February 15, 1999 / Vol. 24, No. 4 / OPTICS LETTERS 265

Multilayer volume holographic optical memory

Vladimir Markov, James Millerd, James Trolinger, and Mark Norrie

MetroLaser Inc., Suite 100, Skypark Circle 18010, Irvine, California 92614

John Downie and Dogan Timucin

NASA Ames Research Center, M/S 269-3, Moffett Field, California 94035

Received October 2, 1998

We demonstrate a scheme for volume holographic storage based on the features of shift selectivity of a specklereference-wave hologram. The proposed recording method permits more-efficient use of the recording mediumand yields greater storage density than spherical or plane-wave reference beams. Experimental results ofmultiple hologram storage and replay in a photorefractive crystal of iron-doped lithium niobate are presented.The mechanisms of lateral and longitudinal shift selectivity are described theoretically and shown to agreewith experimental measurements. 1999 Optical Society of America

OCIS codes: 210.0210, 090.0090, 210.2860, 030.6140, 090.4220.

Holographic memory has been a subject of interest fordecades since it was suggested by van Heerden.1 Highinformation density, parallel access, and high-speedretrieval are among the features that make this tech-nique of data storage so attractive. Selective proper-ties of volume holograms that are due to angular2,3

or wavelength4 deviation from the Bragg conditionas well as to reference-beam phase encoding5,6 aremethods that are frequently used for data input andretrieval. The combination of reference-beam phaseencoding with spatial-shift multiplexing was shown tobe an eff icient approach for high-density holographicinformation storage.7,8 A similar technique that usesa reference beam comprising many plane waves (ora spherical wave) was suggested and experimentallydemonstrated.9 Although all these methods permithigh-density storage of the holograms, the longitudinalshift component of the volume recording medium hasnot been considered for coding the individual pages ofinformation. Recently a method of multilayer opticalstorage was discussed in which information is recordedat different depths within the medium, similar to thatof a magnetic-disk stack currently used in PC’s.10,11 Itwas demonstrated that holograms can be recorded asthin layers within the volume of the medium to providelarge information storage capacity and fast data trans-fer rates.12 In this Letter we discuss and demonstratea single-volume, multilayer holographic optical mem-ory based on the features of three-dimensional spatial-shift selectivity in a volume hologram recorded with aspeckle-encoded reference beam (SRB).

For our analysis we consider the case in which thehologram is recorded by a plane-wave signal beamSosrd and a SRB Rosrd with a divergence angle duSP ,as shown in Fig. 1. The two recording beams inter-sect at an angle u0, forming an interference patternwith a grating spacing L ­ lysinsu0d, assuming aSRB incidence angle uRo ­ 0. It was shown13 that,in the first Born approximation, the diffracted waveamplitude Ssrd, when it is reconstructed with aSRB that is different from the recording beam [i.e.,

0146-9592/99/040265-03$15.00/0

Rsrd fi Rosrdg, can be described as

Ssrd ­ ko2

ZZZV

d´sr0dRsr0dexpfikosr 2 r0dg

4pjr 2 r0jd3r0 .

(1)

Here d´sr0d is the modulated component of the record-ing medium’s permittivity d´srd ~ SosrdRo

psrd and Vis the volume of the hologram. Equation (1) is validif the hologram is a volume hologram and its thick-ness T exceeds the longitudinal speckle size, i.e.,T .. lysduSPd2 .. ly2uo. Then, by assuming a plane-wave signal beam Sosrd ­ expsikosrd and a recon-structed signal beam Ssrd propagating in the samedirection, we can reduce Eq. (1) to

Ssrd ­ expsikosrdZZZ

VCsr, r0d d3r0 . (2)

Fig. 1. Schematic of multilayer speckle–reference-beam-encoded hologram recording. Abbreviations are definedin text.

1999 Optical Society of America

266 OPTICS LETTERS / Vol. 24, No. 4 / February 15, 1999

It is assumed here that the speckle pattern inten-sity distribution has Gaussian statistics and that itsspatial autocorrelation function Csr, r 0d is determinedby mutual intensity of the recording and reconstruct-ing SRB’s,14 i.e., Csr, r0d ­ kRo

psrdRsr0dl.Contrary to the usual practice for a phase-encoded

holographic memory, we consider the case when thespatial amplitude–phase distribution of reconstruc-tion beam Rsrd remains identical to that of recordingbeam Rosrd. The difference between Rsrd and Rosrd isdue to the mutual spatial shift of the hologram andthe reconstructing beam, i.e., Rsrd ­ Rosr 1 Dd, whereD ­ D'q 1 DkZ, D' and DP are transverse and longi-tudinal components of the shift, respectively, and q andz are unity vectors in the same directions.

As the experimentally measured value is the dif-fracted beam intensity ID ­ jSj2, it is convenient tointroduce the parameter of relative diffracted beamintensity IDN sDd ­ ID sDdyIDsD­0d, where the measureddiffracted intensity ID sDd is normalized by its peakvalue at zero shift, IDsD­0d. By incorporating the three-dimensional correlation function Csr, r0d derived inRef. 13 and using the Fresnel–Kirchhoff diffraction in-tegral, we can express the dependence IDN sD'd as

IDN sD'd ­ID sD'dIDsD'­0d

­

ØØØØØØØZ T

0exp

√ikonD'

2

2ddh

! Z 1`

2`

ZjKD sqdj2exp

√2

ikonddh

qD'

!d2q dz

ØØØØØØØ2

T2Z 1`

2`

Zj KD sqdj2 d2q

,

(3)

here KD sqd is the diffuser aperture function, ko ­2pyl, q ­ qxx 1 qyy , n is refractive index of therecording medium, and ddh is the diffuser–hologramdistance.

It follows from Eq. (3) that any lateral mismatchbetween the hologram and reconstruction beam Rsrdleads to a decrease in the intensity of the diffractedbeam. Figure 2 shows the falloff in IDN sDd thatoccurs for lateral shift sDk ­ constantd. One ofthe important features of this type of selectivity isthat no ripples are observed as a function of spatialmismatch, unlike in the case of angular or spec-tral selectivity of volume holograms recorded withplane or spherical waves. The monotonic decreasein diffraction efficiency as a function of shift dis-tance results in much less cross talk between storedimages than can be obtained by use of other formsof multiplexing. Furthermore, the spatial decorre-lation is symmetric within the plane perpendicularto the Z direction, whereas other forms of multi-plexing have high selectivity only in the disper-sion plane.

Because the speckle pattern has a three-dimensionalnature, the longitudinal shift also results in spatialdecorrelation between the hologram and the recon-structing speckle beam, and thus a third dimensioncan be used to multiplex information. It can be shownthat, analogously to IDN sD'd, the diffracted beam in-tensity IDN sDkd ! 0 when the shift distance Dk exceeds

the longitudinal correlation length kskl (see Fig. 2).The longitudinal shift selectivity opens the possibil-ity of implementing several virtual layers of hologramswithin the same volume of the recording medium.

SRB holograms were recorded in 2.8-mm-thickFe:LiNbO3 s0.02% Feymold crystal by three-dimensional multiplexing. The crystal, with itsC axis lying in the plane of the recording beams,was set onto an XYZ computer-controlled positioningtable, which had a precision of 0.025 mm in the X, Y ,and Z planes. A 1-cm-diameter cw argon laser beam(l ­ 515 nm, P ­ 40 mWycm2) was used as the co-herent light source for hologram recording. The SRBhad a lateral speckle size ks'l ø 3 mm and intersectedthe plane-wave signal beam at an angle of u0 ­ 35±

(uRo ­ 0± and uSo ­ 35±). The diffracted beam inten-sity was measured with a p–i–n photodetector.

The diffraction efficiency of the hologram in itsoriginal position sD ­ 0d was approximately 1023.After each hologram was recorded, a lateral shift ofD' ­ 10 mm was introduced to record the next pageof information. The raster scan sequence was used tomultiplex images in X, Y , and Z, as shown in Fig. 1.During reconstruction, proper mutual repositioning ofthe hologram and the SRB resulted in informationretrieval. A typical sequence of 30 holograms storedin the form of a 6 3 5 matrix is shown in Fig. 3.The scan step length for this matrix reconstructionwas 0.25 mm. Notice the symmetric nature of theselectivity in both the X and the Y directions that ischaracteristic of use of a SRB.

Fig. 2. Calculated diffracted beam intensity IN sDd as afunction of lateral D' and longitudinal Dk shifts fora hologram recorded and reconstructed with a speckle-encoded reference beam.

Fig. 3. Measured diffraction eff iciency of 30 hologramsmultiplexed with lateral shift D' ­ 10 mm between suc-cessive recordings.

February 15, 1999 / Vol. 24, No. 4 / OPTICS LETTERS 267

Fig. 4. Measured diffracted beam intensity as a functionof spatial shift in the X, Y , and Z directions for two layersof holographic recordings that have a longitudinal shift of30 mm between layers. Each layer is composed of a 3 3 3matrix of holograms. The contour lines correspond to 7%increments normalized to the largest measured intensity.For clarity, the Z dependence for only two of the hologramsis shown.

Once recording of the first layer, L1, was completed,we formed the next layer, Li, by shifting the recordingmedium (or the diffuser that generated the speckle pat-tern) along the central axis of the speckle-beam propa-gation. The shift magnitude, as discussed above,should satisfy the condition that Dk $ kskl, which,for our experimental setup, was ,30 mm. In thisway a new layer, L2, could be recorded with the samelateral shift selectivity, and thus a new matrix ofnL2 3 mL2 holographic pages was formed. The effectof longitudinal shift selectivity was measured fortwo holograms and is shown in Fig. 4 as a contourplot of diffracted intensity. A longitudinal shift(Z direction) of Dk ­ 30 mm was introduced betweensuccessive recordings. Figure 4 also shows an ex-ample of the diffracted signal reconstructed from atwo-layer structure, in which each layer is composedof a 3 3 3 matrix. These results agree with ouranalysis and show that use of a speckle-wave refer-ence beam permits holographic shift multiplexingin three spatial dimensions with a selectivity deter-mined by the average transverse and longitudinalspeckle size.

We now estimate the storage density for the tech-nique of holographic data multiplexing describedabove. The number of holograms N' to be recordedin one layer can be calculated as the ratio betweenan effective area F of the recording medium andunitary lateral shift area sD'd2 in this plane, i.e.,N' ø slx 3 lydysD'd2, where lx and ly are lateraldimensions of the recording medium. The number

of available layers is proportional to TyDk. Thetotal number of holograms that can be recordedwith a shift selectivity scheme can be estimatedas NSP ­ VyfsD'd2 3 Dkg. This number leads toNSP , 4 3 109 holograms for a 1 cm 3 1 cm 3 1 cmcrystal for the experimental conditions describedabove sks'l ø 3 mm, kskl ø 30 mmd. In a practicalsystem the dynamic range of the refractive-indexvariation and the signal-to-noise ratio of the recon-structed image further limits the maximum storagedensity. The average signal-to-noise ratio for each ofthe holograms reconstructed in these experiments was#45, measured as the ratio of the Fourier-filtered dccomponent of the diffracted beam to the collected scat-tered light that propagates in the same direction. Atfixed experimental conditions, such as recording-beamratio, exposure level, and form of the aperture in thediffuser plane, the value of the signal-to-noise ratiodepends on the ratio of the introduced shift D', k tothe magnitude of the correlation radius ks', kl in thecorresponding direction.

In conclusion, we have demonstrated the possibil-ity of creating a multilayer holographic memory in aphotorefractive crystal based on the three-dimensionalspatial-shift selectivity of speckle-encoded referencewaves. The method achieves high-density data stor-age with a simple storage-retrieval architecture.

This research was supported in part by the NASAAmes Research Center. The authors thank MichaelDang for technical assistance. V. Markov’s e-mailaddress is vmarkov@metrolaserinc.com.

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