Edwin Jan Klein - Universiteit Twente

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Chapter 2 index. Although this can be a time consuming process when many resonators need to be trimmed it can be a valuable tool in the “fine tuning” process of a resonator. This can be especially important in passive micro-resonators that have no other means of tuning or in very small resonators where even small variations in the index can cause a large deviation of the resonance frequencies as will be shown later in Equation (2.44). 2.8.2 Wavelength tuning range All of the effects mentioned in the previous paragraph create a change in the index in one or all of the materials that make up a waveguide. Together, these changes constitute a change in the effective refractive index Neff of the waveguide by ∆Neff. Using Equation (2.11) this can be translated to a change in group index ∆ng. An expression that determines the shift in resonance wavelength ∆λs as a function of this parameter can be found by first combining the resonance condition (2.1) and the expression of the roundtrip phase (2.10) into: ( 2π ) 2 2π ϕ r = m ⋅ 2π = ⋅ R ⋅ ng m = ⋅ R ⋅ ng λ0 λ0 34 , m ∈ Ν (2.39) This equation can then be rearranged to provide the shift in the resonance wavelength ∆λs as a function of the change in the group index ∆ng for a certain fringe order m: 2π ⋅ R ⋅ ( n g m + ∆ng ) = λ + ∆λ Substituting (2.39) for a given m back into in Equation (2.40) then gives: λ0. ∆n ∆λ s = n g g 0 s (2.40) (2.41) This equation shows that the resonance shift is only proportional to the change in group index of the resonator waveguide and is independent of its radius. It is therefore not possible to change the radius of the resonator in order to get a larger tuning range of the resonant wavelength. A larger radius will at most enlarge the relative tuning range ∆λmax/FSR. Ultimately the maximum tuning range is limited by the maximum of ∆ng which will be different depending on what tuning method is used. This is not a problem in most thermo-optically tuned devices where, depending on the materials and geometry used, the tuning range might be as large as 40 nm at a wavelength of 1550 nm. In fact, thermally tuned resonators with a heater on top of the resonators can actually benefit from a smaller radius as the power consumption in the proportionally smaller heater drops. In electro-optically or opto-optically tuned devices, however, the effects are generally very small. The tuning range is therefore generally limited to values well below 1 nm. Although this excludes these devices from applications where large tuning ranges of several nm are required, such as for instance add-drop multiplexers and routers the range may still be large enough for use in resonator based modulators.
35 The Micro-Resonator Whether or not the tuning range is large enough can be determined by looking at the modulation depth that is possible for a given maximum ∆ng. The modulation depth ∆Mod (in dB) is the difference between the power dropped by a resonator that is in full resonance at a certain wavelength λ0 and the power dropped at that same wavelength when the resonator is tuned by ∆ng, as illustrated in Figure 2.20. P Drop /P In (dB) 0 -5 -10 -15 The modulation depth is given by: ⎛ ⎜ P ∆Mod = 10log ⎜ ⎝ Pλ 0 , ng ng+∆ng Figure 2.20. Modulation depth and resonance shift. λ 0 ∆n g ⎞ ⎟ ⎛ = 10log ⎜ ⎜1+ F ⎟ ⎠ ⎝ C 2 2π ⎞ sin ( π ⋅ R ⋅ ∆n ) ⎟ g λ0 ⎠ (2.42) Where Pλ0 is the maximum power at resonance wavelength λ0 and Pλ0,∆ng is the power at that wavelength when ng changes by ∆ng. This equation can be rewritten to give the change in group index that is required to achieve a certain modulation depth: ∆ ∆Mod ⎛ ∆Mod ⎞ ⎜ ⎛ ⎞ ⎜ 10 F ⎟ 2 = λ ⎟ 0 ⋅ arcsin ⋅ R ⎜ ⎜ 10 −1 ⎟ / / 2π (∆Mod
Page 1 and 2: DENSELY INTEGRATED MICRORING- RESON
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Page 17 and 18: Chapter 1 Introduction The devices
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Page 25: 9 Introduction these basic paramete
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Page 32 and 33: Chapter 2 ∆ = ⎛ β r − β g
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Page 36 and 37: Chapter 2 FC 4µ 1µ 2 ⋅ χr = 2
Page 38 and 39: Chapter 2 P Through /P In (dB) 0 -1
Page 40 and 41: Chapter 2 The figure shows that it
Page 42 and 43: Chapter 2 In − jϕr1 2 Figure 2.1
Page 44 and 45: Chapter 2 differences between the f
Page 46 and 47: Chapter 2 M = ⋅ FSR = N ⋅ FSR F
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Page 56 and 57: Chapter 3 3.1 Introduction The most
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Page 86 and 87: Chapter 4 4.1 Introduction As was s
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Page 90 and 91: Chapter 4 Under the condition that
Page 92 and 93: Chapter 4 Figure 4.4. Screenshot of
Page 94 and 95: Chapter 4 The equations required to
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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 -
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Chapter 4 Figure 4.27a. OADM with r
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Chapter 4 will propagate through th
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Chapter 4 As demonstrated by these
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Chapter 4 What is more interesting
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Chapter 4 method it does allow time
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Chapter 4 complex than the interact
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Chapter 5 5.1 Introduction The mate
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Chapter 5 wafer is used (step 1). T
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Chapter 5 range of 0.9 to 1.1 µm.
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Chapter 5 The process flow with the
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Chapter 5 5.3.3 Mask layout The big
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Chapter 5 5.4. Fabrication and mask
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Chapter 5 1. Definition of the vert
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Chapter 5 5.4.2 Fabrication The fab
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Chapter 5 Figure 5.21. Process flow
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Chapter 5 removed using lift-off of
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Chapter 6 6.1 Introduction About ha
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Chapter 6 In early, comparatively s
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Chapter 6 that the TEOS has a very
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Chapter 6 The most important aspect
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Chapter 6 6.2.3 Chromium heater des
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Chapter 6 Therefore, even if the si
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Chapter 6 Next, the heater was heat
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Chapter 6 6.3 Characterization of s
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Chapter 6 polarization maintaining
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Chapter 6 the resonators in this gr
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Chapter 6 Although the fitted coupl
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Chapter 6 a cladding thickness of 3
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Chapter 6 6.4 A wavelength selectiv
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Chapter 6 A possible explanation fo
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Chapter 7 Densely integrated device
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Densely integrated devices for WDM-
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7.2.2 Spectral measurements Densely
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Power Densely integrated devices fo
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7.3.4 Characterization Densely inte
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Figure 7.31a. Eye pattern of the re
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Chapter 8 8.1 Introduction In most
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Chapter 8 amount of power will be d
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Chapter 8 Another problem that may
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Chapter 8 halves that are each comp
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Chapter 9 Discussion and Conclusion
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Appendix A. Mason’s rule Several
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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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