microspheres, photonic atoms and the physics of...

The transfer of energy between neigh-boring molecules plays a pivotal

role in nature. In photosynthesis, for ex-ample, a plant fuels its metabolism andgrowth with sunlight by taking advan-tage of a curious physical phenomenonthat allows energy to hop from onechlorophyll molecule to another situat-ed about a half a nanometer away. Acouple of hundred chlorophyll mole-cules pass the energy they collect fromthe sun in this way to a single reactioncenter, the starting point for subsequentchemical reactions. Without this mech-anism for transferring energy betweenmolecules, photosynthesis would large-ly cease, and we would likely starve.

About 15 years ago I began to won-der whether similar forms of energytransfer could influence photochem-istry within aerosol particles. In partic-ular, I wanted to know whether thereare subtleties in the way energy is con-veyed between molecules in an isolat-ed droplet about 10 micrometers in di-ameter. To most physicists, the ideamust have seemed crazy. After all, therange of the longest substantial ex-change of this sort, as Nobelist JeanPerrin had discovered and TheodoreFörster had described in quantum-mechanical terms decades ago, is only

about 5 nanometers. The vessels I wasproposing to use would be 2,000 timeslarger. So there was no obvious reasonto expect that their tiny size wouldhave any influence at all. Still, researchelsewhere with similar microscopicparticles hinted of interesting physicaleffects, and I urged one of my graduatestudents, Lorcan Folan, to investigate.Little did I know that the results weand others were soon to obtain woulddistinguish the lowly aerosol particleas a high-tech item.

Such microscopic particles nowstand poised to serve in a variety ofways, from lasers of exceptional effi-ciency to optical filters of unprecedent-ed purity and chemical probes of tinysize—to name just a few obvious appli-cations. But before delving into howtiny spheres can provide such valuablefunctions, it is worthwhile to reviewhow this rapidly evolving creature of21st-century technology first arose froma primordial soup of basic research.

Peering at ParticlesProbing something as subtle as thetransfer of energy between moleculesmay seem daunting, but in truth theprocedure is straightforward. You firstenergize one type of molecule, knownas a donor, by illuminating it with lightfrom a properly tuned laser, whichkicks ground-state electrons to a higherenergy level. Then you look for a trans-fer of this energy to another type ofmolecule, known as an acceptor, bysensing the characteristic color of lightit gives off when its excited electronsfall back to a lower-energy state (a fa-miliar enough process called fluores-cence). If no energy passes betweendonors and acceptors, only the donor

molecules will fluoresce, giving offtheir own particular color. So the ratioof acceptor to donor fluorescence pro-vides a convenient way to gauge theamount of energy transferred.

To perform the measurement on amicroscopic droplet, one simply mixesin the appropriate donors and accep-tors and observes the spectrum oflaser-induced fluorescence. The not-so-minor complication is that it is diffi-cult to hold a 10-micrometer sphere ofliquid in place long enough to studyit. Lorcan and I solved this problemby constructing an apparatus in whichhe could levitate and contain an elec-trically charged particle indefinitely us-ing electrostatic force to balance gravi-ty (Figure 1), just as Robert Millikanhad done decades before in his famousoil-drop experiment. But Millikan’sscheme alone does not provide a“trap”—the particle can wander freely.To prevent such drift, Lorcan’s appara-tus superimposed an oscillating elec-tric field on the constant levitationfield, following the example of Wolf-gang Paul, who had shown with hisNobel Prize–winning work of the1950s that a dynamic field can be usedto trap an atomic ion (Figure 2). With aproperly fashioned oscillating field, amicroscopic droplet just hangs there inair, an easy target to hit with a laserand to view through a microscope.

The first spectrum Lorcan obtainedfrom a levitated droplet sent a wave ofsurprise through our laboratory. Hehad planned a series of experiments atvarying concentrations, starting on thedilute side where the average distancebetween donors and acceptors was 20times the maximum range for Försterexchange. So we did not expect any en-

414 American Scientist, Volume 89

Microspheres, Photonic Atomsand the Physics of Nothing

Light can become trapped within tiny, transparent spheres. The surprising propertiesthat result may turn “microsphere photonics” into an important new technology

Stephen Arnold

Copyright © 2001 American Scientist

Stephen Arnold is director of the MicroparticlePhotophysics Laboratory and Thomas PottsProfessor of Physics at the Polytechnic Universityin New York. Arnold has also held visiting appoint-ments at Caltech, the University of Tokyo and theÉcole normale supérieure in Paris. He is a Fellow ofthe American Physical Society and the OpticalSociety of America. Address: Department ofPhysics, Polytechnic University, 6 MetrotechCenter, Brooklyn, NY 11201. Internet: [email protected]

ergy transfer to be apparent. Yet the ra-tio of acceptor to donor fluorescenceproved to be more than 10 percent.

As Lorcan increased the concentra-tion of acceptor molecules in a series ofdroplets under study, we became in-creasingly puzzled. Had the well-known Förster mechanism operated,the amount of energy transferred insuch dilute solutions should have beenproportional to the concentration of ac-ceptors. But these experiments re-vealed a range of concentrations nearlytwo orders of magnitude wide forwhich we saw little change in theamount of energy conveyed between

molecules (Figure 3). What is more, inthe light spectra for both donors and ac-ceptors, we observed spikes that wereas obvious as fence pickets (Figure 4).Such distinctive features had never ap-peared in experiments that probed thesevery same molecules in a centimeter-scale test tube. Although the explanationwas not immediately obvious, these twopieces of evidence were ultimately to re-vamp our view of how energy was be-ing passed between molecules.

At the outset, we were planning toprobe the subtleties of Förster transfer,whereby the energy in an excited elec-tron shifts to another molecule without

ever generating a photon. How, onemight reasonably ask, does that hap-pen? Such transfer takes place becausean excited molecule behaves some-thing like a transmitting radio anten-na. Close to this nanoscopic source, theoscillating electric field is especiallyintense (although it drops off extreme-ly rapidly, with the cube of the dis-tance). This field can, in fact, be suffi-ciently strong to induce oscillation inthe electron cloud of a nearby mole-cule, and this coupling conveys energyif the acceptor sits close enough thatthe probability of transfer overwhelmsthe natural probability for the donor to

2001 September–October 415Copyright © 2001 American Scientist

Figure 1. Charged droplet of glycerol floats motionlessly between two metallic electrodes as it is irradiated from the left with laser light. The au-thor and his students used this experimental arrangement to study how energy passes between two different kinds of dye molecules mixed intothe droplet. Their discovery that optical energy moved from one kind of molecule to the other with surprising efficiency prompted them to in-vestigate the intriguing physics of light traveling within microscopic spheres made of liquid, plastic and glass. The novel optical properties of suchmicrospheres suggests their use in many different applications, from signal processing to biological sensing. (Photograph courtesy of the author.)

fluoresce. Photons are not involved insuch an exchange; that is to say, thedonors do not have to give off electro-magnetic radiation. The Förster processis thus akin to what happens to peoplewho mysteriously hear radio programsbecause the electric field of a nearby ra-dio transmitter is so powerful that it in-duces currents to flow in their fillings.

Of course, radio transmitters are notbuilt to energize the mouths of peoplestanding nearby: They depend on theirantennas broadcasting electromagneticwaves to far-flung receivers. So too

with excited molecules. If the donor hasno near-field neighbors to capture thisenergy, the excited molecule emits aphoton into the far field (at least onewavelength away). An acceptor look-ing back at the donor from this distancenormally finds itself so far away thatthe probability of being struck by thephoton and absorbing its energy is as-tronomically small. Yet this was thescale of separation between donors andacceptors in Lorcan’s first experiment.

What was going on? Given the lowconcentration of donor and acceptormolecules within the droplet, we knewthat Förster transfer was not operating.Photons must have been leaving thedonors and hitting the acceptors, butthey were doing so with an unexpectedefficiency. The only reasonable expla-nation was that each of the emittedphotons was returning many times tothe same region, so that it had manychances to collide with an acceptor.The spikes we saw in the spectra gaveus a good clue to the mechanism.

These spikes are resonance peaks,which correspond to special electro-magnetic modes for the entire particle.The situation is akin to a violin string,which supports vibrational modesonly at those frequencies that providefor an integral number of half wave-lengths along its length. The electro-magnetic modes of small particles—commonly known as Mie resonancesor whispering-gallery modes—are

analogous and are normally describedby their wave character, too, in a waythat takes full account of such compli-cations as polarization and diffraction.However there is a more visceral de-scription of these modes that clearlyunderscores the ability of a photon torevisit a region many times. H. M.Nussenzveig of the Universidade Fed-eral do Rio de Janeiro realized that ifthe sphere is much larger than thewavelength of light involved, whisper-ing-gallery modes can be representedas geometrical orbits. With diffractionstripped away, photons can be thoughtof as bouncing around inside the parti-cle in well-defined trajectories, con-fined by total internal reflection—thesame phenomenon that makes the sur-face of a swimming pool look like amirror when you peer up from underwater and look to the side (Figure 5).

The swimming-pool effect arises be-cause rays hitting the surface from un-derneath at a shallow angle reflectcompletely back into the water. To alarge extent this is also true inside atransparent particle, so long as it ismuch larger than the wavelength.When a ray of light strikes the spheri-cal surface at a shallow angle, it justbounces back inside. A ricochetingphoton thus remains within the parti-cle for much longer than it would oth-erwise. Ultimately the photon lifetimeis limited by diffraction, which causesphoton trajectories to be less certain, al-

416 American Scientist, Volume 89 Copyright © 2001 American Scientist

�

to microscope,camera andspectrometer

laser beam

picopipette

Figure 2. Custom-designed “picopipette” generates one charged 10-micrometer droplet of glycerol, which passes through an access holeinto the experimental chamber. This tiny sphere is then irradiatedwith a laser, and the resulting emissions are observed through a mi-croscope to which a spectrometer is coupled. It can be studied in thisway because it is levitated in air using three electrodes. A large, con-stant electric force (blue arrow) balances the downward force of grav-ity (orange arrow). But according to a well-known theorem of physics,a static electric field cannot be fashioned to hold a charged object inplace without drifting. An alternating saddle-shaped potential can,however, be used to create an electric field that switches back andforth (green arrows), trapping the droplet. During his Nobel address in1988, Wolfgang Paul, who first constructed such traps to study atom-ic ions, used a mechanical analogue (above) to illustrate how such anoscillating saddle can be made to contain a small ball. (Photographby Hans-Joachim Becker, courtesy of the Deutsches Museum.)

Förstertransferflu

ores

cenc

e ra

tio (

perc

ent)

0.1

1

10

100

acceptor concentration(moles per liter)

10–8 10–7 10–6 10–5

Figure 3. Transfer of energy between donor andacceptor dye molecules (as measured by theirfluorescence) proved to be much larger (dots)than predicted according to Förster theory (line).This discrepancy, and the weak dependenceon concentration over much of the range, ledthe author and his students to consider otherways that energy could flow from one mole-cule to another within a levitated droplet.

lowing the energy eventually to “leak”out. The effects of diffraction grow asthe particle shrinks, and when the ra-dius approaches the wavelength oflight passing through the interior, reso-nances are lost altogether.

With these considerations in mind,we began to make sense of the obser-vations and started to appreciate theimportance of the special electromag-netic modes of a tiny droplet. We calledthem photonic-atom modes, because thetrajectories of the photons resemble theorbits of electrons in atoms. It turns outthat the longest-lived modes have pho-tons traveling along simple polygons(Figure 6), whereas for the shorter-livedmodes the paths close after more thanone revolution around the interior. Us-ing our data and the photonic-atompicture, we estimated that before beingabsorbed or leaking out, the photonscirculating within an acceptor-freedroplet of 10-micrometer radius covera total distance of about 0.6 meter—30,000 times the width of the sphere!

Just as with an electron in a Bohratom, the photon in a microsphere, or“photonic atom,” has a quantized amountof orbital angular momentum. Photonshave momentum? Indeed they do. Ein-stein had shown long ago that a photonhas momentum proportional to its ener-gy, which in turn is proportional to theoptical frequency. The orbital angularmomentum of a photon in a photonicatom is just the momentum Einstein hadshown times the inner radius of thepolygon (which for grazing photons isnearly the same as the particle radius).So having modes separated by a con-stant increment of angular momentumis equivalent to their being regularlyspaced in frequency—the spectral fencepickets Lorcan had uncovered.

One can think of a given mode as awave that circumnavigates the interiorof the tiny sphere and returns in stepwith the oscillations at its starting point.The mode with the next higher valueof angular momentum has a frequencyincreased by just the right amount tosqueeze an additional wavelength intothis circuit. Such properties of photonicatoms seemed neatly to explain whatwe were seeing in our experiments.

Steve Holler, an undergraduate stu-dent I was advising at the time, setabout to shore up the hypothesis bytaking pictures of a glowing micro-droplet through discriminating colorfilters that captured the light of donorand acceptor emissions separately

(Figure 7). His acceptor image boostedour confidence enormously, becauselight was concentrated close to the sur-face, where the photons in a photonicatom circulate. Holler’s donor imagewas less interesting, with almost all ofthe interior aglow, but it displayed adistinctive asymmetry, which arose be-cause the spherical droplet focusedmuch of the incident laser light onto itsback side. Surprisingly, the acceptorimage showed no difference betweenback and front. Rather, it revealedtwo curious bright spots, diametricallyopposed.

The cloud of mystery eventually dis-sipated when we realized that donormolecules excited preferentially at theback of the droplet launch photons atevery “azimuth.” Imagine a busy air-port sending jets in every direction,with each of the pilots instructed to flya great-circle route. These aircraft willeventually converge at the antipodalpoint on the other side of the globe.Unless they collide in midair, they willthen return to their starting point, andso forth. Similarly, the concentration ofthe donor emission at the back of a mi-crosphere sends photons on great-circletrajectories, which intersect at two an-tipodal points, seen as bright points inthe image of acceptor fluorescence. Be-cause our image averaged many revo-lutions of the photons from one sideof the sphere to the other, we saw acompletely symmetrical picture—justas if we had taken a time exposure of aswinging pendulum over an intervalmuch longer than one oscillation.

The overall efficiency of energytransfer we measured for a sphere wasabout 10 percent. But the acceptor im-age showed that this transfer only takesplace in a thin shell near the surface;most donor molecules do not partici-pate. Indeed, only one out of five areinvolved, indicating that for these thetransfer efficiency is about 50 percent.Noel Goddard, a master ’s studentworking in my lab, was later able to ob-tain such an enhanced efficiency by em-bedding all donor molecules just underthe surface of the droplet. But even withall donors in the right place, a key ques-tion remains: Why should they emitphotons so efficiently into the special di-rections needed for photonic-atommodes? The answer requires a brief con-sideration of why an excited atom ormolecule emits light in the first place.

Much Ado About NothingWhen I took quantum mechanics as agraduate student, I recall being told bymy professor that the excited states ofhydrogen are mathematically station-ary. I realized that the atom shouldemit a photon and so asked, “Does thismean that if I put an excited hydrogenatom in my pocket, go home and comeback tomorrow, it will still be excited?”The instructor confirmed that it wouldnot, showing some discomfort aboutwhere the discussion was headed. Still,I pushed on: “How long, then?” Hesaid it was on the order of nanosec-onds, prompting me to reply, “That’sstationary?” My professor had littlemore to offer except to remind me that


540 550 560 570wavelength (nanometers)

fluor

esce

nce

Figure 4. Spectrum of light emitted by acceptor molecules within a droplet reveals a series ofpeaks, corresponding to resonant electromagnetic modes. The peaks shown represent modesof three families (pink, blue and yellow) with different polarizations or radial order. For eachfamily, the peaks are regularly spaced, which reflects the quantization of angular momentumfor the photons circulating within.

we had already done calculations onstimulated emission.

In stimulated emission, a passingphoton induces an excited electron toreturn to the ground state. The energyof the triggering photon must match thedifference between these two levels, andthe emission produces a second, identi-cal photon. Although this processmakes lasers possible, it is not nearly asinteresting to me as spontaneous emis-sion, which provides almost all of thelight we see. The sun, incandescentbulbs, fluorescent lamps, even firefliesshine without requiring external pho-tons to trigger their emissions. Einsteinused thermodynamic arguments toshow the need for both stimulated andspontaneous emission, but he was notable to offer an explanation for the lat-ter. Nor could the mechanism be ob-tained from the quantum mechanics ofatoms. The answer appeared only af-ter 1948, when physicists began to ap-preciate that the electromagnetic fieldof empty space is quantized.

As high school students, we weretaught to think that if we removed allthe atoms, molecules and photons froma vessel, it would then contain nothing.But this notion is incorrect. Even in acold enclosure held near absolute zero,an excited atom is bathed in electromag-netic fluctuations, which are particularlyintense when the atom’s emission wave-length matches a resonant mode. Theyare the result of an electromagneticHeisenberg uncertainty principle: Theproduct of the electric and magneticfields of a mode has a fixed minimum—both fields cannot simultaneously be

zero. Even in a completely dark, emptyenclosure, each electromagnetic modewill have a residual “zero-point energy,”equal to a constant times its frequency.

The time-varying fields associatedwith zero-point energy trigger sponta-neous emission, which in this sense isquite similar to stimulated emission, al-though the source of stimulation israther subtle. Such quantum fluctua-tions also apply pressure, as the Dutchphysicist H. B. G. Casimir realizeddecades ago. Two neutral metallic plates,for example, attract each other with aforce that increases as their separationdiminishes. A simple explanation isthat the limited space between theplates supports fewer electromagneticmodes than the surrounding regions,giving rise to a net inward push.

The universe is thought to have aninfinite number of electromagneticmodes and a zero-point energy densitythat increases continuously with fre-quency. Within an enclosure, the spec-trum of the energy density becomesbunched around discrete frequencies,each one associated with a particularmode. As the container is reduced insize, a mode of a given frequency occu-pies a smaller volume and consequent-ly has a higher zero-point energy den-sity. If the physical enclosure measuresjust a few wavelengths on a side, thezero-point energy densities within amode can exceed the energy densitiesof free space by orders of magnitude.As a result, an excited molecule, whichwould otherwise radiate over a broadband of frequencies, is easily inducedto emit photons into such a mode—so

long as the emission band contains thefrequency required for that mode.

Although the tiny droplets my stu-dents and I were studying are notevacuated cavities per se, they confinephotons within modes in a small re-gion and thus act in essentially thesame way. So it is not surprising thatthe physics of nothingness applies tothem as well. Indeed, detailed calcula-tions confirm that enhanced quantumfluctuations within the photonic-atommodes account for the efficiency of theenergy transfer we observed. Consis-tent with this, we find experimentallythat the energy-transfer efficiency is in-creased even further as the particle sizeis reduced to a diameter of 5 microme-


Figure 5. Light rays refract as they pass from air into water or vice versa. Beyond a critical angle, the light one sees while viewing the surface ofa pool from below comes from total internal reflection (pink line, left). The outside of the pool is visible only within a circle overhead; elsewhereone sees reflections from within the pool (right).

Figure 6. Light rays skimming at a shallowangle below the surface of a spherical dropletare subject to total internal reflection. In theexample shown here, a photon completes arevolution of the sphere with eight bouncesand follows an octagonal trajectory. A typicalphoton might orbit in this way many thou-sands of times within a microscopic dropletbefore it is absorbed or “leaks” out.

Stev

e T

hom

ton/

Cor

bis

ters. This is a result of the so-called cav-ity quantum electrodynamic effect.

An important application of this ef-fect involves miniature lasers. Everyoneis familiar with these semiconductordevices, which are found in laser point-ers, laser printers and compact-discplayers. Indeed examples are now socommonplace that many people forgetwhat the word laser means: light ampli-fication by stimulated emission of radi-ation. A fair fraction of the power fedinto semiconductor lasers is wasted be-cause there is a threshold current need-ed to start the lasing process. But powerlosses associated with this thresholdcan be much diminished by taking ad-vantage of the cavity quantum electro-dynamic effect. How? By making smalllasers even smaller.

Laser action always begins withspontaneous emission. But in tradition-al devices, only a tiny fraction of thespontaneously generated photons—fewer than one in a thousand—go into alasing mode. Thus considerable poweris needed to ensure that an adequatenumber of these photons will be avail-able to start the laser going. Here iswhere shrinking dimensions and thecavity quantum electrodynamic effect

help out. Reducing the size of the lasercavity limits the number of availablemodes. In principle, the cavity can bemade small enough that the emissionspectrum of the laser material will over-lap just one mode. The tiny size of thecavity then provides enhanced quan-tum fluctuations and rapid emissioninto this mode. Thus very little power isneeded to start the laser working.

Recently investigators at several labo-ratories have used the confinement ofphotons in small spherical particles tocreate such low-threshold lasers (Figure8). This elegant approach does, however,have its limits, because mode confine-ment is lost as the size of the sphere ap-proaches the wavelength of the light. Soit may not be possible to eliminate thethreshold current completely. Still, thesemicrospheres make quite efficient lasers.

Microspheres also provide opticalfilters of exceptional spectral purity, be-cause they hold the energy of a photonover a long time in comparison withthe period of one oscillation in the cor-responding light wave. A tiny sphere isthus something like a fine wineglass,which tapped with a spoon will soundan extended note, although each acousticoscillation lasts just a millisecond or so.

A correlate of this property is that sucha wineglass responds to external stim-ulation over a narrow range of fre-quency—so narrow that it takes an EllaFitzgerald to sing just the right pitchand shatter the glass. Microspheres,too, respond to excitation over a slimrange of frequencies.

For quantum optical systems, thisbasic physical notion is containedwithin another Heisenberg uncertaintyprinciple. In a refined form, this rela-tionship says that for a given mode, theproduct of the frequency width and thelifetime of a photon has a minimumvalue, 1⁄2 π. We determined from our en-ergy-transfer experiments that a pho-ton typically bounces around the inte-rior of a 10-micrometer microspherefor about 3 nanoseconds before it is ab-sorbed by the material or flies out.Consequently, the corresponding mini-mum frequency width is around 50megahertz. Although this may seemlike a lot of bandwidth to a radio engi-neer, for optical communication it is re-ally quite small. To understand justhow narrow 50 megahertz is in thiscontext, consider using such spheres tosort transmissions carried by light overan optical fiber.


a

c

b

d e

intensity

Figure 7. Light emitted from donor moleculeswithin a droplet shows a distinct asymmetry(a), because the laser beam that excites them isfocused at the left (b). Light emitted from theacceptor molecules reveals a ringlike pattern(c), which demonstrates that they are excitedonly near the surface of the droplet. Most ofthe light emitted by donor molecules escapesbefore intercepting an acceptor. Only photonsin a resonant mode, which circulate just be-neath the surface (d), remain within thedroplet long enough to have an appreciablechance of colliding with acceptor molecules.Many ringlike orbits are possible, but they allcome together at two antipodal points (e), cor-responding to the two diametrically opposedbright spots in the acceptor image (c). (Imagesa and c courtesy of the author.)

How would one do something likethis? The ideal way would be to usemultiple microspheres of slightly dif-ferent sizes, so that each one wouldserve to select a particular band of in-formation. The number of separatechannels available depends on distin-guishing one resonance on a givensphere from the adjacent modes (thosehaving the next higher or lower al-lowed value of angular momentum).For a sphere that is about 10 microme-ters in radius, these modes are 3,000 gi-gahertz apart. So in principle one coulddistinguish (3 × 1012)/(5 × 107) or60,000 different channels. In practice,distortion of the sphere would proba-bly reduce the number of channels tosomething closer to 10,000, whichwould still constitute a technical tourde force (although I suspect that if thisscheme were ever employed to selectfrom among television transmissions,there might still be nothing to watch).

In 1995, two members of my re-search group—Ali Serpenguzel andGiora Griffel—and I reported a meansfor sorting optical signals in just thisway. The technique involves anotherquantum-mechanical principle calledtunneling. When a microsphere—made,say, of glass or plastic—is placed with-in a wavelength of the core of an opti-cal fiber, a photon traveling throughthe fiber has a fair probability of excit-ing a photonic-atom mode in thesphere, so long as the frequency of thisphoton corresponds to that of themode. Physicists say the photon tun-nels resonantly across this gap.

Photons circumnavigating the spherecan also tunnel into the fiber, if they do

not just leak out first. Although suchleakage might seem a bad thing, in fact itis very convenient, because it providesinformation about what is going on in-side the microsphere. Indeed, we firstinvestigated the phenomenon of tunnel-ing by observing light leaking out of apolystyrene microsphere (Figure 9). Wehad placed the tiny plastic sphere on anoptical fiber that was polished so as toeliminate all but the slimmest sliver ofcladding. We then shined a tunable laserinto the fiber and varied the frequencyof light while viewing the microsphereat right angles. At most frequencies thescene was completely dark, except forsome faint glints of light scattering fromthe polished surface of the fiber, butwhen the frequency of the laser matcheda photonic-atom mode, the sphere litup, thanks to leaking photons.

Within a month of our publishing anarticle about this work, physicists atthe École normale supérieure in Parissaw a different sort of evidence for thetunneling of photons between an opti-cal fiber and a microsphere. They mea-sured a diminution in the light trans-mitted through the fiber when thefrequency was set equal to a photonic-

atom mode. Such dips in transmissionarise in part because leakage and ab-sorption in the sphere reduce the prob-ability of the photon returning to thefiber. But this simple picture of photonsjumping between sphere and fiber ne-glects the wave character of light andthus misses an important physical ef-fect: the destructive interference thatcan take place when light reenters thefiber after having made a relativelylong visit to the sphere. Griffel and Ifirst described this phenomenon in1996. More recently, another group ofinvestigators led by Kerry Vahala at theCalifornia Institute of Technology ob-tained nearly 100 percent efficiency forthe coupling of light from an opticalfiber to a microsphere. With their ex-perimental arrangement, there is hard-ly any transmission at all through thefiber at resonance.

Many Points of LightOur experiments with tiny plasticspheres and optical fibers helpedlaunch a field that is best described bythe phrase “microsphere photonics.”The centers of work in this area arenow at Caltech and MIT, and many


598 600 602 604 606 608 610 612 614wavelength (nanometers)

inte

nsity

laser

water

core

cladding microsphere

Figure 8. Microsphere laser glows brightly in aring, where most of the photons circulate. Thisgeometry arises because an optical fiber in theplane of the ring touches the sphere at onepoint along the equator. Photons sent throughthe fiber pass into the sphere, exciting laser ac-tion for this particular electromagnetic mode.(Image courtesy of Kerry Vahala, Caltech.)

Figure 9. Microsphere placed within one wavelength of the core of an optical fiber readily ab-sorbs photons when the frequency of light passing through the fiber matches a resonant modeof the sphere (top). At resonance, photons enter the sphere and eventually leak out in all di-rections, causing distinct peaks in the intensity of light seen coming from the sphere as afunction of the wavelength of laser excitation (bottom).

applications have emerged. One of themost intriguing came from Vahala’slaboratory at Caltech, where workersinduced photons of a specific frequen-cy to tunnel resonantly into a sphereand then into a second fiber. This pho-tonic device constitutes what is calledan add-drop filter, because it can be usedeither to add or to remove the signalcarried on a given optical channel (Fig-ure 10). With it, one can route informa-tion between optical fibers at select fre-quencies, without having to employelectronic circuitry at all.

Plastic microspheres can also serveas sensors, because their photonic-atommodes change in frequency when thetemperature varies or when they comein contact with material of similar opti-cal properties—for example, DNA mol-ecules attached to their surfaces—apossibility I am now investigating withmy colleague Iwao Teraoka and withFrank Vollmer of Rockefeller Universi-ty. The idea here is to affix to a micro-sphere many strands of DNA carryingone particular base sequence. Geneticmaterial having the complementary se-quence can readily bind to the surfaceof such a sphere. When it does, theadded coating (like the expansion thataccompanies heating) alters the effec-tive radius of the particle, which forcesthe resonant frequency of a given modeto shift. Other kinds of oscillators aresensitive to changes in dimension aswell. For instance, the frequency of apendulum changes when the rod con-necting the bob to the pivot expandsthermally. But pendula do not makevery good thermometers, so it mightcome as something of a surprise thatmicrospheres would have high sensi-tivity. They do, at least in principle.

The constancy of angular momen-tum for a particular mode dictates thatthe fractional decrease in frequency

must be the same as the fractional in-crease in dimension, and vice versa.The minimum size change that can bedetected is the smallest measurablefractional change in frequency timesthe radius of the sphere. One can easilyobserve a full line-width shift, some 50megahertz, which at a typical opticalfrequency corresponds to a fractionalchange in size of one part in 10 million.So one can potentially discern a changein radius for a 10-micrometer sphere of10–12 meters—one-hundredth of anatomic diameter. This exquisitely highsensitivity opens the door for a rangeof applications, from thermometry tobiochemical sensing, for which multi-ple probes specific enough to detect theactivity of particular genes could be in-terrogated over a single optical fiberusing spheres of different sizes.

Thinking of tiny spheres as photonicatoms indeed appears to be a fruitfulendeavor, but one can go a step furtherand push the analogy into the molecu-lar realm. Just recently, scientists work-ing with Makoto Kuwata-Gonokami atthe University of Tokyo built the pho-tonic equivalent of a hydrogen mole-cule. In H2, two protons share two elec-trons in a covalent bond, which givesrise to a splitting of the atomic elec-tronic states. Gonokami and his re-search collaborators touched two near-ly identical fluorescent microspherestogether and recorded a similar split-ting in photonic-atom modes. Appro-priately, the researchers dubbed theircreation a photonic molecule.

Physicists continue to search forclever ways to benefit from the opticalproperties of tiny spheres. One can, forexample, imagine that grouping morethan two spheres together will offer yetmore interesting or useful opticalmodes. Photonic “polymers” mighteven be in the future. Whatever further

advances grow out of this research, Itake great pleasure in remembering theexperiments of 1980s that led me intothe field of microsphere photonics inthe first place—attempts to probe howenergy is transferred between mole-cules without photons. In that quest Ifailed, which I realize now was the bestthing I could have hoped for.

BibliographyArnold, S., and L. M. Folan. 1989. Energy trans-

fer and the photon lifetime within anaerosol particle. Optics Letters 14:387–389.

Cai, Ming, Guido Hunziker and Kerry Vahala.1999. Fiber-optic add–drop device based ona silica microsphere-whispering gallerymode system. IEEE Photonics Technology Let-ters 11:686–687.

Arnold, S., S. Holler and S. D. Druger. 1996.Imaging enhanced energy transfer in a levi-tated aerosol particle. Journal of ChemicalPhysics 104:7741–7748.

Folan, L. M., S. Arnold and S. D. Druger. 1985.Enhanced energy transfer within a micro-particle. Chemical Physics Letters 118:322–327.

Haroche, Serge, and Jean-Michel Raimond.1993. Cavity quantum electrodynamics. Sci-entific American 268(4):54–62.

Mukaiyama, T., K. Takeda, H. Miyazaki, Y. Jim-ba and M. Kuwata-Gonokami. 1999. Tightbinding photonic-molecule modes of reso-nant bispheres. Physical Review Letters82:4623–4625.

Nussenzveig, H. M. 1992. Diffraction Effects inSemiclassical Scattering. New York: Cam-bridge University Press.

Serpenguzel, A., S. Arnold and G. Griffel. 1995.Excitation of morphological resonancesfrom individual microparticles and clustersin contact with an optical fiber. Optics Letters20:654–656.


Links to Internet resources for“Microspheres, Photonic Atoms and thePhysics of Nothing” are available on the

American Scientist Web site:

http://www.americanscientist.org/articles/01articles/arnold.html

drop add

input output

Figure 10. Microsphere coupled to two optical fibers (left) constitutes an add-drop filter. An optical signal sent toward the sphere along one fiber(green arrow, upper right) is added to the many signals traveling along the other fiber (blue arrows). This device can also be used to extract (or“drop”) a signal (red arrow, upper left) that was originally traveling through a fiber along with many others. (Image courtesy of Kerry Vahala.)

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