Optimization and Design Numerical Modeling and Advances in Fabrication Technologies To Optical Performance
Optimization and Design Numerical Modeling and Advances in Fabrication Technologies To Optical Performance
Optimization and Design Numerical Modeling and Advances in Fabrication Technologies To Optical Performance
AbstractPhotonic crystals and Nano photonics have received a great deal of attention over the last decade, largely due to improved
numerical modeling and advances in fabrication technologies. To this day, fabrication and optical behavior remain decoupled during the design
phase and numerous assumptions are made about perfect geometry. As research moves from theory to real devices, predicting device behavior
based on realistic geometry becomes critical. In this dissertation, a set of numerical tools was developed to model micro and nano fabrication
processes. They were combined with equally capable tools to model optical performance of the simulated structures. Using these tools, it was
predicted and demonstrated that 3D nanostructures may be formed on a standard mask aligner. A space-variant photonic crystal filter was
designed and optimized based on a simple fabrication method of etching holes through hetero-structured substrates. It was found that hole taper
limited their optical performance and a method was developed to compensate. A method was developed to tune the spectral response of guided-
mode resonance filters at the time of fabrication using models of etching and deposition. Auto cloning was modeled and shown that it could be
used to form extremely high aspect ratio structures to improve performance of form-birefringent devices. Finally, the numerical tools were
applied to metallic photonic crystal devices.
__________________________________________________*****_________________________________________________
299
IJRITCC | July 2016, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 4 Issue: 7 296 - 302
____________________________________________________________________________________________________________________
V. MAXWELLS EQUATIONS AND THEOREMS take many forms. To understand optical behavior in nano-
Maxwells equations are the fundamental laws that govern optical elements, it is necessary to have an understanding of
behavior of all electromagnetic energy. They are based on a Maxwells
macroscopic view of how waves interact with matter and may
equations and how they are applied. A summary of Maxwells density (W/m2), and magnetic field intensity (A/m)
equations is provided in Table 1. respectively. Electric charge density v (C/m3) and electric
current density J G (A/m2) represent sources that can induce
A. Time-Domain Form electromagnetic fields or be induced by the fields.All materials
The most widely used form of Maxwells equations are are comprised of charged particles that are displaced in the
differential equations, as opposed to integral equations. In time- presence of an applied electric field. Accelerating charges
domain form [24], these are: radiate fields that combine out of phase with the
D (t ) v (t ) (1)
applied wave. The overall effect is to modify propagation so
waves behave differently than they would in a vacuum. To
B (t ) 0 (2) incorporate these effects in a simplified manner, they are
treated macroscopically through the constitutive parameters
B (t )
x E (t ) (3) (t),(t) , and sometimes (t). In general, these are time-varying
t tensor quantities that relate to the fields through the following
D (t ) equations that involve convolutions.
x H (t ) J (4)
t
(5)
The field parameters D , B , Eand E represent electric flux
density (C/m2), electric field intensity (V/m), magnetic flux
300
IJRITCC | July 2016, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 4 Issue: 7 296 - 302
____________________________________________________________________________________________________________________
C. Wave Equations
Perhaps the most significant aspect of Maxwells equations is
(6)
that they predict propagating waves. The curl equations show
that time changing electric fields induce curling, or
(7) circulating, magnetic fields in the immediate vicinity.
The dielectric permittivity characterizes how well a material Likewise, time changing magnetic fields induce circulating
electric fields. In this manner, oscillating fields continue to
can store energy imposed by an electric field. Permeability induce other
quantifies how efficiently energy is stored due to an applied oscillating fields and a wave is formed. To better understand
magnetic field. The conductivity arises from free charges the wave phenomenon, it makes sense to combine Maxwells
that form electrical currents in the presence of an applied curl equations since it is the interaction of these two equations
electric field. that
B. Frequency-Domain Form predicts propagation. The combined equation is called a wave
Transforming Eqs. (1) - (7) to the frequency-domain equation and it is possible to derive it in terms of just the
simplifies the mathematical framework by reducing magnetic field or just the electric field. Wave equations enable
convolutions to simple products. fully rigorous analysis of electromagnetic problems using a
single equation while incorporating all
(8) information from both of Maxwells curl equations.
To begin deriving full vector wave equations, Eqs. (21) and
(9)
(22) are written as
(10)
(23)
(11)
(24)
(12) Taking the curl of these equations leads to:
(13) (25)
(14)
(26)
In this form, it is possible to eliminate the terms D , Band J The curl operations on the right side of these equations can be
from Maxwells equations. replaced using the original curl equations. This leads to the full
vector wave equations.
(15)
(16) (27)
(17)
(28)
(18)
The wave equations can be written in terms of the free space
Most often permittivity and permeability are not tensor
wave number k0, where k /c .
quantities. In addition, charge vis usually ignored and 0
(19)
(30)
(20)
VI. CONCLUSION
This manuscript designed and optimized several nano-optical
(21)
elements by considering how fabrication affects their optical
(22) behavior. Background was given to understand device
theory. Numerical tools were discussed and detailed
formulations were provided for each along with block diagrams
301
IJRITCC | July 2016, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 4 Issue: 7 296 - 302
____________________________________________________________________________________________________________________
summarizing their implementation. To better understand [12] S. P. Simonaho and R. Silvennoinen, "Sensing of wood density
electromagnetic theory of nano-optical elements and concepts by laser light scattering pattern and diffractive optical element
used to develop numerical models, background information based sensor," J. Opt. Technol., vol. 73, pp. 170- 174, 2006.
[13] V. Emiliani, D. Cojoc, E. Ferrari, V. Garbin, C. Durieux, M.
was provided to introduce Maxwells equations from which
Coppey-Moisan, and E. D. Fabrizio, "Wave front engineering for
wave equations were derived. These were used to explain
microscopy of living cells," Opt. Exp., vol. 13, pp. 1395-1405,
scaling theories and introduce the concept of left-handed 2005.
materials.Microscopic models of the response of materials were [14] E. D. Fabrizio, D. Cojoc, and S. Cabrini, "Diffractive optical
presented in the form of the Lorentz oscillator model for elements for differential interference contrast x-ray microscopy,"
dielectrics and the Drude model to metals. From these, basic Opt. Exp., vol. 11, pp. 2278-2288, 2003.
properties of bulk optical materials were identified and [15] F. Niklaus, P. Enoksson, E. Kalveston, G. Stemme: Void-free
described. full-wafer adhesive bonding, J. Micromech. Microeng. 11, 100
REFERENCES 107 (2000)
[1] R. Rumpf and E. G. Johnson, "Fully three-dimensional modeling [16] Y. Orihara, W. Klaus, M. Fujino, and K. Kodate, "Optimization
of the fabrication and behavior of photonic crystals formed by and application of hybrid-level binary zone plates," Appl. Opt.,
holographic lithography," Journal of the Optical Society of vol. 40, pp. 5877-5885, 2001.
America A, vol. 21, pp. 1703-1713, 2004. [17] W.H. Ko, J.T. Suminto, G.J. Yeh: Bonding techniques for
[2] R. C. Rumpf and E. G. Johnson, "Modeling the formation of microsensors. In: Micromachining andMicropackaging for
photonic crystals by holographic lithography," presented at Transducers, ed. by W.H. Ko
Proceedings of SPIE Micromachining Technology for Micro- (Elsevier, Amsterdam 1985)
Optics and Nano-optics III, Bellingham, WA, 2005. [18] H. Sasaki, I. Fukuzaki, Y. Katsuki, and T. Kamijoh, "Design
[3] P. Srinivasan, R. C. Rumpf, and E. G. Johnson, "Fabrication of 3- considerations of stacked multilayers of diffractive optical
D photonic crystals by two-step dry etching of layered media," elements for optical network units in optical subscribernetwork
presented at SPIE Micromachining Technology for Micro-Optics applications," Appl. Opt., vol. 37, pp. 3735-3745, 1998.
and Nano-Optics IV, San Jose, CA, 2006. [19] S. Jeon, G. P. Wiederrecht, and J. A. Rogers, "Photonic systems
[4] Z. Li and X. Zhang, "Fragility of photonic band gaps in inverse- formed by proximity field nanopatterning," Proceedings of the
opal photonic crystals," Phys. Rev. B, vol. 62, pp. 1516-1519, SPIE on Micromachining Technology for Micro-Optics and
2000. Nano-Optics III, vol. 5720, pp. 187-195, 2005.
[5] H. P. Herzig, Micro-optics: Elements, systems and applications. [20] W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson,
Philadelphia: Taylor &Francis Inc., 1998. "Selective Excitation of the TE01 Mode in Hollow-Glass
[6] D. L. Dickensheets, "Imaging performance of off-axis planar Waveguide Using a Subwavelength Grating," IEEE Phot. Tech.
diffractive lenses," J. Opt. Soc. Am. A, vol. 13, pp. 1849-1858, Lett., vol. 17, pp. 1441-1443, 2005.
1996. [21] A. Schilling, H. P. Herzig, L. Stauffer, U. Vokinger, and M.
[7] K. Yamada, W. Watanabe, Y. Li, and K. Itoh, "Multilevel phase- Rossi, "Efficient beam shaping of linear, high-power diode lasers
type diffractive lenses in silica glass induced by filamentation of by use of micro-optics," Appl. Opt., vol. 40, pp. 5852-5859,
femtosecond laser pulses," Opt. Lett., vol. 29, pp. 1846-1848, 2001.
2004. [22] M. R. Wang and X. G. Huang, "Subwavelength-resolvable
[8] C. Gimkiewicz, D. Hagedorn, J. Jahns, E. B. Kley, and F. Thoma, focused non-Gaussian beam shaped with a binary diffractive
"Fabrication of microprisms for planar optical interconnections optical element," Appl. Opt., vol. 38, pp. 2171-2176, 1999.
by use of analog gray-scale lithography with high-energy-beam- [23] Y. Zhao, Y. P. Li, and Q. G. Zhou, "Vector iterative algorithm for
sensitive glass," Applied Optics, vol. 38, pp. 2986-2990, the design ofdiffractive optical elements applied to uniform
1999.J.L. Vossen: Thin Film Processes (Academic, New York illumination," Opt. Lett., vol. 29, pp. 664-666, 2004.
1976) 8.9 M. Gad-el-Hak (Ed.): The MEMS Handbook (CRC, [24] A. Chutinan and S. Noda, "Effects of structural fluctuations on
Boca Raton 2002) the photonic band gap during fabrication of a photonic crystal: a
[9] J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Metallic study of a photonic crystal with a finite number of periods," J.
surface-relief on-axis and off-axis focusing diffractive cylindrical Opt. Soc. Am. B, vol. 16, pp. 1398-1402, 1999.
mirrors," J. Opt. Soc. Am. A, vol. 16, pp. 113- 130, 1999.
[10] G.T.A. Kovacs: Micromachined Transducers Sourcebook Nadeem Khargan Alhareeb was born in
(McGraw Hill, New York 1998)P. Rai-Choudhury (Ed.): Nasiriyiahcity,Thi-Qar province, Iraq,
Handbook of Microlithography, Micromachining and on November 1981. Received his B.S.
Microfabrication. Vol.2: Micromachining and degrees in Electrical Engineering from
Microfabrication(SPIE/IEE, Bellingham, Washington/London Al Mustansiriyah University, Baghdad
1997)
,Iraq, in 2007. Received his M.SC
[11] J. Rasanen and K. E. Peiponen, "On-line measurement of the
degree in the department of
thickness and optical quality of float glass with a sensor based on
a diffractive element," Appl. Opt., vol. 40, pp. 5034-5039, 2001. Communication Engineering. Currently; he become as a
Lecturer in Biomedical Engineering department, university of
ThiQar, Iraq
302
IJRITCC | July 2016, Available @ http://www.ijritcc.org
_______________________________________________________________________________________