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

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As can be seen in Figure 1.2, with increase in crystal thickness, the transmission response for some frequencies rapidly approaches zero. However, at the same time, the widths of these troughs decrease. One-dimensional systems in photonic crystals are actually tailor made to provide either reflection or anti-reflection coatings. This is done by careful choice of the materials used, their thickness and the number of layers. One of the other tools frequently used with the photonic band gap (PBG) subject area is that of the band structure diagram. In order to introduce this concept, the best example would be one dimension. One of the most important relations in electromagnetics, especially in reflection to PBG (Photonic Band Gap) apart from Maxwell's Equations is the dispersion relation: (ω=angular frequency, n=refractive index, c=speed of light in vacuum, k=wave vector). To start with, consider a 'piece' or 'block' of air. We do not have to worry about waveguides or bits of metal or PBG crystal for the moment. For the sake of comparison and for comprehension, what happens can be seen if a block of dielectric material and not air is present. What modes are present then? From the two diagrams in Fig. 1.3, it can see that there is a diamond shape that repeats. The number of diamonds is different between the air and dielectric, because in free space dispersion relation wn=ck, if n is changed, then the gradient of the line changes. Since a block of air has been chosen with an artificial periodicity, the expected straight line of gradient gets folded up. When it reaches the side of the plot, it continues with the same gradient by folding and this explains the diamond shape.
7 Figure 1.3 Air and Dielectric Block Band Diagrams¹² The Bragg stack¹² mentioned above is a mixture of two materials, and if the ratios are right, then useful gaps in the band diagram, which are the called "Photonic Band Gaps" are created. It can be concluded from the band diagrams and transmission plots that, if materials, along with their associated dielectric constants and their thickness are chosen correctly, useful PGBs can be obtained. One dimensional photonic band gap structures such as 'Bragg Stacks' are used within laser cavities and for optical coatings. Generally, a one dimensional gap is only of use if the application is going to be restrained to a specific, or small range of angles for a source embedded within the dielectric medium.
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 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 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
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56 decreases to a minimum in a cert
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58 only be carried in one dimension
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Figure 6.9 Simulated transmission t
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62 Fig 6.10 Transmission spectra fo
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64 Figure 6.11(b) Transmission spec
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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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