February 1, 2005 / Vol. 30, No. 3 / OPTICS LETTERS 305

One-beam recording in a LiNbO3 crystal

Jung-Ping Liu

Institute of Optical Sciences, National Central University, Chung-Li 320, Taiwan

Hsiao-Yi Lee

Department of Optoelectronic System Engineering, Minghsin University of Technology, Hsinchu 304, Taiwan

Hon-Fai Yau and Yin-Zhong Chen

Institute of Optical Sciences, National Central University, Chung-Li 320, Taiwan

Chi-Ching Chang

Department of Applied Physics, Chung Cheng Institute of Technology, National Defense University, Taoyuen 335, Taiwan

Ching Cherng Sun

Institute of Optical Sciences, National Central University, Chung-Li 320, Taiwan

Received July 1, 2004

We propose a new way to record images in a photorefractive LiNbO3 crystal. This method involves only asingle object light without any reference light. We believe that the recording is attained by fanning hologramsthat result from interference between the object light and its scattered light. Although volume gratings areinvolved, the recorded pattern can be viewed not only with a laser light beam that is incident over a certainangular range but also with white light. © 2005 Optical Society of America

OCIS codes: 050.7330, 090.2900, 160.3730, 190.5330, 210.0210.

Photorefractive LiNbO3 crystals have been widely dis-cussed because of the distinguished performance in op-tical storage and other applications.1 In the standardprocess of recording information in a LiNbO3 crystal,a reference beam in addition to the object beam isneeded to form an interference pattern. This patternis recorded in the crystal via the photorefractive effect,and the object beam can be reconstructed only with theoriginal reference beam. Although this holographicmethod can record the complete information on an ob-ject, it requires a light source of good coherence andrelatively large space for attainment of interference.One-beam holographic recording was demonstrated byKukhtarev et al.2 and Naruse et al.3 In the formercase, Kukhtarev et al.2 demonstrated that the ordinaryand extraordinary components of a single light beamcould form interference gratings through the photo-voltaic effect in a BaTiO3 crystal. In the latter case,Naruse et al.3 directed a light beam into a cubic crys-tal from one corner; the beam then automatically splitinto two beams that crossed each other in the crystal,and the object beam was recorded. In this Letter wepropose an even simpler way to record a pattern in aLiNbO3 crystal directly without any reference beam.In contrast with the methods proposed by Kukhtarevet al.2 and Naruse et al.3, our method has no require-ment for the polarization state, the incident angle, orthe incident position of the object beam, and thus itshould be easier to implement.

The experimental setup is shown in Fig. 1. Thestorage medium is a 500-parts-in-106 photorefractiveLiNbO3:Fe crystal of 20 mm 3 20 mm 3 20 mm size.

0146-9592/05/030305-03$15.00/0

The c axis of the crystal is normal to the incident beam.The light source is a Verdi laser �l � 532.5 nm�. Therecording configuration is a 1:1 imaging system withthe image plane inside the crystal. The input pat-tern (5 mm 3 5 mm in size) was first projected on thecrystal with a collimated laser light of 50-mW�cm2

intensity. The polarization state of the input lightwas set as extraordinarily polarized (e-polarized), andthe exposure time was 10 min. It can also be set as

Fig. 1. Schematic of the setup in the recording stage: SF,spatial f ilter; Ls, lenses; P, input pattern. The diameter ofthe imaging lens is 5.4 cm, and its focal length is 32.5 cm.The inset is the schematic for reading; u is the angle ofincidence of the reading beam.

© 2005 Optical Society of America

306 OPTICS LETTERS / Vol. 30, No. 3 / February 1, 2005

ordinarily polarized (o-polarized), but the recordingtime is three to four times longer. One can see therecorded pattern instantaneously after it is recordedbehind the crystal by illuminating the crystal with acollimated laser beam (see the inset in Fig. 1). Fig-ure 2 shows photographs of the observed image takenbehind the LiNbO3 crystal for various incident anglesof the reading beam. The resulting image usually ap-pears as a positive replica of the original object. How-ever, it turns into a negative replica when the incidentangle is zero.

We believe that the recording is achieved via thefanning effect.4 –6 It should be emphasized that onlythe bright region of the image of the input patterninduces fanning in the crystal through interferencebetween the object light and its scattering light, thusbuilding fanning gratings. In the viewing processthe fanning gratings in the region corresponding tothe bright portion of the input pattern diffract light,whereas the remaining portion of the crystal does not,because there is no fanning grating. As a result thediffracted light yields the image of the input patternin some direction. We arrive at this model becauseour experiments showed that a successful recordingwas always accompanied by the occurrence of thefanning phenomenon. For instance, when the c axisof the crystal was set along the propagation directionof the object beam or opposite to it, no fanning oc-curred, and no recording succeeded. Other examplesare that neither a low-doping LiNbO3 crystal nor athin LiNbO3 crystal plate gives rise to the fanningphenomenon in any configuration because of theirlow coupling strength5 (gL, where g is the couplingconstant and L is the coupling length), and we havenever achieved any successful recording in this man-ner. This model can also explain the experimentalfact that the recording time when one is using ano-polarized light is longer than when e-polarized lightis used. In our experiments the coupling constant forthe e-polarized wave is proportional to ne

3r33, which isthree times larger than that for the o-polarized wavethat is proportional to no

3r13. Therefore, to achievethe same change in refractive index, the recordingtime with o-polarized light is three or four timeslonger than with e-polarized light.

According to the model above, when an object beamenters a crystal, numerous sets of gratings are formedthrough the interference of the object beam and thefanning light. These kinds of gratings are oftenknown as fanning holograms,7,8 and their gratingvectors can be expressed as

K � ko 2 kf , (1)

where ko and kf are the wave vectors of the objectbeam and the fanning light, respectively, and K is thegrating vector of the fanning grating. In Eq. (1) onlythe 11 order of the gratings is considered, becauseother orders do not give rise to signif icant results inpractice. When these fanning gratings are read witha reading beam of wave vector kr , diffracted beamstake place with their wave vector equal to

kd � kr 1 K . (2)

Combining Eqs. (1) and (2), we obtain an equation re-lating the various wave vectors:

kd � kr 1 ko 2 kf . (3)

Note that in Eq. (3) kf is in fact a group of vectors invarious directions, whereas kr and ko are definite vec-tors. Equation (3) explains the experimental resultsshown in Fig. 2. In these experiments we alwaysobserve the image of the recorded pattern in the crys-tal, regardless of the incident direction of the readingbeam. These results can be understood by theexplanation that each image in Fig. 2 is produced by aspecific but different group of fanning gratings. Thisspecific set of kf is equal to kr, and thus kd is equalto ko according to Eq. (3). Accordingly, the diffractedlight gives rise to an image of the object. According tothis analysis, it looks as if we should see the recordedinput pattern in the crystal with a reading beam inany direction, because presumably there are fanninggratings in every direction. In practice, however, fan-ning occurs in only a limited range of directions in thestorage process. Therefore the diffracted image cantake place only with reading beams incident within alimited range of directions. In our experimental ob-servation we could see the image in the crystal whenthe reading beam was in an angular range of 615±

measured outside the crystal. When the incidentangle was bigger than 15±, the image became too faintto be observed. This result is consistent with theobservation that fanning occurred in an angular rangeof only 615± in the storage process. When the readingbeam is perpendicularly incident on the crystal, thefanning grating unavoidably diffracts some portions ofthe incident light out of its original propagation direc-tion, while the remaining part of the crystal transmits

Fig. 2. Photos of the input pattern and the final images.(a) Image of the input pattern taken at plane B. Theinput pattern is the Chinese character for electric.(b), (c), (d) Photos of the f inal images when u is 5±,10±, and 15±, respectively. (e) Photos of the final imagewhen the reading beam is incident perpendicularly on thecrystal. (f ), (g), (h) Photos of the f inal images when u is25±, 210±, and 215±, respectively.

February 1, 2005 / Vol. 30, No. 3 / OPTICS LETTERS 307

Fig. 3. Relation between the incident angle of the readingbeam and the emerging angle of the diffracted beam ob-tained by calculation.

Fig. 4. Photos of the final images when a white-light lampis used as the reading light source. Reading angles of(a) 5±, (b) 10±, (c) 15±, (d) 25±, (e) 210±, (f ) 215±.

Fig. 5. Demonstration of the spatial resolution witha U.S. Air Force resolution chart as the input pattern.(a) Image of the input pattern taken in plane B. In therecording stage the light source is a Verdi laser. (b) Finalimage obtained with a beam of white light.

the incident light without obstruction. Thus, lookingfrom the back of the crystal, the part of the crystalwhere the fanning grating is located appears darkerthan its surroundings. Remember that the fanninggrating spreads over the region where the image of

the object is located, and therefore a negative image ofthe object is observed.

The direction of the diffracted beam with respect tothe direction of the reading beam can be estimated byuse of the treatment proposed by Magnusson and Gay-lord.7 Results for three reading wavelengths (450,532, and 650 nm) for the same recording wavelengthat 532 nm are presented in Fig. 3. The incident angleof the reading beam is positive when the reading beamis below the crystal normal. The diffracted angle ispositive when the reading beam is above the diffractedbeam. All the angles here were measured inside thecrystal, so they became larger outside. (The 15± inci-dence angle outside the crystal is an �6.8± incidenceangle inside the crystal). It can be seen from Fig. 3that the diffracted angle for light at l � 450 650 nmis practically the same when the incident angle iswithin 615± outside the crystal. This result impliesthat we can use white light to view an image, althoughthis device actually employs volume gratings and theBragg condition must be satisfied. This expectationis confirmed by our experiment, and this observationis shown in Fig. 4. Comparing Fig. 4 with Fig. 2, onecan see that white-light reading is superior to laserreading because in the former there is no specklenoise in the image. Finally, we have examined theresolution of this method. The resulting resolution is�8 line pairs�mm, as shown in Fig. 5.

In conclusion, we have experimentally demonstrateda method of recording images in a LiNbO3 crystal byuse of the object beam alone. We believe that therecording is achieved by means of the photorefractivefanning effect. Accordingly, volume gratings takeplace in the bright region of the image, and one canexploit these volume gratings to yield the image of theobject with white light as well as laser light.

The authors thank the National Science Council ofthe Republic of China for the support of this research(contract NSC-92-2215-E-008-017). Thanks are alsodue to W. H. Ip for his encouragement for the pub-lication of this work. J.-P. Liu’s e-mail address isjpliu@ios.ncu.edu.tw; H.-F. Yau’s e-mail address isyauhf@ios.ncu.edu.tw.

References

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3. S. Naruse, A. Shiratori, and M. Obara, Appl. Phys. Lett.71, 4 (1997).

4. J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).5. P. Yeh, Introduction to Photorefractive Nonlinear Optics

(Wiley, New York, 1993).6. M. Goulkov, S. Odoulov, J. Imbrock, M. Imlau,

E. Krätzig, C. Bäumer, and H. Hesse, Phys. Rev. B 65,195111 (2002).

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