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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coherent effects in semiconductor optics ： ウィキペディア英語版 Coherent effects in semiconductor optics The interaction of matter with light, i.e., electromagnetic fields, is able to generate a coherent superposition of excited quantum states in the material. ''Coherent'' denotes the fact that the material excitations have a well defined phase relation which originates from the phase of the incident electromagnetic wave. Macroscopically, the superposition state of the material results in an optical polarization, i.e., a rapidly oscillating dipole density. The optical polarization is a genuine non-equilibrium quantity that decays to zero when the excited system relaxes to its equilibrium state after the electromagnetic pulse is switched off. Due to this decay which is called ''dephasing'', coherent effects are observable only for a certain temporal duration after pulsed photoexcitation. Various materials such as atoms, molecules, metals, insulators, semiconductors are studied using coherent optical spectroscopy and such experiments and their theoretical analysis has revealed a wealth of insights on the involved matter states and their dynamical evolution. This article focusses on coherent optical effects in semiconductors and semiconductor nanostructures. After an introduction into the basic principles, the semiconductor Bloch equations (abbreviated as SBEs)〔Schäfer, W.; Wegener, M. (2002). ''Semiconductor Optics and Transport Phenomena''. Springer. ISBN 3540616144.〕〔Haug, H.; Koch, S. W. (2009). ''Quantum Theory of the Optical and Electronic Properties of Semiconductors'' (5th ed.). World Scientific. ISBN 9812838848.〕〔Meier, T.; Thomas, P.; Koch, S. W. (2007). ''Coherent Semiconductor Optics: From Basic Concepts to Nanostructure Applications'' (1st ed.). Springer. ISBN 3642068960.〕〔Lindberg, M.; Koch, S. (1988). "Effective Bloch equations for semiconductors". ''Physical Review B'' 38 (5): 3342–3350. doi:(10.1103/PhysRevB.38.3342 )〕〔Schmitt-Rink, S.; Chemla, D.; Haug, H. (1988). "Nonequilibrium theory of the optical Stark effect and spectral hole burning in semiconductors". ''Physical Review B'' 37 (2): 941–955. doi:(10.1103/PhysRevB.37.941 )〕 which are able to theoretically describe coherent semiconductor optics on the basis of a fully microscopic many-body quantum theory are introduced. Then, a few prominent examples for coherent effects in semiconductor optics are described all of which can be understood theoretically on the basis of the SBEs. ==Starting point== Macroscopically, Maxwell's equations show that in the absence of free charges and currents an electromagnetic field interacts with matter via the optical polarization $$. The wave equation for the electric field $$ reads $(\backslash nabla\; \backslash cdot\; \backslash nabla\; -\; \backslash frac\; \backslash frac)\; (,t)\; =\; \backslash mu\_0\; \backslash frac\; (,t)$ and shows that the second derivative with respect to time of $$, i.e., $\backslash frac$, appears as a source term in the wave equation for the electric field $$. Thus, for optically thin samples and measurements performed in the far-field, i.e., at distances significantly exceedng the optical wavelength $\backslash lambda$, the emitted electric field resulting from the polarization is proportional to its second time derivative, i.e., $\backslash propto\; \backslash frac$. Therefore, measuring the dynamics of the emitted field $(t)$ provides direct information on the temporal evolution of the optical material polarization $(t)$. Microscopically, the optical polarization arises from quantum mechanical transitions between different states of the material system. For the case of semiconductors, electromagnetic radiation with optical frequencies is able to move electrons from the valence ($v$) to the conduction ($c$) band. The macroscopic polarization $$ is computed by summing over all microscopic transition dipoles $p\_$ via $=\; \backslash frac\backslash sum\_\; (\_\; p\_\; +\; \backslash mathrm\; )$,〔 where $\_$ is the dipole matrix element which determines the strength of individual transitions between the states $v$ and $c$, $\backslash mathrm$ denotes the complex conjugate, and $V$ is the appropriately chosen system's volume. If $\backslash epsilon\_c$ and $\backslash epsilon\_v$ are the energies of the conduction and valence band states, their dynamic quantum mechanical evolution is according to the Schrödinger equation given by phase factors $\backslash mathrm^$ and $\backslash mathrm^$, respectively. The superposition state described by $p\_$ is evolving in time according to $\backslash mathrm^$. Assuming that we start at $t=0$ with $p\_(t=0)\; =\; p\_$, we have for the optical polarization $(t)\; =\; \backslash sum\_\; (\; \_\; p\_\; \backslash ,\; \backslash mathrm^\; +\; \backslash mathrm\; )$. Thus, $(t)$ is given by a summation over the microscopic transition dipoles which all oscillate with frequencies corresponding to the energy differences between the involved quantum states. Clearly, the optical polarization $(t)$ is a coherent quantity which is characterized by an amplitude and a phase. Depending on the phase relationships of the microscopic transition dipoles, one may obtain constructive or destructive interference, in which the microsopic dipoles are in or out of phase, respectively, and temporal interference phenomena like quantum beats, in which the modulus of $(t)$ varies as function of time. Ignoring many-body effects and the coupling to other quasi particles and to reservoirs, the dynamics of photoexcited two-level systems can be described by a set of two equations, the so-called optical Bloch equations.〔 Allen, L.; Eberly, J. H. (1987). ''Optical Resonance and Two-Level Atoms''. Dover Publications. ISBN 0486655334.〕 These equations are named after Felix Bloch who formulated them in order to analyze the dynamics of spin systems in nuclear magnetic resonance. The two-level Bloch equations read $\backslash mathrm\; \backslash hbar\; \backslash frac\; p\_\; =\; \backslash Delta\; \backslash epsilon\; \backslash ,\; p\_\; +\; \backslash cdot\; I$ and $\backslash mathrm\; \backslash hbar\; \backslash frac\; I\; =\; 2\; \backslash cdot\; (\; p\_\; -\; p\_^\backslash star\; ).$ Here, $\backslash Delta\; \backslash epsilon=(\backslash epsilon\_c\; -\; \backslash epsilon\_v)$ denotes the energy difference between the two states and $I$ is the inversion, i.e., the difference in the occupations of the upper and the lower states. The electric field $$ couples the microscopic polarization $p$ to the product of the Rabi energy $\backslash cdot$ and the inversion $I$. In the absence of the driving electric field, i.e., for $=\; \backslash mathbf$, the Bloch equation for $p$ describes an oscillation, i.e., $p\_\; (t)\; \backslash propto\; \backslash mathrm^$. The optical Bloch equations enable a transparent analysis of several nonlinear optical experiments. They are, however, only well suited for systems with optical transitions between isolated levels in which many-body interactions are of minor importance as is sometimes the case in atoms or small molecules. In solid state systems, such as semiconductors and semiconductor nanostructures, an adequate description of the many-body Coulomb interaction and the coupling to additional degrees of freedom is essential and thus the optical Bloch equations are not applicable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Coherent effects in semiconductor optics」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.