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Optics Letters

Spatial-harmonic gratings at high modulation depths in photorefractive quantum wells

Q. N. Wang, M. R. Melloch, David D. Nolte

Published Dec 15, 1991• 16 citations
Publisher

Abstract

High-order spatial harmonics of photorefractive gratings are detected directly in multi wave mixing experiments in photorefractive AlGaAs/GaAs quantum wells operating in the Franz-Keldysh geometry. We have observed diffraction signals from the first-, second-, and third-harmonic refractive-index gratings. The quadratic electro-optic effect in the quantum wells second-spatial-harmonic grating.

DOI
10.1364/ol.16.001944

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Applied Physics Letters•Nov 25, 1996•8 citations
High-order spatial harmonics of photorefractive gratings are detected directly in multi wave mixing experiments in photorefractive AlGaAs/GaAs quantum wells operating in the Franz-Keldysh geometry. We have observed diffraction signals from the first-, second-, and third-harmonic refractive-index gratings. The quadratic electro-optic effect in the quantum wells second-spatial-harmonic grating.
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 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 demonstrate for the first time, to our knowledge, second harmonic optical phase conjugation, using the second spatial harmonics of a nonsinusoidal grating formed in a photorefractive material. The possibility of harmonic phase conjugation has been considered previously for artificial Kerr media.1 We have applied the same idea to barium titanate, since the existence of the higher-order gratings in this material has been known to us for some time. In our experiment, two 1.06-µm cw Nd:YAG laser beams wrote a grating in a poled photorefractive barium titanate crystal. Then a second harmonic of the YAG at 0.532 µm read out the grating in a counterpropagating direction to one of the writing beams. In this geometry, the usual Bragg condition is not satisfied. The reflectivity of the 0.532-µm signal was rather weak, ~0.01%, with ~0.1-mW reading beam power. The buildup time was around 3 s, with loosely focused writing beams with 50-mW power in each beam. The same experiment with a SBN crystal showed no significant harmonic phase conjugation. Finally, we stress that this effect is different from the previously published result.2
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.
Nonreciprocal energy transfer between two coherent laser beams during two-wave mixing requires a photorefractive phase shift between the interference pattern and the resulting space charge. The symmetry of the Stark geometry photorefractive quantum wells forbids a phase shift using either dc or ac fields. We present the first experimental demonstration of nonreciprocal energy transfer during two-wave mixing using moving gratings. Optical energy exchange is observed in photorefractive p-i-n quantum well diodes with photorefractive gains approaching 1000 cm−1 and exhibiting complex spatio-temporal dynamics.