1. Introduction

Volume holographic memory has attracted great attention due to its potential of high storage density and fast data transfer rate [1]. To increase the storage density, many multiplexing methods, such as angle multiplexing [2,3], shift multiplexing [4–6], wavelength multiplexing [7,8], and polarization multiplexing [9–11], etc., have been proposed and investigated previously. Most of these methods require a sequential recording of the holograms. Although wavelength multiplexing can potentially record more than one hologram in each exposure, it will require more than one laser source and a complicated alignment system. Practically, polarization multiplexing is the only mechanism that allows simultaneous recording and retrieval of two holograms.

Several methods of implementing polarization multiplexing have been studied in LiNbO₃ crystals and other photo-induced anisotropic materials. Su et al. [9] recorded two holograms sequentially in the same position of a LiNbO₃ crystal using a polarization multiplexing method based on the photovoltaic effect and the photorefractive effect. Todorov et al. [10] demonstrated another polarization multiplexing method in photo-induced anisotropic materials where the spatial modulations of polarization resulted in spatially modulated anisotropy and, consequently, in refractive index modulation. In Ref. [10], the reference and signal beams had orthogonal circular polarizations (left-hand and right-hand), and the two polarization holograms were superimposed sequentially in the common volume of a methyl orange/PVA film. Another kind of photo-induced anisotropic film, bacteriorhodopsin film, was also used to record two polarization multiplexed holograms by Koek et al [11]. In their system, the polarization of the reference beam remained unchanged during the two exposures, while the polarizations of the object beams of the two holograms were orthogonal. However, all of these polarization multiplexing schemes demonstrated only the simultaneous readout of the two polarization multiplexed holograms using the reference beam with a specific polarization. And no simultaneous recording and high density memory systems have been reported due to the following limitations: (1) the hologram generated via the photovoltaic effect in Ref. [9] is much weaker than that generated via the general photorefractive effect in LiNbO₃ crystals, and (2) the recorded holograms are volatile due to dark decay [12] in LiNbO₃ crystals and thermal relaxation [11] in photo-induced anisotropic materials.

In this paper we demonstrate a novel dual-channel holographic recording technique, in which the holograms of the two channels can be operated simultaneously in both the recording and the retrieving processes. The recording material employed in this work is the isotropic cationic ring-opening photopolymer (CROP polymer) [13] developed by Aprilis Inc. The grating evolution during the dual-channel holographic recording process is evaluated both theoretically and experimentally. The simultaneous recording and concurrent readout with equal diffraction intensities and negligible inter-channel crosstalk are demonstrated in a high-density holographic memory system based on the dual-channel holographic recording technique and a speckle shift multiplexing method. The simultaneous nature of new scheme provides the ability for the users to interact with the storage medium from an additional channel, and offers a faster data transfer rate in both the recording and reading processes.

2. Grating evolutions in dual-channel holographic recording

2.1. Theoretical analysis

Figure 1 shows the basic geometry of our dual-channel holographic recording in a CROP photopolymer with thickness d in the z direction. In this scheme, the recording beams are separated into the p- and s-polarization channels so that the polarization states of the two channels are mutually orthogonal. Specifically, the p-polarization channel consists of the recording beam pair, E _rp(r) and E _op(r), with the p-polarization; and the s-polarization channel consists of the other recording beam pair, E _rs(r) and E _os(r), with the s-polarization. During the holographic recording exposure, the photo-induced polymerization profile of the CROP polymer is directly proportional to the spatial modulation of the exposure intensity, which leads to the corresponding modulation of refractive index [15]. Therefore, the holographic exposure in this scheme simultaneously records two (and only two) volume holograms which are produced by the two interferences of the recording beam pairs in the s-and p-polarization channels, respectively. Moreover, these two holograms are distinguished by the Bragg selectivity, where a separation angle between the two reference beams much larger than the Bragg angular selectivity (Δθ_B ) is applied. The incidence angles of the reference beams, E _rp(r) and E _rs(r), in the recording material, are θ_p and θ_s , respectively. For simplicity, θ_p =-θ_s is adopted, thus the separation angles is |2θ_p |(|2θ_p |≫Δθ_B ). In addition, the two object beams are both propagating along the direction of the z-axis that is normal to the surface of the recording material.

 

Fig.1. . eometry of the dual-channel holographic recording by plane waves in a photopolymer: d, thickness of the photopolymer medium; PBS, polarizing beam splitter; E _rp(r), E _op(r), E _rs(r), and E _os(r), electric fields of the recording beams; θ_p and θ_s , incidence angles of the reference beams in the medium. Here the subscript symbols: o, object beam; r, reference beam; p, p-polarization (in the x-z plane) recording channel (shows in blue); s, s-polarization (along the direction of the y-axis) recording channel (shows in red).

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Under the diffusion free condition with a low exposure intensity in the CROP polymer, where the diffusion of the monomer is much faster than the polymerization, high values of index modulation can be recorded with high fidelity and the dark reaction effect can be neglected [16]. In this case, the diffusion-reaction model [17,18] is applicable to the CROP polymer [16]. Thus we can obtain the temporal evolutions of diffraction index modulations [18] of p- and s-polarization channels in the proposed scheme respectively, as:

where, Δn_p (t) and Δn_s (t) are the temporal modulations of the refraction index, E_rp, E_rs, E_op , and E_os are the amplitudes of the reference and object beams of the p- and s-polarization channels, respectively. $I_0=\sum _{i=r,o}\sum _{j=s,p}{E}_{\mathit{ij}}^2$ is the average recording intensity, αM is the maximum available modulation index, γ is a positive constant responsible for the time evolution, and τ(τ∝$I_0^{-1}$) is the time constant.

The temporal evolutions of the grating strengths (ν_p and ν_s ) of these two gratings can be described as [19]:

where, λ is the wavelength of the probe wave, θ_bp , θ_bs are the Bragg diffraction angles of the probe waves for the p- and s-polarization channels respectively, and θ_bp=-θ_sp , due to θ_p =-θ_s .

According to Eqs. (1) and (2), it can be seen that the temporal evolutions of the grating strengths of the two channels are similar in form. The only difference is a reductive coefficient of cos(θ_p ) cos(θ_bp ) in the p-polarization channel. However, in practice, equal grating strengths can be achieved easily by using small θ_p (θ_bp=θ_p when the beam with the same wavelength is used for reading) and slightly higher intensities for the corresponding beams of the p-polarization channel.

2.2. Experimental results of grating evolutions

To verify the theoretical predictions, we recorded gratings with the dual-channel holographic recording scheme shown in Fig. 1 in the CROP polymer. A diode pumped laser (wavelength λ=532nm) is used to generate laser beams for the dual-channel holographic recording. The polarization of each beam is carefully adjusted as in Fig. 1. The recording intensity of each beam is about 0.8mW/cm². The incidence angle of the reference beam measured in the air is 25° for the s-polarization channel, and -25° for the p-polarization channel. Using the CROP polymer index n=1.545, we can calculate the corresponding incidence angle in the material, which is θ_s =15.87° and θ_p =-15.87° respectively. Since the material has low sensitivity and absorption at wavelengths longer than 600nm, a diode laser at the wavelength of 650nm is used to monitor the evolution of gratings in real time by Bragg-matched probing: one exposure process for the s-polarization channel using an s-polarized probe beam at the probe angle of θ_bs =17.62°, and the other for the p-polarization channel using a p-polarized probe beam at the probe angle of θ_bp =-17.62°. The temporal evolution of each grating is

where I_d (t) and I_t (t) are the intensities of the diffracted and transmitted beams, respectively.

 

Fig. 2. Grating evolutions during dual-channel holographic recording

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The dotted curves in Fig. 2 illustrate the grating evolutions of the s- and p-polarization channels. We extracted ν_p.sat =0.471, γ=2.10 and τ=13.5s from the experimental data of the p-polarization channel, and ν_s.sat =0.523, γ=2.14 and τ=13.5s from that of s-polarization channel by minimizing the sum of the squares of the difference between experimental data points and theoretical predictions. The values of γ and τ of the two gratings are similar, just as the theoretical predictions. The ratio of ν_p.sat and ν_s.sat is 0.90, which agrees with the theoretical value (r=ν_p.sat/ν_p.sat =cos(θ_p )cos(θ_bp )=0.91).

3. Holographic memory with dual data-channel

3.1. System setup

The optical setup of the dual-channel holographic memory system is shown in Fig. 3. The linearly polarized light at the wavelength of 532nm generated from a diode-pumped laser source passes through a half-wave plate HP1 and a polarized beam splitter PBS1, the light is then divided into the reference and object arms. In the object arm, the PBS3 divides the light into two parts to illuminate the two spatial light modulators, SLM1 and SLM2 (1280×768 arrays of 13.2µm×13.2µm), respectively. One is the p-polarization data-channel. And the other is the s-polarization data-channel. In the reference arm, the PBS2 divides the light into reference beams of the p- and s-polarization channels. A quarter-wave plate QP and an adjustable mirror are added to compensate the path-length difference between the object and reference beams in the p-polarization data-channel. The half-wave plates HP1, HP2 and HP3 are employed to adjust the intensities of the four recording beams. And the HP4 is used to adjust the reference beam polarization. The diffusers, D1 and D2, with FHWM=5°, generate random speckle modulation in reference beams for speckle shift multiplexing. The corresponding effective NA (numerical aperture) of each reference beam is about 0.1. The recording material is Aprilis HMC-series polymer with the thickness of 300µm, which features a high dynamic range, high recording sensitivity, and very low volumetric shrinkage [20], and is regarded as one of the most promising WORM material for nonvolatile holographic memory [14]. This material is mounted onto a positioning system composed of two linear translation stages which can perform addressing in sub-micrometer scale along the x- and y directions at the Fourier plane of the SLMs, respectively. The reconstructed beams are separated by the PBS4 and then captured by CCD1 and CCD2 which receive the data from p- and s-polarization data-channels.

 

Fig. 3. Experimental setup for dual data-channel holographic memory: DPL, diode-pumped solid-state laser; HP, half-wave plate; PBS, polarizing beam splitter; SF, spatial filter; EL, beam-expanding lens; QP, quarter-wave plate; D, diffuser; SLM, spatial light modulator; FL, Fourier transfer Lens; WP, wedge prism; L, lens; M, mirror; HMC, holographic media card; CCD, charge coupled device.

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3.2. Experimental results

According to the analysis of grating evolutions in our dual-channel holographic recording scheme, in order to achieve equal diffraction intensity for the two channels, the reference (readout) power of the p-polarization channel is adjusted to a slightly higher level than that of the s-polarization channel. In the experiment, the powers of the s- and p-reference beams are 81µW and 100µW, and those of the signal beams are 38µW and 34µW, respectively. The diameter of the recorded spot is around 5mm. And the incidence angles of the reference beams are 25° and -25°, respectively.

 

Fig. 4. (a).Shift selectivity of a hologram recorded using speckle shift multiplexing in dual-channel system. (b). Readout of 30 holograms per channel superimposed by speckle shift multiplexing.

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Shift multiplexing method based on speckle correlation is adopted here, in order to perform high density holographic multiplexing in the whole volume of the material. The one dimensional shift selectivity of a hologram in the dual-channel system is plotted in Fig. 4(a), by measuring the diffraction intensities of the reconstructed holograms every 0.425µm shift interval (50 shifting steps of the linear translation stage with the step resolution of 0.0085µm).

The shift selectivity is about 6µm, which is in good agreement with theoretical results [5] in single-channel systems. The deviation of the experimental curve from the theoretical one in the tails of the diffraction efficiency curve is mainly caused by the noises of speckle field and the I/O devices. Moreover, the speckle noise intensity will increase linearly with the increasing number of multiplexed holograms, since the previously recorded holograms are still reconstructed randomly under an optical speckle field [14] in the speckle shift multiplexing. Thus a shift interval of 170µm is chosen in both the x and y directions to minimize the crosstalk and the speckle noise. 1800 (30×30×2) holograms with 0.96-Mpixels data each are recorded in a local square area by using the dual-channel technique and the speckle shift multiplexing method. The resulting density is about 20pixels/µm². The diffraction intensity of each hologram in the first row is plotted in Fig. 4(b). It shows that the average diffraction intensities of the p- and s-channels are similar, and the diffraction intensities of sequentially recorded holograms in the same channel are almost uniform with a fluctuation of ±7%. This is mainly caused by the fluctuation of the laser power and the tiny non-uniformity of polymer composition system. One pair of simultaneously reconstructed data pages is shown in Fig. 5. It can be seen that a good separation of the data pages of the two channels is achieved, and no evidence of inter-channel crosstalk is observed, as in Fig.5 (a) and Fig.5 (b). The overlapped data page captured by CCD1 without PBS4 is shown in Fig. 5 (c). It shows the diffraction intensities of two channels are almost equal. This implies that the parameters chosen for dual data-channel holographic memory are feasible.

 

Fig. 5. Readout pages in dual data-channel holographic memory: (a) p-channel data page; (b) s-channel data page; (c) the overlapped p- and s-channel data pages without PBS4.

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4. Conclusions

A dual-channel holographic recording technique that allows simultaneously access of two orthogonally polarized holograms, in both recording and reading processes, with negligible inter-channel crosstalk is proposed. The grating evolution in the dual-channel holographic recording scheme is theoretically analyzed, and experimentally validated. A holographic memory system with equal diffraction intensities is demonstrated by combining the proposed technique with a speckle shift multiplexing method. In addition, our system uses only one 4-f optical head to transfer the pair of data pages with orthogonal polarization. This simultaneous nature of the two channels offers a compact system with a faster data transfer rate in both the recording and reading processes.

The result reported here is obtained with Aprilis CROP polymer but it is valid for most isotropic photopolymerizable recording media without photo-induced anisotropy in general. And in this kind of dual-channel system, the pair of pages recorded simultaneously can be independent data from different data sources, e.g., one from an analog device and the other from a digital source; or they can be related data from correlated data sources. For example, one potential application of the dual-channel holographic memory system is the holographic projector [21] for stereoscopic video.