Edwin Jan Klein - Universiteit Twente

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Chapter 3 3.2.3 Filter bandwidth In Chapter 2.5 it was already shown that there is a direct tradeoff between the resonator filter rejection ratio and its bandwidth. In Equation (2.31) the bandwidth was already expressed in terms of the free spectral range and SRR but it does not provide a clear relation to the cavity losses and coupling coefficients required. This is therefore done in Equation (3.4) which can be found by combining (2.22) and (2.30): ∆ λ FWHM 2 FSR( 1− µ 1µ 2χ r ) λ0 ( 1− µ 1µ 2χ r ) ≈ = 2 π µ µ χ 2n . R. π µ µ χ 1 2 r 44 g 1 2 r (3.4) Figure 3.6 shows the filter bandwidth of a resonator with ng=1.5 at λ0=1550 nm for a number of cavity losses. FWHM (GHz) 1000 100 10 1 0.03 dB 0.16 dB 0.62 dB 0.1 0.0 0.2 0.4 0.6 0.8 Field coupling coefficient Figure 3.6. Filter bandwidth vs. coupling coefficient for three different roundtrip losses. For low coupling coefficients the cavity roundtrip loss is clearly an important parameter to be considered as it affects the filter bandwidth quite significantly. The increase of bandwidth for an increase in losses is, however, due to an overall reduction of resonator performance, including the finesse and the dropped power. For moderate to large coupling (>0.4) the effect of the cavity losses is relatively minor and the bandwidth is mainly determined by the coupling coefficients. In 3.1.1 and 3.1.2 it was already stated that for practical uses in telecom the coupling coefficients should not be chosen too high or too low. By choosing a particular filter bandwidth this range can be narrowed down even further. A bandwidth of 10 GHz (≈0.08 nm) will for instance require the field coupling κ to be >0.2. For a bandwidth of 40 GHz the coupling needs to be increased even further to >0.4 (at a roundtrip loss of 0.03 dB). Another way to increase the filter bandwidth, as follows from Equation (3.4), is to decrease the radius of the resonator. The added benefit of this is that it will keep some of the other resonator parameters, such as for instance the SRR, more or less unchanged whereas these would be greatly affected by a change of the coupling. In many instances, however, a reduction in radius will not be possible as was explained in Chapter 2.6.
3.2.4 Channel Crosstalk 45 Design An ideal optical telecom system provides a large bandwidth as well as a high filter rejection ratio. The high rejection ratio is required in order to keep the channel crosstalk as low as possible. The adjacent channel crosstalk (CT) is the measure by which an optical signal in one channel can interfere with a signal in an adjacent channel. This is illustrated in Figure 3.7. In which the vertical lines show the locations of different channels on, in this instance, the ITU grid [103]. P Drop /P In (dB) 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 1547 1548 1549 1550 1551 1552 1553 1554 Wavelength (nm) Figure 3.7. Definition of the adjacent channel crosstalk. The adjacent channel crosstalk is here defined as the relative power fraction of a signal that is present on a channel adjacent to the channel λc on which this signal is transmitted. Following the derivation given in Appendix B the crosstalk can be expressed in terms of the channel separation ∆λcs, the Finesse and the Free Spectral Range: CT ≡ P ( = + ∆ ) 2 drop λ λc λcs ⎛ sin ( π. ∆λ / FSR) ⎞ 10. log( = −10log ⎜ ⎜1+ ⎟ 2 Pdrop ( λ = λc ) ⎝ sin ( π / 2F ) ⎠ (3.5) Figures 3.8a and 3.8b respectively show the crosstalk of a single resonator at an ITU channel spacing of 50 GHz and 100 GHz (∆λcs≈0.8 nm) for a resonator with R=50 µm and ng=1.5 at λ0=1550 nm. These figures show that the crosstalk can potentially be a major problem when a micro-resonator is used as a filter in applications that use these channel spacings. Although very low crosstalk values of
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DENSELY INTEGRATED MICRORING- RESON
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DENSELY INTEGRATED MICRORING- RESON
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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 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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