Edwin Jan Klein - Universiteit Twente

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Chapter 6 the resonators in this group is identical and it becomes possible to not only determine the resonator parameters κ1, κ2 and αdB for a given response but also its alignment. Normalized drop response (dB) Normalized through response (dB) 0 -2 -4 -6 -8 -10 -12 -14 -16 0 -2 -4 -6 -8 -10 -12 -14 1542 1544 1546 1548 1550 1552 1554 1556 1558 Wavelength (nm) s = 0 s = 0.4 s = 0.8 s = 1.2 s = 1.6 148 s = 0 s = 0.4 s = 0.8 s = 1.2 s = 1.6 -16 1542 1544 1546 1548 1550 1552 1554 1556 1558 Wavelength (nm) Figure 6.19. Through (bottom) and drop (top) response as a function of the port waveguide offset s for a Si3N4 microring resonator with a radius of 25 µm. Coupling coefficient κ 2 0.8 0.6 0.4 0.2 0.0 2 κ1 2 κ2 @ 100 dB/cm 2 κ2 @ 140 dB/cm 2 κ2 @ 185 dB/cm 0.0 0.4 0.8 1.2 1.6 2.0 Heater +heater pads Figure 6.20. Mask layout of the group of resonators that was measured. Offset s (µm) a) b) Figure 6.21. Fitted coupling coefficients κ1 and κ2 (κ1≠κ2) as a function of the offset s of the fabricated resonator (that has a misalignment) a). In b) the coupling coefficients of a simulated resonator have been calculated as a function of the offset s for a resonator that is perfectly aligned (κ1=κ2). The arrows indicate offset positions that are roughly equivalent in the fabricated and simulated resonators.
149 Microring-resonator building blocks In Figure 6.21a the values of the coupling coefficients κ1 and κ2 are given as a function of the port waveguide offset s. To obtain these values the DropZone tool was used to solve Equations 4.22 and 4.23. As was previously discussed in Chapter 4.4, only κ1 can be determined directly. In order to determine the other coupling constant, κ2, an estimate of the losses has to be made. Using the Selene mode solver these losses were determined to be 200 dB/cm. However, when fitting the responses for the offset of 1.6 µm, the maximum limit for the loss is 185 dB/cm because κ2 then becomes zero. Therefore the actual losses have to be at least below 185 dB/cm but, considering the Selene simulation results, probably not far below that value. Figure 6.21a shows the fitted values of κ2 for the maximum loss of 185 dB/cm as well as for two lower bend losses of 140 and 100 dB/cm. As can be seen in the figure, there is a spread of 0.3 in the values of κ2 at s=1.6 µm. However, at s=0 µm there is a convergence for all bend losses to a value of ≈0.7, making the uncertainty in the fitted value κ2 less for this offset. Interestingly, the maximum values of κ1 and κ2 are not equal, as might be expected based on resonator symmetry, but show values of 0.5 and 0.7 respectively. In fact, the maximum of κ2 is likely to be even higher for a negative offset but no resonators with that offset were available. The difference can be explained by examining the CMT simulations of this resonator shown Figure 6.21b where the coupling coefficient is plotted as a function of the offset s and the thickness of the separation layer hsep. These simulations show that when to coupling between the resonator and port waveguides is very high, which in these simulations occurs for h=0.8 µm, there can be more than one maximum. The reason for this is that within a certain range of offsets the coupling length is so long that part of the power is coupled back into the port waveguide. Although this effect is seen only for a thickness of 0.8 µm in the simulations and the thickness of the separation layer in the fabricated device was 1.0 µm, neither the device not the simulations are perfect. For the fabricated device there will always be a variation in thickness and, since many approximations are used in the CMT simulation tool, coupling coefficients predicted by the simulation also been seen as an indication rather than solid fact. Keeping this in mind it is then possible to estimate the offset of the resonator from the measurement data. Assuming that the maximum in the curve of κ2 at s=0 µm corresponds to the simulated offset of 2 µm and that the maximum of κ1 at s=0.8 µm corresponds to the simulated offset of -3 µm as indicated by the arrows, then the misalignment can be estimated to be ≈2.1 µm towards the second coupler. To give a better idea of this misalignment it is illustrated by the drawing in Figure 6.22. For reference the arrows indicate the positive axis of all parameters. Figure 6.22. Exaggerated drawing of a resonator with a misalignment of 2.1 and an offset s=0 for both port waveguides.
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DENSELY INTEGRATED MICRORING- RESON
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DENSELY INTEGRATED MICRORING- RESON
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To my parents…
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esonators is limited by the spacing
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iv Samenvatting Dit proefschrift be
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schakelaar “aan” is, dan is de
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3.6.2 Overlap loss reduction.......
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Chapter 1 Introduction The devices
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1.2 Broadband to the home 3 Introdu
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1.3 Bringing Fiber to the Home 5 In
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Figure 1.5. The technological scope
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9 Introduction these basic paramete
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Chapter 2 2.1 Introduction Integrat
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Chapter 2 light Icav2 in the cavity
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Chapter 2 ∆ = ⎛ β r − β g
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Chapter 2 2.3.3 Combined model The
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Chapter 2 FC 4µ 1µ 2 ⋅ χr = 2
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Chapter 2 P Through /P In (dB) 0 -1
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Chapter 2 The figure shows that it
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Chapter 2 In − jϕr1 2 Figure 2.1
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Chapter 2 differences between the f
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Chapter 2 M = ⋅ FSR = N ⋅ FSR F
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Chapter 2 the heat will therefore f
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Chapter 2 index. Although this can
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Chapter 2 resonators for instance h
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Chapter 2 a rather complex MEMS bas
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Chapter 3 3.1 Introduction The most
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Chapter 3 3.2.1 Drop port on-resona
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Chapter 3 3.2.3 Filter bandwidth In
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Chapter 3 (resulting in a higher ba
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Chapter 3 Figure 3.11. Residual cha
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Chapter 3 3.3 Geometrical design ch
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Chapter 3 resonator and the port wa
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Chapter 3 Another important fact wh
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Chapter 3 The flowchart of the desi
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Chapter 3 While the resonator in th
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Chapter 3 3.6.1 Port waveguide and
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Chapter 3 overlap losses are only 0
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Chapter 3 3.7 Component design cons
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Chapter 3 By maximizing the power t
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Chapter 3 important, due to the fac
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Chapter 4 4.1 Introduction As was s
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Chapter 4 4.2.1 Transient response
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Chapter 4 Under the condition that
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Chapter 4 Figure 4.4. Screenshot of
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Chapter 4 The equations required to
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Chapter 4 using an approach based o
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Chapter 4 4.5.1 Architecture The Au
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Chapter 4 4.5.2 Simulation method A
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Chapter 4 Figure 4.9. A Primitive w
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Chapter 4 Listing 4.3. Pseudo code
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Chapter 4 Listing 4.4. Pseudo code
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Chapter 4 simulated output spectra
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Chapter 4 Figure 4.21. The reflecto
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Chapter 4 P Drop /P In (dB) 0 -10 -
Page 114 and 115: Chapter 4 Figure 4.27a. OADM with r
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Page 118 and 119: Chapter 4 As demonstrated by these
Page 120 and 121: Chapter 4 What is more interesting
Page 122 and 123: Chapter 4 method it does allow time
Page 124 and 125: Chapter 4 complex than the interact
Page 126 and 127: Chapter 5 5.1 Introduction The mate
Page 128 and 129: Chapter 5 wafer is used (step 1). T
Page 130 and 131: Chapter 5 range of 0.9 to 1.1 µm.
Page 132 and 133: Chapter 5 The process flow with the
Page 134 and 135: Chapter 5 5.3.3 Mask layout The big
Page 136 and 137: Chapter 5 5.4. Fabrication and mask
Page 138 and 139: Chapter 5 1. Definition of the vert
Page 140 and 141: Chapter 5 5.4.2 Fabrication The fab
Page 142 and 143: Chapter 5 Figure 5.21. Process flow
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Page 148 and 149: Chapter 6 In early, comparatively s
Page 150 and 151: Chapter 6 that the TEOS has a very
Page 152 and 153: Chapter 6 The most important aspect
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Page 158 and 159: Chapter 6 Next, the heater was heat
Page 160 and 161: Chapter 6 6.3 Characterization of s
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Page 175 and 176: Chapter 7 Densely integrated device
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Page 191 and 192: 7.3.4 Characterization Densely inte
Page 195 and 196: Figure 7.31a. Eye pattern of the re
Page 197: Densely integrated devices for WDM-
Page 200 and 201: Chapter 8 8.1 Introduction In most
Page 202 and 203: Chapter 8 amount of power will be d
Page 204 and 205: Chapter 8 Another problem that may
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Page 209 and 210: Chapter 9 Discussion and Conclusion
Page 211 and 212: Appendix A. Mason’s rule Several
Page 213 and 214: Appendix B. Crosstalk Derivation Th
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List of Acronyms ADSL - Asymmetric
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List of Symbols Q - Quality Factor
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Bibliography [1] Dan Schiller, “E
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Regions,” IEEE Photonics Technolo
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[66] B. E. Little, S. T. Chu, J. V.
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[97] H. Haeiwa, T. Naganawa and Y.
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[135] A. Driessen, D. H. Geuzebroek
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[165] T. Barwicz, M. R. Watts, M. A
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Publication List Patents (pending)
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R. Dekker, L.T.H.Hilderink, M.B.J.
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Networks (BB Photonics),” Interna
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Dankwoord/Acknowledgements Zo, dit
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Edwin Jan Klein - Universiteit Twente

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