Optical properties of photonic crystals - New Jersey Institute of ...

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20 2.2.1 Transfer Matrix Method Theoretical studies using the Transfer Matrix Method (TMM) 29 have been crucial to the design and characterization of these PBG materials. TMM calculates the transmission and reflection coefficients of a plane wave incident on a PBG structure. It is computationally very demanding, with simulations covering long time spans and requiring large system sizes, especially for studying defects and disordered states. The TMM code is run on a Cray T3E, as well as an older Paragon and some clusters of workstations. The larger memory and faster processors in the Cray T3E and IBM SP permit to simulate much larger systems and further the ability to study disordered systems. 2.2.2 Finite Difference Time Domain method Utilizing a Fabry Perot cavity between two photonic crystals, an exceptionally directional antenna can be fabricated. Using a dipole antenna source within the cavity, exceptionally directional beams can be obtained from the antenna, at the resonant frequency of the cavity. The beam has a half power width of less than 10° when compared to the normal. Finite-difference simulations are used to design a planar waveguide in the 3-dimensional layer-by-layer crystal with a 90° bend with 100% transmission through the bend. A similar L-shaped waveguide has also been simulated using a metallic photonic crystal with only 3 unit cells thickness needed for 85% transmission efficiency. The performance of waveguides in two-dimensional PBG structures has been simulated and the guiding efficiency is optimized as a function of the structural parameters. Such structures are important in all-optical photonic crystal devices.
21 2.3 Performance of the FDTD code The FDTD code29 uses a typical finite difference method with a 2D spatial decomposition. This requires passing data to the 4 neighboring nodes during each iteration. The communication load is fairly small compared to the computational load, so this code scales very well on even the most challenging multiprocessor machines. The scaling curves shown here are for a small cluster of 64 PCs connected only with Fast Ethernet. This demonstrates that the code scales well even for small system sizes on a cluster where the interprocessor communication rate is much lower than for traditional MPPs such as the Cray T3E and IBM SP. On these larger systems, this code scales ideally to very large numbers of nodes. 2.4 Waveguide Bends in Photonic Crystals In conventional waveguides such as fiber-optic cables, light is confined by total internal reflection (also known as index confinement, a more accurate term when the guide diameter is on the order of the wavelength) 20. One of the weaknesses of such waveguides, however, is that creating bends is difficult. Unless the radius of the bend is large compared to the wavelength, much of the light will be lost. This is a serious problem in creating integrated optical "circuits," since the space required for large-radius bends is unavailable.
Page 1 and 2: Copyright Warning & Restrictions Th
Page 3 and 4: ABSTRACT BAND -GAP CHARACTERISTICS
Page 6 and 7: APPROVAL PAGE OPTICAL PROPERTIES OF
Page 8 and 9: This Thesis is dedicated to my fami
Page 10 and 11: TABLE OF CONTENTS Chapter Page 1 IN
Page 12 and 13: TABLE OF CONTENTS (Continued) Chapt
Page 14 and 15: LIST OF FIGURES Figure Page 1.1 Str
Page 16 and 17: LIST OF FIGURES (Continued) Figure
Page 18 and 19: 2 The friction between the photonic
Page 20 and 21: 4 progress towards all-optical inte
Page 22 and 23: As can be seen in Figure 1.2, with
Page 24 and 25: 8 1.1.2 Two Dimensional Photonic Cr
Page 26 and 27: 10 future. They may provide a novel
Page 28 and 29: CHAPTER 2 BACKGROUND AND SIGNIFICAN
Page 30 and 31: 14 transfer and computing. Applicat
Page 32 and 33: 16 Chigrin and Lavrinenko in collab
Page 34 and 35: 18 component of the wave vector rem
Page 38 and 39: Figure 2-3 Structure of a 2D photon
Page 40 and 41: 24 enhancing the efficiency of lase
Page 42 and 43: 26 Figure 2-6 A perfect waveguide i
Page 44 and 45: CHAPTER 3 FUNDAMENTALS OF OPTICAL P
Page 46 and 47: 30 the square of its amplitude--i.e
Page 48 and 49: 32 3.2 Control of Properties of Mat
Page 50 and 51: 34 Figure 3.3 Spontaneous-emission
Page 52 and 53: 36 current it generated. But the fi
Page 54 and 55: 38 be used in a solar cell, generat
Page 56 and 57: 40 4.1.3 Spectral Range The spectra
Page 58 and 59: 42 beyond the scope of MultiRad. Th
Page 60 and 61: 44 c. It considers only Silicon as
Page 62 and 63: Figure 5.1 Schematic of bench top e
Page 64 and 65: 48 radiative properties of interest
Page 66 and 67: 50 The final structure of the 3D cr
Page 68 and 69: 52 The wafers are then planarized b
Page 70 and 71: 54 Fig 6.2 Block diagram showing di
Page 72 and 73: 56 decreases to a minimum in a cert
Page 74 and 75: 58 only be carried in one dimension
Page 76 and 77: Figure 6.9 Simulated transmission t
Page 78 and 79: 62 Fig 6.10 Transmission spectra fo
Page 80 and 81: 64 Figure 6.11(b) Transmission spec
Page 82 and 83: 66 As can be seen from the above ta
Page 84 and 85: Fig 6.14 Simulated reflectance spec
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Fig 6.16 Simulated transmittance sp
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72 7.2 Recommendations Much of the
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1.4 54.9 58.3 44.6 64.1 1.5 62.4 70
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11.2 60.3 64 53.8 48.2 11.3 59.7 62
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APPENDIX A2 RAW DATA This appendix
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APPENDIX A2 (CONTINUED) 80 0.232 5.
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APPENDIX A2 (CONTINUED) 8Z 0.221 2.
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BIBLIOGRAPHY [1] E. Yablonovitch, "
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96 [25] G. E. Jellison, F. A. Modin
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