at
the exit side of the PCWs.
PC is cooperated along with the PCW
to increase the coupling efficiency.
The wide beam was squeezed down
prior to being fed to the PCW by
taking advantage of the focusing effect
of the GRIN PC.
The FDTD based
simulations were supported by the
and a 5
increment in the
coupling efficiencies were estimated
using eq. (1)
in the simulations and
microwave experiments, respectively.
Figures 5&6 show the regarding
improvements in t
efficiency to the PCW.
Fig. 3 GRIN structure and its
Fig. 4Photonic Crystal Waveguide
Fig. 5 GRIN incorporated with
Fig. 6 Intensity distribution at the exit side of the PCW. (a) Simulation
s, (b) Experimental results.
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