GRADED INDEX PHOTONIC CRYSTALS The developments of ...

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Nov 15, 2013 (3 years and 7 months ago)

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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
periodic
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

the

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

the focusing
power of the GRIN PC
. The response of the structure to spatially wide incident
beams is investigated and
a
strong fo
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
th
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

(PCWs)
.
The beams diverge quickly at
the exit side of the PCWs.
Th
e GRIN
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
experi
mental results.


5
2
5
5
2
5
y
GRIN PCW
y
PCW
E
E

 


 



Eq. (1)


A 6.35
dB
and a 5
dB

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
he coupling
efficiency to the PCW.


Fig. 3 GRIN structure and its
focusing abilities

Fig. 4Photonic Crystal Waveguide
structure





Fig. 5 GRIN incorporated with
the PCW


Fig. 6 Intensity distribution at the exit side of the PCW. (a) Simulation
result
s, (b) Experimental results.


References:

1
P. Russel, Science
299
, 358 (2003).

2
C. M. Soukoulis, Nanotechnology
13
, 420 (2003).

3
D. W. Prather, S. Shi, j. Murakowski, G. J. Schneider, A. Sharkawy, C.
Chen, B. L. Miao, and R. Martin, J. Phys. D.
40
, 2635
(2007).

4
H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato,
and S. Kawakami, Appl. Phys. Lett.
74
, 1212 (1999).

5
J. Witzens, M. Loncar, and A. Scherer, IEEE J. Sel. Top. Quantum
Electron.
8
, 1246 (2002).

6
L. Wu, M. Mazilu, and T. F. Kraus
s, J. Lightw. Technol.
21
, 561 (2003).

7
H. Kurt and D. S. Citrin, Opt. Express
15
, 1240 (2007).

8
H. Kurt and D. S. Citrin, IEEE Photon. Technol. Lett.
19
, 1532 (2007).


Related Publications:

1)
H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, Appl.

Phys.
Lett.
93
, 171108 (2008).

2)
Atilla Ozgur Cakmak, Evrim Colak, Humeyra Caglayan, Hamza Kurt,
and Ekmel Ozbay, J. Appl. Phys.
105
, 103708 (2009).