Cryostat Beamsplitters
5 Conclusion and recommendations
The goal of this project was to provide a proof of principle for the change of the Quality-factor of a photonic crystal nanocavity using two coupled cavities. Several devices have been constructed and measured where this effect has indeed been observed. A change in Q-factor of up to around 50%
has been found in this way.
Apart from that the ideal structure to achieve the Q-tuning had to be found. From theoretical investigations this was found to be when the total losses and the coupling rate are both comparable.
This would be exactly at the transition regime between weak and strong coupling. The measured cavities already showed the behaviour of both these regimes showing that it would indeed be possible to reach this regime. This is also shown schematically in Figure 46 where the positions of some of the measured cavities is shown in the losses/coupling regime.
2 4 6 ideal coupling regime. These values have been estimated from the peak separation in the strong coupling or from fitting with the coupled mode theory model in the weak coupling case.
Time-resolved PL showed a decrease in decay rate of the emitter of a factor 3, when the two cavites where brought into resonance. This is to our knowledge the first time that the dynamic behaviour of a PhC cavity has been tuned statically.
Finally time-resolved measurements also showed that indeed the decaytime of an emitter inside a coupled cavity can be modified by bringing the cavity in resonance. Apart from that high-power pumping showed the fast blue-shift caused by carrier injection, which could be used in the future to get dynamic tuning of the Q-factor.
The time-resolved measurements also showed some effects which have not been fully understood yet. Further investigation would be needed to completely clarify these. One of these effects could be the increase of mode volume as a result of the coupling.
In this study, it has been shown that (This project shows) the possibility of dynamically tuning the confinement in a cavity for Cavity Quantum ElectroDynamics (CQED), thus opening up a whole new
52 range of possibilities in solid state CQED applications. Apart from that it is to our knowledge the first demonstration of static tuning of the Q-factor in photonic crystal cavities.
5.1 Recommendations
Since the results of this project open up a whole new spectrum of possibilities a lot can be done to extend the work of this project. First the dynamic behaviour has to be understood completely in order to ensure that all the effects taking place in the coupled cavities are known. This should mainly be a theoretical study.
To really use this study for CQED the effect on a single quantum dot should be studied. To do this the material should be changed to GaAs. In this way the change in Purcell factor for a single emitter could really be studied and the possibilities to use this for for example a single-photon emitter.
For most CQED applications dynamic tuning is required and the thermal tuning used in this project should thus be replaced by tuning through carrier injection. Since these carriers could especially influence the single photon behaviour special measures have to be taken to preven this as well.
53
Appendix A
This derivation is an adaption of the derivation used in [18].
The derivation of the coupled mode equations start out from the wave equation, which all modes should obey:
Now we assume two modes with electric fields according to:
The total electric field is now a superposition of the two modes:
Plugging this field into the wave equation we get:
The spatial derivatives should still obey the wave equation for the uncoupled modes with a different refractive index (ε1 and ε2 respectively): theory is a perturbation theory and will break down if these components are no longer negligible).
When the two modes couple each mode will influence the other mode, changing the propagation condition for both modes. This can be represented by using a new dielectric constant for the coupled mode εt.[42] Combining all this and plugging it into the wave equation gives:
54 Taking the scalar product with E1,coupled and E2,coupled respectively and using the orthonormality of the solutions gives:
Where Δω is ω1- ω2 and Δε1,2=εt-ε1,2. The off-diagonal matrix elements are now given by the ratio between one component and the time derivative of the other component. To find these components the equation is rewritten to:
Ignoring the phase difference since we are working in steady state, the difference in refractive index for the two modes and defining
as the normalized effective mode overlap we get:
Q.E.D.
55
Appendix B
This appendix gives an indication how the equations can be derived.
First we define the Hamiltonian for our system. This is similar to the Hamiltonian for the coupled
Plugging this into Heisenberg’s equation of motion we get:
56
57
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59
Acknowledgements
May you always know the truth And see the lights surrounding you
May you always be courageous Stand upright and be strong May you stay forever young Bob Dylan – Forever young
This project would not have been possible without the help of many people. First of all I would like to express my gratitude to my supervisor Andrea Fiore for allowing me to work on this project and to assist me in every step. His guidance and supervision made me learn a lot more about science and about working on a scientific project, lessons which I will carry with me for the rest of my life.
Secondly I would like to thank Chaoyuan Jin. With his guidance and insight I was always able to take the right steps in the project. He introduced me to many subjects in physics, even if they were only closely related to the subject. Apart from that he introduced me to the Chinese language and culture. He also put countless effort in fabrication of the samples, enabling me to do my experiments. This thesis would not have existed without all the effort he put in.
For the experimental part I would like to express my sincere gratitude to “Master” Thang Hoang, who never seized to help me with the experimental setup and who helped me a lot in using and adapting it. Even after some mistakes made from my side, which he would always have to fix. For experimental part I would also like to thank Matthias Skacel and Shartoon Fattahpoor, who also helped me considerably when I would be performing measurements which were not that standard.
Het gaat jullie goed jongens!
For the help in gaining fundamental understanding of the subject and his general guidance over the project I would sincerely like to thank Robert Johne. He often felt like a third supervisor, guiding and advising me with every step I would take. I would also like to thank Leonardo Midolo in this sense, for his help with the simulations and in using Matlab and Comsol.
The technicians Jos van Ruijven, Martine van Vlokhoven and helped me considerably with preparing a vessel to fill the cryostat with liquid nitrogen. Without their efforts the time-resolved experiments would not have been possible. I would also like to thank Rob van der Heijden, Mehmet Dündar and Bowen Wang for their assist in useful discussions and for letting us use their equipment and their SNOM setup.
Finally I would like to thank all the other people in PSN, especially Döndü, Francesca, Francesco, Giulia, Saeedah, Tian, Yoon, and Zili for the great times shared and for always be ready to help me.
This project would not have been as enjoyable without the help of you all. This project did not only teach me a lot about science, but also about myself and it turned me from “Baby Milo” to the guy I am now. And although this was not always an easy process, with people like you to assist me with every step it was never a hard journey to follow.