doctoralThesis Publikationsserver der Universitätsbibliothek Marburg Universitätsbibliothek Marburg Microscopic Investigations of the Terahertz and the Extreme Nonlinear Optical Response of Semiconductors Physik Golde, Daniel Golde Daniel https://doi.org/10.17192/z2010.0461 2010-06-22 Intrabandübergang Fano, U., " Effects of configuration interaction on intensities and phase shifts, " Phys. Rev. 124, 1866 (1961). M. Kira and S. W. Koch, " Many-body correlations and excitonic effects in semiconductor spectroscopy, " Prog. Quantum Electron. 30, pp. 155–296, 2006. Luo, C. W., Reimann, K., Woerner, M., Elsaesser, T., Hey, R., and Ploog, K. H., " Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation, " Phys. Rev. Lett. 92, 047402 (2004). M. Kira, W. Hoyer, and S. W. Koch, " Microscopic theory of the semiconductor terahertz response, " phys. stat. sol. (b) 238, pp. 443–450, 2003. J. R. Danielson, Y.-S. Lee, J. P. Prineas, J. T. Steiner, M. Kira, and S. W. Koch, " Interaction of strong single-cycle terahertz pulses with semiconductor quantum wells, " Phys. Rev. Lett. 99, p. 237401, 2007. R. H. M. Groeneveld and D. Grischkowsky, " Picosecond time-resolved far-infrared experiments on carriers and excitons in GaAs-AlGaAs multiple quantum wells, " J. Opt. Soc. Am. B 11, pp. 2502–2507, 1994. 2. J. ˇ Cerne, J. Kono, M. S. Sherwin, M. Sundaram, A. C. Gossard, and G. E. W. Bauer, " Terahertz dynamics of excitons in GaAs/AlGaAs quantum wells, " Phys. Rev. Lett. 77, pp. 1131–1134, 1996. R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, " How many-particle interactions develop after ultrafast excitation of an electron-hole plasma, " Nature 414, pp. 286–289, 2001. R. Huber, C. Kübler, S. Tübel, A. Leitenstorfer, Q. T. Vu, H. Haug, F. Köhler, and M.-C. Amann, " Fem- tosecond formation of coupled phonon-plasmon modes in InP: Ultrabroadband THz experiment and quan- tum kinetic theory, " Phys. Rev. Lett. 94, p. 027401, 2005. C. Kübler, R. Huber, and A. Leitenstorfer, " Ultrabroadband terahertz pulses: generation and field-resolved detection, " Semicond. Sci. Technol. 20, pp. S128–S133, 2005. M. C. Peter P. Yu, Fundamentals of Semiconductors: Physics and Materials Properties , 3rd ed. (Springer, Berlin, Germany, 2005). Lindberg, M. and Koch, S. W., " Effective bloch equations for semiconductors, " Phys. Rev. B 38, 3342–3350 (1988). M. Kira and S. W. Koch, " Exciton-population inversion and terahertz gain in semiconductors excited to resonance, " Phys. Rev. Lett. 93, p. 076402, 2004. M. Kira, W. Hoyer, T. Stroucken, and S. W. Koch, " Exciton formation in semiconductors and the influence of a photonic environment, " Phys. Rev. Lett. 87, p. 176401, 2001. I. Galbraith, R. Chari, S. Pellegrini, P. J. Phillips, C. J. Dent, A. F. G. van der Meer, D. G. Clarke, A. K. Kar, G. S. Buller, C. R. Pidgeon, B. N. Murdin, J. Allam, and G. Strasser, " Excitonic signatures in the photoluminescence and terahertz absorption of a GaAs/Al x Ga 1−x As multiple quantum well, " Phys. Rev. B 71, p. 073302, 2005. Bonvalet, A., Nagle, J., Berger, V., Migus, A., Martin, J.-L., and Joffre, M., " Femtosecond infrared emission resulting from coherent charge oscillations in quantum wells, " Phys. Rev. Lett. 76, 4392 (1996). Müller, T., Parz, W., Strasser, G., and Unterrainer, K., " Influence of carrier-carrier interaction on time- dependent intersubband absorption in a semiconductor quantum well, " Phys. Rev. B 70, 155324 (2004). Steiner, J. T., Microscopic Theory of Linear and Nonlinear Terahertz Spectroscopy of Semiconductors, PhD thesis, Philipps-University Marburg (2008). J. E. Sipe and E. Ghahramani, " Nonlinear optical response of semiconductors in the independent-particle approximation, " Phys. Rev. B 48, pp. 11705–11722, 1993. PRL 102, 127403 (2009) PHYSICAL REVIEW LETTERS week ending 27 MARCH 2009 127403-4 T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, " Room-temperature semiconductor mod- ulators for free-space signal transmission with THz waves, " in Nanosensing: Materials and Devices, M. S. Islam and A. K. Dutta, eds., Proc. SPIE Int. Soc. Opt. Eng. 5593, pp. 521–532, 2004. J. E. Sipe and A. I. Shkrebtii, " Second-order optical response in semiconductors, " Phys. Rev. B 61, pp. 5337– 5352, 2000. S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, " Semiconductor excitons in new light, " Nature Mat. 5, pp. 523–531, 2006. Leinß, S., Kampfrath, T., v. Volkmann, K., Wolf, M., Steiner, J. T., Kira, M., Koch, S. W., Leitenstorfer, A., and Huber, R., " Terahertz coherent control of optically dark para excitons in, " Phys. Rev. Lett. 101, 246401 (2008). S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, " Terahertz detection of plasmons and their many-body signatures in a two-dimensional electron gas. " to be published. M. Kira, W. Hoyer, and S. W. Koch, " Terahertz signatures of the exciton formation dynamics in non- resonantly excited semiconductors, " Sol. Stat. Comm. 129, pp. 733–736, 2004. The electrons experience a wiggling motion also in the growth direction due to the tilting of the confinement potential. Krieger, J. B. and Iafrate, G. J., " Time evolution of bloch electrons in a homogeneous electric field, " Phys. Rev. B 33, 5494–5500 (1986). M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, " Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy, " Phys. Rev. B 62, pp. 15764–15777, 2000. Cerne, J., Kono, J., Sherwin, M. S., Sundaram, M., Gossard, A. C., and Bauer, G. E. W., " Terahertz dynamics of excitons in GaAs/AlGaAs quantum wells, " Phys. Rev. Lett. 77, 1131–1134 (1996). Kersting, R., Bratschitsch, R., Strasser, G., Unterrainer, K., and Heyman, J. N., " Sampling a terahertz dipole transition with subcycle time resolution, " Opt. Lett. 25, 272 (2000). Heyman, J. N., Kersting, R., and Unterrainer, K., " Time-domain measurement of intersubband oscillations in a quantum well, " Appl. Phys. Lett. 72, 644–646 (1998). M. Tonouchi, " Cutting-edge terahertz technology, " Nature Photonics 1, pp. 97–105, 2007. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, World Scientific, Singapore, fourth ed., 2004. K. K. N. Simon and M. Sze, Physics of Semiconductor Devices, 3rd ed. (John Wiley and Sons, Hoboken, NJ, USA, 2006). 2011-08-10 terahertz physics Niederdimensionaler Halbleiter In the major part of this Thesis, we discuss the linear THz response of semiconductor nanostructures based on a microscopic theory. Here, two different problems are investigated: intersubband transitions in optically excited quantum wells and the THz plasma response of two-dimensional systems. In the latter case, we analyze the response of correlated electron and electron-hole plasmas. Extracting the plasma frequency from the linear response, we find significant deviations from the commonly accepted two-dimensional plasma frequency. Besides analyzing the pure plasma response, we also consider an intermediate regime where the response of the electron-hole plasma consists of a mixture of plasma contributions and excitonic transitions. A quantitative experiment-theory comparison provides novel insights into the behavior of the system at the transition from one regime to the other. The discussion of the intersubband transitions mainly focuses on the coherent superposition of the responses from true THz transitions and the ponderomotively accelerated carriers. We present a simple method to directly identify ponderomotive effects in the linear THz response. Apart from that, the excitonic contributions to intersubband transitions are investigated. The last part of the present Thesis deals with a completely different regime. Here, the extreme nonlinear optical response of low-dimensional semiconductor structures is discussed. Formally, extreme nonlinear optics describes the regime of light-matter interaction where the exciting field is strong enough such that the Rabi frequency is comparable to or larger than the characteristic transition frequency of the investigated system. Here, the Rabi frequency is given by the product of the electrical field strength and the dipole-matrix element of the respective transition. Theoretical investigations have predicted a large number of novel nonlinear effects arising for such strong excitations. Some of them have been observed in experiments performed on semiconductors. Previous theoretical works often modeled the semiconductor as an ensemble of independent two-level systems. Such an approach does surely not account for many-body interactions among the carriers. Only very few publications exist that include Coulomb effects in the extreme nonlinear regime. Furthermore, these studies concentrated exclusively on the optically induced interband transitions. For the strong fields considered here, however, the ponderomotive intraband acceleration of the photo-excited carriers cannot be neglected a priori. In our discussion of the extreme nonlinear optical response of semiconductors, we will analyze both the influence of the Coulomb interaction and the effect of carrier accelerations. The Thesis is organized as follows. In Chap. 2, we give an overview of our microscopic theory that has been used to obtain the results presented in this work. Chapter 3 discusses intersubband transitions of optically excited quantum wells. Besides a purely theoretical analysis of excitonic effects, a detailed experiment-theory comparison is presented. Chapter 4 deals with the intraband dynamics in two-dimensional semiconductor systems. Here, our results are also compared to recent experiments. In Chap. 5, we explore the extreme nonlinear optical response of semiconductor nanostructures. Finally, we summarize our findings and give a short outlook in Chap. 6. https://archiv.ub.uni-marburg.de/diss/z2010/0461/cover.png English ths Prof. Dr. Koch Stephan W. Koch, Stephan W. (Prof. Dr.) optical properties Interbandübergang Physics Physik Optische Eigenschaft Mikroskopische Untersuchungen zur Terahertz- sowie zur extrem nichtlinearen optischen Antwort von Halbleitern opus:3001 urn:nbn:de:hebis:04-z2010-04612 Die vorliegende Arbeit befasst sich mit der Berechnung den optischen Eigenschaften von Halbleiterstrukturen sowohl im sichtbaren wie auch im Terahertz-Spektralbereich. Die mikroskopische Theorie, die fuer Berechnungen der in dieser Arbeit diskutierten Resultate verwendet wurde, wird in Kapitel 2 vorgestellt. Sie basiert auf einer Bewegunsgleichungsmethode, bei der die auftauchende Vielteilchenhierarchie mit einer sogenannten Clusterentwicklung konsistent abgebrochen wird. In Kapitel 3 untersuche ich Intersubbanduebergaenge zwischen den zwei niedrigsten Leitungssubbaendern in optisch angeregten GaAs Quantenfilmen. Dabei regt das THz-Feld nicht nur Elektronen von einem Subband in das andere an, sondern kann auch an die vorhandenen kohaerenten Exzitonen koppeln und somit Uebergaenge zwischen Exzitonen, die zu verschiedenen Subbaendern gehoeren, induzieren. Interessanterweise zeigen die differentiellen THz-Transmissionsspektren eine charakteristische asymmetrische Linienform des Intersubbanduebergangs, die stark an eine Fano-Resonanz erinnert. Dieses Verhalten kann auf eine kohaerente Ueberlagerung der durch Intersubbanduebergaenge und ponderomotive Dynamik induzierten Felder zurueckgefuehrt werden. Kaptitel 4 befasst sich mit der Untersuchung der Intrabanddynamik in zwei unterschiedlichen Systemen: dem Elektron-Loch-Plasma in einem optisch angeregten Quantenfilm sowie einem zweidimensionalen Elektrongas (2DEG). Mithilfe einer Plasmon-Pol-Analyse kann die Plasmafrequenz aus der dielektrischen Funktion des Systems extrahiert werden. Fuer beide betrachtete zweidimensionale Systeme stellt sich heraus, dass die THz-Antwort durch eine dreidimensionale Plasmafrequenz bestimmt wird. Weiterhin wird die Antwort des Quantenfilms fuer Bedingungen untersucht, bei denen nahezu alle Elektronen und Loecher zu Exzitonen gebunden sind. Indem die Ladungstraegerkonzentration kontinuierlich erhoeht wird, kann nun der Uebergang zum korrelierten Elektron-Loch-Plasma untersucht werden. Eine weiterfuehrende theoretische Analyse der 2DEG-Daten zeigt, dass die Antwort hier sehr stark sowohl von ponderomotiven Effekten als auch von der Elektron-Ion-Streuung beeinflusst wird. Als Konsequenz der grossen Streubeitraege kann die Antwort des 2DEG nicht mit einem einfachen Drude-Modell erklaert werden. In Kapitel 5 beschaeftige ich mich mit der extrem nichtlinearen Antwort von Halbleiternanostrukturen. In diesem Regime der Licht-Materie-Wechselwirkung sind die vorhandenen Felder so stark, dass die Rabifrequenz vergleichbar oder sogar groesser ist als die charakteristische Uebergangsfrequenz des betrachteten Systems. Dabei ist die Rabifrequenz definiert als das Produkt aus dem Dipolmatrixelement des entsprechenden Uebergangs und der elektrischen Feldstaerke. Hierzu berechne ich die kohaerent emittierte Strahlung des Systems bei optischer Anregung mit Feldstaerken von 50 MV/cm und mehr. In diesem Regime werden viele neuartige nichtlineare Effekte erwartet. Fuer reine Interbanddynamik werden hier unter anderem die Carrier-Wave Mollow-Aufspaltung und die Erzeugung von hoeheren harmonischen beschrieben. Sobald die Intrabandbeschleunigung eingeschaltet wird, veraendern sich die Emissionsspektren dramatisch. Insbesondere die Erzeugung hoher Harmonischer wird deutlich verstaerkt. 2010 ppn:225757680 theoretical physics inter- and intraband transitions Philipps-Universität Marburg 2010-08-02 application/pdf Fachbereich Physik Terahertzbereich low-dimensional semiconductors Theoretische Physik monograph