Determination of the time constant of fast photorefractive materials using the phase modulation technique
Applied Physics Letters
We present a method to determine the dielectric relaxation time using a phase-modulation technique. The predictions were checked using a GaAs crystal. The experimental results agree well with the theory. © 1995 American Institute of Physics. Semiconductors as photorefractive materials sensitive to infrared light are among others advantageous since they have small response times. Typically these time constants are in the range of milli-down to microseconds depending on parameters like
... ers like illuminating intensity, temperature, dopant concentration, or grating spacing. An exact knowledge of this material constant is important for the characterization of the material under investigation. The first possibility to determine the time constant is a direct one by measuring the diffraction efficiency during erasure of a holographic grating as a function of time. 1,2 However, this erasure technique is sometimes difficult to perform. A beam-coupling technique was demonstrated in Ref. 3. A further possibility was presented recently. 4 It is based on the phase modulation technique. 5 Hereby the phase of one of the two beams in a beam-coupling experiment is slightly modulated with a certain frequency. This makes vibrating the light interference pattern on the crystal. The light intensity of the beams measured behind the crystal contains higher harmonics depending on the phase shift between the light interference pattern and the holographic grating and on the fact whether the grating is a refractive index grating or an absorption grating. It is obvious that the modulated signal depends on the modulation frequency. If the frequency is much smaller than the inverse response time, the hologram can be recorded instantaneously. Thus, no modulated signal can be observed. If the modulation frequency is large enough, however, the material cannot follow the oscillation of the light intensity pattern. As a consequence the resulting modulated signal becomes independent of the modulation frequency and saturates. In between there is a characteristic dependence of the amplitude of the modulated signal on the modulation frequency. This behavior has been used in Ref. 4 to determine the time constant. In this letter we show that there is a second possibility, namely to exploit the fact that also the phase between the modulation and the higher harmonics depends on the modulation frequency and can be used to get information about the time constant. The basic formulas of the phase modulation technique were already derived in Refs. 4 and 5. Here only a short summary is given as far it is necessary to present the main idea of this letter. The periodic light intensity pattern in a beam-coupling experiment of two beams S and R ͑see Fig. 1͒ can be written as where the complex conjugate of the modulation m has to satisfy m*(K,t)ϭm(ϪK,t) since the intensity I is a real quantity. The phase of beam S is now modulated. As a consequence m can be written as In the approximation ͉m͉Ӷ1 the time evolution of a space charge field E sc is governed by assuming a purely diffusion driven mechanism with E D as diffusion field. The time constant under investigation is . The general, inhomogeneous solution of Eq. ͑3͒ is where m (K,)ϭ(1/2)͐ Ϫϱ ϱ m(K,t)exp(Ϫit) dt is the Fourier transformation of m(K,t). The homogeneous solution of a͒ Electronic mail: firstname.lastname@example.org FIG. 1. Sketch of experimental arrangement. The phase of beam S is modulated. The interference of the transmitted part of beam S and the diffracted part of beam R is analyzed.