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International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
20
A DESIGN AND SIMULATION OF OPTICAL PRESSURE SENSOR
BASED ON PHOTONIC CRYSTAL IN SUB-MICRON RANGE
[1]
Rajeshwari S, [2]
Indira Bahaddur, [3]
Dr. Preeta Sharan, [4]
Dr. P C Srikanth
[1]
Department of ECE, Malnad College of Engineering, Hassan, India,
[2]
Department of ECE, Assistant Professor, Malnad College of Engineering, Hassan, India
[3]
Department of ECE, Professor, The Oxford College of Engineering, VTU, Bangalore, India
[4]
Department of ECE, Professor, Malnad College of Engineering, Hassan, India
ABSTRACT
MOEMS based micro-sized pressure sensor can be developed to detect even
sub-micron range dimension change using the photonic crystal. The applied pressure on the
object will change the dimension of the waveguide carved in the photonic crystal. As a result,
this change in spacing can alter the propagation feature of electromagnetic waves that pass
through them that is changing the transmission spectrum. So, this change can directly be
mapped to pressure on the observed object. In this paper, the pressure sensor using photonic
crystal has been modeled and analyzed.
Keywords: FDTD, MOEMS, Micro-optics, Photonic crystal, Photonic sensing technology,
Pressure Sensor
I. INTRODUCTION
Integrated photonics has opened a way to develop sensor systems which can replace the
conventional electronic pressure sensors. The miniaturization, extreme efficiency and high
sensitivity has made photonic sensor most viable solution to the conventional pressure sensor
with limitations like inefficiencies in harsh environment, high cost and low sensitivity.
Opto-mechanical micro sensor technology can be explored to develop pressure sensor. MEMS
merged with Micro-optics involves sensing or manipulating optical signals on a very small size
scale using integrated mechanical, optical, and electrical systems, giving rise to a new class of
MOEMS technology.
IJECERD
© PRJ
PUBLICATION
International Journal of Electronics and Communication
Engineering Research and Development
(IJECERD)
ISSN 2248– 9525 (Print)
ISSN 2248 –9533 (Online)
Volume 4, Number 2, April- June (2014), pp. 20-27
© PRJ Publication, http://www.prjpublication.com/IJECERD.asp
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
21
Photonic sensing technology is innovative approach to identify and measure physical
variables. Photonic crystal is array of periodic change in refractive index which can engineer
the flow of light passing through it. The slightest change in the arrangement of index of
refraction and corresponding dimension alters the transmission spectrum, which provides the
photonic crystal very sensitive detection capability. Stable alignment, thermal stability, low
cost, low energy requirement, faster response and compatibility with fiber-optic cable makes
photonic sensor for pressure sensing have applications in various field from structural health
monitoring, underwater applications, bio-medical applications to aerospace engineering.
In this paper, we propose a model for photonic crystal based pressure sensor. The model
consists of a waveguide carved in two dielectric slabs surrounded by photonic crystal. The
dielectric slabs are mobile. The photonic crystal is mounted on the object under observation. As
such its pressure can be coupled to the movement of the dielectric slabs in the photonic crystal
and pressure variation can be mapped to the separation of these slabs and thus measured. As a
consequence the optical properties of the photonic crystal like the transmission spectrum
change. The altered transmission spectrum act as a signature of the pressure applied. The
spectral analysis has been done to detect the change in the pressure.
II. THEORY
The photonic crystal is defined as periodic profile of refractive index which allows the
controlled flow of the light through it. The artificial photonic crystal structures can be
fabricated using immensely developed CMOS technology. It appears in one-dimension,
two-dimension and three dimensions. It exists in two configurations: rods in air configuration
and holes in slab configuration. The photonic crystal appears in different lattice structures
example square lattice and hexagonal lattice. In this paper, two works are carried out. One is
using two-dimensional square lattice photonic crystal with rods in air figuration and another is
using two-dimensional hexagonal lattice photonic crystal with holes in slab configuration.
The defect engineering is an important aspect of the photonic crystal which is
responsible for the controlled propagation of light through it. Defect engineering is the
controlled change in the index profile of the photonic crystal to modify course of the
electromagnetic waves passing through it. The line defect and point defect are the two types of
defect popularly used and are very useful for creating band gap structures for different
applications.
The photonic band gap property can be explored for the sensing applications. The band
gap is referred to as an optical insulator. The bandgap property is precisely dependent on the
refractive index arrangement of the photonic crystal. The smallest change in the refractive
index profile example change in radius of holes or change in the dimension of the waveguide,
there is a precise change in the band gap property. Thus the band gap structures are efficient and
highly sensitive sensor devices.
FDTD (Finite Difference Time Domain) Method: FDTD method provides a solution to
Maxwell's equation. In FDTD method a finite rectangular grid is divided into space and time.
These equations are solved using MEEP simulation tools. MEEP implements FDTD method to
compute transmission spectrum.
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
22
The model of photonic crystal consist waveguide carved with the help of two dielectric
slabs, with the upper plate mobile. As the pressure is applied on the photonic crystal, the
dielectric slab moves and change the dimension of the waveguide. As a result the index profile
of the photonic crystal is altered and thus changing the spectral property. This change in optical
property is directly proportional to the applied pressure.
III. DESIGNS
1. Pressure sensor using rods in air configuration photonic crystal:
The first design of Pressure sensor is a two dimensional, square lattice photonic crystal
with a line defect in rods in air configuration. The model consists of waveguide carved with the
help of two dielectric slabs. The upper dielectric slab is mobile with respect to the pressure
applied.
Following points explain the design parameters of the modeled pressure sensor:
a) Rods in air configuration.
b) Radius of rods 0.17µm.
c) Square Lattice.
d) Lattice constant 'a'=1µm.
e) Dielectric constant of dielectric slab is 11.56.
f) The length of each plate is 10µm and width is 1µm.
g) Dielectric constant of the waveguide is 1 (Air).
h) Height of slab is infinity
i) Light source: Unit Gaussian Pulse with center frequency at 0.4, width of the pulse is
0.3.
j) Minimum distance between dielectric slabs is zero µm and the maximum distance
between dielectric slabs is 2µm
The structure of the design-1 model is illustrated in the Figure 1 with maximum
separation and figure 2 with minimum separation between dielectric slabs.
Figure 1: Model of the pressure sensor (rods in air configuration)
Pressure applied
Light
Source
Spectrum
Analyzer
Mobile
dielectric
slab
Waveguide
Photonic
Crystal
Separation
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
23
Figure 2: Model of the pressure sensor with minimum separation
(rods in air configuration)
2. Pressure sensor using holes in slab configuration photonic crystal
The second design of Pressure sensor is a two dimensional, hexagonal lattice photonic
crystal with a line defect in holes in slab configuration. The model consists of waveguide
carved with the help of two dielectric slabs. The upper dielectric slab is mobile with respect to
the pressure applied.
Following points explain the design parameters of the modeled pressure sensor:
a) Holes in slab configuration.
b) Holes in slab 0.40µm.
c) Hexagonal Lattice.
d) Lattice constant 'a'=1µm.
e) Dielectric constant of dielectric slab is 11.56.
f) The length of each plate is 10µm and width is 1µm.
g) Dielectric constant of the waveguide is 1 (Air).
h) Height of slab is infinity
i) Light source: Unit Gaussian Pulse with center frequency at 0.4, width of the pulse is 0.3.
j) Minimum distance between dielectric slabs is zero µm and the maximum distance
between dielectric slabs is 0.5µm
The structure of the design-2 model is illustrated in the Figure 3 with maximum
separation and figure 4 with minimum separation between dielectric slabs.
Figure 3: Model of the pressure sensor (holes in slab configuration)
Photonic
Crystal
Pressure applied
Mobile
dielectric
slab
Spectrum
Analyzer
Light
Source
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
24
Figure 4: Model of the pressure sensor with minimum separation
(holes in slab configuration)
The modeling and simulation has been done with the help of MEEP simulation tool.
MEEP tool works in time domain and provides implementation of Finite Difference Time
Domain Method. MEEP is MIT Electromagnetic Equation Propagation. MEEP is
'dimensionless' tool where µ0, 0, c are unity. The output of MEEP is the transmitted power; the
transmission spectrum is obtained using output from MEEP.
Operation: The Gaussian light pulse is passed through one end of the photonic crystal while the
spectrum analyzer is placed in the other end. The applied pressure moves the mobile plate
reducing or increasing the distance between two dielectric slabs. The movement of the plate is
considered in 20 steps, each step of 0.1µm for design1 and for design2 we have considered in 5
steps, each step of 0.1µm. The changed dimension of the waveguide alters the light propagation
and thus changing the transmission spectrum. The transmission spectrum is observed at each
step of 0.1µm increase or decrease in distance between the two dielectric slabs.
IV. RESULTS
The transmission spectrum is plotted as shown in figure 5 given below.
Figure 5: The transmission spectrum for zero separation between the dielectric slabs in
design-1
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
25
Figure 6: The transmission spectrum for 0.1, 0.2, 0.3, 0.4, 0.5 dimension(µm) of the
waveguide in design-1
Figure 6: The transmission spectrum for 0.6, 0.7, 0.8, 0.9, 1 dimension (µm) of the
waveguide in design-1
Figure 7: The transmission spectrum for 1.1, 1.2, 1.3, 1.4, 1.5 dimension (µm) of the
waveguide in design-1
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
26
Figure 8: The transmission spectrum for 1.6, 1.7, 1.8, 1.9, 2 dimension (µm) of the waveguide
in design-1
.
Figure 9: The transmission spectrum for 0.5, 0.4, 0.3, 0.2, 0.1, and 0 dimension (µm) of the
waveguide in design-2
V. CONCLUSION
In this paper, we are successful in modeling and analyzing pressure sensor using photonic
crystal in sub-micron range. The varying spectrum of the waveguide can suitably and
efficiently represent and measure pressure applied on the object. Further, it can be designed and
fabricated to measure expansion or compression or both.
REFERENCES
[1] An article 'Recent advancement in sensor technology for underwater environment' by
Mohd Rizwal Arsad, Indian Journal Of Marine Sciences, Vol. 38(3), September 2009,
pp. 267-273
[2] 'Optical Fiber Sensor for Chemical Detection', US patent number 4834496, May
30,1989
[3] 'Sensor Device', by Mitsuro Sugita, US patent number US7391945, 2008
International Journal of Electronics and Communication Engineering Research and Development
(IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014)
27
[4] 'Two-Dimensional Photonic Crystal', by Susumu Noda et al. US patent number
US7853111B2, 2010.
[5] http://abinitio.mit.edu/wiki/index.php
/Meep_Introduction/Transmission.2Freflection_spectra
[6] 'Photonic Crystals: Modeling The Flow Of Light', by John D. Joannopoulos, Steven G.
Johnson, Robert D. Meade.
[7] 'A Novel Method for Switching and Tuning of PBG Structures', Jack Wu, S. N. Qiu, C.
X. Qiu,2 and I. Shih, Department of Electrical and Computer Engineering McGill
University, 2004.
[8] 'Photonic Crystals: Modeling The Flow Of Light', by John D. Joannopoulos ,Steven G.
Johnson, Robert D. Meade.
[9] http://en.wikipedia.org/wiki/Photonic_ crystal # Fabrication_challenges
[10] http://ab-initio.mit.edu/MEEP/Tutorial.

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A design and simulation of optical pressure sensor based on photonic crystal in sub micron range

  • 1. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 20 A DESIGN AND SIMULATION OF OPTICAL PRESSURE SENSOR BASED ON PHOTONIC CRYSTAL IN SUB-MICRON RANGE [1] Rajeshwari S, [2] Indira Bahaddur, [3] Dr. Preeta Sharan, [4] Dr. P C Srikanth [1] Department of ECE, Malnad College of Engineering, Hassan, India, [2] Department of ECE, Assistant Professor, Malnad College of Engineering, Hassan, India [3] Department of ECE, Professor, The Oxford College of Engineering, VTU, Bangalore, India [4] Department of ECE, Professor, Malnad College of Engineering, Hassan, India ABSTRACT MOEMS based micro-sized pressure sensor can be developed to detect even sub-micron range dimension change using the photonic crystal. The applied pressure on the object will change the dimension of the waveguide carved in the photonic crystal. As a result, this change in spacing can alter the propagation feature of electromagnetic waves that pass through them that is changing the transmission spectrum. So, this change can directly be mapped to pressure on the observed object. In this paper, the pressure sensor using photonic crystal has been modeled and analyzed. Keywords: FDTD, MOEMS, Micro-optics, Photonic crystal, Photonic sensing technology, Pressure Sensor I. INTRODUCTION Integrated photonics has opened a way to develop sensor systems which can replace the conventional electronic pressure sensors. The miniaturization, extreme efficiency and high sensitivity has made photonic sensor most viable solution to the conventional pressure sensor with limitations like inefficiencies in harsh environment, high cost and low sensitivity. Opto-mechanical micro sensor technology can be explored to develop pressure sensor. MEMS merged with Micro-optics involves sensing or manipulating optical signals on a very small size scale using integrated mechanical, optical, and electrical systems, giving rise to a new class of MOEMS technology. IJECERD © PRJ PUBLICATION International Journal of Electronics and Communication Engineering Research and Development (IJECERD) ISSN 2248– 9525 (Print) ISSN 2248 –9533 (Online) Volume 4, Number 2, April- June (2014), pp. 20-27 © PRJ Publication, http://www.prjpublication.com/IJECERD.asp
  • 2. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 21 Photonic sensing technology is innovative approach to identify and measure physical variables. Photonic crystal is array of periodic change in refractive index which can engineer the flow of light passing through it. The slightest change in the arrangement of index of refraction and corresponding dimension alters the transmission spectrum, which provides the photonic crystal very sensitive detection capability. Stable alignment, thermal stability, low cost, low energy requirement, faster response and compatibility with fiber-optic cable makes photonic sensor for pressure sensing have applications in various field from structural health monitoring, underwater applications, bio-medical applications to aerospace engineering. In this paper, we propose a model for photonic crystal based pressure sensor. The model consists of a waveguide carved in two dielectric slabs surrounded by photonic crystal. The dielectric slabs are mobile. The photonic crystal is mounted on the object under observation. As such its pressure can be coupled to the movement of the dielectric slabs in the photonic crystal and pressure variation can be mapped to the separation of these slabs and thus measured. As a consequence the optical properties of the photonic crystal like the transmission spectrum change. The altered transmission spectrum act as a signature of the pressure applied. The spectral analysis has been done to detect the change in the pressure. II. THEORY The photonic crystal is defined as periodic profile of refractive index which allows the controlled flow of the light through it. The artificial photonic crystal structures can be fabricated using immensely developed CMOS technology. It appears in one-dimension, two-dimension and three dimensions. It exists in two configurations: rods in air configuration and holes in slab configuration. The photonic crystal appears in different lattice structures example square lattice and hexagonal lattice. In this paper, two works are carried out. One is using two-dimensional square lattice photonic crystal with rods in air figuration and another is using two-dimensional hexagonal lattice photonic crystal with holes in slab configuration. The defect engineering is an important aspect of the photonic crystal which is responsible for the controlled propagation of light through it. Defect engineering is the controlled change in the index profile of the photonic crystal to modify course of the electromagnetic waves passing through it. The line defect and point defect are the two types of defect popularly used and are very useful for creating band gap structures for different applications. The photonic band gap property can be explored for the sensing applications. The band gap is referred to as an optical insulator. The bandgap property is precisely dependent on the refractive index arrangement of the photonic crystal. The smallest change in the refractive index profile example change in radius of holes or change in the dimension of the waveguide, there is a precise change in the band gap property. Thus the band gap structures are efficient and highly sensitive sensor devices. FDTD (Finite Difference Time Domain) Method: FDTD method provides a solution to Maxwell's equation. In FDTD method a finite rectangular grid is divided into space and time. These equations are solved using MEEP simulation tools. MEEP implements FDTD method to compute transmission spectrum.
  • 3. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 22 The model of photonic crystal consist waveguide carved with the help of two dielectric slabs, with the upper plate mobile. As the pressure is applied on the photonic crystal, the dielectric slab moves and change the dimension of the waveguide. As a result the index profile of the photonic crystal is altered and thus changing the spectral property. This change in optical property is directly proportional to the applied pressure. III. DESIGNS 1. Pressure sensor using rods in air configuration photonic crystal: The first design of Pressure sensor is a two dimensional, square lattice photonic crystal with a line defect in rods in air configuration. The model consists of waveguide carved with the help of two dielectric slabs. The upper dielectric slab is mobile with respect to the pressure applied. Following points explain the design parameters of the modeled pressure sensor: a) Rods in air configuration. b) Radius of rods 0.17µm. c) Square Lattice. d) Lattice constant 'a'=1µm. e) Dielectric constant of dielectric slab is 11.56. f) The length of each plate is 10µm and width is 1µm. g) Dielectric constant of the waveguide is 1 (Air). h) Height of slab is infinity i) Light source: Unit Gaussian Pulse with center frequency at 0.4, width of the pulse is 0.3. j) Minimum distance between dielectric slabs is zero µm and the maximum distance between dielectric slabs is 2µm The structure of the design-1 model is illustrated in the Figure 1 with maximum separation and figure 2 with minimum separation between dielectric slabs. Figure 1: Model of the pressure sensor (rods in air configuration) Pressure applied Light Source Spectrum Analyzer Mobile dielectric slab Waveguide Photonic Crystal Separation
  • 4. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 23 Figure 2: Model of the pressure sensor with minimum separation (rods in air configuration) 2. Pressure sensor using holes in slab configuration photonic crystal The second design of Pressure sensor is a two dimensional, hexagonal lattice photonic crystal with a line defect in holes in slab configuration. The model consists of waveguide carved with the help of two dielectric slabs. The upper dielectric slab is mobile with respect to the pressure applied. Following points explain the design parameters of the modeled pressure sensor: a) Holes in slab configuration. b) Holes in slab 0.40µm. c) Hexagonal Lattice. d) Lattice constant 'a'=1µm. e) Dielectric constant of dielectric slab is 11.56. f) The length of each plate is 10µm and width is 1µm. g) Dielectric constant of the waveguide is 1 (Air). h) Height of slab is infinity i) Light source: Unit Gaussian Pulse with center frequency at 0.4, width of the pulse is 0.3. j) Minimum distance between dielectric slabs is zero µm and the maximum distance between dielectric slabs is 0.5µm The structure of the design-2 model is illustrated in the Figure 3 with maximum separation and figure 4 with minimum separation between dielectric slabs. Figure 3: Model of the pressure sensor (holes in slab configuration) Photonic Crystal Pressure applied Mobile dielectric slab Spectrum Analyzer Light Source
  • 5. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 24 Figure 4: Model of the pressure sensor with minimum separation (holes in slab configuration) The modeling and simulation has been done with the help of MEEP simulation tool. MEEP tool works in time domain and provides implementation of Finite Difference Time Domain Method. MEEP is MIT Electromagnetic Equation Propagation. MEEP is 'dimensionless' tool where µ0, 0, c are unity. The output of MEEP is the transmitted power; the transmission spectrum is obtained using output from MEEP. Operation: The Gaussian light pulse is passed through one end of the photonic crystal while the spectrum analyzer is placed in the other end. The applied pressure moves the mobile plate reducing or increasing the distance between two dielectric slabs. The movement of the plate is considered in 20 steps, each step of 0.1µm for design1 and for design2 we have considered in 5 steps, each step of 0.1µm. The changed dimension of the waveguide alters the light propagation and thus changing the transmission spectrum. The transmission spectrum is observed at each step of 0.1µm increase or decrease in distance between the two dielectric slabs. IV. RESULTS The transmission spectrum is plotted as shown in figure 5 given below. Figure 5: The transmission spectrum for zero separation between the dielectric slabs in design-1
  • 6. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 25 Figure 6: The transmission spectrum for 0.1, 0.2, 0.3, 0.4, 0.5 dimension(µm) of the waveguide in design-1 Figure 6: The transmission spectrum for 0.6, 0.7, 0.8, 0.9, 1 dimension (µm) of the waveguide in design-1 Figure 7: The transmission spectrum for 1.1, 1.2, 1.3, 1.4, 1.5 dimension (µm) of the waveguide in design-1
  • 7. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 26 Figure 8: The transmission spectrum for 1.6, 1.7, 1.8, 1.9, 2 dimension (µm) of the waveguide in design-1 . Figure 9: The transmission spectrum for 0.5, 0.4, 0.3, 0.2, 0.1, and 0 dimension (µm) of the waveguide in design-2 V. CONCLUSION In this paper, we are successful in modeling and analyzing pressure sensor using photonic crystal in sub-micron range. The varying spectrum of the waveguide can suitably and efficiently represent and measure pressure applied on the object. Further, it can be designed and fabricated to measure expansion or compression or both. REFERENCES [1] An article 'Recent advancement in sensor technology for underwater environment' by Mohd Rizwal Arsad, Indian Journal Of Marine Sciences, Vol. 38(3), September 2009, pp. 267-273 [2] 'Optical Fiber Sensor for Chemical Detection', US patent number 4834496, May 30,1989 [3] 'Sensor Device', by Mitsuro Sugita, US patent number US7391945, 2008
  • 8. International Journal of Electronics and Communication Engineering Research and Development (IJECERD), ISSN 2248-9525(Print), ISSN- 2248-9533 (Online) Volume 4, Number 2, April-June (2014) 27 [4] 'Two-Dimensional Photonic Crystal', by Susumu Noda et al. US patent number US7853111B2, 2010. [5] http://abinitio.mit.edu/wiki/index.php /Meep_Introduction/Transmission.2Freflection_spectra [6] 'Photonic Crystals: Modeling The Flow Of Light', by John D. Joannopoulos, Steven G. Johnson, Robert D. Meade. [7] 'A Novel Method for Switching and Tuning of PBG Structures', Jack Wu, S. N. Qiu, C. X. Qiu,2 and I. Shih, Department of Electrical and Computer Engineering McGill University, 2004. [8] 'Photonic Crystals: Modeling The Flow Of Light', by John D. Joannopoulos ,Steven G. Johnson, Robert D. Meade. [9] http://en.wikipedia.org/wiki/Photonic_ crystal # Fabrication_challenges [10] http://ab-initio.mit.edu/MEEP/Tutorial.