Coaxial polarization holographic data recording on a polarization-sensitive medium

Teruyoshi Nobukawa; Takashi Fukuda; Daisuke Barada; Takanori Nomura

doi:10.1364/OL.41.004919

Polarization holography is capable of recording and retrieving amplitude, phase, and polarization of a beam in a material [1,2]. By introducing polarization holography to a holographic data storage system [3], it is possible to encode digital data in terms of polarization states of a beam, such as the direction of linear polarization [4]. This allows us to carry out multilevel polarization coding [5] and polarization multiplexing [1,6–8], in addition to the well-known angular, shift, and phase multiplexing. These recording techniques based on polarization holography are promising ways for improving the storage capacity and the data transfer rate in holographic data storage. Conventional polarization holographic data storage systems, however, are based on two-axis holography. This recording setup is difficult to downsize. In addition, such optical setup is rather easily influenced by vibration on an installation environment. Unlike two-axis holography, coaxial holographic data storage is compact and robust for vibration because signal and reference beams propagate along a common optical path [9–13]. Conventional coaxial holographic data storage, however, has been designed and developed for encoding digital data solely on the amplitude of a beam. Therefore, it is impossible to record and retrieve a polarization hologram in conventional coaxial systems.

In this Letter, we propose a coaxial polarization holographic data storage system to realize a practical polarization holographic data recording. In the proposed system, we generate an arbitrary vector beam using a phase hologram technique [14–16]. To record the polarization hologram of a vector beam, we use a polarization-sensitive medium containing a photodegradative aromatic ketone derivative (AK1) [17,18]. The medium with the AK1 is initially isotropic, and illumination with a polarized beam results in linear anisotropy of the medium via axis-selective photoreaction [17,19]. The AK1 is reported to exhibit large photoinduced linear birefringence, as compared with conventional polarization-sensitive medium containing phenanthrenequinone [19–21]. By using the proposed system, we aim to investigate the fundamental characteristics of coaxial polarization holographic data storage. In particular, we experimentally evaluate the effect of an introduction of a random phase mask [10,11] on reconstructed images by means of a signal-to-noise ratio (SNR) and a symbol error rate (SER).

Figure 1 shows an optical setup for coaxial polarization holographic data storage. Referring to Fig. 1, we describe the recording and retrieving processes of polarization coaxial holographic data storage. A mode-hop-free single-mode laser (405 nm) was used as a light source. A polarization direction was adjusted at 45° from a horizontal direction using a half-wave plate and a polarizer. A spatial filter was applied to the beam to obtain a collimated beam. The resulting beam was divided into two beams using a non-polarizing beam splitter, and each beam was incident on each phase-only spatial light modulator (SLM) which has $800 \times 600$ pixels with a pixel pitch of 20 μm (X10468-01, Hamamatsu Photonics K. K.). In general, the use of phase holograms displayed on two transmissive SLMs allows us to spatially modulate amplitude, phase, and polarization distribution of a beam [22]. The technique presented in [22] is based on a cascaded architecture in which one transmissive SLM imaged on the other. Alternatively, in our proposed system shown in Fig. 1, two reflective SLMs are arranged in the L-shaped arrangement for coherent polarization addition (LCPA) layout. The working directions of SLMs for a linearly polarized beam are set to be orthogonal with each other. The phase holograms [14–16] to be displayed on SLMs are designed as follows. An arbitrary vector beam can be described by the superimposition of two orthogonal linearly polarized beams $E_{1} (x, y)$ and $E_{2} (x, y)$ on the basis of the Jones formalism:

(\begin{matrix} E_{1} (x, y) \\ E_{2} (x, y) \end{matrix}) = (\begin{matrix} a_{1} (x, y) \exp {i φ_{1} (x, y)} \\ a_{2} (x, y) \exp {i φ_{2} (x, y)} \end{matrix}),

where

a_{1}

and

a_{2}

are amplitudes, and

φ_{1}

and

φ_{2}

are phases of horizontal and vertical linearly polarized beams, respectively. To generate each complex amplitude

E_{n} (x, y)

(

n = 1, 2

), each SLM displayed a phase hologram

ψ_{n} (x^{'}, y^{'})

(

n = 1, 2

):

ψ_{n} (x^{'}, y^{'}) = A_{n} (x^{'}, y^{'}) {Φ_{n} (x^{'}, y^{'}) + φ_{c} (x^{'}, y^{'})},

where

A_{n}

and

Φ_{n}

denote functions to determine amplitude

a_{n}

and phase

φ_{n}

, respectively.

φ_{c}

is a linear phase distribution to separate a desired component from unnecessary diffracted beams in the Fourier plane, as described later. The divided beams from a non-polarizing beam splitter were modulated with each SLM according to Eq. (2). Each phase-modulated beam

\exp {i ψ_{n} (x^{'}, y^{'})}

was Fourier transformed by a lens. In the Fourier plane, there were diffracted beams of the phase-modulated beams. Owing to the linear phase distribution,

φ_{c}

, the desired components correspond to the first-order beams of the diffracted beams. Only the first-order beams are extracted through the aperture which is twice as large as the Nyquist size, since the rest of the diffracted beams are unnecessary. In the conjugate plane of the SLMs, each first-order beam is given by

E_{n} (x, y) = \frac{\sin {1 - A_{n} (x, y)} π}{{1 - A_{n} (x, y)} π} \cdot \exp [i {Φ_{n} (x, y) - (1 - A_{n} (x, y)) π}] .

Note that the polarization states of

E_{1} (x, y)

and

E_{2} (x, y)

in Eq. (3) are orthogonal with each other because the working directions of SLMs for a linearly polarized beam are set to be orthogonal as described before. By comparing Eqs. (1) and (3), the coefficient of the exponential function can be regarded as an amplitude value

a_{n}

, or

\frac{\sin {1 - A_{n} (x, y)} π}{{1 - A_{n} (x, y)} π} = a_{n},

and its inverse function is given by

A_{n} (x, y) = 1 - {sinc}^{- 1} (a_{n}),

where

{sinc}^{- 1}

is the inverse of

\sin (k π) {(k π)}^{- 1}

. Similarly, the exponential term

{Φ_{n} (x, y) - (1 - A_{n} (x, y)) π}

in Eq. (3) can be regarded as a phase value

φ_{n}

, or

Φ_{n} (x, y) = φ_{n} + {1 - A_{n} (x, y)} π .

Therefore, the desired vector signal and reference beams can be obtained in the conjugate plane of the SLMs by designing the phase holograms on the basis of Eqs. (2), (5), and (6). This phase hologram technique can remove undesired zeroth-order beams [23] that are caused by the surface reflection and the imperfection of the SLMs and, thus, it is possible to generate a high-quality beam. A detailed description and other functions for the phase hologram

ψ_{n}

are presented in [14] and [15].

Fig. 1. Optical setup for coaxial polarization holographic data storage. HWP, half-wave plate; $P i$ , polarizer; SF, spatial filter; $L i$ , lens; BS, beam splitter; $SLM i$ , phase-only spatial light modulator; M, mirror.

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These resulting beams were Fourier transformed again and interfered in the medium with a thickness of 500 μm. The vector beam recording principle in our medium is attributed in the photoinduced birefringence [17]. During the retrieving process, the volume polarization hologram was illuminated by the reference beam and, thereby, the signal beam was reconstructed. Although the reconstructed amplitude ratio between $a_{1}$ and $a_{2}$ is changed depending on the material parameters and the recording conditions [2,24,25], both a scalar complex amplitude and a polarization of a signal beam can be retrieved from a volume polarization hologram. The intensity distribution of a reconstructed signal beam was captured with a CMOS camera which has $2592 \times 1944$ pixels and a pixel pitch of 2.2 μm. The polarization component of a reconstructed signal beam was detected through a polarizer.

As a preliminary experiment, we first demonstrated recording a volume intensity hologram to evaluate the effect of a random phase mask on our medium. Note that we refer to an interference pattern of beams with the same polarization state as a volume intensity hologram to distinguish a volume polarization hologram. In general, a random phase mask makes the Fourier spectra of signal and reference beams uniform and increases an interference efficiency [10]. Moreover, a random phase mask reduces the width of the point spread function in a coaxial system [11,26,27]. The use of a random phase mask, therefore, results in a high-quality reconstructed image. Previous experimental studies on coaxial holographic data storage have shown the capability of a random phase mask in photopolymer materials [10,11,16]. Taking into consideration this aspect, here we verify that a random phase mask is also useful in our medium before recording a volume polarization hologram. Figure 2 shows the complex amplitude distribution of signal and reference beams. Each image consists of $512 \times 512$ pixels. The polarization states of the signal and reference beams are the same linear polarization. Figure 2(a) consists of a ring pattern for a reference beam and a data page. The data page is designed based on a $1 ∶ 4$ coding method [28]. In the coding method, a single symbol consists of one ON and three OFF cells in $2 \times 2$ cells. Each ON and OFF cell consists of $8 \times 8$ pixels. Figure 2(b) shows a random phase mask that has binary phase values, 0 and $π$ . The signal and reference beams were generated using the SLM1. (The SLM2 was not operated in the volume intensity hologram recording experiment.) These beams were recorded in the medium as a volume intensity hologram.

Fig. 2. Complex amplitude distribution of signal and reference beams with a horizontally linear polarization component. (a) Amplitude distribution and (b) random phase mask for signal and reference beams.

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Figure 3 shows the reconstructed images without and with a random phase mask. As is clearly found out, a clear reconstructed image is obtained when a random phase mask is applied. The quality of the reconstructed image is evaluated with an SNR and an SER. The SNR is evaluated by the following equation:

SNR = \frac{μ_{on} - μ_{off}}{{(σ_{on}^{2} + σ_{off}^{2})}^{1 / 2}},

where

μ_{on}

and

μ_{off}

are the means, and

σ_{on}^{2}

and

σ_{off}^{2}

are the variances, of the ON and the OFF pixels in a reconstructed image, respectively [3]. The SER is given by

SER = \frac{E_{symbol}}{N_{symbol}} \times 100 [%],

where

E_{symbol}

and

N_{symbol}

denote the number of error and the total symbols in a reconstructed image. The SNRs and SERs of the reconstructed images are shown in the top of Fig. 3. The values are effectively improved from 0.91 to 2.92 in the SNR, and from 14% to 0% in the SER. These improvements are consistent with the knowledge of previous studies on coaxial holographic data storage. From these experimental results, we confirmed that the introduction of the random phase mask, in recording a volume intensity hologram via coaxial optical setup, works even in our polarization-sensitive medium, as well as in the conventional photopolymer materials.

Fig. 3. Reconstructed images of volume intensity holograms (a) without and (b) with the random phase mask.

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Succeeding the preliminary confirmation on the effect of the random phase mask in our medium, we go for a demonstration of the coaxial polarization holographic data recording. For a proof-of-principle experiment, we generated a vector signal beam that consists of two independent data pages with horizontally and vertically linear polarized components. The data pages with each polarization are shown in Figs. 2(a) and 4(a). In contrast, the polarization state of a reference beam was fixed as horizontally linear. These signal and reference beams were recorded in the medium as a polarization volume hologram. A reconstructed signal beam was captured with a CMOS camera. Figures 5(a) and 5(b) show reconstructed images that are recorded without and with the random phase mask, respectively. Similar to the results in the volume intensity hologram experiment as described above, a clear reconstructed image can be obtained by using a random phase mask. These reconstructed images contain horizontally and vertically linear polarization components. Inserting a polarizer in an observation path as indicated as the position of P2 in Fig. 1, each linear polarization was separated depending on the angle of the transmission axis, as shown in Figs. 5(c)–5(f). The quality of the reconstructed image was quantitatively evaluated with the SNR and the SER. The SNRs and SERs are shown in the top of each reconstructed image. The SNRs are improved from 0.76 to 2.38 in the reconstructed images of a horizontally linear polarization component, and from 1.07 to 2.43 in the reconstructed images of a vertically linear polarization component. The SERs are completely suppressed from 20% and 11% in each linearly polarized beam. As confirmed in the previous experiment of the volume intensity hologram recording, the quality of reconstructed images is improved in each polarization state by using a random phase mask. Moreover, the original data pages are successfully retrieved without any error in the proposed system. Interestingly, although the reconstructed image with a vertically linear polarization component is orthogonal to the polarization state of the reference beam, its SNR and SER are affected and improved by the random phase mask. These experimental results insist that the introduction of a random phase mask is effective for coaxial polarization holographic data storage since the random phase mask improves a point spread function and interference efficiency, regardless of the polarization state of a signal beam.

Fig. 4. Complex amplitude distribution of a signal beam with a vertically linear polarization component. (a) Amplitude distribution and (b) random phase mask for a signal beam.

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Fig. 5. Experimental results of volume polarization holograms: reconstructed images (a) without and (b) with the random phase mask. Images (c) and (d) are horizontally linear polarization components in (a) and (b), respectively. Images (e) and (f) are vertically linear polarization components in (a) and (b), respectively.

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Note that the SNRs of the reconstructed images with a vertically linear polarization component (1.07 and 2.43) are higher than those of the reconstructed images with a horizontally linear polarization component (0.76 and 2.38). The major reasons for this result can be explained as follows. In general, the reference beam is scattered after passing through a medium [10]. This is well known for the noise in the coaxial holographic data storage. In these experiments, the reference beam had only a horizontally linear polarization component. Therefore, in Figs. 5(e) and 5(f), the scattered reference beam was suppressed by using an orthogonal polarizer to the polarization state of a reference beam.

In conclusion, we have proposed a coaxial polarization holographic data recording for the first time, to the best of our knowledge. In our system, an arbitrary vector beam is generated by using the LCPA layout to make the use of a phase hologram technique. As a proof-of-principle experiment, we recorded data pages encoded on horizontal and vertical linear polarized beams. Each of the data pages was successfully retrieved without any error. The proposed system allows us to realize a compact, simple, and stable optical setup for a polarization holographic data recording, since the signal and reference beams propagate along a common optical path. To the best of our knowledge, the effect of a random phase mask on a volume polarization hologram has not been discussed previously. The experimental results clearly indicated that the introduction of a random phase mask is considerably effective for improving the SNR and the SER in recording volume polarization holograms, as well as in recording volume intensity holograms.

Funding

Japan Society for the Promotion of Science (JSPS) (15J11996); Japan Science and Technology Agency (JST) under the Strategic Promotion of Innovation Research and Development Program.

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Coaxial polarization holographic data recording on a polarization-sensitive medium

Abstract

Funding

REFERENCES

Cited By

Figures (5)

Equations (8)

Optics Letters