S. I. Bozhevolnyi and I. I. Smolyaninov Vol. 12, No. 9 /September 1995 /J. Opt. Soc. Am. B 1617

Characterization of phase-conjugated near-field light spots

Sergey I. Bozhevolnyi and Igor I. Smolyaninov*

Institute of Physics, University of Aalborg, Pontoppidanstræde 103, DK-9220 Aalborg, Denmark

Received October 28, 1994; revised manuscript received April 4, 1995

Using degenerate four-wave mixing in a Fe:LiNbO3 0.04-wt. % crystal and incremental recording, we haverealized phase conjugation of light emitted by a fiber tip (of a near-field microscope) alternately placed at twoclose positions near the crystal surface. We observe with the near-field microscope that the phase-conjugatedlight forms two subwavelength-sized spots near the surface; the spots are elongated in the direction of thecrystal optical axis. It is demonstrated that phase-conjugated light spots formed 240 nm apart in the directionperpendicular to the crystal optical axis can still be resolved.

Scanning near-field optical microscopy (SNOM) has al-ready found a number of applications (besides pure imag-ing) in which subwavelength resolution provided by thetechnique can be advantageously exploited. Applicationsof SNOM include but are not limited to spatially resolvedspectroscopy, biochemical sensing, fluorescence imaging,and magneto-optic storage.1,2 Recently we reported thefirst experimental results for phase conjugation of lightemitted by an uncoated fiber tip of a reflection scanningnear-field optical microscope (RSNOM).3 It has been ob-served that the phase-conjugated light can produce asubwavelength-sized spot image in the RSNOM. Onemight suggest that this effect be used for high-densitydata storage. However, there are many problems to besolved before this possibility can be seriously considered.

Here we present further experimental results obtainedwith practically the same setup,3 which has been im-proved with respect to stability and signal-to-noise ratio.We develop a procedure to form two phase-conjugatednear-field light spots at a given distance. Light intensitydistributions across these spots are measured and theirresolution limit is discussed.

The experimental setup described in detail in our previ-ous publication3 consists of the RSNOM with an uncoatedfiber tip4 and Fe:LiNbO3 0.04-wt. % crystal pumped bytwo counterpropagating laser beams of wavelength l ø633 nm. A 10-mW He–Ne laser is used both to launchthe light in the single-mode fiber of the RSNOM andto provide the pump beams for the degenerate back-ward four-wave mixing. In addition to the experimen-tal arrangement used previously,3 we have introducedan acousto-optic Bragg cell into the path of the pumpbeams. This enables us to modulate the power of thepump beams at a frequency of 20 kHz and to use syn-chronous detection of the phase-conjugated reflected lightwith the help of a lock-in amplifier, thus increasing thesignal-to-noise ratio. The RSNOM includes a shear-forcefeedback system,5 which is used to maintain a constanttip–surface distance (,5 nm) and to image the surfacetopography while simultaneously recording a near-fieldoptical image. (Operation of our SNOM with the shear-force feedback system is described in detail elsewhere.6)Mechanical construction of the RSNOM has been modi-fied so that in the present experiments the sample drift3

0740-3224/95/091617-04$06.00

with respect to the piezotranslator controlling the fibertip position was less than 3 nmymin. This value can beregarded as negligibly small for our experiments, sincetypical exposure and readout times were ,5 and 2 min,respectively.

The geometry of light interactions during phase conju-gation in our experiments is displayed schematically inFig. 1. Phase conjugation in photorefractive crystals oc-curs owing to diffraction of either of the pump beams bya volume hologram (of a signal wave) recorded with an-other pump beam as a reference wave. We have esti-mated that for the phase-conjugated light power to be,0.1 nW under our experimental conditions3 the recordedholograms should be at least a few micrometers in size.This means that to yield several phase-conjugated lightspots at subwavelength distances the appropriate holo-grams should be multiplexed within practically the samevolume. For this purpose we have used an incrementalrecording technique7 by writing the holograms of two dif-ferent signal waves (emitted with the fiber tip placed attwo different positions) with a series of short exposures.Owing to the large recording–erasure time constants ofphotorefractive Fe:LiNbO3 crystals,8 we could observe thephase-conjugated reflected light in the absence of the sig-nal wave.3

First, we studied more carefully the distribution of thephase-conjugated reflected light in an individual spot,which can be produced when the fiber tip is kept at thesame place during the recording procedure. Typical top-ographical and near-field optical images obtained imme-diately after the exposure are shown in Fig. 2. It shouldbe noted that the time characteristics of the recordingand the erasing processes were measured to be similarto those reported previously,3 and we used an exposuretime of ,5 min for the recording of a single spot. Typicaldistributions of the detected phase-conjugated light inten-sity in two orthogonal directions across an individual spotare shown in Fig. 3. It turned out that the elongation ofthe spot image observed previously3 is in fact the charac-teristic feature of phase conjugation in our experiments.Typical values of spot widths in the directions perpendicu-lar and parallel to the crystal optical axis were found tobe ,180 to 250 nm, respectively (Fig. 3).

The observed elongation of the spot image along the

1995 Optical Society of America

1618 J. Opt. Soc. Am. B/Vol. 12, No. 9 /September 1995 S. I. Bozhevolnyi and I. I. Smolyaninov

Fig. 1. Schematic representation of light interactions duringthe recording process in our experiments. The polarization ofthe light is perpendicular to the figure plane, and the crystaloptical axis c is in the figure plane parallel to the crystal surface.

Fig. 2. Gray-scale near-field (a) optical and (b) topographicalimages, 4 mm 3 4 mm, taken immediately after exposure; duringexposure the fiber tip was kept at the same place. The maxi-mum depth of the topographical image is 123 nm. The crystaloptical axis is oriented in the vertical direction.

crystal optical axis has yet to be understood, but onecan expect that different wave components of a compli-cated signal wave (such as the wave emitted by the fibertip) should experience phase conjugation with differentefficiencies.9 On the other hand, the smallest measuredspot width of ,180 nm can be explained as follows.10

The optical field of the signal wave emitted by the fibertip, which is located near the crystal (Fig. 1), can bedecomposed at the surface plane into propagating andevanescent components with respective numerical mag-nitudes kk of the wave vector projection onto this planeof appropriately kk , 2pyl and kk . 2pyl. However,an appreciable part of the evanescent wave components,namely, that satisfying the criterion 2pnyl . kk . 2pyl

(n is the refractive index of the crystal), gives rise topropagating waves in the crystal. These waves shouldexperience phase conjugation with the same efficiency asthe propagating waves having kk , 2pyl. This meansthat the waves with kk , 2pnyl, which propagate in-side the crystal, can contribute equally to the phase-conjugated light, even though some of these waves areevanescent outside the crystal (in air). The situation isentirely different for the waves with kk . 2pnyl, whichare evanescent inside the crystal as well as in air. Forthese waves the interaction length is limited by the pen-etration depth dp ­ fskkd2 2 s2pnyld2g20.5, which meansthat their contribution in the phase-conjugated reflectedlight decreases rapidly with the increase of kk. There-fore the size of the phase-conjugated light spot should belimited by ly2n, which is ,140 nm in our case. Takinginto account that the RSNOM has a resolution limit of,100 nm,6,11,12 one can presume that the actual value ofthe smallest spot width obtained in our experiments is,150 nm. This value agrees well with the above esti-mation of the spot size limit.

In another series of experiments we recorded phaseconjugation of light emitted by the fiber tip, which wasrepeatedly moved during the exposure between two givenpositions near the crystal surface. The incrementalrecording technique is known7 to provide uniform diffrac-tion efficiencies for multiplexed holograms if the incre-ment time for the recording of an individual hologram issignificantly smaller than the material’s response time.We used an increment time of 10 s and a total exposuretime of ,10 min, but the brightness of the obtained spots

Fig. 3. Typical distributions of the phase-conjugated (PC) lightintensity measured across an individual spot a, perpendicularand b, parallel to the crystal optical axis.

S. I. Bozhevolnyi and I. I. Smolyaninov Vol. 12, No. 9 /September 1995 /J. Opt. Soc. Am. B 1619

Fig. 4. Gray-scale near-field optical images, 2.4 mm 3 2.1 mm,of two phase-conjugated light spots taken (a) immediately afterexposure and (b) 5 min later. The spot separation is ,500 nmalong the crystal optical axis.

were slightly different anyway. It was also observedthat the level of the optical signal detected outside thelight spots was higher than during the experiments witha single spot. These effects as well as the dynamics ofthe erasure process during the readout can be seen fromthe optical images shown in Fig. 4. The images alsodemonstrate the two phase-conjugated light spots placedonly ,500 nm apart are well resolved. This indicatesthe possibility of mutiplexing holograms (responsible forphase conjugation) of at least two subwavelength-sizedlight sources. Judging from the size of a single phase-conjugated light spot (Fig. 3), one can expect that twospots should be resolved even at half of these distances.We have recorded phase conjugation when the distancebetween two fiber tip locations was ,240 nm in the di-

rections perpendicular [Fig. 5(a)] and parallel [Fig. 5(b)]to the crystal optical axis. Distributions of the detectedphase-conjugated light intensity show that the spots arebarely resolved in the first case (Fig. 6) and nearly re-solved in the second case (Fig. 7). Again, given the reso-lution limit of the RSNOM,6,11,12 one can expect that theactual spots are sufficiently resolved in both cases.

The spot images shown in Fig. 5 are noticeably lessbright than those in Fig. 4. There may be several rea-sons for this. It is clear, for example, that spatial fre-quencies of a composite hologram that is to be recordedtend to increase when two positions of the fiber tipapproach each other. This can eventually result ina decrease of the efficiency and the quality of phase

Fig. 5. Gray-scale near-field optical images, 1.7 mm 3 1.7 mm,of two phase-conjugated light spots taken immediately afterexposure. The spot separation is ,240 nm (a) perpendicularand (b) parallel to the crystal optical axis.

1620 J. Opt. Soc. Am. B/Vol. 12, No. 9 /September 1995 S. I. Bozhevolnyi and I. I. Smolyaninov

Fig. 6. Distributions of the phase-conjugated (PC) light inten-sity measured across two spot images from Fig. 5(a), a, perpen-dicular and b, parallel to the crystal optical axis.

Fig. 7. Distributions of the phase-conjugated (PC) light inten-sity measured across two spot images from Fig. 5(b), a, perpen-dicular and b, parallel to the crystal optical axis.

conjugation because of the limited spatial resolutionof a particular photorefractive crystal. Actually theexperiments with phase conjugation of light fromsubwavelength-sized sources can provide a direct assess-ment of a photorefractive material with respect to thedispersion in its grating-vector response.

In summary, we have developed a procedure for form-ing two phase-conjugated near-field light spots at a givendistance near the surface of Fe:LiNbO3 0.04-wt. % crystal.We have characterized the light intensity distributionsin such spots and demonstrated that the spots formed240 nm apart in the direction perpendicular to the crys-tal optical axis can be still resolved in our RSNOM.It seems that there is a resolution limit of ,ly2n inthe present experimental arrangement that is due to theinherent volume nature of phase conjugation in pho-torefractive crystals. We believe that the resolutioncan be increased beyond this limit by phase conjuga-tion in thin photorefractive films. Using sufficientlythin films, one can try to increase the contribution (inthe phase-conjugated light) of the evanescent wave com-ponents with kk . 2pnyl, where n is the refractive in-dex of the film. The aforementioned argument with the

penetration depth dp now implies the resolution limit,pfs1ytd2 1 s2pnyld2g20.5, where t is the thickness ofthe film and the evanescent waves with dp . t are as-sumed to experience phase conjugation with the sameefficiency as do the propagating waves. Photorefrac-tive polymers13 might be suitable for the fabrication ofappropriate films. Our experiments indicate that it ispossible to form several phase-conjugated light spots atsubwavelength distances. This possibility can be usedto investigate various interesting phenomena. One maycreate a phased array of pointlike sources by varying thephase of light in the fiber when changing the fiber posi-tion during the recording procedure. Two spots formeda few nanometers apart with opposite phases should ex-hibit radiation properties close to those of an electricquadrupole, which is itself an interesting object to study.

*On leave from the Institute of Spectroscopy, RussianAcademy of Sciences, 142092, Troitsk, Russia.

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