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

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18 component of the wave vector remains constant throughout the crystal. The tangential component of the wave vector lies between zero for normal incidence and (n w / c) for grazing incidence. Therefore, only values of the tangential component of the wave vector, which are inside the range, need to be considered. For this limited range (the shaded area on the wave vector axis), there is the frequency region (the shaded area on the frequency axis) which is completely inside the forbidden gaps of the photonic crystal both for TE and TM polarization. No propagating mode is allowed in the photonic crystal for any propagating mode in the ambient medium within this frequency region. The total omnidirectional reflection arises for both TE and TM polarization^18. Though conceptually simple, photonic crystals have been difficult to fabricate for operation in the visible spectrum because the feature sizes involved have to be of the order of the wavelengths of visible light if they are to work. Though IC microlithography can now reach the required resolution, the crystals produced are limited in depth, which restricts their effectiveness. The new technique does not have those restrictions. Instead of building up a series of patterns on a substrate, the entire three-dimensional crystal is recorded at once by causing an interference of four coherent laser beams. By choosing the appropriate direction, intensity and polarization relationships among them, the structure of the resulting interference pattern can be manipulated as required. The key to this new generation of optoelectronic devices lies in the design of the photonic crystal materials, which may be used to control the light - or indeed any electromagnetic radiation. These are composites, made of two materials with different refractive indices, organized into a periodic structure in three dimensions. If the periodicity is comparable in its length scale with the wavelength of light, say around 0.5 micrometers, then there are
19 'band gaps', i.e. frequency bands in which propagation is not allowed, and the photonic crystal is a perfect reflector. The real technological interest lies in the properties of defects in the crystal, which create localized electromagnetic modes at certain defined frequencies in the band gap. These defect modes can be controlled to form a very efficient laser, a photonic switch or a waveguide. Such waveguides could incorporate very sharp bends on the micron scale thereby allowing the construction of microscopic photonic integrated circuits. 2.2 Simulation methods of Photonic Crystals A joint effort between the Condensed Matter Physics group, the Microelectronics Research Center, and the Department of Materials Science and Engineering at Oxford has been investigating photonic crystals and their properties. These materials may have photonic band gaps (PBG) in the microwave, millimeter, infrared, or optical wavelengths depending on their physical dimensions. The fabrication of photonic crystals with gaps in the optical wavelengths is being pursued. Either colloidal systems or advanced silicon processing techniques are used (silicon processing has been performed by Lin's group at Sandia Labs). Secondly, in the microwave and millimeter wavelengths (where photonic crystals already exist), antennas made from photonic crystals ^25, waveguides in photonic crystals, and filters using photonic crystals are being fabricated. The theoretical investigations have led to experimental fabrication and testing of new structures, which in turn drive further advances in their design.
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 36 and 37: 20 2.2.1 Transfer Matrix Method The
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
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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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