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

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26 Figure 2-6 A perfect waveguide intersection terms of coupling through a resonant cavity at the center. If the resonant cavity can be prevented by symmetry from decaying into the crossing waveguide, then the situation reduces to one-dimensional resonant tunneling, and crosstalk will be prohibited. This situation is achieved by requiring simple symmetries in the waveguide and resonant modes, as shown in fig.2.6. Here, the solid-line waveguide modes only couple with the solid-line resonant cavity modes, and similarly for the dashed-line modes. Essentially, there are three requirements that must be met: • The waveguides must have mirror symmetry about their axis, and they must be single-mode in the frequency range of interest. (This mode will be either even or odd.) • The resonant cavity in the center of the intersection, which governs coupling between the waveguides, must respect the mirror planes of both waveguides. • In the frequency range of interest, the resonant modes must be odd with respect to one waveguide and even with respect to the other.
27 All three of these conditions are easily achieved. (In particular, the third condition is automatic for degenerate modes in intersections with sufficient symmetry [the symmetry group of the square].) The resulting transmission profile will be the typical spectrum of resonant tunneling--a Lorentzian (bell-shaped) curve centered on the resonance frequency. The width of the resonance is inversely proportional to the quality factor Q of the resonant mode (Q is proportional to the decay lifetime).
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 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 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
Page 86 and 87: Fig 6.16 Simulated transmittance sp
Page 88 and 89: 72 7.2 Recommendations Much of the
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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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