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Comparison of Confined Modes in L1 and L3
Photonic Crystal Nanocavities in terms of Fill Factor
Foroogh Khozeymeh Sarbisheh ,Soheil Sharifi and Ahmadreza Daraei

kind of photonic insulators, through which specific
wavelengths of light cannot propagate due to a photonic
bandgap.
When two or more substances that have a large difference in
their refractive indices are arranged alternately with a period of
a half wavelength, a band gap structure, through which the light
of the certain wavelength cannot propagate, is formed. Light
within a photonic bandgap cannot propagate through a photonic
crystal, but when defects are introduced into the crystal to
disturb the periodic structure, light can propagate through the
photonic crystal via the defects.The defects creat localized
modes within the photonic band gap. The defects in photonic
crystal, (which divided in two groups of point and line defects),
as a nanocavity or a resonator, are realized. The photonic
crystal linear nanocavities Ln, such as L1 and L3 with high
confinement have many applications in many areas of physics
and engineering, including coherent electron–photon
interactions [6], ultra-small filters [7,8], low-threshold lasers[9],
photonic chips[10], nonlinear optics[11] and quantum
information processing[12].
In this work, we theoretically investigated L1 nanocavity, L1
nanocavities with reduced radius of two ends air-holes and L3
nanocavity. Variations in fill factor of the L1 nanocavity by
radius reduction in that, cause changes in various properties of
confined cavity mode. Also closing characteristics of this mode,
to the confined mode characteristics existed in L3 nanocavity,
have been discussed.
Abstract— the first L1 nanocavity in a semiconductor slab has
been simulated in a hexagonal lattice of air-holes (radius r) with
lattice constant a=270 nm and constant fill factor (r/a=0.29), by
using BandSOLVE and FullWAVE software from RSoft
Photonics CAD package. With calculation of photonic energy
band gap for mentioned structure, L1 nanocavity and then, L1
nanocavities with reduced radius of two ends air-holes with
different fill factors are created in five steps. The resonant cavity
mode isn’t observed for high air-holes radius. But, a resonant
mode would be appeared by the decreasing of the air-holes radius.
Finally, various resonant mode properties, (confined in the
modified L1), such as: quality factor, wavelength and two
dimensional field profiles are compared with resonant mode
confined in the L3 nanocavity. Graphs of the wavelength and
quality factor variations of resonant mode have been analyzed in
this work.
Index Terms— Confined Mode, L1 nanocavity, L3 nanocavity,
Photonic Crystal, Quality Factor
I. INTRODUCTION
T
HE photonic crystal linear nano-cavities Ln, such as L1 and
L3 with high confinement has many applications in
different fields such as waveguide, low-threshold nanolasers,
single-photon emitters for quantum communications, and etc.
Performing cavity quantum electrodynamics experiments
(CQED), in nanostructures in range of light wavelengths are
difficult, because it require to structures in order of light
wavelengths. Nowadays these problems hav been simplified
with use of fabrication technologies of semiconductors devices
[1].
The various kind of nanocavities such as semiconductor
micropillar,microdisk,photoniccrystal nanocavity, microsphere
and microring, have been suggested and fabricated[1-2].
Among of all, photonic crystal nanocavities are more suitable
than others, because they have small modal volume, v, and high
quality factor, Q, [3-5]. In addition, they are very useful in
wavelength tuning of cavity mode, the control of polarization,
conductivity and waveguiding capability in through of lattice
structure tuning and variety in design. Photonic crystals are a
II. SIMULATIONS
The L1 nanocavity is the simplest kind of photonic crystal
linear nanocavities Ln, which is created with omitting of one air
hole, (creation of one point defect), in center of a favorite
photonic crystal lattice. In this paper, a L1 nanocavity with a
hexagonal lattice of air-holes (with refractive index n = 1 and
radius r =78.3 nm), has been simulated in a GaAs
semiconductor slab, (with refractive index n=3.09). The lattice
constant and fill factor are considered respectively, a =270 nm
and r/a=0.29. A schematic of simulated L1 nanocavity is shown
in Figure1.
This work was supported in part by the University of Sistan and
Baluchestan”.
Address: Ahmad reza Daraei is with the Department Physics at University
of Sistan and Baluchestan, Zahedan, Iran (e-mail: daraei@phys.usb.ac.ir ).
Soheil sharifi was with Department Physics at University of Sistan and
Baluchestan, Zahedan, Iran
(e-mail:
sharifi@phy.usb.ac.ir
or
soheil.sharifi@gmail.com ).
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resonant mode with use of FDTD method, is realized and then,
quality factor of this mode with use of its radiation spectrum
and relation Q=λ/Δλ, (λ is wavelength maximum and Δλ is half
width of wavelength maximum), is calculated.
In any stage, wavelength and quality factor of the resonant
cavity mode, have changed. At first, no resonant mode is
appeared in the photonic band gap but, in first step of radius
reduction, a small mode with low intense and small Q, is
observed in initial of the gap. However, with fill factor
variation and radius reduction in each step, wavelength and
quality factor of this resonant mode, increase slowly. These
variations have been simulated and analyzed and their
resultants have been imported in table 1.
(a)
If L3 nanocavity with structure properties similar to L1
nanocavity, would be simulated directly, after calculations, we
(b)
TABLE I
WAVELENGTH AND QUALITY FACTOR VARIATIONS IN DIFFERENT STEPS OF
SIMULATION.
Quality Factor,
Radius of two end
Wavelength of resonant mode,
Q
air holes, r)nm)
λ )nm)
Fig. 1. a) Scanning electron micrograph (SEM) of L1 nanocavity (one missing
air-holes in the center is not etched), and b) illustration of dielectric canstant
distributions in L1 nanocavity.
With calculation of photonic band gap, (range of forbidden
wavelengths or frequencies), for two dimensional photonic
crystal slab, (structure which is existed in part a figure 1, but
without omitting of central air hole), L1 nanocavity with
wavelength operating within the photonic band gap, is created.
The photonic band gape is formed for wavelengths in range of
931 -1179 nm.
Then, L1 nanocavities with two end holes with decreased
radius, (modified L1s with changed r/a), are simulated in five
steps. A schematic of a L1 nanocavity and radius reduction
steps at this naocavity, is shown in Figure2.
(a)
(b)
(c)
(d)
(e)
(f)
78.3
62.7
47.1
31.5
15.9
0.3
940.1
966.8
996.5
1081.9
1026
1105.9
6905.8
7665.7
5409.5
10260
understand that it has one fundamental resonant mode with
wavelength λ=1026 nm in the photonic band gap, and quality
factor Q=10260. These quantities are in correspond with
obtained quantities for L1 nanocavity with decreased radius r =
0.3 nm, (see last row in table 1). It means that L1 nanocavity
with decreased radius r=0.3 nm is almost equivalent to L3
nanocavity. To show this subject better, vertical two
dimensional (2d) patterns of electromagnetic field of resonant
cavity mode in ML1s and L3 nanocavities, have been plotted in
vertical direction in figure 3.
Fig. 2. Schematics of a) L1 nanocavity with radius r= 78.3 nm, b) Modified L1
or ML1 with decreased radius r = 62.7nm, c) ML1 with r = 47.1 nm, d) ML1
with r = 31.5 nm, and e) ML1 with r= 15.9 nm, f) L1 nanocavity with decreased
radius r= 0.3 nm or ≈ L3 nanocavity (three missing air-holes in a line).
A quantity which can show the strength of nanocavity in
resonant mode confinement is Quality factor (Q). Allowed
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with r = 0.3 nm, and f) vertical 2d patterns of electromagnetic field of resonant
mode in L3 nanocavity.
It is observable that vertical 2d patterns of electromagnetic
field of resonant cavity mode in different steps of simulation,
have been changed slowly, (a, b, c and d in figure 3) and finally
in last step ML1 nanocavity with r= 0.3 nm, have exactly
resonant cavity mode pattern which is existed in L3 nanovavity,
as we expected, (similarity between part e and f in figure 3). As
radius of two end holes is decreased, volume of the cavity mode
is increased and therefore, intensity distribution of cavity mode
concentrate in a bigger volume with respect to cavity wales and
then in final stage, has redistributed in the center of nanocavity
with high localization. The benefit of this phenomenon is lower
dissipation or more quality factor. Wavelength and quality
factor variations of resonant mode have been examined and
plotted in figure 4.
(a)
Wavelength(nm)
(b)
(c)
1100
1080
1060
1040
1020
1000
980
960
940
920
0
10
20 30 40 50
Radius(nm)
60
70
60
70
(a)
quality factor
10000
(d)
8000
6000
4000
2000
0
0
10
20
30 40 50
Radius(nm)
(b)
Fig. 4. variation of a) wavelength and b) quality factor of resonant cavity mode,
in terms of radius reduction of two end air holes, r (nm).
(e)
As it can be seen in figure 4 part a, with radius reduction in
range of r= 78.3 to 15.9 nm, wavelength has an increasing
procedure but in radius r= 0.3 nm, suddenly wavelength
decrease to 1026 nm, (number amount of confined mode
wavelength in L3 nanocavity). Also, quality factor in range of
r= 78.3 to 47.1 nm, has almost an increasing procedure but in
radius r= 15.9 nm, decrease to 5409.5, and then in r= 0.3 nm has
been reached to 10260 (number amount of confined mode Q in
L3 nanocavity), (figure 4 part b). Variations in quality factor
can bee due to change of maximum wavelength half width of
confined mode.
(f)
Fig. 3. Schematic of vertical 2d patterns of electromagnetic field of cavity
mode in a) Modified L1 or ML1 with decreased radius r = 62.7nm, b)Modified
L1 with r = 47.1nm, c) ML1 with r=31.5 nm, d) ML1 with r = 15.9 nm, e) ML1
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III. CONCLUSION
With reduction of fill factor, (or reduction of radius), in L1
nanocavity, quality factor and wavelength variations of
confined mode were examined. As the whole, when radius of
two end air holes in linear Ln nanocavities, is decreased, the
examined structure is gotten very similar to the structure of
L(n+2) nanocavites. In this paper with radius reduction of two
end holes in L1 nanocavity, when variation of structure
parameters reached to an appropriate conditions, confined
mode has appeared and with continuation of uniform procedure
of radius reduction, wavelength and quality factor of this mode,
almost have increased. In other words, with change of fill factor
in L1 nanocavity, related structure parameters were similar to
structure parameters of L3 nanocavity; so that amounts of
wavelength and quality factor of resonant mode in L1
nanocavity with decreased radius r= 0.3 nm, are similar to
amounts of wavelength and quality factor of resonant mode in
L3 nanocavity. Also, 2d patterns of electromagnetic field of
resonant cavity mode in two mentioned structure, were similar.
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