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Journal of the Optical Society of America B

Theory of the photorefractive effect for multiple-quantum-well structures in perpendicular field ref lection grating geometry

Vladimir V. Shkunov, Mark V. Zolotarev

Published May 1, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1364/josab.12.000913

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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.

Photorefractive Effects, Materials, and Devices•Jan 1, 1991•0 citations
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.
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.
An interaction between optical signal guided in a photorefractive multiple quantum well planar waveguide and two external waves is considered. The external waves create a refractive index grating in the waveguide core which can be applied for frequency selective switching of guided signals. The influence of free carriers generated by the signal wave on the stability of photorefractive grating is analyzed. Full Text: PDF References D.D. Nolte, "Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications", [CrossRef] M. Wichtowski, A. Ziółkowski, E. Weinert-Rączka, "A general approach to the space–charge field solution in photorefractive materials in a TWM geometry", J. Opt. 12, 065201 (2010) [CrossRef] E. Weinert-Rączka, M. Wichtowski, A. Ziółkowski, G. Staroń, "Photorefractive Grating in Multiple Quantum Well Planar Waveguide", Acta Phys. Pol. A 103, 229 (2003) A. Ziółkowski, E. Weinert-Rączka, "Dark screening solitons in multiple quantum well planar waveguide", [CrossRef] A. Ziółkowski, "Temporal analysis of solitons in photorefractive semiconductors", J. Opt. 14, 035202 (2012) [CrossRef] M. Wichtowski, E. Weinert-Rączka, "Photorefractive Multiple Quantum Well Waveguide as a Bragg Reflector ", Acta Physica Polonica A 103, 239 (2003) Q. Wang, R. M. Brubaker, D. D. Nolte and M. R. Melloch, "Photorefractive quantum wells: transverse Franz—Keldysh geometry", J. Opt. Soc. Am. B 9, 1626 (1992) [CrossRef] D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, "Resonant photodiffractive effect in semi-insulating multiple quantum wells", A.M. Glass. J. Opt. Soc. Am. B 7, 2217 (1990) [CrossRef] D.D. Nolte, M. R. Melloch : In: Photorectractive effects and Materials, ed. by D. D. Nolte (Kluwer, Dordrecht 1995) L. F. Magaňa, F. Agulló-López and M. Carrascosa, "Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells", J. Opt. Soc. Am. B 11, 1651 (1994) [CrossRef] Q. Wang, R. M. Brubaker, D. D. Nolte, "Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures", J. Opt. Soc. Am. B 9, 1773 (1994) [CrossRef] P. Vaveliuk, B. Ruiz, N. Bolognini, "Analysis of the steady-state photorefractive harmonic gratings", Phys. Rev. B, 59, 10985 (1999) [CrossRef] D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, "Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures", IEEE J. Quantum. Electron. 20, 265 (1984) [CrossRef] D.D. Nolte, Q. Wang, "Robust infrared gratings in photorefractive quantum wells generated by an above-band-gap laser", Appl. Phys Lett. 58, 2067 (1991) [CrossRef]
A model of wave mixing is developed for photorefractive multiple-quantum-well structures in quantum-confined Stark effect geometry. This optical model takes into account both absorption and index gratings and is based on the nonlocal character of the optical nonlinearity in the direction of the applied electric field. A coupling gain is defined that depends only on the imaginary part of the relative permittivity grating. It is shown that self-starting gratings can appear when a certain threshold condition on the coupling gain is verified, with this condition being similar to the threshold condition for double phase-conjugate mirror operation in bulk photorefractive materials. The possibility of obtaining with actual devices the relatively high optical nonlinearity necessary to reach the threshold is discussed. Double phase conjugation with multiple-quantum-well structures in a two-zone configuration is envisaged.
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.