Figure 5.4: Nonlinear reflectance spectra obtained by above-band pump experiments [296] look very similar to those obtained by resonant pumping, compare for Fig. 5.2.
the pronounced deep dip below the hh exciton resonance gradually disappears from the spectra once the excitation level is risen. Comparison between the measured and cal-culated reflectance spectra shows excellent agreement. Specifically, the observed overall peak and valley structure is nicely reproduced.
5.3 Excitation Conditions
In this section, we will address the question why the single-beam experiments are so nicely matched by calculations from a theory based on the assumption of pump-probe conditions. To do so, we compare resonant and above-band excitation conditions. In particular, we start that inspection by an examination of the absorption properties of the sample FIB13.
Figure 5.3(a) shows the scaled spectra of experimentally applied pulses for resonant (dark gray) and above-band (light gray) excitation as shaded areas. The calculated true-absorption probabilitiesA(ω) = 1−R(ω)−T(ω) for low excitation (blue line) and high excitation (red line), where the reflection [transmission] probability is given by R(ω) [T(ω)], are plotted in the same frame. The respective true absorption resulting from
the multiplication of the pulse spectrum with the true-absorption probability is plotted in Fig. 5.3(b) for low and high excitation levels after both, resonant and above-band excitation. The reddish curves correspond to high excitation and the bluish ones to low excitation. Specifically, the light colored lines refer to spectra for above-band pump while the darker colored lines refer to spectra for on-resonance pump, respectively.
As one can see, considerable absorption is observed in a wide spectral range for all ex-citation conditions. In particular, resonant and above-band exex-citation yield very similar absorption spectra. Moreover, most of the absorption generates free carriers under both excitation conditions due to the strong continuum-absorption contributions. In conse-quence, the experimental spectra obtained by above-band excitations, Fig. 5.4, look very similar to the spectra obtained after resonant excitation, Fig. 5.2(b), when the respective pump powers are comparable.
That similarity can be understood as follows. From pulsed nonlinear experiments of QWs one has learned that carriers which have been created by the near band edge absorption of 100fs pulses can be adequately described by an equilibrium carrier dis-tribution with a carrier temperature of 40−50K. Especially, only negligible cooling or redistribution of these carriers occurs within 100fs. Hence, the excited system can be described by an appropriately chosen carrier density and temperature for above-band excitation conditions.
In particular, the difference that originates from the two different excitation schemes is a creation of coherent polarization by the resonant pump while the above-band excitation generates carriers incoherently. Nevertheless, the microscopic treatment of the carrier-carrier scattering guarantees an appropriate description of the density-dependent QW nonlinearity, and thus of the EID. Moreover, the self-consistent treatment of light-matter interactions ensures the correct inclusion of the corresponding broadening of the spectral features which change only relatively slowly with the density, as the simulations show.
Under above-band excitation conditions, the effect of the carriers, generated incoher-ently by the non-resonant pump, on resonant spectral features is monitored by the weak resonant part of the pulse. That resonant tail of the off-resonant pulse serves here as the probe pulse that is assumed in the theory, which establishes the link between theory and non-resonant conditions. As we have seen previously, spectra obtained by non-resonant excitation are very similar to spectra after resonant excitation due to similar absorp-tion characteristics. Thus, the very good agreement between theory and resonant-pump experiments can be understood. At the same time, one has to remark that a detailed comparison of the exact carrier densities becomes meaningful only once the excitation conditions are modeled closer to the experiment.
6
Numerical Studies
The very good agreement of our theory with the experimental results found in the linear as well as in the nonlinear regime confirms an appropriate modeling of the investigated samples and thus the predictive power of the theory. Therefore, further entirely nu-merical studies shall now deepen the understanding of the spectral properties of the Fibonacci-spaced MQW samples. In particular, investigation of effects and conditions that cannot be achieved or that are at least very difficult to achieve in experiments can be performed by numerical simulations in an easy way. The same sample parameters which have successfully been used in the previously discussed theory-experiment com-parisons are used in all following computations unless the usage of deviating parameters is stated.
Specifically, the focus of the investigations will be on the sharp minimum in the linear reflectance spectrum. Sharp spectral features like the observed reflectance minimum are possible candidates for optical applications. For instance, the optical Stark effect [336]
can be used to shift the entire spectrum in a short time so that the present sample, i.e.
the sharp dip, could be used as a high-speed optical switch [337–339]. The dip also has possible applications to slow light similar to the case of interference fringes observed in the spectral stopband of a very large number of slightly detuned excitonic Bragg periodic QWs [340, 341]. Thus, we will now aim at an understanding of the properties as well as of the origin of that reflectance minimum.
6.1 Origin of Sharp Reflectance Minimum
In order to study the origin or the pronounced, sharp minimum in the reflectance spec-trum close to the 1s hh-resonance, a switch-off analysis of the QW susceptibility is performed. Since that reflectance minimum is most pronounced in the linear spectrum of FIB13, we focus on that case. Therefore, we show as a shaded area in Fig. 6.1 the already discussed linear reflectance spectrum obtained from the full calculation. That reflectance spectrum is compared to the results of identical computations except that either the real part of the QW susceptibility (blue line), or its imaginary part (red line),
1517 1523 1529 0
0.2 0.4 0.6 0.8
energy [meV]
reflectance R(ω)
Figure 6.1: A switch-off analysis shows a disappearance of the stopbands with entirely switched-off QW susceptibility (black line). While the inclusion of only the imaginary part of the susceptibility (blue line) reveals a smoothly peaked spectrum, the corresponding real part (red line) almost completely repro-duces the highly structured spectrum of the full simulation (shaded area) of FIB13 in the linear regime.
or the whole QW susceptibility (black line) is artificially set to zero. If the QW sus-ceptibility is neglected completely, the stopbands disappear and the remaining almost constant reflectance originates only from the array of dielectric layers. In particular, the reflection of light at the sample-air interface strongly contributes to the observed total reflectance of the sample in the whole spectral range if there is no ARC added to that interface.
Switching on the imaginary part of the QW susceptibility, one finds that additional absorption peaks are introduced to the reflectance. These peaks are located at the resonance positions and are additive to the spectrum obtained with vanishing QW sus-ceptibility. The observed spectral shape clearly differs from the full computation.
In contrast, all the main spectral features of the full computation agree with the spectrum obtained when only the real part of the QW susceptibility is considered. In particular, the stopbands as well as the valley between the hh and the lh resonance originate from the real part of the susceptibility. Moreover, the spectral shape of the full computation is completely matched in the spectral region energetically below the sharp reflectance minimum. In addition, even the spectral shape of that reflectance minimum is observed to be in nice agreement with the spectrum from the full computation as well.
Close to the resonance positions, a number of additional very sharp peaks and dips is observed. In the full computation, the imaginary part causes some of these extremely sharp features to smear out. At the same time, the imaginary part of the QW
suscep-6.2 Sensitivity of Spectra to Average Spacing and Ratio of QW-QW separations