We report the anisotropic focusing characteristics of a spherically configured region of micro-domains that have been induced within a cubic shaped crystal of Ce:doped Sr0.61Ba0.39Nb2O6. The internal spherical structure focuses extraordinary polarised light, but not ordinary polarised. The spherical region, which is easily observed via scattering, is formed as the crystal cools down, after a repoling cycle through the Curie temperature, with an applied field. Analytic modelling of the thermal gradients that exist within the crystal during cooling reveals a small (&lt; 1°) temperature difference between the central and outside regions. The similarity in shape between these temperature profiles and the observed scattering region suggests a possible mechanism for the growth of this spherical micro-domained structure

Brown, Paul T.

Daniell, Geoffrey J.

Eason, Robert W.

Ross, Graeme W.

Smith, Peter G.R.

English

Southampton (e-Prints Soton)

1Southampton SO17 1BJ, UKTelephone: +44 1703 593150e-mail: light@orc.soton.ac.ukOptoelectronics Research CentreUniversity of SouthamptonAnisotropic Focusing Characteristics of Micro-domain Structures within Crystalline Sr Ba Nb O : The Crystal Ball 0.61 0.39 2 6P.G.R.Smith, G.W.Ross, P.T.Brown, R.W.Eason and G.J.DaniellAbstractWe report the anisotropic focusing characteristics of a spherically configured region of micro-domains thathave been induced within a cubic shaped crystal of Ce:doped Sr Ba Nb O . The internal spherical structure 0.61 0.39 2 6focuses extraordinary polarised light, but not ordinary polarised. The spherical region, which is easily observedvia scattering, is formed as the crystal cools down, after a repoling cycle through the Curie temperature, withan applied field. Analytic modelling of the thermal gradients that exist within the crystal during cooling revealsa small (<1 ) temperature difference between the central and outside regions. The similarity in shape betweenothese temperature profiles and the observed scattering region suggests a possible mechanism for the growthof this spherical micro-domained structure. IntroductionStrontium barium niobate (SBN:x, Sr Ba Nb O ) is a crystalline material which is a solid solution x 1-x 2 6of strontium and barium niobates [1]. For values of x in the range 0.5-0.75, crystals are readilyavailable with good optical quality for applications in photorefraction, optical memories, electro-optic devices and phase conjugation. SBN is one of several glassy ferroelectric crystals that haveunusual structural (and micro-structural) properties [2]. The phase transition from ferroelectricto paraelectric states is diffuse, and as such, the values reported for Curie temperature , T , range cquite widely in the literature. Single domain crystals are obtained by heating through T with an capplied field present larger than the coercive field, and subsequently letting the crystal cool downbelow T . Experimentally, however, the exact procedure adopted for this, namely duration of capplied field, rate of crystal cooling, whether the nominal value for T is reached, and very cimportantly, the previous crystal repoling history, all affect both the net dipole moment obtained,and the extent of formation of any regions of micro-domains.Recent studies using the technique of X-ray diffraction imaging have revealed the extent to whichdomains, and micro-domains, may be present in nominally well poled samples of SBN. For arange of different crystals, 180 anti-parallel domains were observed, predominantly near theocrystal edges , with an average size of the order of 10 µm or less [3]. For SBN:50, rapid coolingthrough T can produce domains with average widths of 100D, while subsequent annealing for ca few days at lower temperatures can change this value to the order of microns [4]. Othermaterials such as lead magnesium niobate, Pb(Mg Nb )O , also reveal this variation in domain 1/3 2/3 3size: field cooling (FC) and zero field cooling (ZFC) produce distinctly different domain sizedistributions [5]. SBN will always tend to show this variability of domain sizes, the preciselength and width of which is a strong function of the poling procedure adopted, and earlierpoling/repoling cycles. Scattering experiments have been performed for SBN which allow domain size distributions tobe inferred [6]. The experiments reported used two nominally identical crystals of SBN:61 whichwere subjected to differing poling treatments. Crystal number one remained unpoledthroughout the measurements. Crystal number two however was given an initial FC thermalpoling, followed by several ZFC thermal cycles. The Rayleigh scattering, viewed at 90 , differedo2 C-axis ------>Figure 1. Central ball region ofSBN:61 crystal, viewed throughimaging of scattered light. Figure (a)shows a top view, for o-polarisedlight incident normal to the c-axis.Figure (b) is a view at 45, along acrystal edge, showing that thescattering region is spherical, andcan be viewed simultaneously fromtwo sides of the crystal. The crystalwas 5 x 5 x 5 mm, and the centralball is approximately 3 mm diameter.markedly between the two crystals, both in intensity and polarisation dependence. Thehundredfold difference reported for the scattered light intensity between the two crystals isindicative of their respective domain size, as Rayleigh scattering depends strongly on dimensionsof the scatterer. The crystal we discuss in this paper however,contains a spherical micro-domain structure thatrepresents both of the above cases reported in [6],but within a single crystal. The central region is anefficient scatterer, and the visual appearance isstriking: the crystal contains a scattering ‘ball’ whichis completely enclosed within the crystal cube. Also,unlike the results reported in [6], the scattering iseasily observable with the naked eye. While thepolarisation properties of the scattered light aresimilar, the intensity of the scattering is many ordersof magnitude larger, measurable with standardoptical power meters, rather than using photoncounting. The anisotropic focusing we observe isgenerated by the presence of this spherical regionwithin the uniaxial SBN crystal structure. Anisotropic properties of the crystal ballFigure 1 shows the scattered light generated fromthe central region of the crystal. Fig 1(a) wasobtained by viewing at 90 to the incident beamodirection, which was provided from either an Ar ion+laser operating at 514.5nm or a He-Ne laser at633nm. Figure 1(b) shows the scattering viewedalong a crystal edge direction, the two imagesclearly showing the volume nature of the scatteringregion. An analyser placed in the path of thescattered light revealed a polarisation dependence asindicated in figure 2. O-polarised light was scattereduniquely as e-polarised, whereas e-polarised lightyielded almost equal intensity contributions of bothe-polarised, and o-polarised light. The scattering ballappeared following a normal FC poling cycle. Thefield applied was 2 kV across the crystal c axis, andthe cooling cycle took the crystal from atemperature of typically 120 C to roomotemperature (~25 C), over a time period of ~2ohours. The crystal was situated within a thermalenclosure, so the cooling curve showed exponentialbehaviour. The scattering ball was observed eachtime the crystal was FC poled in this way.Subsequent room temperature electrical repoling3Figure 2. Schematic of the anisotropicscattering observed. Incident o-polarisedlight is scattered as e-polarised. Incident e-polarised light is scattered with equalintensity into both polarisations. Thenotation , e.g. X(YZ)Y, is taken from use in[6], and refers to, left to right, incident k-vector direction, incident polarisation,scattered polarisation, scattered k-vector.could be used to make the scattering balldisappear, but a FC cycle was required toproduce the structure. The exact location ofthe centre of the ball could be shifted laterallyalong the crystal c-axis by # 1mm, dependingon the poling field polarity, but the overall sizeremained constant however. The origin of the scattering and anisotropicfocusing lies in the orientation and size of themicrodomains present within this uniaxialmedium. We have performed two-beamcoupling experiments using the ‘Swiss cheese’arrangement [7] in which the signal beampropagates down the c-axis, and a pump beamis incident at an arbitrary angle (45 in ourocase) to the crystal entrance face. This beamcoupling arrangement allows visualisation ofthe domain orientation, as coupling will eitheraugment or deplete the signal beam intensity,depending on the domain polarity. For SBN,the largest electro-optic coefficient normallyaccessed is r but for the Swiss cheese 33,coupling experimental set-up, this is notpossible. Additionally, when viewing normalto the c-axis direction, circular interferencepatterns were observed, generated by the ball,which masked the outline of the central region, viewed through conventional beam coupling inthe symmetric orientation utilising r . A unity beam intensity ratio was used, and the transiently 33diffracted light was captured with a frame grabber and CCD camera. Figure 3 shows the optimumresults obtainable, using the smaller r coefficient. The image shows a central approximately 13circular region which is noticeably darker than the outer regions, indicating less overall couplinghas taken place here. This is indicative of the simultaneous presence of 0 and 180 domainso owithin this region. Note that while the shape of the microdomain region is very similar to thatshown in figure 1, due to the difference in physical processes involved in scattering and beamcoupling, there is no reason for an exact match. Measurement of the angular dependence of He-Ne laser light diffracted from within the ballalsolead to the conclusion that the central region consists of a spherically configured array ofparallel and anti-parallel domains, with transverse widths at the sub-micron to few microns scalelength. Light was diffracted as a wide angular fan, rather than as discrete points, indicating thepresence of a distribution of domain widths. The peak intensity within this diffracted fan indicateda modal width of ~2µm. No significant scattering was observed along the c-axis directionhowever, indicating that the length of domains greatly exceeds their width. Additionally, no suchdiffraction was observed when He-Ne light was directed at regions of the crystal outside thecentral spherical region.4Figure 3. Image of ball, viewed by transient two-beam coupling, showing thecentral region of disordered microdomains. Coupling occurred down thecrystal c-axis, hence coupling efficiency was not optimal. Birefringent focusingWhen the crystal is illuminated with collimated light from a He-Ne laser, the internal microdomainregion acts as a converging lens for e-polarised light, but not for o-polarised. The focal lengthachieved at the He-Ne wavelength of 633 nm was measured to be ~140cm, producing a spot size,T, of 290µm, measured using a beam profiler. Experimentally however, the incident Gaussianbeam overfilled the crystal input aperture, so that the normal conditions applicable to diffractionlimited Gaussian beam focussing (lens not acting as a limiting aperture) do not apply. Forcomparison however, using an average value of ball diameter of 3mm, obtained from scatteringand beam coupling observations respectively, we deduce a diffraction limited value of spot sizeof ~ 190µm, for the measured focal length of 140cm.There was no focusing action at all for o-polarised incident light. To our knowledge, no othersuch birefringent focusing structures have been reported, in this passive compact form. It is, ofcourse, possible to assemble such a birefringent device, using specially constructed doublets, madefrom differently orientated anisotropic elements. However, the crystal here achieves this in a singleelement. One additional advantage is that this lens is field erasable. A room temperature repolingfield makes the ball disappear. By further optimised field cooling procedures, lens structures maybe achievable with larger dimensions, and smaller values of focal length. DiscussionThe scattering observed reflects the underlying lack of single domain ordering within thecentral region. The presence of 0 and 180 domains, with associated domain boundaries,o ointernal stresses, and charge compensation than can occur at the ends of domains, all affect thebulk properties of a ferroelectric. When a region of microdomained material exists within abulk single domain crystal, then the microscopic structure can have a pronounced affect on themacroscopic optical properties, such as refractive index and birefringence. In our case,5Figure 4. Results of analytic modelling of 3-dimensional heat diffusion problem withinthe SBN crystal. Two iso-temperaturesurfaces are shown, to illustrate theirincreasingly spherical nature towards thecentral region of the crystal. The calculationswere performed assuming isotropic heat flow.More detail on the analytic solution is givenin the appendix.while the exact cause for formation of thisball is uncertain, we suggest that thethermal cycling required to FC pole thecrystal also influences the domain growthhabit, through the finite temperaturedifferences that exist between the centraland outside regions. The spherical shapesuggests that some diffusion process may beinvolved. Material in- or out-diffusion isunlikely, as the ball could be formed anderased many times, and the temperaturesinvolved in poling were only of order 100 oC. Furthermore, the lateral poling fieldpolarity dependent shift that was observed,suggests a more general explanation. It isknown in SBN that domain size is afunction of external pressure [8]. There isalso a small, but systematic temperaturedifference between the central and outerregions of the crystal following a FCpoling. In figure 4 we show the results of ananalytic solution to the 3- dimensional heatflow equation within the SBN, following aheating cycle to beyond its Curietemperature, and slow cooling to roomtemperature. The calculation assumed thatheat diffusion was isotropic, and used theknown value for thermal diffusivity in SBN(D= 6.77 x 10 cm s [9]). A more-3 2 -1complete discussion of the analytic solution to this problem is given in an appendix. Two equaltemperature contours are shown within the crystal. It can be seen that there is a good similaritybetween the inner contour plot and the region showing pronounced optical scattering, shown infigure 1. This can be qualitatively understood by considering heat loss from the outside faces ofthe crystal cube. There will be a systematic thermal smoothing of the temperature contours,resulting in a quasi-spherical shape as the centre of the cube is reached. The maximum calculatedtemperature difference between the centre and outside edges of the crystal does not exceed ~ 0.2K at any time during the cooling period. As stated earlier, it is known however that the dielectricoproperties and value of Curie temperature for SBN are sensitive to external factors, and wesuggest here that this temperature difference, while small, may have a pronounced affect on thegrowth habit experienced by the central region, which will be under constant stress during thecooling phase. We observe a progressive increase in the scattered light intensity from the central region ratherthan a sudden onset at a specific temperature, as the crystal cools. We conclude therefore that themicrodomained central region grows through continuous response to forces such as pressure, orstress. As the material cools through the Curie temperature, the transition from the paraelectricto the ferroelectric anisotropic phase will occur first at the cooler outer crystal regions.Progressive cooling may exert further pressure on the central region, which in turn affects theinternal structure, and the whole process continues. In this way, there can be a large internal stress6accumulated within the crystal, which as stated earlier, is a known method for microdomainformation. Although it may seem surprising that this can occur from such a small value oftemperature difference, such glassy ferroelectrics are known to be very sensitive to smalltemperature differences at, for example, their domain freezing temperature [10]. ConclusionsIn conclusion, the scattering central ball we have grown within the cube shaped SBN crystaldisplays interesting optical properties. E-polarised light is selectively focussed by the centralregion, while o-polarised light is unaffected. The underlying mechanism for the formation of thisregion in not certain, but may well be due to temperature gradients experienced during cooling,following a poling cycle. If the domain size could be controlled dynamically, then variable focallength optical elements could be constructed by this route. Further work is in progress concerningthis aspect. AcknowledgementsWe would like to acknowledge Dr N.I.Zheludev of Southampton University for useful discussionsconcerning the non-reciprocal nature of the scattering observed within the crystal. We alsoacknowledge the Engineering and Physical Sciences Research Council (EPSRC) for funding undergrant no. GR/K 28251.T(x,y,z,t)’64B3j j jodd p, q, r(&1)p%q%rpqrcos pBx2Lcos qBy2Lcos rBz2L× exp &DB2t4L 2 [p 2%q 2%r 2] .T(t)’(Ti&Tf) e &"t % Tf t>0Ti t<0Tf % (Ti&Tf )($e &"t & "e &$t)($ & ").64"L 2(Tf&Ti)e &"tDB5 j j jodd p q r(&1)p%q%rcospBx2LcosqBy2LcosrBz2Lpqr[p 2%q 2%r 2]7AppendixFigure 4 shows the results of analytically modelling the heat flow. As a starting point, a solutionof the diffusion equation in a cube of edge 2L isAt t=0 the temperature T is uniform except on the surface x=±L, y=±L, z=±L where T is alwayszero. This solution therefore corresponds to the physical situation where the initial temperatureof the cube is unity and the surface temperature makes a step function change to T=0 at t=0.If the temperature of the oven containing the crystal changes from T to T according to i fthe response of the crystal can be obtained by replacing each factor of the form exp(!$t) byIn the experiment " was 5.834 10 s , D was taken as 6.77 10 cm s [9], and assumed to be-4 -1 -3 2 -1isotropic, and L=2.5 mm These values give the minimum value of $, corresponding to p=q=r=1as 0.801; it follows that for times greater than a few seconds after the start of cooling exp(!$t)is negligible; also "L /DB << 1. With these approximations the temperature difference between2 2 the crystal surface and the point x,y,z, at time t, isThe value of the triple sum at the centre of the cube is 1.27 and with the constants above, thetemperature difference between the crystal faces and the centre of the cube never exceeds 0.19K.Figure 4 has been generated by plotting equal temperature contour shells from the 3 dimensionalmatrix of points derived from the analytic solution above, and two such shells are illustrated, toshow the increasingly spherical shape obtained.8References1. R.R.Neurgaonkar, W.K.Cory, ‘Progress in photorefractive tungsten bronze crystals’,JOSA B 3, pp274-282, (1986)2. G.Burns, ‘Crystalline ferroelectrics with a glassy polarisation phase’, Phase Trans., 5,pp261-276, (1985)3. 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G.W.Ross, R.W.Eason, ‘Temperature sensitivity of repoling in strontium barium niobate near to the glassy transition’,

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R.R.Neurgaonkar, ‘Anisotropic glasslike characteristics of strontium barium niobate relaxors’,

Rayleigh-scattering in Sr Ba Nb O '

T.G.Xi, Y.Fei, C.F.Shao, ‘Specific-heat and thermal-diffusivity of strontium barium niobate (Sr Ba Nb

temperature, and frequency-dependence of the dielectric-properties of strontium barium niobate’

Anisotropic focusing characteristics of micro-domain structures within crystalline Sr0.61Ba0.39Nb2O6 : the crystal ball

Anisotropic focusing characteristics of micro-domain structures within crystalline Sr<sub>0.61</sub>Ba<sub>0.39</sub>Nb<sub>2</sub>O<sub>6</sub> : the crystal ball

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