Investigation Effects of Filling Rate on the Bands Gaps of Two Dimensional Photonic Crystals
TELKOMNIKA, Vol.14, No.3A, September 2016, pp. 27~32
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v14i3A.4414
27
Investigation Effects of Filling Rate on the Bands Gaps
of Two Dimensional Photonic Crystals
1,2,3
Baohe Yuan*1, Qi Xu2, Linfei Liu3, Xiying Ma4
North China University of Water Resources and Electric Power, Zhengzhou 450011, China
4
Shaoxing College of Arts and Sciences, Shaoxing 312000, Zhejiang Province, China
*Corresponding author, e-mail: [email protected]
Abstract
The influences of the filling rate on the photonic band gap properties of the two dimensional hex
photonic crystals are investigated using the finite-difference time-domain method. When the filling rate f
varies from 0.227 to 0.735 reminding the refractive index as 5, the number of the photonic band gaps
decreases from 5 to 2 bands, the width of the photonic band gap between the transmit peaks become
narrow; but for larger f > 0.445, the transmit intensity is very low in the high frequency region, it can be
consider as a larger photonic band gap region, the onset of this larger photonic band gap shifts toward low
frequency. At the same time, the onset transmit peaks shift toward low frequency also. The simulation
results show that the photonic band gap can be effectively changed by the filling rate.
Keywords: photonic crystal, photonic band gap, filling rate, finite-difference time-domain
Copyright © 2016 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Photonic crystals (PCs) have gained much attention in the past decade due to the great
applications in luminescence and communication fields [1-3]. A lot of efforts have been devoted
to design materials so that can affect the properties of photons [4-5]. And striking progress has
been achieved in three-dimensional (3D) photonic crystal fabrications from microwave to visible
to obtain a complete photonic band gap (PBG) [6-7]. However, serious technological problems
and high cost still restrict the applications of 3D materials especially in visible range [8-9]. Twodimensional (2D) photonic crystal structures are the most advanced and fast developing areas
owing to mature fabrication methods and envisioned broad applications [10-12]. The main
factors that determine the properties of 2D photonic crystals are the refractive index contrast,
the filling rate of materials in the lattice and the arrangement of the lattice elements [13-15].
Systematically investigate the action of refractive index and filling rate on PBG is necessary.
Several methods, such as planer wave, transfer matrix and the finite-difference time-domain
(FDTD), have been used to model the propagation of electromagnetic waves in photonic
crystals and achieved many useful results [16-17]. However, plane wave cannot be used when
the structure containing defects that break the periodicity and induce localized modes. Since
FDTD method makes use of the periodicity of the lattice, it is perfectly well suited for band
structure calculations [18-19].
In this work, the finite-difference time-domain (FDTD) is developed to examine the
effect of the filling rate on PBG behavior of the hex lattice photonic crystals in the TE
electromagnetic waves. The PCs transmit features of hex lattices have been simulated as the
filling rate f ranging from 0.227 to 0.735.
2. Theoretical Modeling
A PBG is most easily obtained when the Bravais lattice is the face centered cubic (FCC)
in 3D and the hexagonal lattice in 2D. In addition, a high refractive index contrast is required
(typically greater than 2). Therefore, we consider a two dimensional hex PCs structures
composed of air spheres surrounded with a dielectric medium (shown in Figure 1). The filling
rate f of the hex structure various from 0.227 to 0.735 which can exhibits the evolutionary
Received March 19, 2016; Revised July 24, 2016; Accepted August 1, 2016
28
ISSN: 1693-6930
process of PBG for TE mode electromagnetic radiation. The radius of the air sphere is 0.25 m,
the lattice constant is 1 m, and the refractive index of the medium is 5.
The 2D TE electromagnetic mode of the photonic crystals are taken to propagate in x-z
plane, Hx, Ey, Hz nonzero components propagate along z, transverse field varies along x in
lossless media and the magnetic field parallels to the y axis, Maxwell’s equations take the
following form:
E y
t
1 H x H z H x
1 E y H z
1 E y
,
(
),
x
z
t
t
0 z
0 x
(1)
where =0r is the dielectric permittivity, r is the dielectric constant of the medium, and
the refractive index is n0 r , 0 and 0 is the vacuum dielectric constant and the magnetic
permeability, respectively.
Figure 1. The Schematic diagram of the fcc (a) and hex (b) lattices. The radius of the air sphere
and the lattice constant a are 0.25 m and 1 m, respectively
The total set of numerical equation (1) takes the from:
E yn (i, k ) E yn 1 (i, k )
t
z
[ H xn 1 / 2 (i, k 1 / 2) H xn 1 / 2 (i, k 1 / 2)]
(2)
t
[ H zn 1 / 2 (i 1 / 2, k ) H zn 1 / 2 (i 1 / 2, k )]
x
H xn 1 / 2 (i, k 1 / 2) H xn 1 / 2 (i, k 1 / 2)
H xn 1 / 2 (i 1 / 2, k ) H xn 1 / 2 (i 1 / 2, k )
t
0 z
[ E yn (i, k 1) E yn (i, k )]
t
[ E yn (i 1, k ) E yn (i, k )]
0 x
(3)
(4)
The superscript n labels the time steps while the indices i and k label the space steps
and x and z along the x and z direction, respectively. This is the so-called Yee’s numerical
method applied to the 2D TE case [18, 20-21]. It uses central difference approximation for the
numerical derivatives in space and time, both having second order accuracy. Typically, the
sampling in time is selected to ensure numerical stability of the algorithm, 10 to 20 steps per
wavelength are needed, and the time step is determined by the Courant limit:
t 1 /(c 1 /( x) 2 1 /( z ) 2 )
The power of TE mode incidence in the both 2 D lattice photonic crystals is 1 V/m with
the wavelength of 1.9 m.
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 27 – 32
TELKOMNIKA
ISSN: 1693-6930
29
3. Results and Discussion
Figure 2 shows the normalized transmit intensity verses the frequency as filling rate
f=0.227 and the refractive index as 5 of a hex lattice for TE mode normal incidence. The
transmit spectrum is consist of five proportional spacing transmit bands, the transmit intensity is
very low between each transmit band, this is the so-called PBG region in which the TE mode
cannot propagate [22, 23]. Therefore, there are five PBG regions located at 295-347, 385.6-447,
482-534, 569-621 and 662-711 THz. The width of these 5 PBGs is 52, 62, 52, 52 and 49 THz
determined from the FWHM (full width at half maximum) of the bands. It indicates that the five
PBG are almost equidistance.
Figure 2. The normalized transmit intensity verses frequency spectrum of a hex lattice
with f =0.227 and refractive index as 5 for TE mode at normal incidence. There are five PBG
bands
In Figure 3 shows the transmit intensity verses the frequency as the filling rate f=0.327.
Similar to Figure 2, there are also five PBGs that located at 340-382, 447-486, 548-586.6, 645683 and 749-791 THz, respectively, the width of them is 42, 39, 38.6, 38 and 42 THz,
respectively. Compare with Figure 2, the width of PBG bands decrease about 10 THz. At the
same time, the transmit spectrum turns up fine structure, each transmit band contains double
transmit peaks. The intensity of the transmit peaks decreases from 0.85 for the first peak down
to 0.52 for the fifth peak, showing a reducing by 0.32.
Figure 3. The normalized transmit spectrum of a hex structure for f =0.327. Five PBGs
are located at 340-382, 447-486, 548-586.6, 645-683 and 749-791 THz, respectively, the width
of them is 42, 39, 38.6, 38 and 42 THz, respectively
For the filling rate f=0.445 in a hex lattice, the transmit spectrum for TE mode is shown
in Figure 4. The spectrum contains two larger transmit bands and four very smaller peaks, and
each larger band contains double peaks, the wide of them becomes two times as large as that
of Figure 2. Clearly, as frequency over 330 THz, the transmit intensity of TE mode
electromagnetic wave is very low, indicating TE mode cannot propagated in this large frequency
region. This can be considered as a large PBG region, Therefore, there are two PBG regions,
Investigation Effects of Filling Rate on the Bands Gaps of Two Dimensional … (Baohe Yuan)
30
ISSN: 1693-6930
the first one is centered at 205 THz, and the other is the larger region for frequency over 330
THz. Compare with Figure 2 and Figure 3, the number of PBG decreases from 5 to 2, at the
same time, the larger PBG band shift to high frequency region, the onset transmit peak sharply
shift towards low frequency.
Figure 4. The normalized transmit spectrum of a hex for f =0.445. There are two PBG regions,
the first one is centered at 205 THz, and the other is large region for frequency over 330 THz
In the case of f=0.581 and 0.735, the corresponding transmit spectrum is shown in
Figure5 and Figure6. These two spectra is very similar, both contain two transmit peaks; there is
a small PBG between the two peaks. Similar to Figure 4, when frequency is over 200 THz in
Figure 5 and 140 THz in Figure 6, the transmit intensity is very low, it can be considered as
PBG regions. This indicates that most frequency region is hold up by PBG for larger f, the TE
electromagnetic wave for frequency over 200 THz and 140 THz may not propagated in these
hex lattices, most electromagnetic wave is reflected or absorbed by the lattice. In addition, the
onset transmit peaks sharply shift towards low frequency.
Figure 5. The normalized transmit spectrum of a hex for f =0.581. There are two PBG regions,
the first one is centered at 105 THz, and the other is large region for frequency over 200 THz
Figure 6. The normalized transmit spectrum of a hex for f =0.735. There are two PBG regions,
the first one is centered at 100 THz, and the other is large region for frequency over 140 THz
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 27 – 32
TELKOMNIKA
ISSN: 1693-6930
31
In view of the gaps of above hex structures, the existence of multiple photonic band
gaps is rather interesting. With the filling rate increasing, the number of PBG bands decreases,
more and more frequency region is hold up by PBG, this tendency offers more freedom in
designing multi-channel photonic crystals devices.
4. Conclusion
The influences of the filling rate on the PBG properties of 2D hex photonic crystal are
investigated using the FDTD method. With the filling rate increasing, the number of PBG bands
decreases from 5 to 2 bands, for larger f (>0.445), the transmit intensity is very low in high
frequency region, it can be consider as a larger PBG region. At the same time, the onset
transmit peaks shift toward low frequency. It shows that the photonic band gap can be
effectively influenced by the filling rate. The changes in hex lattice are especially interesting and
helpful in designing multi-channel PCs devices.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
Yablonovitch E. Inhibited spontaneous emission in solid state physics and electronics. Phy. Rev. Lett.
1987; 5: 2059-2062.
Vlasov YA, Luterova K, Pelant I, Honerlage B, Astratov VN. Optical gain of CdS quantum dots
embedded in 3D photonic crystals. Thin Solid Films. 1998; 318(4): 93-95.
Dowling JP, Scalora M, Bloemer MJ, Bowden CM. The photonic band edge laser: A new approach to
gain enhancement. J. Appl. Phys. 1994; 75(2): 1896-1899.
Ohnishi D, Okano T, Imada M, Noda S. Room temperature continuous wave operation of a surfaceemitting two-dimensional photonic crystal diode laser. Optics Express. 2004; 12(8): 1562-1568.
Ferrando A, Zacarés M, Córdoba PF, Monsoriu A. Spatial soliton formation in photonic crystal fibers.
Optics Express. 2003; 11(5): 452-459.
Ye YH, Le Blanc F, Hache, Truong VV. Self-assembling three-dimensional colloidal photonic crystal
structure with high crystalline quality. Appl. Phys. Lett. 2001; 78(1): 52-54.
Chutinan A, Noda S. Highly confined waveguides and waveguide bends in three-dimensional
photonic crystal. Appl. Phys. Lett. 1999; 75(12): 3739-3741.
Noda S. Three-dimensional Photonic Crystals Operating at Optical Wavelength Region. Physica B.
2000; 279(2): 142-149.
Vlasov YA, Astratov VN, Karimov OZ, Kaplyanskii AA, Bogomolov VN, Prokofiev AV. Existence of a
photonic pseudogap for visible-light in synthetic opals. Phys. Rev. B. 1997; 55(5): 13357-11360.
Zoorob ME, Charltona MDB, Parker GJ, Baumberg JJ, Netti MC. Experimental investigation of
photonic crystal waveguide devices and line-defect waveguide bends. Mate. Sci. and Eng. B. 2000;
74(7): 168-174.
Rakhshani MR, Mansouri-Birjandi MA. Tunable Channel Drop Filter using Hexagonal Photonic
Crystal Ring Resonators. TELKOMNIKA Indonesian Journal of Electrical Engineering. 2013; 11(1):
513-516.
Kácik D, Turek I, Martincek I, Canning J, Issa NA, Lyytikäinen K. Intermodal interference in a
photonic crystal fibre. Optics Express. 2004; 12(8): 3465-3470.
Mohammad EJ, Abdullah GH. TM-Polarization One-Dimensional Photonic Crystal Design.
International Journal of Advances in Applied Sciences. 2013; 2(3): 165-170.
Krauss Thomas F, Richard M, De La Rue. Optical and confinement properties of two-dimensional
photonic crystals. Prog. Quan. Elect. 1999; 23(1): 51-96.
Ghadrdan M, Mansouri-Birjandi MA. All-Optical NOT Logic Gate Based on Photonic Crystals.
International Journal of Electrical and Computer Engineering (IJECE). 2013; 3(4): 478-482.
Centeno E, Felbacq D. Light propagation control by finite-size effects in photonic crystals. Phys. Lett.
A. 2000; 269(1):165-169.
Modinos A, Stefanou N, Yannopapas V. Applications of the layer-KKR method to photonic crystals.
Optics Express. 2001; 8(1): 197-202.
Meade RD, Brommer KD, Rappe AM, Joannopoulos JD. Electromagnetic Bloch waves at the surface
of a photonic crystal. Phys. Rev. B. 1991; 44(11): 10961-10964.
Rakhshani MR, Mansouri-Birjandi MA. Wavelength Demultiplexer using Heterostructure Ring
Resonators in Triangular Photonic Crystals. TELKOMNIKA Indonesian Journal of Electrical
Engineering. 2013; 11(4): 1721-1724.
Yee KS. Numerical solution of initial boundary value problems involving Maxwell's equations in
isotropic media. Antennas Propagation. 1966; 17(5): 302-307.
Bierwirth K, Schulz N, Amdt F. Finite-difference analysis of rectangular dielectric waveguide
structures. IEEE Trans. Microwave Theory Technol. 1986; 34(12): 1104-1114.
Investigation Effects of Filling Rate on the Bands Gaps of Two Dimensional … (Baohe Yuan)
32
ISSN: 1693-6930
[22] Feng SS, Shen LF, He SL. A two-dimensional photonic crystal formed by a triangular lattice of square
dielectric rods with a large absolute band gap. Acta Physica Sinica (in Chinese). 2004; 53(5): 15401545.
[23] Zhu ZH, Ye WM, Yuan XD, Zeng C, Wang H. A Numerical Method to Calculate and Analyze of
Defect Modes in Two 2Dimensional Photonic Crystal. Acta Optica Sinica (in Chinese). 2003; 23: 522525.
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 27 – 32
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v14i3A.4414
27
Investigation Effects of Filling Rate on the Bands Gaps
of Two Dimensional Photonic Crystals
1,2,3
Baohe Yuan*1, Qi Xu2, Linfei Liu3, Xiying Ma4
North China University of Water Resources and Electric Power, Zhengzhou 450011, China
4
Shaoxing College of Arts and Sciences, Shaoxing 312000, Zhejiang Province, China
*Corresponding author, e-mail: [email protected]
Abstract
The influences of the filling rate on the photonic band gap properties of the two dimensional hex
photonic crystals are investigated using the finite-difference time-domain method. When the filling rate f
varies from 0.227 to 0.735 reminding the refractive index as 5, the number of the photonic band gaps
decreases from 5 to 2 bands, the width of the photonic band gap between the transmit peaks become
narrow; but for larger f > 0.445, the transmit intensity is very low in the high frequency region, it can be
consider as a larger photonic band gap region, the onset of this larger photonic band gap shifts toward low
frequency. At the same time, the onset transmit peaks shift toward low frequency also. The simulation
results show that the photonic band gap can be effectively changed by the filling rate.
Keywords: photonic crystal, photonic band gap, filling rate, finite-difference time-domain
Copyright © 2016 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Photonic crystals (PCs) have gained much attention in the past decade due to the great
applications in luminescence and communication fields [1-3]. A lot of efforts have been devoted
to design materials so that can affect the properties of photons [4-5]. And striking progress has
been achieved in three-dimensional (3D) photonic crystal fabrications from microwave to visible
to obtain a complete photonic band gap (PBG) [6-7]. However, serious technological problems
and high cost still restrict the applications of 3D materials especially in visible range [8-9]. Twodimensional (2D) photonic crystal structures are the most advanced and fast developing areas
owing to mature fabrication methods and envisioned broad applications [10-12]. The main
factors that determine the properties of 2D photonic crystals are the refractive index contrast,
the filling rate of materials in the lattice and the arrangement of the lattice elements [13-15].
Systematically investigate the action of refractive index and filling rate on PBG is necessary.
Several methods, such as planer wave, transfer matrix and the finite-difference time-domain
(FDTD), have been used to model the propagation of electromagnetic waves in photonic
crystals and achieved many useful results [16-17]. However, plane wave cannot be used when
the structure containing defects that break the periodicity and induce localized modes. Since
FDTD method makes use of the periodicity of the lattice, it is perfectly well suited for band
structure calculations [18-19].
In this work, the finite-difference time-domain (FDTD) is developed to examine the
effect of the filling rate on PBG behavior of the hex lattice photonic crystals in the TE
electromagnetic waves. The PCs transmit features of hex lattices have been simulated as the
filling rate f ranging from 0.227 to 0.735.
2. Theoretical Modeling
A PBG is most easily obtained when the Bravais lattice is the face centered cubic (FCC)
in 3D and the hexagonal lattice in 2D. In addition, a high refractive index contrast is required
(typically greater than 2). Therefore, we consider a two dimensional hex PCs structures
composed of air spheres surrounded with a dielectric medium (shown in Figure 1). The filling
rate f of the hex structure various from 0.227 to 0.735 which can exhibits the evolutionary
Received March 19, 2016; Revised July 24, 2016; Accepted August 1, 2016
28
ISSN: 1693-6930
process of PBG for TE mode electromagnetic radiation. The radius of the air sphere is 0.25 m,
the lattice constant is 1 m, and the refractive index of the medium is 5.
The 2D TE electromagnetic mode of the photonic crystals are taken to propagate in x-z
plane, Hx, Ey, Hz nonzero components propagate along z, transverse field varies along x in
lossless media and the magnetic field parallels to the y axis, Maxwell’s equations take the
following form:
E y
t
1 H x H z H x
1 E y H z
1 E y
,
(
),
x
z
t
t
0 z
0 x
(1)
where =0r is the dielectric permittivity, r is the dielectric constant of the medium, and
the refractive index is n0 r , 0 and 0 is the vacuum dielectric constant and the magnetic
permeability, respectively.
Figure 1. The Schematic diagram of the fcc (a) and hex (b) lattices. The radius of the air sphere
and the lattice constant a are 0.25 m and 1 m, respectively
The total set of numerical equation (1) takes the from:
E yn (i, k ) E yn 1 (i, k )
t
z
[ H xn 1 / 2 (i, k 1 / 2) H xn 1 / 2 (i, k 1 / 2)]
(2)
t
[ H zn 1 / 2 (i 1 / 2, k ) H zn 1 / 2 (i 1 / 2, k )]
x
H xn 1 / 2 (i, k 1 / 2) H xn 1 / 2 (i, k 1 / 2)
H xn 1 / 2 (i 1 / 2, k ) H xn 1 / 2 (i 1 / 2, k )
t
0 z
[ E yn (i, k 1) E yn (i, k )]
t
[ E yn (i 1, k ) E yn (i, k )]
0 x
(3)
(4)
The superscript n labels the time steps while the indices i and k label the space steps
and x and z along the x and z direction, respectively. This is the so-called Yee’s numerical
method applied to the 2D TE case [18, 20-21]. It uses central difference approximation for the
numerical derivatives in space and time, both having second order accuracy. Typically, the
sampling in time is selected to ensure numerical stability of the algorithm, 10 to 20 steps per
wavelength are needed, and the time step is determined by the Courant limit:
t 1 /(c 1 /( x) 2 1 /( z ) 2 )
The power of TE mode incidence in the both 2 D lattice photonic crystals is 1 V/m with
the wavelength of 1.9 m.
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 27 – 32
TELKOMNIKA
ISSN: 1693-6930
29
3. Results and Discussion
Figure 2 shows the normalized transmit intensity verses the frequency as filling rate
f=0.227 and the refractive index as 5 of a hex lattice for TE mode normal incidence. The
transmit spectrum is consist of five proportional spacing transmit bands, the transmit intensity is
very low between each transmit band, this is the so-called PBG region in which the TE mode
cannot propagate [22, 23]. Therefore, there are five PBG regions located at 295-347, 385.6-447,
482-534, 569-621 and 662-711 THz. The width of these 5 PBGs is 52, 62, 52, 52 and 49 THz
determined from the FWHM (full width at half maximum) of the bands. It indicates that the five
PBG are almost equidistance.
Figure 2. The normalized transmit intensity verses frequency spectrum of a hex lattice
with f =0.227 and refractive index as 5 for TE mode at normal incidence. There are five PBG
bands
In Figure 3 shows the transmit intensity verses the frequency as the filling rate f=0.327.
Similar to Figure 2, there are also five PBGs that located at 340-382, 447-486, 548-586.6, 645683 and 749-791 THz, respectively, the width of them is 42, 39, 38.6, 38 and 42 THz,
respectively. Compare with Figure 2, the width of PBG bands decrease about 10 THz. At the
same time, the transmit spectrum turns up fine structure, each transmit band contains double
transmit peaks. The intensity of the transmit peaks decreases from 0.85 for the first peak down
to 0.52 for the fifth peak, showing a reducing by 0.32.
Figure 3. The normalized transmit spectrum of a hex structure for f =0.327. Five PBGs
are located at 340-382, 447-486, 548-586.6, 645-683 and 749-791 THz, respectively, the width
of them is 42, 39, 38.6, 38 and 42 THz, respectively
For the filling rate f=0.445 in a hex lattice, the transmit spectrum for TE mode is shown
in Figure 4. The spectrum contains two larger transmit bands and four very smaller peaks, and
each larger band contains double peaks, the wide of them becomes two times as large as that
of Figure 2. Clearly, as frequency over 330 THz, the transmit intensity of TE mode
electromagnetic wave is very low, indicating TE mode cannot propagated in this large frequency
region. This can be considered as a large PBG region, Therefore, there are two PBG regions,
Investigation Effects of Filling Rate on the Bands Gaps of Two Dimensional … (Baohe Yuan)
30
ISSN: 1693-6930
the first one is centered at 205 THz, and the other is the larger region for frequency over 330
THz. Compare with Figure 2 and Figure 3, the number of PBG decreases from 5 to 2, at the
same time, the larger PBG band shift to high frequency region, the onset transmit peak sharply
shift towards low frequency.
Figure 4. The normalized transmit spectrum of a hex for f =0.445. There are two PBG regions,
the first one is centered at 205 THz, and the other is large region for frequency over 330 THz
In the case of f=0.581 and 0.735, the corresponding transmit spectrum is shown in
Figure5 and Figure6. These two spectra is very similar, both contain two transmit peaks; there is
a small PBG between the two peaks. Similar to Figure 4, when frequency is over 200 THz in
Figure 5 and 140 THz in Figure 6, the transmit intensity is very low, it can be considered as
PBG regions. This indicates that most frequency region is hold up by PBG for larger f, the TE
electromagnetic wave for frequency over 200 THz and 140 THz may not propagated in these
hex lattices, most electromagnetic wave is reflected or absorbed by the lattice. In addition, the
onset transmit peaks sharply shift towards low frequency.
Figure 5. The normalized transmit spectrum of a hex for f =0.581. There are two PBG regions,
the first one is centered at 105 THz, and the other is large region for frequency over 200 THz
Figure 6. The normalized transmit spectrum of a hex for f =0.735. There are two PBG regions,
the first one is centered at 100 THz, and the other is large region for frequency over 140 THz
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 27 – 32
TELKOMNIKA
ISSN: 1693-6930
31
In view of the gaps of above hex structures, the existence of multiple photonic band
gaps is rather interesting. With the filling rate increasing, the number of PBG bands decreases,
more and more frequency region is hold up by PBG, this tendency offers more freedom in
designing multi-channel photonic crystals devices.
4. Conclusion
The influences of the filling rate on the PBG properties of 2D hex photonic crystal are
investigated using the FDTD method. With the filling rate increasing, the number of PBG bands
decreases from 5 to 2 bands, for larger f (>0.445), the transmit intensity is very low in high
frequency region, it can be consider as a larger PBG region. At the same time, the onset
transmit peaks shift toward low frequency. It shows that the photonic band gap can be
effectively influenced by the filling rate. The changes in hex lattice are especially interesting and
helpful in designing multi-channel PCs devices.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
Yablonovitch E. Inhibited spontaneous emission in solid state physics and electronics. Phy. Rev. Lett.
1987; 5: 2059-2062.
Vlasov YA, Luterova K, Pelant I, Honerlage B, Astratov VN. Optical gain of CdS quantum dots
embedded in 3D photonic crystals. Thin Solid Films. 1998; 318(4): 93-95.
Dowling JP, Scalora M, Bloemer MJ, Bowden CM. The photonic band edge laser: A new approach to
gain enhancement. J. Appl. Phys. 1994; 75(2): 1896-1899.
Ohnishi D, Okano T, Imada M, Noda S. Room temperature continuous wave operation of a surfaceemitting two-dimensional photonic crystal diode laser. Optics Express. 2004; 12(8): 1562-1568.
Ferrando A, Zacarés M, Córdoba PF, Monsoriu A. Spatial soliton formation in photonic crystal fibers.
Optics Express. 2003; 11(5): 452-459.
Ye YH, Le Blanc F, Hache, Truong VV. Self-assembling three-dimensional colloidal photonic crystal
structure with high crystalline quality. Appl. Phys. Lett. 2001; 78(1): 52-54.
Chutinan A, Noda S. Highly confined waveguides and waveguide bends in three-dimensional
photonic crystal. Appl. Phys. Lett. 1999; 75(12): 3739-3741.
Noda S. Three-dimensional Photonic Crystals Operating at Optical Wavelength Region. Physica B.
2000; 279(2): 142-149.
Vlasov YA, Astratov VN, Karimov OZ, Kaplyanskii AA, Bogomolov VN, Prokofiev AV. Existence of a
photonic pseudogap for visible-light in synthetic opals. Phys. Rev. B. 1997; 55(5): 13357-11360.
Zoorob ME, Charltona MDB, Parker GJ, Baumberg JJ, Netti MC. Experimental investigation of
photonic crystal waveguide devices and line-defect waveguide bends. Mate. Sci. and Eng. B. 2000;
74(7): 168-174.
Rakhshani MR, Mansouri-Birjandi MA. Tunable Channel Drop Filter using Hexagonal Photonic
Crystal Ring Resonators. TELKOMNIKA Indonesian Journal of Electrical Engineering. 2013; 11(1):
513-516.
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