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Optics Letters

How fast is excitonic electroabsorption?

Stefan Schmitt-Rink, D. S. Chemla, W. H. Knox, David A. B. Miller

Published Jan 1, 1990• 65 citations
Publisher

Abstract

Many semiconductor light modulators rely on changes in excitonic absorption induced by electric fields. We study their temporal response in the framework of a one-dimensional model, for which we solve exactly the timedependent Schrödinger equation. For a homogeneously broadened system, the electroabsorption response time is found to be simply the inverse of the (field-induced) exciton linewidth, which can be as short as 50 fsec.

DOI
10.1364/ol.15.000060

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Many semiconductor light modulators rely on changes in excitonic absorption induced by electric fields. We study their temporal response in the framework of a one-dimensional model, for which we solve exactly the timedependent Schrödinger equation. For a homogeneously broadened system, the electroabsorption response time is found to be simply the inverse of the (field-induced) exciton linewidth, which can be as short as 50 fsec.
One-dimensional semiconductors are characterized by strongly bound excitons. Therefore, the Frenkel regime of excitons localized within a few unit cells is readily reached and traditional Wannier exciton models become inadequate. In the presence of strong electric fields, excitons are polarized and, in extreme cases, ionized. Such strong-field effects have previously been described analytically for Wannier excitons. In the present work, we show that analytical results can be extended to the more involved Frenkel case as well. Hence, by analytically solving the difference equation describing Frenkel excitons in electric fields, we derive close-form expressions for resonances providing Stark shifts and ionization rates. Moreover, closed-form results for exciton electroabsorption spectra and dynamic polarizability are obtained.
Semiconductor quantum well electroabsorption modulators are widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1 terahertz (THz). Here, the NIR absorption of undoped quantum wells was modulated by strong electric fields with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency- and power-dependent NIR absorption line. Nonperturbative theory and experiment indicate that the THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quantum coherence may yield new applications for quantum well modulators in optical communications.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.
We have identified several physical processes by which below-gap photons can modify excitonic absorption in GaAs quantum wells.1-3 These different phenomena can be distinguished by their temporal response times, which range from tens of nanoseconds to less than one picosecond. Our experiments also show that the relative contributions of these mechanisms to below-gap optical modulation of exciton absorption depend strongly on temperature as well as on the wavelength of the below-gap modulating beam. The size of the modulation indicates that a new class of absorptive and dispersive devices for optical signal processing is possible in which signals propagate in the transparent region of the crystal and experience negligible attenuation. In order to successfully interpret and calculate the magnitude of these exciting new effects, we show that it is necessary to take into account the special properties of two-dimensional excitons in semiconductor quantum wells.
An approach for solving the excitonic absorption in a semiconductor quantum well driven by an intense terahertz field is presented. The formalism relies on the stationary single-photon Schrodinger equation in the full quantum mechanical framework. The optical absorption dynamics in both weak and strong couplings are discussed and compared. The excitonic absorption spectra show the Autler—Townes doublets for the resonance terahertz field, a replica peak for the non-resonance terahertz field, and the electromagnetically induced transparency phenomenon for modulating the decay rate of the second electron state in the weak coupling. In particular, the electromagnetically induced transparency phenomenon window range is discussed. In the strong coupling region, the multi-order energy level resonance splitting due to the strong optical field is found. There are three (non-resonance terahertz field) or four (resonance terahertz field) peaks in the optical absorption spectra. This work provides a simple and convenient approach to deal with the optical absorption in the exciton system.