光子晶體是一種不同折射率材料呈週期性排列的光學介質結構，經由模擬設計，可以實現調控電磁波的傳導來符合需求。在本篇論文中，共研究了兩個主題。

第一個是利用轉移矩陣法（TMM）來設計出以矽為基板的抗反射層（ARC），此ARC主要的波段為可見光到紅外線的範圍，力圖將反射率降至最低，提升整體的效率。經由不同的角度來觀察 TE、TM模式下的反射光譜。

第二個主題是利用金屬與介電質材料來設計出光學量子井（PQW）結構，我們分析銀、鋁、銅這三種金屬是否皆具有量子井的特性，結構上都以反對稱結構(AB)^m(MC)^n(AB)^m 為主，A=B=C=介電質，M=金屬，量子井的特性是可做為多通道的濾波器，可藉由調控缺陷的週期來實現，並在最後的分析找出濾波器的工作頻段。

Photonic crystals, artificially periodic layered structures, have attracted much attention in the past two decades in the photonic community. In this thesis, based on the use of photonic crystal structures, we propose two filter structures which could be of technical use in photonic applications.

The first part is to exploit the transfer matrix method（TMM）to design and simulate the filtering properties of antireflection coating (ARC) on silicon substrate.
We have made several analyses on the three-layer and four-layer ARC structures. The ARC filter is designed to be suitable from visible to infrared. It is designed to have the lowest reflectivity in a wider frequency range. The angular dependence of antireflection for both TE and TM modes is also given.

The second subject is to design a multichannel filter. We employ the photonic quantum well (PQW) structure made of dielectric and metallic materials. Three different metals, silver (Ag), aluminum (Al), and copper (Cu), will be used to
comparatively study. In this study, asymmetric PQW structure, (AB)^m(MC)^n(AB)^m , is considered in our design. Here, layers of A, B, and C are dielectric slabs and M is a slab of metal. It is found that the number of channels is equal to the number of periods of central PQW. The proposed multichannel filter can be operated in the UV range.

[1] M. Chen, H.C. Chang, A.P. Chang, S.Y. Lin, J.Q. Xi and E.F. Schubert, “Design
of optical path for wide-angle gradient-index antireflection coating,” Applied
Optics, Vol. 46, 6533–6538, 2007.
[2] G.E. Jellison Jr., R.F. Wood, “Antireflection coatings for planar silicon solar
cells,” Solar Cells, Vol. 18, 93–114, 1986.
[3] P.A. Young and W.G. Thege, “Two-layer laser anti-reflection coatings,” J. Phys.
D：Appl. Phys., Vol. 4, 64–71, 1971.
[4] L. Wang, F. Chen,“Optimization of wide angle MgF2/ZnS/Al2O3 passivation and
antireflection film for silicon solar cells,” Journal of optoelectronics and
advanced materials, Vol. 14, 929–934, 2012.
[5] M.A. Green, “High efficiency silicon solar cells / edited by Martin A. Green,”
Aedermannsdorf, Switzerland：Trans Tech, 1987.
[6] S.M. Sze, “Semiconductor Devices：Physics and Technology,” John Wiley＆
Sons Inc, 2012.
[7] S. John, California Institute of Technology, “On a method of decreasing the
reflection from nonmetallic substances,” J.O.S.A., Vol. 26, 73–74, 1936.
[8] A. Mussett and A. Thelen, “Multilayer antireflection coatings,” Progress In
Optics, Vol. 8, 203–237, 1970.
[9] J. Zhao and M.A. Green, “Optimized antireflection coatings for high-efficiency
silicon solar cells,” IEEE Transactions On Electron Devices, Vol. 38, 1925–1934,
1991.
[10] K.L. Jiao, W.A. Anderson, “SiO2/TiO2 double-layer antireflective coating
deposited at room temperature for metal/insulator/n-Si/p-Si solar cells,” Solar
Cells, Vol. 22, 229–236, 1987.
[11] M.A. Green, A.W. Blakers, J. Shi, E.M. Keller, and S.R. Wenham,“19.1％
efficient silicon solar cell,” Appl. Phys. Lett., Vol. 44, 1163–1164, 1984.
[12] P. Nubile, “Analytical design of antireflection coatings for silicon photovoltaic
devices,” Thin Solid Films, Vol. 342, 257–261, 1999.
[13] M.J. Minot, “Single-layer, gradient refractive index antireflection films effective
from 0.35 to 2.5 u,” J. Opt. Soc. Am., Vol. 66, 515–519, 1976.
[14] W.H. Southwell, “Scaling rules for quantic refractive index matching
semi-infinite-band antireflection coatings,” SPIE, Vol. 3133, 65, 1997.
[15] J.R. Jacobsson, “Review of the optical properties of inhomogeneous thin films,”
SPIE, Vol. 2046, 2, 1993.
[16] R. Jacobsson, “Light reflection from films of continuously varying refractive
index,” Progress In Optics, Vol. 5, 247–286, 1966.
[17] M.J. Minot, “The angular reflectance of single-layer gradient refractive-index
films,” J. Opt. Soc. Am., Vol. 67, 1046–1050, 1977.
[18] A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, C. Zanke, B. Blasiet al.,
“Grazing with very high solar transmittance,” Sol. Energy, Vol. 62, 177–188,
1998.
[19] A. Ghosh, P.K. Bandyopadhyay, “Board band antireflection coating on silicon
from 1.5 to 6 um spectral band,” Infrared Physics＆ Technology, Vol. 46,
408–411, 2005.
[20] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and
Electronics,” Phys. Rev. Lett., Vol. 58, 2059–2062, 1987.
[21] S. John, “Strong Localization of Photons in Certain Disordered Dielectric
Superlattices,” Phys. Rev. Lett., Vol. 58, 2486–2489, 1987.
[22] R. Sapienza, M. Leonetti, L.S. Froufe-Pérez, J.F. Galisteo-López, C. Conti, C.
López, “Optical amplification enhancement in photonic crystals,” Phys. Rev. A,
Vol. 83, 023801, 2011.
[23] D.S. Wiersma, R. Sapienza, S. Mujumdar, M. Colocci, M. Ghulinyan, L. Pavesi,
“Optics of nanostructured dielectrics,” J. Opt. A: Pure Appl. Opt., Vol. 7,
S190–S197, 2005.
[24] S.W. Shao, X.S. Chen, W. Lu, M. Li, and H.Q. Wang, “Fractal independently
tunable multichannel filters,” Appl. Phys. Lett., Vol. 90, 211113, 2007.
[25] J. Lumeau, L.B. Glebov, and V. Smirnov, “Tunable narrowband filter based on a
combination of Fabry–Perot etalon and volume Bragg grating,” Opt. Lett., Vol.
31, 2417–2419, 2006.
[26] C.J. Wu, Y.H. Chung, and B.J. Syu, “Band gap extension in a one-dimensional
ternary metal-dielectric photonic crystal,” PIER, Vol. 102, 81–93, 2010.
[27] J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the
Flow of Light, Princeton University Press, Princeton, NJ, 1995.
[28] K. Sakoda, Optical Properties of Photonic Crystals, Springer–Verlag, Berlin,
2001.
[29] S.J. Orfanidis, Electromagnetic Waves and Antennas, Rutger University, 2008,
www.ece.rutgers.edu/orfanidi/ewa.
[30] 光學中的半導體– 光子晶體, 中國科學院半導體研究所, 2008,
http://www.semi.cas.cn/kxcb/kpwz/200811/t20081105_2286672.html
[31] L.D. Bonifacio, B.V. Lotsch, D.P. Puzzo, F. Scotognella, G.A. Ozin, “Stacking
the nanochemistry deck: structural and compositional diversity in
one-dimensional photonic crystals,” Adv. Mater., Vol. 21, 1641–1646, 2009.
[32] C. Lopez, “Materials aspects of photonic crystals,” Adv. Mater., Vol. 15,
1679–1704, 2003.
[33] J.E.G.J. Wijnhoven, W.L. Vos, “Preparation of photonic crystals made of air
spheres in titania,” Science, Vol. 281, 802–804, 1998.
[34] O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus al.,
“Two-dimensional photonic band-gap defect mode laser,” Science, Vol. 284,
1819–1821, 1999.
[35] F. Scotognella, D.P. Puzzo, A. Monguzzi, D.S. Wiersma, D. Maschke, R. Tubino
al., “Nanoparticle one-dimensional photonic-crystal dye laser,” Small, Vol. 5,
2048–2052, 2009.
[36] A. Mekis, J.C. Chen, J. Kurland, S. Fan, P.R. Villeneuve, J.D. Joannopoulos,
“High transmission through sharp bends in photonic crystals waveguides,” Phys.
Rev. Lett., Vol. 77, 3787–3790, 1996.
[37] J. Serbin, M. Gu, “Experimental evidence for superprism effects in
three-dimensional polymer photonic crystals,” Adv. Mater., Vol. 18, 221–224,
2006.
[38] V. Morandi, F. Marabelli, V. Amendola, M. Meneghetti, D. Comoretto,
“Colloidal photonic crystals doped with gold nanoparticles: spectroscopy and
optical switching properties,” Adv. Funct. Mater., Vol. 17, 2779–2786, 2007.
[39] K. Busch, S. Lölkes, R.B. Wehrspohn, H. Föll (Eds.), Photonic crystals:
Advances in design, fabrication and characterization, Wiley, Weinheim, 2004.
[40] P. Yeh, Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.
[41] X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of
omnidirectional total reflection frequency range in one–dimensional photonic
crystals by using photonic heterostructures,” Appl. Phys. Lett., Vol. 80,
4291–4293, 2002.
[42] J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission
in one–dimensional photonic quantum well structures,” Appl. Phys. Lett., Vol. 73,
2084–2086, 1998.
[43] R. Srivastava, S. Pati, and S.P. Ojha, “Enhancement of omnidirectional reflection
in photonic crystal heterostructures,” Progress in electromagnetics Research B,
Vol. 1, 197–208, 2008.
[44] S.K. Awasthi, U. Malaviya, and S.P. Ojha, “Enhancement of omnidirectional
total–reflection wavelength range by using one–dimensional ternary photonic
bandgap material,” J. Opt. Soc. Am. B: Optical Physis, Vol. 23, 2566–2571,
2006.
[45] S.K. Awasthi, and S.P. Ojha, “Design of a tunable optical filter by using a
one–dimensional ternary photonic bandgap material,” Progress in
electromagnetics Research M, Vol. 4, 117–132, 2008.
[46] A. Banerjee, “Enhanced temperature sensing by using one–dimensional ternary
photonic bandgap structures,” Progress in electromagnetics Research Letters,
Vol. 11, 129–137, 2009.
[47] A. Banerjee, “Enhanced refractometric optical sensing by using one–dimensional
ternary photonic crystals,” PIER, Vol. 89, 11–22, 2009.
[48] H. Contopanagoes, E. Yablonovitch, and N.G. Alexopoulous, “Electromagnetic
properties of periodic of periodic multilayers of ultrathin metallic films from dc
to ultraviolet frequencies,” J. Opt. Soc. Am. A, Vol. 16, 2294–2306, 1999.
[49] H. Contopanagoes, N.G. Alexopoulous, and E. Yablonovitch, “High–Q
radio-frequency structures using one-dimensionally periodic metallic films,”
IEEE Trans. Microwave Theory Technol., Vol. 46, 1310–1312, 1998.
[50] L. Qi, Z. Yang, X. Gao, F. Lan, Z. Shi, and Z. Liang, “Bandgap extension of
disordered one–dimensional metallic–dielectric photonic crystals,” IEEE
International Vacuum Electronics Conference, 158–159, 2008.
[51] Z.S. Wang, L. Wang, Y.G. Wu, L.Y. Chen, X.S. Chen, and W. Lu, “Multiple
channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett.,
Vol. 84, 1629–1631, 2004.
[52] S.J. Orfanidis: Electromagnetic waves and Antennas (Rutger University, 2008)
Chap. 7 [www.ece.rutgers.edu/~orfanidi/ewa].
[53] D.R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S.L. McCall, and P.M.
Platzman, “Photonic band structure and defects in one and two dimensions,” J.
Opt. Soc. Am. B, Vol. 10, 314–321, 1993.
[54] G. Boedecker and C. Henkle, “All-frequency effective medium theory of a
photonic crystal,” Opt. Express, Vol. 11, 1590–1595, 2003.
[55] G.J. Schneider and G.H. Watson, “Nonlinear optical spectroscopy in
one-dimensional photonic crystals,” Appl. Phys. Lett., Vol. 83, 5350–5352, 2003.
[56] J.A. Monsoriu, C.J. Zapata-Rofriguez, and E. Silvestre, “Cantor-like fractal
photonic crystal waveguides,” Opt. Commun., Vol. 252, 46–51, 2005.
[57] J. Liu, J. Sun, C. Huang, W. Hu, and D. Huang, “Optimizing the spectral
efficiency of photonic quantum well structures,” Optik, Vol. 120, 35–39, 2009.
[58] J. Liu, J. Sun, C. Huang, W. Hu, and M. Chen, “Improvement of spectral
efficiency based on spectral splitting in photonic quantum-well structure,” IET
Optoelectron, Vol. 2, 122–127, 2008.
[59] C.S. Feng, L.M. Mei, L.Z. Cai, P. Li, and X.L. Yang, “Resonant modes in
quantum well structure of photonic crystals with difference lattice constants,”
Solid State Commun., Vol. 135, 330–334, 2005.
[60] S. Haxha, W. Belhadj, F. Abdelmalek, and H. Bouchriha, “Analysis of
wavelength demultiplexer based on photonic crystals,” IEE Proc. Optoelectron,
Vol. 152, 193–198, 2005.
[61] F. Qiao, C. Zhang, and J. Wan, “Photonic quantum-well structure: multiple
channelled filtering phenomena,” Appl. Phys. Lett., Vol. 77, 3698–3700, 2000.
[62] H.A. Macleod, Thin-Film Optical Filters Fourth Edition, CRC Press, 2010.
[63] J. Benick, A. Richter, M. Hermle, S.W. Glunz, “Thermal stability of the Al2O3
passivation on p-type silicon surfaces for solar cell applications,” Rapid
Research Letter, Vol.3, 233–235, 2009.
[64] J.B. Pendry, “Symmetry and transport of waves in one-dimensional disordered
systems,” Adv. Phys., Vol. 43, 461–542, 1994.