Both the spatial and temporal evolutions of photorefractive (PR) grating formation by field-induced enhancement in Mn:Fe:KTN crystal are visualized in situ and estimated quantitatively by means of digital holographic microscopy. A series of sequential phase maps are retrieved numerically from the recorded digital holograms to explore the quantitative characteristics of the observed procedure. Further investigations reveal that the properties of PR grating, i.e. amplitude of index modulation and writing time of the grating, can be improved drastically by an external field. The improvement PR grating is attributed to enhanced space-charge fields induced by an external field. This effect can be of interest for many relevant applications, such as electroholographic switching, and in situ and real-time monitoring of both the grating structure and its refractive index profile.
© 2016 Optical Society of America
Electroholography (EH) is a high-speed photonic switching method to control optical diffraction by means of a volume phase (Bragg) grating, in which EH switching time below 13 ns has been obtained experimentally [1–4]. The physical basis of EH is the voltage-controlled photorefractive (PR) effect in the paraelectric phase of PR materials where the electro-optic effect is quadratic [5–15], a Bragg grating pre-stored in a crystal is activated upon the application of an electric field, then is reconstructed and the switching operation is implemented by causing diffraction to occur. Generally, the light-induced refractive index change (i.e. the modulation of the refractive index) is evaluated by measuring the gating diffraction efficiency, which is generally measured by two-wave mixing method [6–13]. However, 2D or 3D refractive index distributed in the material cannot be observed by this technique. But what is more significant is the direct observation and manipulating of photorefractive process to learn the exact temporal and spatial behavior, and also the fine structure and formation mechanism of light-induced refractive index grating in the material. However, the index cannot significantly change the intensity profile of the incident light, and therefore, cannot be measured directly. Several phase techniques have been suggested for this purpose [15–20]. For example, the digital holographic microscopy has been proposed to visualize and measure the light-induced change of refractive index in epoxy resin , and grating formation and dynamic behavior in the light-induced holographic process can be obtained by this scheme. Investigated is the refractive index change in photopolymers induced by the dark reaction, and time-lapse phase distribution is measured across the photopolymer by the digital holographic quantitative phase microscopy .
In this paper, we concentrate our interest on the dynamic refractive-index-change behavior of PR grating in a Mn:Fe:KTN crystal and monitoring it quantitatively by digital holographic microscopy (DHM). The index grating is written in a Mn:Fe:KTN crystal, to which an electric field is applied during writing. The effect has been studied by Ref , and the recording time was significantly reduced compared with the case when no electric field is applied. Compared with Ref , more fascinating properties of light-induced refractive index grating in Mn:Fe:KTN crystal under different physical conditions are observed using DHM, which is intriguing and significant, especially for EH switching. Here off-axis image plane holographic system is set up and the reconstructed phase image is retrieved from the recorded digital holograms to visualize the grating structure and refractive index profile on the Mn:Fe:KTN crystal in situ. The temporal evolution of the induced refractive index change is estimated by means of a series of sequential phase difference. The experiments are completed and corresponding theoretical analyses are given.
2. Experimental setup and method
Figure 1 shows the experimental setup schematically for grating formation and in situ monitoring of time evolution of the light-induced refractive index grating in a KTN crystal, which consists of two subsystems: the writing optical system and the probing optical system. For the writing optical setup, in which two writing beams from a semiconductor laser with a wavelength of λw = 532nm can interfere with each other and create refractive index grating in a KTN crystal, and the grating period is. By selecting the intersection angle 2θ between writing beams, index grating with different spacing can be fabricated in a KTN crystal.
The spatial distribution and temporal evolution of light-induced refractive index grating is probed in the probing optical setup, which is based on the Mach-Zehnder digital holographic microscopy arrangement which is usually used in DHM [19, 20]. The light source is a linearly polarized He-Ne laser with wavelength of 632.8nm (Thorlabs HNL050L). A laser beam is expanded and spatially filtered and collimated to an approximate plane-wave of 10mm radius by BE, and then passes through a polarizer and a polarizing beam splitter cube PBS. The horizontally linearly polarized light, i.e. p-polarized light, reflected by reflecting mirror M1 and beam splitter cube BS1, acts as the reference wave; the vertically linearly polarized light, that is s-polarized light, is converted to p-polarized light through a half-wave plate, then is reflected by reflecting mirror M2 and illuminate the object with Bragg match. The object is magnified and imaged on the CCD camera by a microscope objective (MO 40 × , 0.65-N.A.), as the object wave. The object beam is superimposed with the plane reference beam and a Fresnel off-axis image plane hologram is formed and recorded on a CCD. The CCD used is a 14-bit digital CCD camera (GRAS-14S5M/C) with 1384 × 1036 pixels and pixel size of 6.45µm × 6.45µm. The spatial resolution of the DMH system used here is approximately 0.94μm estimated using the resolution target. The temperature of the sample in the experiment is controlled by a temperature control system (TC) we developed with a precision of 0.5°C. DC electric field is applied to the sample by a high-voltage power supply (Agilent N5772A).
The Mn:Fe:KTN single crystal, with Mn0.04:Fe0.15:KTa0.60Nb0.40O3, is grown by the top-seed solution growth method, and the Curie temperature of 27°C. A cube Mn:Fe:KTN sample with dimensions 3.4(x) × 2.0(y) × 0.94(z) mm3 is cut from the as-grown of Mn:Fe:KTN crystal along the crystallographic  axis. Both 3.4(x) × 2.0(y) mm2 faces are optically polished for light propagation. Silver electrodes are plated and two silver conducting wires are attached on both of the 3.4(x) × 0.94(z) mm2 faces, and an electric fieldis applied along the y axis, that is, by the DC-voltage source. For p-polarized light and s-polarized light, the induced index change Δno and Δne by PR effect are different, the value ne of TM mode is larger than that no of TE mode . With no little affected, only Δne is then considered. In the experiment, the writing light and the probe light are p polarized. And to avoid additional index changes by the probe beam in the crystal, the He-Ne laser is operated at much lower power by NF, and a filter with a high transmission wavelength of 633nm is inserted before the CCD camera so that the writing laser beam fails to reach the CCD.
The basics principle of DHM method has been described in detail in . The image plane holograms of the object in different states are recorded and numerically reconstructed, the phase change between and in two different states is given by
3. Experiment and the results analysis
The experimental procedure for observing and monitoring the grating formation inside the crystal is based on determining the phase map in the writing exposure process. A holographic grating is written using two beams with beam intensity of 2 mW each, the angle between the writing beams is about 2θ = 6.6°, which results in a grating period of 4.62 μm and the grating wave vector is parallel to the y-axis, a voltage of U0w = 800 V is applied during writing, temperature is 30°C. The writing process is observed by DHM system in situ and real time, the image plane hologram of the Bragg grating is then recorded on CCD, and numerically reconstructed by taking the Fourier transform, filtering and inverse Fourier transform. A detailed description of the steps is found elsewhere [21, 22]. The phase distribution of Bragg grating inside the crystal is extracted using Eq. (1), filtered by median filter and unwrapped by temporal phase unwrapping . The phase changes of the crystal between the exposure times t≠0 and t = 0 are measured. Figures 2(a)-2(f) show the partial phase map of the index grating with the exposure times of 10, 20, 40, 60, 80 and 120 s, the reading voltage of U = 800 V, respectively. The fine structure of the index grating is visualized and observed, and the phase amplitude increases as the exposure time lengthens, indicating the refractive index of PR grating is subjected to dynamic formation process. The grating spacing is roughly 4.66 μm, and the corresponding intersection angle 2θ = 6.54°, which is almost the same as the experimental result of 6.6° derived as the estimated intersection angle of writing beams. According to Eq. (2), the phase difference distribution measuredis converted to the induced refractive index change, and the spatial and temporal evolution of the grating fromation is estimated, and the amplitidue of the refracive index modulation is determined by analyzing phase distribution shown in Fig. 2. Figure 3 draws the refractive index modulation along y axis for various exposure times. With longer exposure time, subsequently reaches a steady state, for example, the value offor the exposure time of 80s is almost the same as that of 120s.
The refractive index changeis estimated as the average value of peak-to-peak index change for entire grating periods. The refractive index of PR grating subjected to dynamic formation process is a function of time. Figures 4(a)-4(c) show the average Δn as a function of exposure time with the grating period of 4.66 μm for different writing voltage, writing laser powers and temperature, respectively. The dynamic behavior of light-induced refractive index grating of the writing procedure is observed. One can see from Fig. 4, Δn increases with exposure times t, when exposure time t is kept at the same level, Δn increases with the increasing voltage; Δn increases as temperature is close to the Curie temperature, and Δn is little variant with writing laser intensity. Subsequently, Δn saturates after a certain exposure time, and the saturation value Δns depends on the applied electric field, and increases as the electric field strengthens. The writing time constant tw and Δns have been obtained by fitting the Δn-t curves shown in Fig. 4 to the functionFigs. 4(a)-4(c), the red solid fitting curves agree with the experiment data profile, and the fitting parameters are listed in Table 1.
Form Table 1, you notice that for field-induced enhancement effect, tw can be seen as a constant for writing voltage and temperature, and decreases with increasing writing-beam power, the value of tw determines the build-up time of the index grating formation. However, the saturation value Δns is mainly dependent on the writing voltage U0w at the same reading voltage, and increases with the writing voltage rising. To further evaluate the writing time constant tw and the saturation value Δns, we carry out the experiment with the same parameters as in Fig. 4(a) except that no electric field is applied during writing, and the result is shown as in Fig. 4(d) and Table 1, here the reading voltage is 800 V. By comparing two plots in Fig. 4(a) and Fig. 4(d), one can clearly observe that with an enhanced external field (U0w≠0), the writing time constant tw is substantially reduced, as is given in . This is mainly because the drift field induced by the enhanced effect is dominant compared with the diffusion field, which results in that the movement of photo-excited carriers is effected by the drift field rather than diffusion field, namely, the external field stimulates the movement of photo-excited carriers. Another important fact is that the effect of the field-induced enhancement has the bigger amplitude of the refractive index modulation Δn than that of an unenhanced external field (U0w = 0), for Esc is strongly affected by the applied electric field E0w; therefore, the field significantly affects the behavior of the modulation depth. The result implies that high diffraction efficiency can be obtained by applying a relatively low electric field E0w. And the writing time constant tw is independent of writing voltage and temperature for field-induced enhancement effect, which benefits the exposure schedule for EH.
To validate the performance with field-induced enhancement (U0w≠0V) again, we study the average Δn as a function of reading voltage under different writing voltages, writing laser powers and temperatures, and the experimental results are illustrated in Figs. 5(a)-5(c), respectively. All recorded holograms with a grating period of 2.22 μm are written with the grating vector oriented along the y axis, and the exposure time is 100 s, which is saturation. As can be seen from Figs. 5(a)-5(c), ∆n increases as the reading voltage strengthens. When the reading voltage is fixed, ∆n increases with the rising writing voltage and temperature near the Curie temperature; and ∆n is constant with the writing intensity. Compared with an electric field applied on crystal during writing, ∆n has a relatively small value at the same reading voltage when no electric field is applied during writing, which implies that the large Δn can be obtained with the driving voltage of the crystal effectively enhanced.
Each time before grating writing, it is necessary to erase all the original grating using the annealing treatment. We investigate the influence of annealing rate on the refractive index. The sample is heated to 200°C at a rate of 2, 7 and 15°C per minute, and then cools to room temperature at the corresponding rate, and the index grating written in KTN crystal is annealed out. Figure 5(d) depicts the average ∆n as a function of temperature at different annealing rates, respectively, of which the grating period is 2.22 μm at the exposure time of 100 s, the writing voltage of U0w = 600 V, the reading voltage of 600 V and each writing-beam power of 1.5 mW. It should be noticed that for a given temperature, the higher the cooling rate, the bigger ∆n is. ∆n varies very slowly at the very slow cooling rate, 2°C/min, and ∆n grows faster at the faster cooling rate, 15 °C/min. This can be explained that the relatively larger value of electro-optic (EO) coefficients is achieved through the relatively fast cooling rate , and eventually causing significant changes in refractive index. The origin of the large EO coefficients can be expounded by the presence of polar nanoregions (PNRs) in the material which can be affected by an external electric field to enhance the quadratic EO effect. In our experiment, the annealing rate is the same at 10 °C/min.
In addition, it is also of interest to study the dependence of the refractive index change on grating period. The writing angles, 2θ = 5°, 15° and 20°, is examined in detail with an enhanced external field (U0w = 600 V) and with an unenhanced electric field (U0w = 0 V), for comparison. Recording is performed at the writing beam power of 2.0 mW, temperature of 30°C, and exposure time of 100 s and 600 s, respectively. The reconstructed unwrapped phase images by DHM from the light-induced refractive index hologram at U0w = 600 V and U0w = 0 V are shown as in Fig. 6 and Fig. 7, respectively, and the reading voltage is 1000 V. Similarly, the phase distribution measuredis converted to the induced refractive index change using Eq. (2), the spatial variation of along y axis for various grating frequency are plotted, as an insert also shown in Fig. 6 and Fig. 7. From Fig. 6 and Fig. 7, the grating spacing decreases as θ increased, and the value ofwith an enhanced external field is bigger than that of one without an enhanced external field. With grating frequency increasing, increases for the unenhanced effect, while for the enhanced effect, the peak value of is almost the same, independent of grating period (see insert). Figure 8 gives the average Δn with respect to the reading voltages for different grating period with and without electric field applied during writing. Obviously, we can find that, ∆n increases with the increasing reading voltage whether the writing voltage is applied or not, and ∆n is little relevant to the writing angles with the enhanced effect, while significantly different without enhanced effect. When zero electric field is applied during writing, the bigger value of Δn is obtained with the higher grating frequency. With writing angles 2θ increasing, such as 2θ = 61.7°, the grating period is equal to the writing wavelength, sharply decreases due to strongly scattering of the incident light, which is observed in our experiment, so the maximum writing angle is limited due to the writing wavelength. We only consider relative small writing angle in experiment. The solid line in Fig. 8 indicates the theoretical fit obtained using Eq. (4), and fits well with the experimental results.
4. Theoretical analysis
The mechanism of the phenomenon mentioned above will be further discussed in the following section. The transport of charge carriers upon illumination is of basic importance for the PR effect, and the movement of the photoexcited free carriers can be effected by three different mechanisms: diffusion, drift (when an electric field is externally applied) and the photovoltaic effect. For KTN crystals with m3m composition at the paraelectric phase, the amplitude of light-induced index grating is given by 23]Equation (5) is written in the alternative form
Figure 9(a) plots Esc as a function of grating spacing with different writing voltage U0w using Eq. (5). Figure 9(b) and 9(c) show the Δn as a function of reading voltage with different grating periods using Eqs. (4) and (5). The following parameters are used in our calculations: n0 = 2.3, m = 0.8, e = 1.602 × 10−19 C, kB = 1.38 × 10−23 J/K, ε0 = 8.85 × 10−12 Fm−1, NA = 15 × 1024 m−3, T = 303 K, R11 = 5.65 × 10−15 m2/V2, εr = 14208 at 30°C, respectively (The values of R11 and εr are from the experiments).
As Fig. 9 shows, Esc increases as U0w increases, and is independent from θ in a large scope, Δn increases with the increasing Esc and reading voltage U. When the reading voltage U is fixed, Δn in the presence of an applied field (such as U0w = 600 V) is bigger than that in the absence of a field (U0w = 0 V), which is mainly because the E0w field enhances the space-charge field Esc as a result of the drift of the change carriers, eventually greatly increasing the modulation depth of refractive index. Without the enhanced effect (i.e., U0w = 0 V), Δn varies with the grating period Λ, see Fig. 9(c) and Fig. 8(b). The reason is that diffusion is dominant in this case, Esc is purely imaginary and determined by the Eq field and the ED field, and ED and Eq are a function of writing angle, and proportional toand, respectively. For largeθ, (see Eq. (6)). The rate of development of the space-charge field varies strongly with migration length. Thus the optimal writing time is variable because of the difference in the travel distance for the photo-excited carriers (the diffusion length are respectively LD = 0.97, 0.32 and 0.24 μm for 2θ = 5, 15 and 20°). However, when U0w≠0, for example, U0w = 600V, Δn is the same for 2θ = 5, 15 and 20°, see Fig. 8(a) and 9(b), this is mainly because that the Eq field and the ED field are of little help for the space-charge field Esc, the drift field induced by the enhanced effect is significantly larger than the diffusion field caused by the concentration gradient, and. Furthermore, the optimal writing time is the same because the drift lengths (, μ is the mobility, τ is the free carrier lifetime) are the same for different θ, which is highly helpful for angle multiplexing of grating in crystal. The phenomenon simulated is in good agreement with our experimental measurement.
Experimentally, we successfully in situ observe the dynamic behavior of the growth of Bragg grating in a Mn:Fe:KTN crystal, based on the effects of field-induced enhancement, with digital holographic microscopy. Quantitatively, we visualize and monitor the spatial and temporal evolution of PR grating formation by means of phase maps. The process of the grating formation can be artificially controlled to inscribe grating structure desired in PR crystals by DHM, which is intriguing and significant. Additionally, the refractive index change of grating with respect to the cooling rate is also studied, and the large ∆n can be obtained with the fast annealing rate. Experimental results show that bias field can affect PR process significantly, such as shortening writing time, increasing refractive index modulation. Meanwhile, the achieved index modulation amplitude ∆n is independent of grating spacing and writing-beam intensity, a writing time constant tw falls with writing-beam power increasing and is the same for writing voltage and temperature. Importantly, the high diffraction efficiency can be obtained by applying a relatively low electric field. The theoretical analysis is also investigated, results of which agree well with the experimental ones. And a more noteworthy advantage is that the lifetime of non-fixed photorefractive grating can be greatly prolonged by field-induced enhancement effect, which will be reported in a separate paper. In conclusion, the reports in this paper are particularly beneficial for EH, especially, EH switching.
Open Project of State Key Laboratory of Transient Optics and Photonic Technology (No.SKLST201505); National Natural Science Foundation of China (NSFC) (61077072).
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