J.P. Prineas, J.Y. Zhou, J. Kuhl, H.-U. Habermeier, and F. Schartner;
H.M. Gibbs and G. Khitrova (University of Arizona); S.W. Koch (Philipps Universit¨at Marburg);
A. Knorr (Technische Universit¨at Berlin) The modification and control of light-matter
in-teractions in nanostructures with periodic mod-ulation of the complex susceptibility has gener-ated new physical insights and potential appli-cations. Prominent examples include normal-mode coupling of light and excitons in quantum wells embedded into microcavities, the Pur-cell effect in quantum dots embedded into mi-cropillars, and suppressed spontaneous emis-sion as well as waveguiding in photonic crystals for applications such as quantum gates, large-bandwidth light-emitting diodes, thresholdless
A more recent example is the collective re-sponse exhibited by periodic quantum wells coupled by light. For a collection of N quan-tum wells spaced with Bragg periodicity the ra-diative decay time of the excitonic polarization has been shown to vary inversely with the num-ber of quantum wells, due to the formation of a superradiant mode. In the limit of large N, the reflection assumes the square profile of a one-dimensional photonic bandgap, i.e., a di-electric mirror. Unlike the typical passive pho-tonic bandgap structure made from alternating non-resonant layers, the Bragg-periodic
quan-resonant photonic bandgap. For non-linear in-teraction of excitons and light, i.e., sufficiently strong near-resonant pump pulses, the position and width of the resonant photonic bandgap are expected to be modulated on the time scale of the pulse by the ac Stark effect. One can envi-sion using such a structure as a switchable mir-ror that either reflects or transmits a pulse. Fur-thermore, due to the complete suppression of absorption by the fast radiative decay associated with the superradiant mode, the sample fully re-covers after the passage of the pump pulse for both near-resonant and resonant pumping, mak-ing possible a switchable mirror with terahertz bandwidth. Here we present picosecond partial suppression and full recovery of the photonic bandgap formed by an N = 200 Bragg-periodic quantum well structure.
The N = 200 In004Ga096As/GaAs quantum well sample was grown by molecular beam epi-taxy with Bragg periodicity (period half the resonance wavelength). The measured one-dimensional photonic bandgap formed by the periodicity of the quantum well exciton reso-nance is shown in Fig. 64 by the stopband in re-flection (R), the low absorption (A) as well as transmission (T). Note there is no difference in the background index of refraction of the low indium concentration quantum wells and the barriers; the photonic bandgap is realized by the exciton resonance with a greatly increased ra-diative width. Therefore the non-linear interac-tion of light and excitonic polarizainterac-tion is trans-lated directly into the bandgap response.
The non-linear response of the resonant photonic bandgap was investigated at 10 K using pump-probe spectroscopy with 80 fs, transform-limited pulses with a sech2-shape at 80 MHz from a Ti : Sapphire laser. Probe pulses were very weak (5 nJ/cm2) and spectrally broad (16.3 meV). Pump pulses, shaped by a homebuilt pulseshaper in the reflection geome-try using microlithographically patterned re-flection masks, were spectrally narrow, with an 1.08 meV spectral full-width-at-half-maximum
(FWHM) and a 1.6 ps temporal FWHM, (time-bandwidth product of 0.21), and tunable within the bandwidth of the probe pulse. Pump and probe were cross-polarized to eliminate pump light scattered in the probe direction. The yel-low and black lines in Fig. 64 show the pump and probe spectral profiles with respect to the photonic bandgap, respectively.
Figure 64: Measured reflection (R, red) and trans-mission (T, green), and extracted absorption (A, blue) (A = 1 – R – T) of a weak broadband probe from the N = 200 Bragg-periodic quantum well sam-ple. Spectra are normalized with the incident probe spectral profile, indicated as a black line. The pump-pulse profile is also shown (yellow).
Figure 65 shows the spectrally resolved probe reflection from the sample 4 ps before and af-ter the pump pulse is incident on the sample, and at zero delay for the pump pulse positioned within the lower edge of the photonic bandgap as in Fig. 64. The photonic bandgap is par-tially suppressed at zero delay and is subject to a blue shift. Because the shift of the ex-citon resonance means that the quantum wells are no longer exactly Bragg-spaced, coupling to other eigenmodes begins to occur, evidenced by the spectral modulation at zero delay in Fig. 65.
Note while the integrated probe is suppressed by about 10%, portions of the spectrum – in particular the lower energy edge of the pho-tonic bandgap – show an over 90% reduction of probe reflection with compared to without the pump pulse. One can envision using such a non-linearity to create a mirror that can be switched on and off with terahertz bandwidth.
Figure 65: Measured probe spectrum delayed by –4 ps, 0 ps, and +4 ps with respect to the pump. The pump is located at the arrow in Fig. 64 with an in-tensity of 4 µJ/cm2.
Insight may be gained into the physical mech-anisms of the ultrafast response of the pho-tonic bandgap by looking into the theoretical description of the interaction of ultrashort op-tical pulses with semiconductors. Theoreti-cal and experimental investigations have found similarities between simple two-level systems and semiconductors, but also pronounced dif-ferences. In the bandgap structure considered here, the radiative properties of the bare exci-tonic resonances are strongly modified and the response to an external field is dominated by a collective superradiant mode composed of the radiation field and the isolated excitonic polar-ization. This coupled mode exhibits a drasti-cally shortened lifetime (due to the superradiant coupling) which determines the spectral width of the photonic bandgap. The measured re-sponse is determined by the interaction of this superradiant mode and the properties of the ex-ternal light field.
For resonant excitation (external pump pulse spectrally within the bandgap), it is crucial that the superradiant mode has a significantly shorter lifetime than the pulse duration. The medium response is so much faster than the rel-atively slow pump pulse that the polarization and density are in steady state with the pump’s temporal shape (ultrafast adiabatic following).
Therefore, if the pulse is switched off, den-sity and polarization are switched off as well
and the photonic bandgap recovers. This is ex-actly the situation which occurs in Fig. 65. The blueshift and the bleaching of the resonant pho-tonic bandgap are consistent in this situation with the ac Stark effect of the material dynam-ics for cross-polarized pump and probe. How-ever, we note that the dynamics of light and ex-citonic polarization are strongly coupled lead-ing to the superradiant mode. Thus the un-derstanding of this situation requires the non-perturbative analysis of exciton-light coupling, i.e., a quantitative description of the ac Stark ef-fect, modified by light propagation effects.
The dynamics are modified for configurations where the excitation is spectrally detuned from the superradiant mode. For excitation above the photonic bandgap, there is sufficient spec-tral overlap of the pulse with the excitonic con-tinuum which does not – due to its low oscil-lator strength – couple efficiently to the radi-ation field. Therefore, the discussion can be reduced to the description of the material dy-namics alone. The excitation of excitonic con-tinuum states results in excitation of electrons and holes above the bandedge which lose their phase coherence due to non-radiative interac-tions like Coulomb scattering. These processes are not reversible during the switch off of the optical pulse and the sample takes nanoseconds to recover.
In conclusion, we have shown that the resonant active bandgap formed by radiatively-coupled, Bragg-spaced quantum wells can be switched with a low intensity ps pump pulse near the edge of the photonic bandgap. Due to the superradi-ant decay associated with the photonic bandgap, absorption and accumulation of free carriers is fully suppressed for resonant or near-resonant pumping by the accelerated decay of the su-perradiant mode of the light-coupled quantum wells. A mirror that can be switched on and off at a bandwidth limited only by the width of the pump-pulse and the photonic bandgap and which reveals ultrafast recovery with potential terahertz rates has been demonstrated.