White-light photorefractive phase mask

Yuanmei Gao, Simin Liu, Ru Guo, Xiaohua Zhang, and Yi Lu

A volume photorefractive phase mask has been fabricated with incoherent white light from an incan-descent source in LiNbO3:Fe self-defocusing photorefractive crystal for the first time, to our knowledge.It can guide and modulate a probe white light or a laser beam and can be used to transmit an incoherentdark image as the guided modes of the waveguides induced by white-light dark spatial solitons. This alsoproves the existence of photorefractive nonlinearity of white light. © 2005 Optical Society of America

OCIS codes: 230.7370, 210.4680, 190.5330.

1. Introduction

The transmission of images through optically nonlin-ear media has been a challenging task for the pastthree decades.1–6 In a self-focusing medium, when acoherent image is transmitted, both modulational in-stability (MI) and modal dispersion are present. Theywill cause the destruction of the image information,and MI leads to filaments of parts of the image.2

Until 1995, solitons were considered to be solelycoherent entities. However, incoherent solitons thatare formed by partially spatial incoherent light orwhite light were demonstrated experimentally7–9 andinvestigated theoretically.10–15 Not long ago, we re-ported the experimental observation of one-dimensional white-light dark spatial solitons inLiNbO3:Fe crystal.16 A spatially incoherent beam is amultimode or speckled beam for which the instanta-neous intensity distribution varies randomly withtime. Incoherent spatial solitons can exist only innoninstantaneous media with a response time thatgreatly exceeds the characteristic phase fluctuationtime of the beam. Such nonlinearity, therefore, re-sponds only to the time-averaged envelope of thebeam and not to the instantaneous speckle fluctua-tions. In this medium an incoherent soliton is formedwhen the multimode beam induces a multimodewaveguide via the nonlinearity and traps itself in its

own induced waveguide by populating the guidedmodes in a self-consistent fashion.7–9

Recently Kip et al.17 demonstrated incoherent im-age transmission through a self-focusing medium bygradient-index lenses formed by spatially incoherentsolitons. When the image is incoherent, MI occursonly if the nonlinearity exceeds a specific thresholdthat is set by the degree of coherence (correlationdistance). If the correlation distance is short enough,all perturbations are suppressed, and the beam prop-agates in a stable fashion. Its drawback is the finitetransmission distance, which is limited by the modaldispersion.1 Whereas, in a self-defocusing medium,when the image is coherent, MI is absent,18,19 and themodal dispersion is also absent because thewaveguides induced by dark solitons in a saturablenonlinear medium are always single mode.7 Besides,the attractive forces between the adjacent guidedmodes can suppress the repulsion forces between theneighboring dark solitons, leading to the existence ofstationary two solitons.7 Therefore Wen et al.20 couldtransmit the distortion-free image by using coherentlight without a strict limit for the transmission dis-tance in a saturable nonlinear self-defocusing me-dium, LiNbO3:Fe crystal. In fact, most natural lightsources emit light that is incoherent both spatiallyand temporally. When the image is incoherent in aself-defocusing medium, MI is absent.18,19 Modal dis-persion is still present because the waveguides in-duced by incoherent dark spatial solitons composingthe image are multimode. Therefore the transmissionof both spatial and temporal incoherent dark imagesin a self-defocusing medium is a new concept: It re-sembles neither the transmission of a spatially inco-herent bright image in a self-focusing medium17 northe transmission of coherent dark images in a self-defocusing medium.20 If we can transmit thedistortion-free dark image with white light in a

Y. Gao, S. Liu (Liusm@nankai.edu.cn), R. Guo, and X. Zhang arewith The Key Lab of Advanced Technique and Fabrication forWeak-Light Nonlinear Photonics Materials, Ministry of Educa-tion, Department of Physics, Nankai University, Tianjin 300071,China. Y. Lu is with the Department of Automatic Engineering ofTianjin Institute of Technology, Tianjin 300191, China.

Received 10 June 2004; revised manuscript received 4 November2004; accepted 10 November 2004.

0003-6935/05/091533-05$15.00/0© 2005 Optical Society of America

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LiNbO3:Fe crystal, this will be interesting and signif-icant. In this paper we use a simple imaging methodto fabricate the photorefractive phase mask withwhite light from an incandescent source in aLiNbO3:Fe crystal. The phase mask was tested withwhite light and a laser beam and can be used totransmit the dark image distortion free as the guidedmodes of the waveguides induced by white-light darkspatial solitons.

2. Experimental Setup and Results

Our experiment setup is shown in Fig. 1. An ordinaryincandescent lamp (the filament is a line source) withan output power of 25 W was used as the light source.It emits broadband spatially and temporally incoher-ent light. Its frequency band is 380–750 nm in thevisible spectral region. The coherence time of thewhite light is of the order of a few femtoseconds. Thewhite-light beam was initially collimated by lensL1 �f � 135 mm� to form quasi-parallel light and thenpassed through an amplitude mask (O). Two ampli-tude masks, O1 (two Chinese characters) and O2 (res-olution target), were used for comparing the resolvingpower of the images. The image-bearing white-lightbeam was imaged onto the input face of theLiNbO3:Fe crystal (doped with 0.05�wt. % Fe) by lensL2 �f � 135 mm�. To eliminate the influence of theanisotropy of photorefractive crystals, we tilted thecrystalline c axis of the crystal 20° to the horizontaldirection for amplitude mask O1 and 45° for O2. Thecrystal’s dimensions are 3.8 mm � 10 mm � 5 mm.The image-bearing white light propagated along the3.8�mm-long (y-axis) direction. The input face of thecrystal was placed 0.9 cm behind the back focus oflens L2. The intensity of the incident beam at theinput face of the crystal is approximately65 mW�cm2. By moving lens L3 �f � 90 mm�, we im-aged the input or output face of the crystal onto acharge-coupled device (CCD) camera. Attenuator ATwas placed before the CCD to adjust the input inten-sity of the CCD. A He–Ne laser beam (� �633 nm, power of 1 mW, a nonpolarized beam)through spatial filter SF was expanded and colli-mated by lens L4 �f � 135 mm�, then reflected bymirrors M3 and M4, and irradiated on the crystal as a

probe laser beam. When we tested the phase maskwith white light, the quasi-parallel white light wasreflected by mirrors M1, M2, M3, and M4 and irradi-ated on the crystal. M1 and M4 were used only whenthe phase mask was tested by white light as the probebeam (see Fig. 1).

We adjusted the intensity of the incident beam bychanging the image size of the amplitude mask (O) atthe input face of the crystal to control the nonlinear-ity of the photorefractive material. We show that anappropriate condition for forming the photorefractivephase mask with white light as the light source isthat the crystal must be placed within the smallrange of 0.8–1.6 cm behind the back focus of lens L2.When the spacing of the image plane and the backfocus of L2 is less than 0.8 cm, the image is distorted;when the spacing is greater than 1.6 cm, the inten-sity at the incident face is too low to form the phasemask. A typical experimental result is shown in Fig.2. The images of the amplitude mask at the input faceof the crystal are shown in Fig. 2(a). The output im-ages at the illumination using white light as theprobe light are shown in Fig. 2(b); here we can seethat the photorefractive phase mask was not formed.Every half hour we tested the phase mask with whitelight and a laser beam as the probe lights to observethe formation process of the phase mask. The testtime is very short, only a few seconds, so the phasemask is not damaged by the probe beam. The longerthe writing time was, the clearer the output images ofthe phase mask tested by probe beams. After illumi-nation for 7 h, satisfactory images at the output faceof the crystal [Figs. 2(c) and 2(d)] were observed; theirintensity distributions were inverse with those of theinput amplitude masks (O). From the top rows ofFigs. 2(c) and 2(d), we can see that the smaller theincluded angle between the gradient direction of thelight intensity of the image and the c axis is, theclearer the corresponding bright stripe of the outputimage tested by the probe beam. The top row of Fig.2(d) is not clear owing to the presence of the interfer-ence pattern that results because the two faces of thecrystal are parallel to each other. The bottom row ofFig. 2(c) is the output image of the resolution targetwith white light as the probe beam, but the top right

Fig. 1. Experimental setup: He–Ne, laser; lamp, incandescent lamp; SF, spatial filter; M, mirror; L1 and L4, collimating lenses; O,amplitude mask; L2 and L3, imaging lenses; LN, LiNbO3:Fe crystal; C, crystalline c axis; AT, attenuator; CCD, CCD camera.

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corner of the bottom row of Fig. 2(c) is not clear; thesmaller the spacing and construction size of stripesare, the blurrier the stripes. When we fabricated thephotorefractive phase mask of the resolution targetwith white light in this crystal and tested it with thelaser beam, the photorefractive phase mask’s stripeinformation was submersed in the interference pat-terns. This would influence the resolving power.Therefore we used another crystal to fabricate thephotorefractive phase mask of the resolution targetwith white light; this crystal’s two faces are not par-allel by a small tilt angle, and there are no interfer-ence patterns in the bottom row of Fig. 2(d) even withthe laser as the probe light. The storage time of thephase mask was approximately at least one week inthe dark room.

3. Discussion

We fabricated the photorefractive phase mask by us-ing the imaging method with white light based on thephotorefractive photovoltaic effect. When the pho-torefractive material is irradiated, the photogenerat-ing carriers migrate from the bright region to thedark region and are captured. The spatial separatecharges whose spatial distribution corresponds to thedistribution of light intensity form the spatial chargefield Esc. Then the spatial charge field Esc causes therefractive-index change via the linear electro-optical(Pockels) effect. Therefore the main contribution ofthe photorefractive effect is conversion of the spatialdistribution of the intensity of the incident signallight into the spatial distribution of the refractive-index change in the photorefractive crystal. In thephotovoltaic photorefractive medium, in a two-dimensional case, the relation between the refractive-index change �n and input light intensity Iapproximately is21

�n � �12 n3reffEsc � �n2

II � Id

, (1)

where Esc is the space-charge field, n is the linearrefractive index of the medium, reff is the effectiveelectro-optic coefficient, �ns is the saturationrefractive-index change, I is the incident intensity ofwhite light with desirable information, and Id is darkirradiation.

From Eq. (1) we know that the refractive index ischanged in the illuminating bright region and �n� 0 in the self-defocusing LiNbO3:Fe crystal, whereasthe refractive index of the dark region �I � 0� nearlydoes not change. Thus the refractive index of the darkregion is higher than that of the bright region, andthe waveguides are formed in the dark region. Be-cause the input amplitude mask is binary (i.e., in thedark region, I � 0, �n � 0 and, in the bright region,I �� Id, �n � �ns � 0), step-index multimodewaveguides can be written by the method of digitalphase recording in this saturable nonlinear medium(Fig. 3).22 Therefore the waveguides induced by darksolitons from the phase mask. According to the prin-

Fig. 2. White-light phase masks in LiNbO3:Fe-crystal-fabricated amplitude masks: (a) two kinds of input amplitude mask; (b), (c) outputimages of phase masks that use white light as the probe beam at t � 0 and t � 7 h, respectively; and (d) output images of phase masksthat use a laser as the probe beam at t � 7 h. The images in the top row correspond to the crystal with parallel faces, and the images inthe bottom row correspond to the crystal with two faces not parallel by a small tilt angle.

Fig. 3. Sketch of writing and testing the phase mask by use of thebinary amplitude mask: (a) the intensity distribution of writinglight I�x, y�, (b) the index distribution in waveguides written owingto the photovoltaic photorefractive effect, and (c) the output inten-sity distribution of the probe light from the phase mask.

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ciple of the waveguide, when the photorefractivephase mask is tested, the probe light propagating inthe waveguide forms the output bright regions thatcorrespond to the dark region of the writing-lightintensity, whereas the output dark regions corre-spond to the bright region of the writing-light inten-sity. Therefore the intensity distributions of theoutput image are inverse with those of the input im-age. The process is shown in Fig. 3.

Comparing the top and bottom rows of Fig. 2(c), wecan see the former is clearer than the latter. This isbecause the distance between the centers of two ad-jacent waveguides in the top row is larger than thatin the bottom one. The smaller the distance is, theeasier the linear coupling between the adjacentwaveguides. The transfer of the energy generated bythe light field coupling between the adjacentwaveguides blurs the phase mask. The third group ofstripes in the top right corner of the bottom rows ofFigs. 2(c) and 2(d) are fully blurred owing to thesmaller distance of the stripes. When the distance ofthe stripes is less than 25 m in the input face of thecrystal, the output images are blurred. In our exper-iment, if we want to get a clear white-light photore-fractive phase mask, the distance of the stripes in theLiNbO3 crystal must be larger than 25 m. Compar-ing the bottom rows of Figs. 2(c) with 2(d), we can seethe images tested by the white-light probe beam andby the laser probe beam have the same resolvingpower.

Comparing the image of the phase mask tested bythe white-light probe beam [the top row of Fig. 2(c)]with that tested by the laser probe beam [the top rowof Fig. 2(d)], one can see that the former is clearerthan the latter, for there are interference patterns inthe latter and no interference patterns in the former.In addition, we can see there are no interference pat-terns in the bottom rows of Figs. 2(c) and 2(d), for thecrystal’s two faces are not parallel by a small tiltangle.

Comparing the photorefractive phase mask (Fig. 2)written by white light with that written by the laser(Fig. 4, which is from Ref. 7), the contrast of the latteris greater than that of the former. This is because thelatter is composed of single-mode waveguides in-duced by black solitons, whereas the former is com-posed of multimode waveguides induced by graysolitons in which both radiation modes and boundmodes are present.

4. Conclusion

In summary, we first fabricated a volume phase maskby using a simple imaging method with fully incoher-

ent white light that is both temporally and spatiallyincoherent in self-defocusing LiNbO3:Fe. The phasemask can modulate the probe white light or laserbeam and transmit the incoherent dark images. Thecondition for fabricating a clear phase mask is thatthe distance of the adjacent waveguides be largerthan 25 m. The resolving power of the output im-ages of the phase mask with white light as the probebeam is not influenced by the degree of parallelism ofthe crystal’s two faces, whereas that with the laserprobe beam is influenced by the degree of parallelismof the crystal’s two faces. The contrast of a phasemask written by a laser is greater than that writtenby white light. The experimental results can also di-rectly prove the existence of the photovoltaic photore-fractive effect of white light. The white-light phasemask further opens the possibility of studying inco-herent nonlinear optics, fabricating integrated opticsdevices, researching optical information processingthat uses incoherent light sources (for example, in-candescence lamp, sunlight, and light-emitting di-odes), and other applications.

This research is supported by the National NaturalScience Foundation of China (60378013, 60278006,and 10474047).

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