Holographic technique for improving the performances of frequency-domain optical storage

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EISEVIER

I August 1995

OPTICS COMMUNICATIONS Optics Communications

118 ( 1995) 499-504

Holographic technique for improving the performances of frequency-domain optical storage Jin Hui Zhai a, Yu Ruan a, Zai Guang Li b aDepartmerlt of Optoelectronics Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430 074, China b National Experiment of Laser Technology. Wuhan, 430 074, China Received 24 October 1994; revised version received 4 April 1995

Abstract The effects of the holographic technique on frequency-domain optical storage are investigated. The mathematical relations of the system characteristics versus material properties and read/ write conditions are developed for holographic frequency-domain optical storage. The detailed analyses of holography improving the system characteristics, the parameter space of the material and the read/write conditions are presented. The results show that holography will greatly relax the constraints of the system characteristics imposed on the material properties and read/write conditions.

1. Introduction

Spectral hole-burning has become a well-established technique to investigate dynamic properties of solids. It has recently gained considerable interest in technical applications, especially with respect to the frequencydomain optical storage (FDOS) technique [ I]. The additional frequency multiplexing provided by spectral holes theoretically allow for storage densities of the order of lOI bits/cm’. However, the realization of a practical recording system imposes a sort of special requirement on a suitable storage medium, and hole information must be burned very rapidly (30 ns/bit) with tightly focused laser beams (d< 10 pm) [2]. So it is not easy to find a suitable record medium for the FDOS technique, and it is difficult to design a practical FDOS system that needs a precisely locating and servo system [ 31. The holographic hole-burning technique has been proven to be very effective in detecting spectral holes and in accurately determining their widths [ 41. Con0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDfOO30-4018(95)00269-3

sequently, it should be profitable to employ the holographic technique for data storage applications, either for the detection of data bits encoded in spectral holes or even as a holographic memory making use of its imaging properties [ 51. In this work, we try to mathematically relate the system characteristics to the material properties and the read/write conditions when holographic hole-burning is applied for the FDOS technique. The detailed analyses of holography improving the read/write conditions, the parameter space of the materials and the system characteristics are presented.

2. Theory analyses of the holographic holeburning storage system In the holographic hole-burning technique, the sample is illuminated by the interference pattern created by two crossed laser beams. The modulated intensity pattern creates an excited state grating, then a persistent

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grating of the product and educt concentration is formed. Depending on the optical spectra of the products and educts, this leads to frequency and time dependent spatial modulations of the absorption coefficient (Yand refractive index n along the x-axis with period A [ 61. In this section we will theoretically analyze the system characteristics for a holographic frequency-domain optical storage (HFDOS) system. 2. I. The storage densities of the HFDOS system In the holographic hole-burning storage density p is given by

storage system, the

P =foNf A ,

(1)

where A stands for the area of the read/write spot, N for the bit capacity of each hologram,f, for the number of holograms recorded in every spot within the inhomogenous linewidth, which depends on the spectral width of the hole-burning. So the narrower spectral hole should be burned to increase the storage densities. In case of weak electron-phonon coupling, the shape of the spectral hole is a zero-phonon line shape function. The spectral width of the hole-burning is described by ]71.

where r,, stands for the homogeneous linewidth of zero-phonon line shape, Iw for the burning intensity, tw for the burning time, 77for the hole-burning yields, cr for the absorption cross section. For a uniform grating, the diffraction efficiency y = &/I, is given by the ratio of intensities of the diffracted beam and the references beam. When two or more holes are burned successively with the holographic technique at a selected frequency, the total diffraction efficiency must be calculated by taking the square of the sum of the corresponding diffracted field amplitudes. Supposing there are n holograms burned at the same area at a selected frequency, the total diffraction efficiency is given by y(w) = k y, +2 ‘2’ fit’ (A;Ai+j +BiB;+j) coso’Acp> ( i=i i=l

118 (1995) 499-504

with A,(w) =

B,(w) =

+

c

j=i

C j=l

(Ai+jBj-Ai-Bi+j)

sinuAcp)

(% -W)2+(r/2)2'

a, (wb)Lr/2 2 cos 8

wh-w (% - o)2+ (r/2)2’

(4)

(5)

ratio (SNR) of the FHDOS

Assuming that the shot-noise of the detected signal dominates all other noise sources, the achievable SNR for the holographic readout of one hologram is given by SNR=

(6)

where qo stands for the detection quantum efficiency, Z, for the reading intensity, tR for the reading time, ~yo for the absorption coefficient before burning, and H for the relative hole depth which is defined as AN/N,, where No denotes the initial photon populations of the ground states, AIV denotes the change of photon population of the ground states during the process of holeburning. In principle, the SNR can be improved increasing the reading intensity. However, the maximum usable reading intensity is either determined by the specific laser device being used or by the requirement of avoiding excessive spectral broadening of the written holes during reading. Eq. (6) also shows that SNR is greatly affected by the hole depth H. In the case of weak electron-phonon coupling, the relative hole depth is given by

H=I-exp(l+$Lw exp [

(3)

2 cos 8

2.2. The signal-to-noise system

X

11-i

r/2

where yi stands for the diffraction efficiency of the ith hologram, oO( w) and CX~W)stand for the coefficients of the first and second order terms of the Fourier expansion of the absorption coefficient a(x,w), L for the material thickness, q, for the burning frequency.

j=l

n-l

%(%W/2

t)+

1

1+&w

77rc t -exp[ I+ rcigzw (

-car,

+r,-t,]

1. (7)

J.H. Zhai et al. /Optics Communications II8 (1995) 499-503

where uIw stands for the excited rate, &o for the decay rate to burn spectral holes.

Fig. 1 shows the hole broadening as a function of the parameter Cw under various hole-burning yields q. For high 17 (7 > 0.05), it seems justified to restrict the Cw to Cw<2 to control the spectral broadening to Aw, I%), it seems justified to restrict the limits as: t,/Tc > 10. Considering simultaneously the deep holes and high data transfer rate, we take Tc = 10 ns, tw= 1 ps. To analyze the dependence of the hole depth on the writing energy fluency Cw, taking twl TC = 100, Eq. (7) can be written as

3. Holographic hole-burning improves the performances of FDOS system In the frequency-domain optical storage technique, a focused microspot and very short read/write time are required to achieve the performances of the presently developed optical disk recording system, so a suitable storage medium with strictly required material parameters cr, N, and 77must be achieved to gain more deep spectral holes. In the read out process, a fairly high reading intensity and a fairly high hole-burning yield have to be developed in order to achieve the sufficient signal-to-noise ratios. But the excessive reading intensity and hole-burning yield would lead to a spectral broadening of the produced holes, and as aconsequence would affect the performance of the FDOS system. When the holographic hole-burning technique is used to write and read the spectral narrow holes, based on the imaging properties of the holographic technique, images can be stored as spectrally narrow holograms and the data information parallelly accessed from the recording medium each time is more than lo6 bits. So the area of the laser spot can increase to 1 mm2 and the read/write time can be more than 1 JIS without affecting the characteristics of the storage densities and the data transfer rate, which will be more useful to improve the performances of the FDOS system.

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The holographic hole-burning technique is useful in improving the parameter space of the material and the read/write conditions. The deep and narrow spectral holes can be achieved by optimal properties of the holeburning material and the read/write conditions. From Eq. (2), we can conclude that the spectral width of the hole-burning is greatly affected by the saturation power broadening and the excessive photochemistry hole broadening. Defining the writing energy frequency Cw= al&,, the spectral broadening of hole-burning can be described by

(8)

, ,

; !I

.’

I’

0.01

r

1

0.1

I

2

Q

,’

I ,

10

energy

/’

loo

flueJncy

Fig. 1.Hole broadening versus the write/read various hole-burning yields 7.

3. I. Improving the parameter space of the material and the read/write conditions

i

1aoo

c energy fluency under

Om O-06

(

8

3

0.04 .d’

Q

0.02 ._..

f

-

:

.- __+---

,

_

-’

.’

,-

,-

,-

_’

L

0.7

0.1

___ _ ---1 felative

_--

10

loo

loco

burning time tw /Tc

Fig. 2. Relative hole depth versus tw/TC. under various hole-burning yields 7.

502

J. H. Zhai et al. /Optics

Communications

118 (1995) 499-504

2

1017

lo3

1

10" low IO" lo*

I! .Y

iJ.01

0.1

1

writing

energy

10

loo

loo0

fll#8rlcy c

H=l41+:2cJ+ l+*~/cw X[exp(l +~c,)exp[ -(C,+lOO)]

1

. (9)

Fig. 3 shows the relation of H- C, under various hole-burning yields v. The contours show that a large fluency (C, > 100) should be required under the low yield ( 77< 0.0005) to burn the deep holes; however, a low fluency value (Cw< 10) would suffice for r]>O.OOl. From Figs. 1 and 3, it will be illustrated that we can burn the deep and narrow spectral holed under a certain range of writing energy fluency C, in all cases of holeburning yields 7). Even for a very low yield ( 77= 0.0001) , we can burn the required spectral holes with the range 100 < Cc < 5000. For high yield ( 77= 0.05)) the C, is restricted to 0.1 < C, < 2. Now we begin to analyze the reading SNR for a holographic hole-burning system. Assuming the reading bandwidth B = ( 2fR) - ’ = 0.5 MHz, we take a SNR of 40 dB as the required value comparing to the SNR of 50 u 60 dB in a 30 kHz bandwidth for conventional optical storage. Considering the substantial power broadening of the detected hole, we take the absorption coefficient before burning to be a0 = UN,, and the reading energy fluency to be Cn = o-tnZn, then Eq. (6) will be changed as SNR =

77qGA H ---z&N.Lexp(2 d

s), (10)

low

ij;

id

1

id

v

W

Fig. 3. Relative hole depth versus the writing energy fluency under various hole-burning yields 7.

IO"

10'

cft3sssectiono(~)

Fig. 4. Material constraints for hole-burning mediums in order to achieve practical SNR under various 7.

with nl defined as the density-thickness product. Fig. 4 identifies the suitable space material parameters u, N& and q, which result in SNR 240 dB under the read/ write intensity Iv, = lo*’ photons/s. cm*, Z, = 1Or9 photons/s.cm2. The contours show that the parameter space of the material has been obviously improved in HFDOS, especially for the very low holeburning yield. For a low cross section a, because of the shallow depth of the holographic hole-burning, the parameter space shrinks at the upper end of the figure. For a low hole-burning yield, the high saturation intensity is allowed, so we can also achieve a large parameter space, and the parameter space would move to an area of a low NJ value and a high cross section o. Outside the allowed regions, various physical considerations prevent a solution to the material optimization problem

ill. 3.2. Improving the system characterics of the frequency-domain optical storage The holographic hole-burning technique is helpful in solving the technological issues of the frequencydomain optical storage, such as simultaneous high density recording and high reading SNR. To increase the storage densities, the holograms have to be packed as close as possible in frequency dimensions. The minimum separation allowing for wellresolved holograms depends on the spectral width of hole-burning in frequency dimensions. From Eq. (3)) supposing the homogeneous spectral width of the holeburning sample is 0.001 cm-’ and the spectral broad-

J.H. Zhai et al. /Optics Communicarions II8 (19951499-W

01 0

SO3

4 10

P

a0

leaor fraqwrlcy w(aiz) Fig. 5. Normalized diffraction efficiency of thirty holograms stored in the spectral range of 30 GHz.

ening can be controlled to less then 0.01 cm-‘, the spectral width of the hole-burning is of the order of 0.015 cm- ’ (0.45 GHz). When the spectra1 separation between the holograms is 1.0 GHz, Fig. 5 shows that the individual peaks appear to be well resolved and the cross-talk between them is negligible under these conditions. A number of 30 holograms within the wavelength range are accessible with the signal mode dye laser (30 GHz). Extrapolating this storage densities to the whole inhomogenously broadened absorption band, about 30000 images could be stored in a usable range of 1000 cm- ‘. For above 10” bits of capacity of every hologram, the storage densities of the HFDOS system would reach 3 X lOI* bits/cm*, which improves the storage density of the conventional optical disk in the order of 104. From Eq. (6), we know that the SNR will be improved in the holographic hole-burning technique when the hole-burning information is read out in the same reading intensity as in the case of the FDOS system, because of the larger laser spot area and the longer reading time. On the other hand, the advantages of the holographic detection technique: the hologram arises as a narrow peak from a plane of practically zero background, show that the SNR of the holographic signal is much more than that of the transmission signal. Fig. 6 shows the 3D contours of SNR versus cr, NJ for the specific set of parameters: H = 0.005, A = 10 _ * cm’, ~]o =0.75, 8= 30” and C, = 10. The maximum SNR is achieved when UN& is taken to be 2: SNR,,, = 57 dB (signal/noise = 700). Considering the parallel access characteristics of HFDOS, above lo6 bits of capacity can be read out each time width 30 ns, so the data transfer rate can reach 1 GB 1s.

Fig. 6. Three-dimensional

representations of the reading signal-

noise-ratio versus U, NJ..

4. Conclusions In conclusion, a series of mathematical models for relating the system characteristics to material properties and read/write conditions have been developed when the holographic hole-burning technique is applied for FDOS. Due to the large area of optical spot ( 1 mm’), a long read/write time ( 1 I.Ls) and the parallel property of zero background holography, the system characteristics and the parameter space of the hole-burning material will be greatly improved. The storage densities can reach 3 X 1OL2bits/cm*, the data transfer rate can reach 1 GB/s, and the reading SNR will be obviously improved. The deep and narrow holographic holeburning can be achieved in all cases of hole-burning yields 77.Several guidelines for searching the suitable hole-burning materials have been established by identifying appropriate values of important material properties, and read/write conditions, which are shown in Figs. 14. The results show that holography will relax the requirements imposed on spectral hole-burning materials and read/write conditions, which is more useful in searching for a practical storage medium and in establishing a practical HFDOS system.

Acknowledgements This work was mainly supported by the National Defense Science Foundation of China.

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Moemer.

ed.,

Persistent hole-burning:

application (Springer, Berlin, 1988).

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and

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