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PHYSICAL REVIEW A VOLUME 65 013807 Laser action in strongly scattering rare earth metal doped dielectric nanophosphors G R Williams S B Bayram and S C Rand Division of Applied Physics Randall Laboratory University of Michigan Ann Arbor Michigan 481091022 T Hinklin and R M Laine Department ofMaterials Science amp Engineering University ochhigan Ann Arbor Michigan 48109 Received 24 October 200039 revised manuscript received 5 June 200139 published 11 December 2001 We report continuouswave laser action in two oxide nanopowders doped with Ce3 and Pr3 ions To our knowledge these are the rst observations of stimulated emission from electrically pumped random media in which scattering and distributed feedback scale lengths are much shorter than a wavelength The continuous nature of the laser emission in small volumes on the order of a cubic wavelength of these low gain systems and the absence of coherent speckle provide compelling evidence that these results are mediated by strong Anderson localization of light DOI 101103PhysRevA65013807 I INTRODUCTION Previous experiments 179 and theory 1011 on local ization of light and stimulated emission 12716 in scattering media as well as questions regarding the consequences of reCLu rent scattering events 1718 have all heightened cur rent interest in electromagnetic phenomena in multiply scat tering media SLuprisingly few theoretical or experimental papers have been published however that relate to the lim iting regime in which mean free paths and interparticle spac ings are much less than a wavelength Traditionally multiple scattering has been of interest to researchers studying statis tical aspects of weakly localized light 19 coherence 20 or imaging 21 Others have utilized multiple scattering to achieve pulsed laser action in powders where electromag netic propagation is diffusive 258 However at the bOLmd ary between the diffusive and strong scattering regimes where transport distances are on the order of the wavelength fundamental changes are anticipated in the interaction of light with matter that are new and Lmstudied In particular severe scattering is predicted to cause strong localization of light in lossless systems over limited frequency ranges 1011 although such behavior is not evidenced in mean eld calculations 22 Con nement of light by lossless scattering within three dimensional 3D regions of subwavelength dimensions if it were to occur in dense random media would have profound effects on coherence and lightscattering properties of the medium since propagation would then be restricted to dis tances less than an oscillation period llt For Lmab sorbed waves to be localized to the extent that they do not propagate even one wavelength in any direction dramatic changes in propagation parameters have to take place that are not predicted by effectivemedium theory For instance in order for an electromagnetic disturbance to cease oscillating spatially in a nonabsorbing medium the local wave vector must lose its directional character and de nition as a real quantity altogether Consequently computations of coherent superpositions of multiply scattered elds are needed with out the averaging that is customarily performed over one or more wavelengths to de ne constitutive parameters to inves 10502947200165101380762000 65 0138071 PACS numbers 4255Rz 4225Fx tigate optical properties in this regime theoretically Some speci c predictions have already been made however and thresholds for laser action mediated purely by scattering are expected to drop dramatically Lmder strong scattering condi tions 1316 Here we report for the rst time to our knowledge results related to this latter prediction by demonstrating continuous wave electrically pumped powder lasers We have generated ultraviolet and visible laser radiation in dry rareearthdoped nanopowders excited by a continuous lowvoltage and low current electron beam Earlier publications on pulsed laser action in powders were optically pumped experiments in rareearth 258 and polymeric 23 materials in the diffu sive regime and in semiconductor powders 2425 where angular dependences in output spectra and modes were re ported 23725 The angular variations in previous results indicated that different microcavities were responsible for output in different directions The observation of frequency selectivity within the transition bandwidth modes also pro vided clear spectroscopic evidence that the effective lengths of the laser cavities were much greater than half a wave length In Refs 23725 the effective cavity lengths deduc ible from output spectra exceeded ten wavelengths see Note added in proof Since spectral and angular variations re ect nonrandom aspects of material properties and propagation on length scales greater than an optical wavelength these obser vations in earlier pulsed powder lasers showed that the scat tering paths responsible for lasing while short were still too long to randomize laser output completely It may be readily appreciated however that if closed paths providing feedback for lasing are shorter than half a wavelength the constructive and destructive interference of light required to produce fre quency selectivity cannot occur Therefore for effective source volumes smaller than a cubic halfwavelength the stimulatedemission spectrum should be quite different from that of a singlemode coherent laser source occupying the full gain bandwidth and being independent of viewing angle In the phosphors described here we have observed unusual features of this kind in the presence of conventional indica tors of laser action such as sharp thresholds linear output 2001 The American Physical Society WILLIAMS BAYRAM RAND HINKLIN AND LAINE FIG 1 Transmission electron micrograph of 6A1203 nanopar ticles Note the faceted edges and the unaggregated state of par ticles in the sample and spectral quenching of competing transitions from the upper state II EXPERIMENT Our samples consisted of 6alumina nanopowders synthe sized by ame spray pyrolysis and doped with the rareearth metal ions Ce3 and P13 at concentrations of 1000 i 100 ppm 26 Metalloorganic precursors consisting of alumatrane NCH2CHZO3A1 with an equivalent loading of 2 wt A1203 and nitrate equivalents of 0003 wt Ce02 or Pr02 dissolved in ethanol were used to produce powders by combustion at 2000 C in oxygen at rates over 50 gh Particles were collected electrostatically downstream from the ame Particle sizes were estimated using BET 27 sur face areas 80i 1 and 43i 1 m2 g for Ce and Pr and xray line broadening The unaggregated singlecrystal nature of the particles was con rmed by transmission electron micros copy Fig 1 Dopant concentrations achieved in alumina were esti mated to be 75 ions per 20nm particle in the case of Ce and 800 ions per 40nm particle for Pr Asproduced powders were excited by a lowcurrent beam from a KimballPhysics EG14B electron gun to record opticalemission spectra Loose powder samples were lightly pressed into 3 mm shallow recesses of an oxygenfree copper mount in ultra high vacuum lt 6 X 10 10 T and irradiated with electrons in the energy range 1 10 keV over spot diameters of 2 mm Luminescence was collected with f4 fused silica optics and analyzed with a 1m grating spectrometer Scattering conditions in the powder samples were evalu ated using three separate coherent backscattering setups de signed to measure 1 x the mean distance traveled by light prior to directional randomization 12829 In the principal method probe light from an Ar laser 3638 nm overlap ping the Ce3 emission was used to record backscattered intensity through an interference lter using a 1P28 photo multiplier while the sample was rotated through an angular PHYSICAL REVIEW A 65 013807 Emission Intensity 104 countssec 16 2 24 28 32 36 4 Wave number 104 cmquot FIG 2 Cathodoluminescence spectra of Ce 6A1203 nanopar ticles excited by various electronbeam current levels 4 keV 2mm beam diameter range of i300 mrad with a step size 28 mrad that ex ceeded the detection angle 1 mrad Scattering was recorded for light polarized linearly in the scan plane and perpendicu lar to it and in additional runs for circularly polarized inci dent light The photomultiplier was preceded by lensless po larizer and waveplate combinations that detected only polarizationpreserving signals In two other approaches which yielded similar results the detector moved in the scan ning plane on a mechanical arm of xed radius 1 m cen tered on the sample surface In one case the incident laser beam was directed to the scattering surface by a micromirror and in the other by a beamsplitter oriented at 45 to permit intensity measurements over the limited but important back scattering angular range from i 10 to 10 mrad In this way many coherent backscattering CBS experiments were per formed to investigate transport conditions at the wavelengths of importance here III RESULTS The ultraviolet emission spectrum of Ce3 6A1203 Fig 2 consisted of a partly resolved doublet due to 5d4 f inter con gurational transitions of Ce3 30 and did not vary with observation direction The separation of the two components of this feature near 25 500 and 28 000 cm was consistent with the 2F722F52 interval 2100 cmil of the spinorbit split 4f ground term of Ce3 in crystals 3132 However the lowenergy component disappeared once the current was increased above 12 uA This phenomenon is known as spec tral quenching and here signals the onset of stimulated emis sion on the 5d4f2F52 transition This is due to the fact that both components of the 5d4 f 2F 52 2F 72 doublet originate from the same upper state Quenching of one but not the other emissive transition from a single occupied state 0138072 LASER ACTION IN STRONGLY SCATTERING RARE 3975 on 3 o T2 6 39 6 V 3 5 a 39 E 55 FL g 2 l 10 100 cu Current uA S e E El 1 E D 0 1 I 4 I I 0 10 20 30 40 Current uA FIG 3 Peak emission intensity at xem362 nm vs current Solid curves are guides to the eye Inset total linewidth of the composite ultraviolet emission feature from Ce 6AlZO3 nano particles plotted vs current is uniquely attributable to stimulated emission since this is the only process that can alter the relative radiative decay rates of the two 5d4 f transitions This result is remarkable in our experiments because it is obtained with weak continu ous excitation The apparent shift of the highenergy compo nent in Fig 2 to shorter wavelengths as current increased was also consistent with the development of gain on the 5d4f2F52 transition since increasing gain can progres sively offset losses from resonant reabsorption In Fig 3 the intensity of Ce3 emission is plotted versus electron current The sharp break in slope evident at 12 uA between two linear output regimes and the abrupt spec tral quenching of one of the 5d4 f components which sets in at the same current inset are jointly indicative of stimu lated emission with feedback or laser action An important distinction may be made between this behavior and that ex pected for ampli ed spontaneousemission processes ASE in which the output depends exponentially on the pumping rate 1433 Since our small particle sizes preclude optical feedback from highQ morphological resonances either be tween nearneighbor particles or within powder grains a dis tributed feedback mechanism is necessary to account for these characteristics 34 Results of coherent backscattering experiments performed to determine average distances over which light is trans ported in our samples are shown in Fig 4 The upper curve corresponds to data recorded for Ce3ldoped nanoalurnina at 3638 nm For Pr doped samples a HeNe laser 6328 nm was used and results obtained with the same approach are given in the lower curve The inset provides a magni ed view of the cusp obtained using the complementary tech nique described in the preceding section in which the detec tor is scanned through an angular range of 20 mrad collect ing light through a bearnsplitter The sharpness of the CBS cusp in all scans sets a lower limit on the absorption length PHYSICAL REVIEW A 65 013807 3 310 8 390 6 08 2 0639 3 l8 3 5 2317 0 go l39 gm E a 315 1 395 E E 14 02 E 2 i 12 5 0 5 w 0 llllIlllllllll39llllllllllllllllllllllll 200 150 100 50 0 50 100 150 200 Anglemrad FIG 4 Experimental backscattered intensity vs angle at xex 3638 nm upper trace and xex6328nm lower trace from Ce5 AlZO3 and Pr 6AlZO3 nanoparticles respectively incident polarization perpendicular to scan plane Solid curves are best ts see Ref Inset sharp triangular cusp at exact backscattering in Pr 5AlZO3 showing normalized peak intensity of 161 after cor rections for beamsplitter re ectivity of lagt1cm for lineshape analysis 3536 Leastsquares ts 4 to the data then yielded 1 114i 15 nm at 3638 nm and 1 311i 17 nm at 6328 nm the latter value being con sistent with the independent determination from slope analy sis of the inset data This analysis requires that the angle averaged internal re ectivity R of the samples be known at 3638 and 6328 nm Accordingly R was calculated using dispersion data of pure alumina 37 and found to be R 0711 and 0704 respectively with no adjustable pararn eters 4 Experimentally mean free transport distances were therefore found to be less than half a wavelength in both instances These short values nevertheless allow for gain length products for both ions N use gtXlt0003 and N 0561 00008 for saturated Ce3 and Pr3 systems respectively that substantially exceed the estimated losses yll11 lt10 5 IV DISCUSSION In Sec III transport distances 1 shorter than half a wavelength were deduced in conjunction with interparticle spacings of less than 15 at both the experimental wave lengths 3638 and 6328 nm The presence of many par ticles spaced by less than a wavelength on average violates the assumptions of Mie theory even when extended to mul tiply scattering media 38 as well as earlier CBS theories 4 Like previous authors 17 we nevertheless assumed the shape of the backscattering cone and its relation to the trans port distance 1 were unchanged under strong scattering con ditions The maximum height of the cone with respect to the incoherent background is known to decrease in the strong 0138073 WILLIAMS BAYRAM RAND HINKLIN AND LAINE scattering regime 17 so it may not be too surprising that the contrast in our CBS scans is substantially lower than 2 even in the helicitypreserving channel However the short 1 values obtained from analyzing light polarized perpen dicular to the scanning plane and similar results obtained by selecting circular polarization or light polarized parallel to the scan plane indicated that transport distances in the plane of the sample were invariably shorter than xZ Under these conditions despite negligible absorption la is more than four orders of magnitude larger than 1 electromagnetic energy is severely attenuated in less than a single spatial period This implies that the light eld emitted by dopant ions within our samples does not propagate or diffuse at all but assumes a distribution similar to that of a three dimensional evanescent eld as the result of lossless re ec tion between particles The short1 values deduced from our CBS measurements set an upper limit on coherence lengths that is somewhat less than a wavelength This has very im portant implications 39 that should manifest themselves in other ways that we describe next When transport distances are shorter than the spatial scale necessary for interference namely half a wavelength the op tical coherence length 10 is limited to a subwavelength Value lcSllt2 Such a short lc precludes completely coherent scattering apart from that produced by coherent light that never enters the medium but scatters from the sur face itself Hence the intensity uctuations usually referred to as speckle 40 in the scattered light eld of a coherent source should be greatly reduced Experimentally we found that indeed linearly polarized laser light scattered in the backward direction from our samples exhibited only i 30 intensity uctuation during slow angular scans through the central range For coherent input and stationary scatterers this modulation is normally 100 since all scattered light contributions are phasecoherent for a xed con guration 29 Timeaveraging by sample motion is customarily nec essary to extract meaningful eld correlation functions As expected the residual noise in our experiment dropped from i30 to i2 when the sample was rotated about the beam axis at 2 rpm con rming its origin as coherent speckle However the relatively small intensity uctuations in back scattered light made it possible to observe CBS cones with out spinning the sample at all From the angular interval of 063 mrad between peaks and valleys in CBS scans of stationary samples we inferred a limiting coherence aperture for the system of d2A 6 20 mm This was in excellent agreement with the 2mm diameter of the incident beam used to make the measure ments indicating that the speckle derived from re ective particles at the sample surface separated by less than the beam diameter rather than from multiple scattering in the powder interior Very much coarser speckle deriving from multiply scattered light with extremely short 1 was absent in CBS scans over angular ranges of up to 600 mrad when the sample was not rotationally averaged This set a limit on the coherence length of lclt 13 um independently of but in good accord with our CBS measurements Wideangle photographs were also taken of electron excited spots as small as 1 m2 to check for evidence of PHYSICAL REVIEW A 65 013807 2 I I A r l I i 12 E 1 5 39 g 08 E E g I 04 M o 2 2 E L I o I 0 b 2 3 l4 o 6 Wave number10 cm 8 5 I o o quot3 05 o 0 LE z O o o x f o 4 0 WW 0 10 20 30 40 50 60 70 Current HA FIG 5 Emission intensity vs current at xem633 nm in Pr 6A1203 nanoparticles and electron energy 1710 keV Inset emission spectra of Pr 6A1203 illustrating growth of the red tran sition with increasing current at 7 keV speckle in emission A lensless Polaroid Land Film cassette was used outside the vacuum chamber for this purpose No evidence was found for intensity uctuations greater than 10 throughout solid angles as large as 004 sr limited by chamber window size The observation of uniform intensity over such a wide angular range eliminated the possibility of light emission in any given direction arising from coherent laser source regions in the powder with effective cavity lengths greater than the wavelength We are led to conclude that above threshold light from our samples is either gener ated in a fundamentally incoherent manner or it derives from an incoherent assembly of coherent sources that is indistin guishable from an incoherent source The ratio of the coherent peak intensity to the inco herent background was consistently less than 19 in numer ous CBS experiments performed with different samples Low ratios were observed with linear polarizations parallel perpendicular to the scanning plane and with circular polar ization in the helicitypreserving channel This is very much lower than the theoretical value of 2 characteristic of the diffusive regime 17 but may be due to experimental limi tations Experiments are underway with a new CBS appara tus to check whether low contrast in our samples is due to stray light contributions to the background or to recurrent scattering Additional perspective is provided by results for lumines cence in Pr 6A1203 powder excited at various electron en ergies Red emission from P13 exhibits thresholds Fig 5 like that of ultraviolet emission in Ce 6A1203 Changes in slope at threshold are abmpt at low energies They shift to lower currents and become less distinct as electron energy increases Output curves also steepen at higher energies These trends can be explained semiquantitatively by calcu lating electron penetration in A1203 versus energy using the 0138074 LASER ACTION IN STRONGLY SCATTERING RARE Monte Carlo code CASINO 41 In the range 173 keV the average penetration depth was less than the mean transport distance 1 making it less than the length scale over which radiative transport is effective Hence signi cant radiant loss from the excitation volume through the vacuum interface is possible in this energy range On this basis it is understand able that observed thresholds were strongly voltage dependent between 1 and 3 keV being highest for the lowest voltage At a xed current of 20 MA the voltage threshold for laser action was reached experimentally in the neighbor hood of 475 keV The calculated penetration depth at this threshold voltage was comparable to the measured l Under these conditions energy is deposited ef ciently within a vol ume Nl3 from which comparatively little radiant loss is possible through the vacuum interface Over 4 keV the op tical output curves developed more curvature as expected for ampli cation without feedback from a source lying deeper within the inverted medium 33 The inset of Fig 5 contains raw spectral emission data from the Pr sample The separation of dominant features at 15 810 and 16 000 cm 1 is the same as that of the two domi nant spectroscopic sites in PrB AIZO3 so these lines may be assignable either to the 3P0gt3H54964 cm 1 7r and 3P0gt3H54769 cm 1 0 transitions of Pr respectively or to one of these transitions at two different sites 42 Since neither red transition quenches strongly as current is in creased we favor an assignment to one of these transitions at the two distinct sites Most other features in the bluered spectral region arise from 3P0 3P1 and 3P2 emissions transitions from 116 and 1D2 being spinforbidden The three weak ultraviolet bands are tentatively assigned to 1S0 de cays terminating on the 3P 1D and 1G levels 43 V CONCLUSIONS The observations of spectral quenching behavior Fig 2 emission thresholding and linear output above threshold Figs 3a and 5 collectively furnish compelling evidence of Ce3 and Pr laser action in the 174keV range Since con ventional cavities support continuous laser action only with high re ectivity mirrors these observations imply that light experiences nearly total re ection in three dimensions within our samples in agreement with CBS measurements showing directly that scattering is so severe that light propagates for ward less than half a wavelength irrespective of direction or polarization Given that we nd I lt 1 lt in the absence of signi cant absorption kltla these experimental results suggest that light generated by an impurity ion within our powders acquires a spatial distribution that resembles that of a 3D evanescent wave 39 Lacking any other consistent e lanation we conclude this behavior results from strong localization 101144 Emission is evidently stimulated co PHYSICAL REVIEWA 65 013807 herently over distance scales of tens of nanometers in our samples but spatial randomization on length scales of half a wavelength or more precludes directionality or mode selec tivity Backscattered light and laser output appears to be virtually specklefree consistent with its subwavelength ef fective coherence length Finally all frequencies within the luminescent linewidth experience comparable gain and feed back independent of observation angle just as expected for continuous truly random laser action Numerous applications for laser phosphors can be imag ined in conventional lighting and displays Though the brightness of existing phosphors in televisions uorescent lights plasma and eld emission displays is strictly limited by the spontaneousemission rate this limitation can be over come with stimulated emission The absence of speckle could also facilitate largearea submicron optical lithogra phy However while doped dielectric nanophosphors may provide a versatile family of emissive materials for novel light sources many fundamental advances can be expected to emerge from these ndings Confinement of light within subwavelength regions may mediate new or enhanced non linear phenomena associated with ultraslow light recurrent scattering and surface resonances Omnidirectional stimu lated emission will be achieveable on new transitions in new wavelength ranges with excitation methods not previously feasible in dielectrics This prospect is illustrated by our own results for Ce which are the rst to demonstrate continu ous laser action on its ultraviolet transition by any means Studies of pseudogap ltering optical coherence and speckle in the proximity of the localization edge should now be feasible in nanodielectrics Unlike electrons photons do not interact with one another at low energies in vacuum Consequently research on these topics will furnish perspec tives to complement existing knowledge from electron stud ies of wave transport in a wide variety of disordered systems 45 Note added in proof Effective cavity size was also large in research on dyedoped silver colloids inside quartz reso nators that have been reported to support continuous laser action Phys Rev Lett 82 4811 1999 There morphologydependent resonances of a macroscopic cavity determined spectral modes of the output ACIGVOWLEDGMENTS The authors wish to thank K L Schepler S Lipson E Leith and G W Ford for useful discussions and I M Glownia and B Furman for assistance with backscattering measurements We gratefully acknowledge research grants from the National Science Foundation DMR9975542 the Army Research Of ce DAAD199910229 and US DODiAir Force F496209910158 1 M P Van Albada and A Lagendijk Phys Rev Lett 55 2692 1985 2 V M Markushev V F Zolin and Ch M Briskina Sov J Quantum Electron 16 281 1986 3 A Z Genack and N Garcia Phys Rev Lett 66 2064 1991 4 J X Zhu D J Pine and D A Weitz Phys Rev A 44 3948 0138075 WILLIAMS BAYRAM RAND HlNKLlN AND LAlNE 199139 T M Nieuwenhuisen and J M Luck Phys Rev B 48 569 1993 5 C Gouedard D Husson C Sauteret F Auzel and A Migus J Opt Soc Am B 10 2358 1993 6 N M Lawandy R M Balachandran A S L Gomes and 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