A Wavelength Converter Integrated with a Discretely Tunable Laser ...

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26 3. Semiconductor optical amplifier operation and device characterization 3.3.1 Laser condition Laser action occurs if the round trip gain in the laser cavity compensates for the round trip loss. As soon as the gain becomes larger than the loss, for instance due to an increase in the injection current, then the optical power in the cavity increases until the SOA gain saturates enough to put the laser in a steady state condition again, i.e. with a net round trip gain of unity. In the following, an expression for the steady state operation of the laser (the laser condition) in the extended cavity laser (ECL) is presented. The gain in a SOA is provided by the active layer, which has a material gain (cm ). Only a fraction of the optical power of the waveguide mode in the SOA propagates in the active layer itself. This fraction is represented by the confinement factor . The propagation loss of the mode in the active layer and the cladding layers of the SOA is represented by ¡ . Combining the loss and the gain, the net modal gain coefficient can be expressed as Modal gain represents the relative increase of the optical power per unit length of the SOA. Hence ¡ ¤ (3.10) where is the optical power at position along the guide and were we assume that is constant along the amplifier. After integration of 3.11 and by defining the single pass device gain of a SOA of length as (3.11) , we find (3.12) The round trip gain can be found using Eq. 3.12 and including the loss at the facets (mirror loss) with a reflectivity of and ¦ , respectively: ¦ ¦ (3.13) In order to find the round trip gain of the ECL, this equation must be extended with the loss in the passive waveguide sections, which have a length of . In ¡ addition the butt-joint loss must be taken into account, and the round trip gain becomes ¦ ¦ ¦ (3.14) The condition for laser action is that the round trip gain of the mode gain compensates the loss, ¤ thus . Substituting this in Eq. 3.14 and taking the natural logarithm and using Eq. 3.10, we find the laser condition for the modal gain in the ECL The device gain can be expressed in dB instead of ¡ ¢ using £¤¦¥¨§©¡©
3.3 Extended Cavity Lasers and extended waveguide SOAs 27 ¡ ¤ ¡ ¤ ¦ ¡ (3.15) If we define the total distributed mirror ¤ ¦ (§ loss, as cm in a 500 long laser) and, similar, the distributed butt-joint loss for all butt-joints as , then the laser condition in Eq. 3.15 can be expressed as ¤ ¡ ¡ ¡ ¡ ¡ (3.16) As can be seen from this equation, the modal gain in the lasing ECL scales linearly with . ¤ Eq. 3.16 is only useful in SOA characterization if is expressed in a measurable parameter, such as the injection current density . From [54], we find that above threshold the relation between and in bulk and quantum well lasers can be to fitted (3.17) ¡ ), and denotes the differential gain. In general, lasers with quantum well and lasers with strained active bulk layers tend to fit better to this relation than unstrained bulk lasers. The latter tend to show a more linear behavior. Nevertheless, our lasers fit very good to Eq. 3.17 as is shown in Sec. 3.3.2. The logarithm of the threshold current density , i.e. the current density at which laser action starts, scales ¤ linearly with . Indeed, if we substitute Eq. 3.17 at threshold, where denotes the current density at ( transparency , into the expression for the condition for laser action, Eq.3.16, then ¤ ¡ ¡ ¡ ¡ ¡ This relation can be used to derive an expression for the length of the active section at which the threshold current is minimal. We have to solve (3.18) where is the width of the active layer. Taking the exponent of Eq.3.18 and substituting it into Eq. 3.19, we find the laser length with the minimum threshold current: (3.19) ¡ ¡ ¡ which is the slope in Eq.3.18. In practice, is determined by measuring the light power versus current characteristic (LI-curve) of the laser. The LI-curves are treated in the next section. A similar relation can be found for the gain vs. the carrier density. (3.20)
Page 1 and 2: A Wavelength Converter Integrated w
Page 3 and 4: iii
Page 5 and 6: Contents v 4.3 Waveguide components
Page 7 and 8: Chapter 1 Introduction 1.1 Optical
Page 9 and 10: 1.2 Exploiting optical fiber capaci
Page 11 and 12: 1.3 Wavelength conversion in WDM ne
Page 13 and 14: Chapter 2 Wavelength converter over
Page 15 and 16: 2.2 Optical gating 9 λcontrol λpr
Page 17 and 18: 2.2 Optical gating 11 powers (in th
Page 19 and 20: 2.2 Optical gating 13 Michelson Int
Page 21 and 22: 2.3 Coherent wave mixing (FWM, DFG)
Page 23 and 24: 2.5 Summary 17 2.5 Summary The main
Page 25 and 26: Chapter 3 Semiconductor optical amp
Page 27 and 28: 3.2 Amplification in SOAs 21 Table
Page 29 and 30: 3.3 Extended Cavity Lasers and exte
Page 31: 3.3 Extended Cavity Lasers and exte
Page 45 and 46: Chapter 4 Integration of waveguide
Page 47 and 48: 4.3 Waveguide components 41 Table 4
Page 49 and 50: 4.3 Waveguide components 43 4.3.2 P
Page 51 and 52: 4.4 Integration trade-offs 45 the a
Page 53 and 54: 4.4 Integration trade-offs 47 The c
Page 55 and 56: 4.4 Integration trade-offs 49 speed
Page 57 and 58: 4.4 Integration trade-offs 51 resis
Page 59 and 60: 4.4 Integration trade-offs 53 activ
Page 61 and 62: 4.4 Integration trade-offs 55 a) 60
Page 63 and 64: 4.4 Integration trade-offs 57 due t
Page 65 and 66: 4.4 Integration trade-offs 59 The
Page 67 and 68: 4.5 Conclusions 61 4.5 Conclusions
Page 69 and 70: Chapter 5 Technology 5.1 Introducti
Page 71 and 72: 5.2 Epitaxy 65 of the stack Q(1.25)
Page 73 and 74: 5.3 Waveguide processing 67 InP Q(1
Page 75 and 76: 5.3 Waveguide processing 69 h l h S
Page 77 and 78: 5.4 Contact openings and metalizati
Page 79 and 80: 5.4 Contact openings and metalizati
Page 81 and 82: Chapter 6 MWL with absolute wavelen
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6.3 MWL with absolute wavelength co
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6.3 MWL with absolute wavelength co
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6.5 Measurements 81 facet M 1 O4 O3
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6.5 Measurements 83 127 mA, which e
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Chapter 7 MZI wavelength converter
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7.2 Operating principle of the MZI
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7.3 Converter performance 89 Note t
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7.3 Converter performance 91 Chirp
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7.4 Wavelength converter design 93
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7.5 Fabrication 95 1 2 3 4 5 6 7 8
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7.6 Measurements 97 Power out [dBm]
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7.6 Measurements 99 mental and firs
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7.6 Measurements 101 fiber-to-fiber
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7.6 Measurements 103 P out [dBm] P
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7.6 Measurements 105 Power [dBm] -1
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7.6 Measurements 107 Substituting E
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7.6 Measurements 109 7.6.4 BER meas
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7.7 Conclusion 111 output extinctio
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Chapter 8 Wavelength Converter inte
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8.2 Design 115 MWL1 M1 O1 O2 O3 O4
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8.4 Static measurements 117 Control
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8.4 Static measurements 119 The LI-
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8.5 Dynamic operation 121 BER 2.5 G
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8.6 Discussion 123 Wavelength [μm]
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8.6 Discussion 125 lower then the l
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8.7 Conclusions 127 8.7 Conclusions
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Appendix A Mask plates The mask pla
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References [1] H. Takara, E. Yamada
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References 133 [24] R.G. Broeke, J.
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References 135 [51] C.Q. Xu, K. Shi
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References 137 [88] J.J.M. Binsma,
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Summary A wavelength converter inte
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Samenvatting Een golflengte omzette
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Dankwoord Een dankwoord hoort vol m
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echoduo een glas komen claimen, en
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List of Abbreviations AOWC All Opti
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Curriculum Vitae Ronald Broeke was
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List of publications 1. R.G. Broeke
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18. R.G. Broeke A Chirped phased-ar
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