在本論文中，我們採用時域行進波模型解法，來模擬脈波在多模干涉波導半導體光放大器內之動態行為。在此光放大器中，有關單一脈波之傳播、以對撞和擦撞形式入射之脈波對向傳播，另單模波導半導體光放大器內脈波對向傳播，我們均以數值方法作有系統的探討。藉由適當環形共振腔結構的設計，在光放大器內線性耦合及非線性增益飽和現象的交互作用下，脈波經連續數趟的往返碰撞後，將可被有效地壓縮。我們分別以三種脈波入射型式：相同脈波且同時、相同脈波但不同時、不同寬度之脈波等來探究脈波碰撞的特性。一般而言，脈波以對撞形式入射至多模光放大器時，可產生最大的非線性耦合效果。而特別是在單模光放大器內脈波對向傳播所沒有的，只有在多模光放大器中，此種對向傳播之脈波間有彼此牽引的力量。

The dynamics of two counter-propagating pulses in a multimode-interference-waveguide semiconductor optical amplifier (MMI SOA) is numerically studied using time-domain traveling-wave model. The single pulse propagation, two counter-propagating pulses incident on either the same lateral position or different lateral positions in an MMI SOA, and two counter-propagating pulses in a single-waveguide-mode SOA are numerical investigated. In some appropriately designed ring cavities, pulses can be repeatedly compressed after several round trips, as a result of the interplay between linear coupling and gain saturation in the MMI SOA. The characteristics of pulse collision in an MMI SOA are investigated by either launching identical pulses simultaneously, or launching identical pulses at different instants, or launching pulses of different pulse widths. It turns out that the collision of two counter-propagating pulses incident on the same lateral position in an MMI SOA provides the most nonlinear coupling effect. Especially, the amplified short pulses have an attractive force between each other that never appears in a single-waveguide-mode SOA.

Chapter 1 Introduction 1
Chapter 2 Theoretical Formulations 6
2.1 Wave equations for two counter- propagating pulses
in an MMI SOA 7
2.2 Carrier-density rate equation 11
2.3 Power splitting and recombination 15
Chapter 3 Numerical Algorithms 22
3.1 Solution methods of differential equations 22
3.2 Implementation of the time-domain traveling-wave model 25
3.2.1Solutions to wave equations 25
3.2.2 Solution to gain equation 26
Chapter 4 Simulation Results 32
4.1 Single-pulse propagation in an MMI SOA 33
4.2 Two counter-propagating pulses incident on the same
lateral position in an MMI SOA 38
4.2.1Launching identical pulses simultaneously38
4.2.2Launching identical pulses at different instants 40
4.2.3Collision of pulses of different pulse widths 41
4.3 Two counter-propagating pulses incident on different
lateral positions in an MMI SOA42
4.3.1Launching identical pulses simultaneously43
4.3.2 Launching identical pulses at different instants and
collision of pulses of different pulse widths 44
4.4 Two counter-propagating pulses in a single-waveguide-
mode SOA45
Chapter 5 Conclusions85
Appendix 87
References 91

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