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Journal of the Optical Society of America B

Photorefractive quantum wells: transverse Franz–Keldysh geometry

Qiong Wang, M. R. Melloch, Robert M. Brubaker, David D. Nolte

Published Sep 1, 1992• 148 citations
Publisher

Abstract

The photorefractive properties of semi-insulating AlGaAs–GaAs multiple quantum wells are described for the transverse Franz–Keldysh geometry with the electric field in the plane of the quantum wells. Combining the strong electroabsorption of quantum-confined excitons with the high resistivity of semi-insulating quantum wells yields large nonlinear optical sensitivities. The photorefractive quantum wells have effective nonlinear optical sensitivities of n2 ≈ 103 cm2/W and α2/α0 ≈ 104 cm2/W for applied fields of 10 kV/cm. Photorefractive gains approaching 1000 cm−1 have been observed in two-wave mixing under dc electric fields and stationary fringes. The transverse Franz–Keldysh geometry retains the general transport properties and behavior of conventional bulk photorefractive materials. The resonant excitation of free electrons and holes in the quantum wells leads to novel behavior associated with electron–hole competition. We demonstrate that under resonant excitation of electrons and holes the device resolution is fundamentally limited by diffusion lengths but is insensitive to long drift lengths.

DOI
10.1364/josab.9.001626

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The photorefractive properties of semi-insulating AlGaAs–GaAs multiple quantum wells are described for the transverse Franz–Keldysh geometry with the electric field in the plane of the quantum wells. Combining the strong electroabsorption of quantum-confined excitons with the high resistivity of semi-insulating quantum wells yields large nonlinear optical sensitivities. The photorefractive quantum wells have effective nonlinear optical sensitivities of n2 ≈ 103 cm2/W and α2/α0 ≈ 104 cm2/W for applied fields of 10 kV/cm. Photorefractive gains approaching 1000 cm−1 have been observed in two-wave mixing under dc electric fields and stationary fringes. The transverse Franz–Keldysh geometry retains the general transport properties and behavior of conventional bulk photorefractive materials. The resonant excitation of free electrons and holes in the quantum wells leads to novel behavior associated with electron–hole competition. We demonstrate that under resonant excitation of electrons and holes the device resolution is fundamentally limited by diffusion lengths but is insensitive to long drift lengths.
We have observed two-wave mixing in semi-insulating AlGaAs/GaAs multiple quantum well structures at wavelengths near the exciton absorption. The photorefractive index changes are caused by the Franz–Keldysh effect on quantum-confined excitons. Photorefractive gains larger than 200 cm−1 are obtained for the first time at wavelengths near 836 nm using stationary fringes and dc applied fields up to 5 kV/cm. The direction of energy transfer between the two beams is determined by the direction of applied electric field.
The theory of photorefractive grating formation in a semi-insulating GaAs/AlGaAs multiple-quantum-well structure (MQWS) with an electric field applied across the layers and for counterpropagating writing beams is presented. The gain and the response time demonstrate a resonant behavior with respect to variations in both the applied field and the light’s wavelength. For a semi-insulating MQWS such an interaction geometry could provide the highest two-wave mixing gain, as much as 104 cm−1, which exceeds the linear absorption.
Recently, the high speed of semiconductor materials was combined with the large optical nonlinearity of the Franz-Kelydish effect near the quantum confined exciton absorption within semi-insulating multiple quantum well structures (SIMQW)[1]. The diffraction efficiency of four wave mixing obtained in the SIMQW with an optical interaction length of 1.05 µm is comparable with the diffraction efficiency for a semiconductor bulk sample with an optical interaction length of several mm operating under similar conditions. Thus, SIMQW become a ideal candidate to study the diffraction process in the Raman-Nath regime[2]. Here, we report two effects of the second order diffraction in a SIMQW sample under applied field: 1) the direct observation of a strong second order diffraction signal; 2) the intensity of the degenerate four wave mixing signal depends on the direction of applied field when the fringe spacing becomes large.
Electroabsorption has been investigated in semi-insulating asymmetric GaAs/AlGaAs double quantum wells presenting high linear Stark responses, adequate for photorefractive applications. We have used the envelope function approximation to calculate the linear Stark shifts of the energy levels and select a suitable structure for the experimental study. The experimental data indicate that the response to the applied field critically depends on a complicated interplay of effects that compete or cooperate to suppress or enhance the electroabsorption. For positive field polarity, the competing contributions of the overlapping e1–hh1 and e1–hh2 transitions partially cancel the electroabsorption despite large linear Stark shifts. On the other hand, small negative fields induce large electroabsorption because the Stark shifts of the two transitions have opposite signs.