Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings

The photorefractive response to an applied electric field is measured in a photorefractive quantum well, providing evidence in favor of the nonlinear transport in the device due to the hot electrons. The reduced mobility of the hot electrons limits the drift length, and thereby limits fringe overshoot. Thus the nonlinear transport prevents the slowing down of the grating writing rate for increasing fields which is common in bulk photorefractives. The photorefractive phase shift in transverse-field photorefractive quantum wells is measured as a function of the frequency offset between two laser writing beams that generate moving gratings. The two-wave mixing passes through a maximum at an optimum frequency which depends on the magnitude and the sign of the applied dc electric field. The phase shift associated with the moving grating adds or subtracts from the static phase shift induced by hot-electron transport in the semiconductor quantum wells, depending on the sign of the field and the sign of the dominant photocarriers. We observe a linear relationship between the roll-off frequency and the power of the writing beams. PACS: 42.40; 42.65; 78.65 Photorefractive quantum wells operating in the transversefield geometry exhibit a photorefractive phase shift under an applied dc electric field that could not be attributed to trap limitation [1]. The presence of the phase shift led to nonreciprocal energy transfer during two-wave mixing, and produced record photorefractive gains in excess of 1000 cm−1 in these devices [2]. The nonlocal dielectric response produced a “turn-on” voltage signature that was reminiscent of the Gunn-effect mechanism in doped GaAs [3], which led to the suggestion that the photorefractive phase shift in the quantum wells was a consequence of nonlinear transport and electron velocity saturation [4]. This hypothesis was verified Dedicated to Prof. Dr. Eckard Krätzig on the occasion of his 60th birthday. experimentally in 1996 when a direct experimental connection was made between the phase shift and the structure of the conduction band valleys [5]. Clear evidence for the simultaneous onset of transport nonlinearity due to electron heating and the onset of the photorefractive phase shift were seen in experiments performed on several different samples whose band structures had been specifically engineered. The nonlocal dielectric response associated with the electron heating and nonlinear transport has important consequences for applications such as laser-based ultrasound detection. Two-wave mixing in photorefractive quantum wells has been used to perform homodyne detection of surface displacements [6]. In these experiments, the relative phase between the signal wave and the local oscillator must be equal to 90◦. This phase relationship is needed to achieve maximum linear detection of surface displacements. Because the photorefractive quantum well acts as an adaptive beam combiner, the photorefractive phase shift contributes to the relative phase of the signal and local oscillator, and therefore is of practical interest for this application. In this paper, we perform a detailed study of the twowave-mixing dynamics in transverse-field photorefractive quantum wells using running gratings, paying special attention to the role played by the hot-electron photorefractive phase shift. The moving gratings produce an additional shift of the space-charge grating relative to the intensity pattern. This shift can add constructively or destructively with the static hot-electron phase shift, producing changes in the sign for some grating velocities. The principal aspects of the hot-electron phase shift are discussed in Sect. 1, and the device design, fabrication, and characterization are discussed in Sect. 2. The experiments are described in Sect. 3, which has two parts: one that addresses the hot-electron effect on the grating response time in the absence of moving gratings; and one that includes the effects of running gratings. One of the interesting aspects of the hot-electron transport nonlinearity in photorefractive quantum wells is the absence of field-induced slowing down of the grating response time in