Measured extinction spectra of sample #95 (uniform frozen-phonon disorder) are plotted in Fig. 5.1. The individual spectra are shifted upwards for clarity in each panel, also in the following graphs. In TM polarization, two resonances appear in the case of no disorder.
They can be identified as the lower and upper polariton branches [35]. Increasing uniform frozen-phonon disorder causes the peak at high energy to decrease its amplitude further, whereas the peak at lower energies is nearly unaffected. For disorder amounts of more than 80% only one broad peak is observable in the extinction. A slight broadening of the lower polariton branch resonance is attributed to near-field coupling effects of approaching nanowires [23] in the disordered system. The spectral separation between lower and upper polariton branch (polariton splitting) decreases slightly for increasing disorder. Note that the detuning between plasmon and waveguide mode is quite large for this sample. Starting at 420 meV for no disorder, this splitting reduces to about 340 meV for 70% disorder.
For larger amounts the splitting can not be determined due to the vanishing of the upper polariton peak. A detailed analysis and interpretation of this reduced polariton splitting is given later in this chapter. In TE polarization, the typical Fano-like resonance of the quasiguided mode can be observed for no disorder [9, 35]. Increasing disorder reduces the amplitude of this peak, while its width is kept nearly unaffected. For a disorder amount of 90% the peak has completely vanished, indicating that the quasiguided mode is no longer excited. A slight shift of the resonance peak to lower energies is caused by the disorder-influence on the TE-bandstructure [59], as discussed later in this chapter.
These results can be compared with the extinction of sample D11 because both samples have the same disorder type but different distributions D(∆x). For this reason, the influence of thedistribution variation on the optical properties can be directly examined.
As will be shown later, the different periods of the samples (400 nm vs. 430 nm) only slightly affect the principal observations.
The extinction of sample D11 with Gaussian frozen-phonon disorder is plotted in Fig. 5.2. The spectra are similar to the ones from sample #95, except for the diffe-rent energies of the resonances. Especially the polariton branches in TM polarization show a stronger coupling because their energy separation is smaller than for sample #95.
1.4 1.6 1.8 2.0 2.2 2.4 0
4 8 12 16 20
Disorder
Extinction
Energy (eV)
1.4 1.6 1.8 2.0 2.2 2.4 0 2 4 6 8 10
TM TE
100%
0%
Extinction
Energy (eV)
Figure 5.1: Measured extinction of a sample with uniform frozen-phonon disorder (sample #95) at normal light incidence, both in TM and TE polarization.
1.6 1.8 2.0 2.2 2.4 0
2 4 6 8
Disorder
Extinction
Energy (eV)
1.6 1.8 2.0 2.2 2.4 0 1 2 3 4 5
TM TE
100%
0%
Extinction
Energy (eV)
Figure 5.2: Measured extinction of a sample with Gaussian frozen-phonon disorder (sample D11) at normal light incidence, both in TM and TE polarization.
However, increasing Gaussian frozen-phonon disorder also reduces the amplitudes of the upper polariton branch in TM polarization and of the quasiguided mode in TE polari-zation. These resonances vanish for a disorder amount of 60-70% which is less than for sample #95 with uniform frozen-phonon disorder. Additionally, upper and lower TM resonance also decrease their energy separation due to a shift of the resonances to lower and higher energies, respectively.
Now we want to discuss the influence of the disorder type on the optical properties of the structures. The extinction of sample D12 with uniform long-range disorder is
pre-1.4 1.6 1.8 2.0 2.2 2.4 0
2 4 6 8 10
Disorder
Extinction
Energy (eV)
1.4 1.6 1.8 2.0 2.2 2.4 0 1 2 3 4 5 6
TM TE
100%
0%
Extinction
Energy (eV)
Figure 5.3: Measured extinction of a sample with uniform long-range disorder (sample D12) at normal light incidence, both in TM and TE polarization.
1.4 1.6 1.8 2.0 2.2 0 1 2 3 4 5 6 7
TM TE
Extinction
Energy (eV)
1.4 1.6 1.8 2.0 2.2 0
2 4 6 8 10
Disorder
80%
0%
Extinction
Energy (eV)
Figure 5.4: Measured extinction of a sample with Gaussian long-range disorder (sample
#117, periodd0 = 475 nm) at normal light incidence, both in TM and TE polarization.
sented in Fig. 5.3. The spectrum for no disorder in TM polarization shows again the polariton signature. Contrary to the results of samples #95 and D11, both polariton branches are influenced by rising uniform long-range disorder: they are broadened in-homogeneously. Both resonances feature a substructure of several maxima and minima that becomes stronger when the disorder is further increased. The substructure is more pronounced at the upper polariton branch and only hardly visible at the lower polariton branch. This inhomogeneous broadening does not allow the determination of the polari-ton splitting as a function of disorder anymore. The broadened resonances make a clear
determination of the peaks for large disorder amounts difficult. At very large disorder amounts, again only one broad peak is observable. In TE polarization, the resonance peak of the quasiguided mode is also affected by this disorder type. The reduction of the peak’s amplitude is stronger when compared with the spectra of sample #95. It results in a complete vanishing of the peak for an amount of 50-60%, in comparison with an amount of 90% in the frozen-phonon model. Again, the missing of the resonance indicates the missing of the quasiguided mode. Additionally, a strong inhomogeneous broadening of the resonance can be observed. For a disorder amount of only 20% it is not possible to excite a single resonance at the former spectral positions. Rather two pronounced max-ima appear in the extinction, and their number is rising for even higher disorder amounts.
This modification is not just a simple broadening of the original peak. The emphasis of the resonance rather shifts to smaller and higher energies for different disorder amounts.
At first sight, we can speculate about the origin of the additional peaks. One possibility could be localized states [3, 41] that may appear in this disorder model. Later it will be shown in more detail that the excitation of multiple resonances at slightly different energies is the responsible mechanism of the inhomogeneous broadening.
The observed inhomogeneous broadening indeed originates specifically from long-range disorder. This becomes obvious when looking at the extinction of sample #117 with Gaus-sian long-range disorder in Fig. 5.4. Increasing the disorder shows a similar broadening in TE and TM polarization. The substructure on lower and upper polariton branches in TM polarization is more pronounced than that in Fig. 5.3. This also holds for the resonance in TE polarization. Moreover, the strong reduction of the amplitudes is even more drastic than for sample D12. The quasiguided mode in TE polarization vanishes for a disorder amount of 40-50%. The main spectral features and observations are identical with the ones in Fig. 5.3, indicating that long-range disorder affects the optical proper-ties differently than frozen-phonon disorder. The observations are not governed by the distribution D(∆x).
The main effect of the period d0 is to determine the energies of the polariton branches and hence the detuning of plasmon and quasiguided mode (see Fig. 2.10). Therefore, the effects of disorder in samples with the same disorder type but different periods are comparable. Sample #126 only differs by a smaller period from sample #117, both have a Gaussian long-range disorder. The extinction spectra of sample #126 are presented in Fig. 5.5. Unfortunately, the disorder amounts in these samples are not identical. The spectra of sample #126 should be compared with the spectra for 0%, 10%, and 20%
disorder in Fig. 5.4. The spectra are similar with respect to the reduced amplitudes and the broadening of the resonances for increasing disorder. As will be discussed later, the reductions of the energy separation between the polariton branches and of the gaps in the bandstructure crucially depend on the detuning. Consequently, the period has a dramatic influence in disordered systems.
To summarize, we have shown that disorder causes a reduction of the extinction of the
1.4 1.6 1.8 2.0 0
1 2 3
17.8%
8.9%
0%
Extinction
Energy (eV)
1.4 1.6 1.8 2.0
0 1 2 3
Disorder
TE TM
Extinction
Energy (eV)
Figure 5.5: Measured extinction of a sample with Gaussian long-range disorder (sample
#126, d0 = 450 nm) at normal light incidence, both in TM and TE polarization.
quasiguided mode in TE polarization and of the quasiguided mode polariton branch in TM polarization. This reduction is stronger for long-range disorder than for frozen-phonon disorder. Long-range disorder additionally broadens the resonances inhomogeneously.
These spectral effects are caused by the disorder type, neither by the distributionD(∆x) of the position variation nor by the period d0 of the grating arrangement. The energy separation between the polariton branches is reduced for increasing frozen-phonon disor-der. This effect strongly depends on the period, see later on. A clear determination of this polariton splitting is not possible in systems with long-range disorder.