APPLIED PHYSICS LETTERS
VOLUME 81, NUMBER 23
2 DECEMBER 2002
Ultrafast ac Stark effect switching of the active photonic band gap from Bragg-periodic semiconductor quantum wells J. P. Prineas,a) J. Y. Zhou, and J. Kuhl Max Planck Institute for Solid State Research, D-70506 Stuttgart, Germany
H. M. Gibbs and G. Khitrova Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
S. W. Koch Department of Physics and Material Sciences Center, Philipps University, Renthof 5, D-35032 Marburg, Germany
A. Knorr Technische Universita¨t Berlin, Institut fu¨r Theoretische Physik, D-10623 Berlin, Germany
共Received 26 June 2002; accepted 9 October 2002兲 The ultrafast suppression and recovery of an active photonic band-gap structure constructed from the periodic complex susceptibility of quantum well excitons is demonstrated. For resonant pumping, the corresponding superradiant mode is slaved by the external field, and the structure forms a mirror that can be switched on and off at a bandwidth limited only by the width of the pump-pulse and the photonic band gap. Absorption and creation of free carriers is suppressed by the accelerated decay of the superradiant mode of the light-coupled quantum wells. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1526455兴
The modification and control of light–matter interactions in nanostructures with periodic modulation of the complex susceptibility has generated new physical insights and potential applications. Prominent examples include normalmode coupling of light and excitons in quantum wells embedded into microcavities,1 the Purcell effect in quantum dots embedded into micropillars,2 and suppressed spontaneous emission3 as well as waveguiding in photonic crystals,4 for applications such as quantum gates, large bandwidth light-emitting diodes, thresholdless diode lasers, and photonic integrated circuits. A more recent example is the collective response exhibited by periodic quantum wells coupled by light. For a collection of N quantum wells spaced with Bragg periodicity, the radiative decay time of the excitonic polarization has been shown to vary inversely with the number of quantum wells,5,6 due to the formation of a superradiant mode.7 In frequency-resolved reflection, a Lorentzian profile grows in amplitude and linewidth with N. 8 However, the increase with N does not go on indefinitely; in the limit of large N, the reflection reaches 1 共total reflection兲 and assumes the square profile of a one-dimensional photonic band gap, i.e., a dielectric mirror. Unlike the typical passive photonic band gap structure made from alternating nonresonant layers, i.e., real susceptibilities, the Bragg-periodic quantum well excitons presented in this work form an active photonic band gap, i.e., from the complex susceptibility associated with the exciton resonance, excited by an external optical pulse. For nonlinear interaction of excitons and light, i.e., sufficiently strong nearresonant pump pulses, the position and width of the active photonic band gap are expected to be modulated on the time scale of the pulse by the ac Stark effect. One can envision a兲
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using such a structure as a switchable mirror that either reflects or transmits a pulse. An array of such switches could redirect an incoming pulse into an arbitrary direction. Furthermore, due to the complete suppression of real absorption by the fast radiative decay associated with the superradiant mode, the sample fully recovers after the passage of the pump pulse for both near-resonant and resonant pumping, making possible a switchable mirror with terahertz bandwidth. In this letter, we present picosecond partial suppression and full recovery of the photonic band gap formed by an N⫽200 Bragg-periodic quantum well structure. The N⫽200 In0.04Ga0.96As/GaAs quantum well sample 共called DBR28兲 was grown by molecular beam epitaxy with Bragg periodicity 共period half the resonance wavelength兲. The measured one-dimensional photonic band gap formed by the periodicity of the quantum well exciton resonance is shown in Fig. 1 by the stopband in reflection (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 band gap is realized by the exciton resonance with a greatly increased radiative width. Therefore the nonlinear interaction of light and excitonic polarization is translated directly into the band gap response. The nonlinear response of the resonant photonic band gap was investigated at 10 K using pump-probe spectroscopy with 80 fs, transform-limited sech2 pulses at 80 MHz from a Ti:sapphire laser. Probe pulses were very weak (5 nJ/cm2 ) and spectrally broad 共16.3 meV兲. Pump pulses, shaped by a homebuilt pulseshaper in the reflection geometry using microlithographically patterned reflection masks,9 were spectrally narrow, with an 0.54 meV spectral full width at half maximum 共FWHM兲 and a 1.6 ps temporal FWHM, 共time– bandwidth product of 0.21兲, and tunable within the band-
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FIG. 3. Measured probe spectrum delayed by ⫺4, 0, and ⫹4 ps with respect to the pump. The spectra correspond to curve 2 in Fig. 2, and the pump is located at arrow 2 in Fig. 1 with an intensity of 4 J/cm2 . FIG. 1. Measured reflection (R, solid兲 and transmission (T, dot兲, and extracted absorption (A, dash兲 (A⫽1⫺R⫺T) of a weak broadband probe from the N⫽200 Bragg-periodic quantum well. Spectra are normalized with the incident probe spectral profile, indicated as a dash-dot-dot line. Numbered arrows at top indicate pump pulse positions in Fig. 2. The pump-pulse profile is also shown 共dash-dot兲.
width of the probe pulse. Pump and probe were crosspolarized to eliminate pump light scattered in the probe direction. The dash-dot and dash-dot-dot lines in Fig. 1 show the pump and probe spectral profiles with respect to the photonic band gap, respectively. The focused pump FWHM spotsize on the sample was 30 m, with the probe slightly smaller in width. Further, the probe was imaged onto a pinhole after the sample, so that only the inner 20 m of the probe was studied, where pump intensity is more uniform. A 4 J/cm2 pump pulse was spectrally tuned across the photonic band gap, and for each position 共see arrows in Fig. 1兲, the integrated, reflected probe intensity was recorded as a function of the delay with respect to the pump. The results are shown in Fig. 2. For pumping several meV below the
photonic band gap 共1兲, almost no change is induced in the probe reflection for any delay. For pumping within the lowenergy edge of the photonic band gap 共2兲, reflection of the probe is suppressed while the pump pulse is present; as the pump pulse leaves, the sample fully recovers. Curiously, if the pump pulse is exactly centered in the photonic band gap 共3兲, no change is induced in the integrated reflected probe. Finally, if the pump pulse is moved to a region of highabsorption 共4兲, reflection of the probe is suppressed, but the sample does not recover for nanoseconds. The inset to Fig. 2 shows the degree of suppression of the photonic band gap increases with increasing pump pulse intensity for a position as in Fig. 1. For all pump intensities, the integrated reflection fully recovers after passage of the pump pulse. Higher pump intensities could not be explored with our Ti:sapphire due to the heavy losses in reshaping the pulse from 16.4 to 0.54 meV. Figure 3 shows the spectrally resolved probe reflection from the sample 4 ps before and after the pump pulse is incident on the sample, and at zero delay for the pump pulse positioned within the lower edge of the photonic band gap, as in Fig. 1. The photonic band gap is partially suppressed at zero delay and is accompanied by a blueshift. Because the shift of the exciton resonance means that the quantum wells are no longer exactly Bragg spaced, coupling to other eigenmodes begins to occur,8 evidenced by the spectral modulation at zero delay in Fig. 3. Note while the integrated probe is suppressed by about 10%, portions of the spectrum—in particular the lower energy edge of the photonic bandgap— show an over 90% reduction of probe reflection with, in contrast to without, the pump pulse. One can envision using such a nonlinearity to create a mirror that can be switched on and off with terahertz bandwidth. Insight may be gained into the physical mechanisms of the ultrafast response of the photonic band gap by looking into the theoretical description of the interaction of ultrashort optical pulses with semiconductors. Theoretical10 and experimental investigations11–14 have found similarities between simple two-level systems and semiconductors, but also pronounced differences. In the band-gap structure considered here, the radiative properties of the bare excitonic resonances are strongly modified, and the response to an external field is dominated by a collective superradiant mode composed of
FIG. 2. Measured, integrated, reflected probe versus probe delay with respect to the pump for an 0.54 meV, 4 J/cm2 pump located at four different spectral positions, as indicated in Fig. 1. Inset: Maximum pump-induced change in integrated reflected probe versus incident pump-pulse intensity. Pump is centered spectrally as in the dash-dot profile in Fig. 1. For each intensity, recovery is full after passage of the pump pulse. Downloaded 19 Aug 2005 to 61.144.54.42. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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the radiation field and the isolated excitonic polarization.7 This coupled mode exhibits a drastically shortened lifetime 共due to the superradiant coupling兲 which determines the spectral width of the photonic band gap. The measured response is determined by the interaction of this superradiant mode and the properties of the external light field. For resonant excitation 共external pump pulse spectrally within the band gap兲, it is crucial that the superradiant mode has a significantly shorter lifetime than the pulse duration.15 The medium response is so much faster than the relatively slow pump pulse that the polarization and density are in steady state with the pump’s temporal shape 共ultrafast adiabatic following兲. Therefore, if the pulse is switched off, density and polarization are switched off as well, and the photonic band gap recovers. This is exactly the situation which occurs in Fig. 2 at the spectral pump positions 2 and 3. Whereas in position 3 the reflection is 1, and only a very small pump change 共1%兲 is induced, the pump induced reflection change at position 2 is larger 共about 10%兲 due to a better coupling of the pump pulse to the superradiant mode. The blueshift and the bleaching of the strong signal at position 2 are consistent in this situation 共leading to destruction of the photonic band gap兲 with the ac Stark effect of the material dynamics for cross-polarized pump and probe.14 However, we note that the dynamics of light and excitonic polarization are strongly coupled, leading to the superradiant mode. Thus, the understanding of this situation requires the nonperturbative analysis of exciton–light coupling; i.e., a quantitative description of the ac Stark effect, 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 band gap 共compare position 4 in Fig. 1兲, there is sufficient spectral overlap of the pulse with the excitonic continuum which does not, due to its low oscillator strength, couple efficiently to the radiation field. Therefore, the discussion can be reduced to the description of the material dynamics alone. The excitation of excitonic continuum states results in excitation of electrons and holes above the band edge which lose their phase coherence due to nonradiative interactions 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 band gap formed by radiatively-coupled, Bragg-spaced quantum wells can be switched with a low intensity picosecond pump pulse near the edge of the photonic band gap. Due to the superradiant decay associated with the photonic band gap, absorption and accumulation of free carriers is fully suppressed for resonant or near-resonant pumping, and recovery of the sample is full after passage of the pulse. A mirror that can be switched on and off based on this ultrafast recovery effect with potential terahertz rates has been demonstrated. Support is gratefully acknowledged from the Alexander von Humbolt Foundation 共JPP兲; NSF, AMOP, and EPDT 共Tucson group兲; the Deutsche Forschungsgemeinschaft 共SWK and AK兲; and the Max-Planck Program of the Humbolt and Max-Planck Societies 共SWK兲. 1
G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 共1999兲. 2 J. M. Gera´rd, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Theirry-Mieg, Phys. Rev. Lett. 81, 1110 共1998兲. 3 E. Yablonovitch, Phys. Rev. Lett. 58, 2059 共1987兲. 4 S. Y. Lin, E. Chow, V. Hietala, P. R. Vileneuve, and J. D. Joannopoulos, Science 282, 274 共1998兲. 5 E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, Fiz. Tverd. Tela 共St. Petersburg兲 36, 2118 共1994兲 关Phys. Solid State 36, 1156 共1994兲兴. 6 M. Hu¨bner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, Phys. Rev. Lett. 83, 2841 共1999兲. 7 M. Hu¨bner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, Phys. Rev. Lett. 76, 4199 共1996兲. 8 J. P. Prineas, C. Ell, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, Phys. Rev. B 61, 13 863 共2000兲. 9 A. M. Weiner, Rev. Sci. Instrum. 71, 1929 共2000兲. 10 R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 共1990兲. 11 H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Gru¨n, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 共1998兲. 12 N. C. Nielsen, S. Linden, J. Kuhl, J. Fo¨rstner, A. Knorr, S. W. Koch, and H. Giessen, Phys. Rev. B 64, 245202 共2001兲. 13 A. Schu¨lzgen, R. Binder, M. E. Donovan, M. Lindberg, K. Wundke, H. M. Gibbs, G. Khitrova, and N. Peyghambarian, Phys. Rev. Lett. 82, 2346 共1999兲. 14 C. Sieh, T. Meier, F. Jahnke, A. Knorr, S. W. Koch, P. Brick, M. Hu¨bner, C. Ell, J. P. Prineas, G. Khitrova, and H. M. Gibbs, Phys. Rev. Lett. 82, 3112 共1999兲. 15 For the case N⫽10, where reflection is not 1 and the pulse duration is shorter than the superradiant lifetime, real carriers are generated, preventing fast modulation. See M. Hu¨bner, J. Kuhl, S. Haas, T. Stroucken, S. W. Koch, R. Hey, and K. Ploog, Solid State Commun. 105, 105 共1998兲.
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