One beam experiments

Next the experiments described above were also performed on the combined structure described in section 1.4.7. In these structures coupling to the FP modes was expected. For the GaAs sample the lattice constant for the FP cavity was 1.1∙a0. This caused the FP modes to have a big spectral difference with the Noda mode. In the InGaAsP samples both the lattice constant for the FP cavity and the Noda cavity were the same (1.03∙a0), causing the wavelength of the Noda mode to be close to that of the slow-light modes of the FP cavity.

4.2.1 GaAs

The change in Q obtained by changing the pump power of the Noda cavity in the vicinity of an FP cavity is plotted in in Q-factor.

Figure 31. Here the Q-factor as a function of resonant wavelength of the Noda is plotted for both increasing and decreasing pump powers. A periodic behaviour is visible in the Q-factor as would be expected from the coupling with the equidistant FP cavities. Apart from that a linear decrease can be seen which is thought to be caused by heating effects.

However, the spacing between the dips in Q-factor (which should correspond to the spacing between FP modes) is only 0.6nm. This is much smaller than the spacing between FP modes away from the slow light regime. Apart from that the Q only changes by 8%, which is also a much smaller

40 change in Q-factor than expected. Nevertheless, since this effect has never been observed in single Noda cavities it is believed to be a coupling effect.

The apparent discrepancy is thought to be caused because the Noda cavity is not coupling to the even modes of the FP, but to the odd modes. Since the Noda mode has two different polarizations at the same energy it could in principle couple to both modes, but the coupling to the odd mode will be much less efficient due to the spatial distribution of this mode. This could explain the smaller change in Q-factor.

Figure 31: Plot of the Q-factor vs. resonant wavelength of the Noda cavity near an FP cavity in GaAs. The black dots represent points measured when going from low to high power, while the red points are for points measured while decreasing the power. This was done to check for hysteresis effects and to have a reproducibility measurement at the same time. (a) and (b) are both similar measurements performed on different GaAs samples, (a) with a barrier of 10 periods between the Noda cavity and the FP cavity, while (b) was measured on a sample with a barrier of 8 periods. The barrier at the end of the FP cavity was 20 periods in both cases.

When the spectrum of the FP cavity for this structure is plotted (Figure 32) it can be seen that the even slow light FP modes have indeed a much higher wavelength than the Noda mode. However the slow light odd mode is still at higher energies than the Noda mode. From Figure 9 it can be seen that the odd mode has two slow-light regimes, one outside and one inside the light cone. The latter will not emit since it is a leaky mode which is not confined in the third direction. However the Noda mode could still couple to this cavity. The relative position of these two slow-light regimes depends strongly on the crystal parameters and could in principle be around the Noda position.^[41] To check this, the lattice constant of the FP would need to be changed, however due to lack of tuneable

41

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Intensity(a.u.)

Wavelength (nm)

Figure 32: Wavelength spectrum of the FP mode in GaAs for the combined structure. The intensity is on log-scale to clearly show all peaks. The red circle indicates the slow-light regime of the odd modes, while the red line indicates the postion of the Noda mode.

4.2.2 InGaAsP

Figure 33 shows the Q-factor of a Noda mode tuned in resonance with two FP modes determined by lorentzian fitting several spectra taken for different powers. The barrier between the Noda cavity and the FP cavity was 6 periods and the barrier at the end of the FP cavity was also 6 periods. The spectrum of these FP modes is also shown. It can be seen from this graph that the Q-factor of the Noda mode drops with almost 22% when the Noda mode is brought into resonance with the FP mode. The dip in Q overlaps perfectly with the peak of the first FP mode. The second FP mode is at slightly lower wavelength than the dip. This can be explained by the fact that when heating the Noda cavity, the FP cavity will also be heated slightly. This causes a small red shift for the FP cavity, causing the resonance point to slightly red shift as well.

From the spectra of the Noda cavity it can be seen that the Noda mode still overlaps with the FP mode. Therefore this has to be weak coupling between the cavities. However the large change in Q-factor suggest that the coupling is already quite strong. This could therefore be close to the desired regime between weak and strong coupling as described in section 2.1.2. The Q-factor of the FP mode on the left is approximately 3000, while the Q-factor of the FP mode on the right is around 4500.

These Q-factors are different because these modes are close to the bandgap causing the Q-factor to increase the closer the mode is. For the tuning with the second mode the Q-factor drops to approximately the average of the Noda mode and the FP mode, indicating the maximum ΔQ/Q. This is also expected when the barrier at both sides of the FP is equal, because in the ideal case this would cause equal losses and coupling.

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Figure 33: (a) Q-factor of a Noda cavity as a function of wavelength in the vicinity of an FP cavity (black and red dots) and the spectrum of the corresponding FP cavity (black line) taken independently. The black dots are again for increasing power while the red dots are for decreasing power. The FP spectrum is taken at really low power to prevent a red shift caused by heating by the pump beam. (b) spectrum of the Noda cavity at two distinct points. The peak wavelength is shifted to make the two modes overlap. A different linewidth and thus Q-factor is visible

Figure 34 shows the peak wavelength of the modes acquired for different powers for a different combined structure in InGaAsP with the same design parameters as the previous measurements.

The peaks show a clear anticrossing behaviour, indicating strong coupling. The second peak is only pumped when they are spectrally close, indicating that it is pumped by the coupling effect.

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Figure 34: Peak wavelength of two modes in a combined structure as function of laser power. The red spots represent a peak that only came up when the black peak was close. The black spots represent the peak wavelength of the Noda cavity. The insets show the spectra at two distinct points.

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