Photonic atoms and molecules

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Laser & Photon. Rev. 4, No. 2, 179191 (2010) / DOI 10.1002/lpor.200910001 179Abstract Recent advances in the investigation of optical modesin single three-dimensional whispering-gallery microcavitiesand coupled microresonators are reviewed. Due to the smallsize and high quality factor these resonators have the potentialfor development of single-photon emitters, nanojets, sensorsand low-threshold lasers and for fundamental studies of opticalmatter interactions.Photoluminescence confocal image of a spherical whispering-gallery microcavity with monolayer of CdTe quantum dots. 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimPhotonic atoms and moleculesYury P. Rakovich* and John F. DoneganSchool of Physics and Centre for Research on Adaptive Nanostructures and Nanodevices, Trinity College Dublin, Dublin 2, IrelandReceived: 2 January 2009, Revised: 28 February 2009, Accepted: 25 March 2009Published online: 2 June 2009Key words: Photonic atoms, photonic molecules, spherical microcavities, whispering-gallery modes, semiconductor quantum dots.PACS: 42.60.Da, 61.46.Df, 83.85.Ei, 87.85.fk1. IntroductionIn the heart of the Temple of Heaven in Beijing (constructedbetween 1406 and 1420) there is a famous circular stonewall, which surrounds the Imperial Vault. It is named theEcho Wall for its very curious and interesting acousticalproperties a whisper spoken at one end can be heardclearly from the other. In other words, it makes possiblewireless communication between two people separatedby more than 100 m.A comprehensive explanation of this effect has beenprovided by Lord Rayleigh who investigated the propa-gation of acoustic waves over an arch wall surface in theWhispering Gallery under the dome of St. Pauls Cathe-dral [1]. Lord Rayleigh gave an explanation of this phe-nomenon as being due to the curvilinear propagation ofsound, the waves that proceed from a source placed closeto the wall of the gallery clinging to its surface and creep-ing tangentially along it. The phenomenon observed andexplained by Lord Rayleigh has now been observed in circu-lar and spherical optical microresonators. This is the originof the term whispering-gallery modes (WGMs) that iscommonly used to denote electromagnetic modes in theseoptical resonators. Although they did not using this term forthe modes, at the beginning of the 20th century, Debye [2]and Mie [3] derived equations for the eigenfrequencies andscattering resonances of free dielectric and metallic spheres,which naturally take WGMs into account.In the case of dielectric microspheres the closed tra-jectories of light are supported by total internal reflectionwhen boundaries of the microparticles and the air have high* Corresponding author: e-mail: 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim180 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculesFigure 1 (online color at: Light confine-ment inside a microsphere in a geometric-optics picture a) and ina wave-optics description b).refractive index contrast and the radius of curvature of themicrosphere exceeds several wavelengths.In the geometric-optics picture, WGM can be viewedas light rays that, once within the spherical particle, inter-sect repeatedly with the interface above the critical angle,undergoing total internal reflection (Fig. 1a). In a wave-mechanics description, WGMs are internal standing waves,with an integer number of wavelengths circulating near themicrosphere or droplet interface (Fig. 1b).The radiative losses from these small optical micro-cavities can be very small, and the quality factor Q of themicrosphere modes becomes limited only by material atten-uation and scattering caused by geometrical imperfections(e.g., surface roughness). An extremely small linewidth ofthe WGMs (and therefore high values of the Q-factor) werereported in the first experimental observations of WGMsin elastic light scattering from spherical dielectric parti-cles [4, 5]. The strong influence of WGMs on the lumi-nescence and Raman scattering was first studied in [6, 7]and [810], respectively.Microsphere resonators have found applications as ul-trasensitive mechanical [11,12], refractometric [13,14] andbiological [15, 16] sensors, optical waveguides [17, 18],narrowband passive photonic devices such as bandpass fil-ters [19] or add-drop devices [20, 21]. They were also usedto study cavity quantum electrodynamics effects [22,23]. Ifan active material is coupled to whispering-gallery modes,ultralow threshold lasing is achieved [24, 25]. The rangeof WGM microcavity applications is so wide that in thisreview we will restrict ourselves to the case of small (210 m size) spherical microcavities integrated with highlyemitting semiconductor quantum dots.For a much more complete description of the physicsand applications of WGM resonators we refer to otherrecent reviews [26, 27].2. Spherical microcavities as photonic atomsExtending the ideas of the linear combination of atomicorbitals method to the classical wave case, it was recentlysuggested that Mie resonances (WGMs) of a single spheri-cal microcavity play the same role as the atomic orbitals inFigure 2 Schematic ofa spherical microcav-ity, showing distributionand the spatial orienta-tion of modes.the electronic case and the spatial distributions of WGMscan be described by analogy with the orbitals in a hydrogenatom [28]. In the absence of gain, the WGM resonances canbe characterized by a mode number n (angular quantumnumber), a mode order l (radial quantum number), and anazimuthal mode numberm (azimuthal quantum number).The value of n is proportional to the circumference dividedby the wavelength of the light propagating within the micro-sphere, the mode order l indicates the number of maximain the radial distribution of the internal electric field, andthe azimuthal mode numberm gives the orientation of theWGMs orbital plane. The modes offering the highest spatialphoton confinement correspond to high values of angularmomentum n, smaller values of l and to azimuthal quantumnumbersm close to n.The electromagnetic fields confined in a microsphereare given by [29]ETE= jn(nkr)Xnm(; ') ; (1)for modes having no radial components of the electric field(transverse electric or TE modes) andETM= r jn(nkr)Xnm(; ') ; (2)for the transverse magnetic (TM) modes (no radial compo-nent of the magnetic field).Here, Xnm(; ') are the vector spherical harmonicsgiven in spherical polar coordinates, jn(nrkr) and repre-sent the spherical Bessel functions, where k = 2= is thewave number, and is the free-space wavelength.On the other hand, the wavefunctions slmfor the elec-tron confined in the hydrogen atom are given by [30]slm= Rsl(r)lm(; ') ; (3)where Rsl(r) are known as the Laguerre polynomials. Theeigenfunctions (1) and (3) are very similar and their spatialdistributions are characterized by the three integers s, l andm (for the hydrogen atom) and n, l andm (for the micro-sphere), which correspond to total angular, radial and theazimuthal quantum numbers, respectively. Based on all theabove similarities, this approach has enabled small dielec-tric spheres to be considered as photonic atoms [28, 31].However, unlike energy states of electrons in the atom,photonic states in spherical microcavities are not local-ized, due to the finite storage time of photons in the reso-nant mode. This photon lifetime is controlled by qualityfactor Q of the WGMs and therefore can be limited by 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.orgLaser & Photon. Rev. 4, No. 2 (2010) 181Figure 3 (online color at: PL spectra ofcolloidal CdTe QDs (NCs) in water (black) and micro-PL spectrafrom a single melamine formaldehyde (MF) latex microsphereof 3 m diameter covered by one monolayer shell of CdTe NCs(red). PL spectra of QDs were recorded using a Spex Fluorologspectrometer. The micro-PL spectra from the single microspherewere recorded using a RENISHAW micro-Raman system. An Ar+laser ( = 514.5 nm) was used in the micro-PL experiments.diffractive losses, absorption, gain, shape deformation orrefractive index inhomogeneities. As a result, the resonantinternal field of a spherical cavity is not completely con-fined to the interior of the microparticle. Decaying exponen-tially, the evanescent field extends a couple of micrometersinto the surroundings and this field distribution permitsefficient coupling of the emission of semiconductor quan-tum dots (QDs) with WGM by placing the emitter (shellof QDs) on the surface of the high refractive index mi-crosphere. These quantum dots represent the ultimate insemiconductor-based quantum-confined system with atom-like energy levels, large optical transition dipole momentand high photoluminescence quantum efficiency [32]. Dueto their unique optical properties, semiconductor QDs havefound application in biology and photonics [3335].Theory suggests that by placing an excited emitter(such as an atom or molecule or QDs) near the surfaceof a spherical dielectric, the interaction of the emitterwith its self-scattered field can produce enormous enhance-ments in its emission rate at frequencies associated withWGM [36]. This result can be clearly seen in Fig. 3. Thishybrid QDs/microsphere structure was fabricated as de-scribed elsewhere [37].In contrast to the broad, featureless PL band in thespectra of the colloidal nanocrystals (NCs) or quantumdots, the emission spectra of a single melamine formalde-hyde (MF)=CdTe microsphere exhibit a very sharp periodicstructure. The observed WGM peak structure is a result ofcoupling of electronic states in the QDs and photon statesof the microsphere. The placement and spacing betweenWGM peaks presented in Fig. 3 are determined by the sizeand refractive index of the microsphere, while the spectralintensity distribution depends on the parameters of the QDsand can be easily modified by using QDs of different size.The narrow optical resonances presented in Fig. 3 canbe identified as optical modes with TE and TM polariza-tions. For spherically symmetric microparticles the extinc-tion cross section is derivable from the LorenzMie the-ory [38]Cext=2k2Re1Xn=1(2n+ 1) (bn(x; nr) + an(x; nr)) ;(4)where x = 2R= is the size parameter, R is the radiusof the microsphere and the Mie scattering partial waveamplitudes an(x,nr) and bn(x,nr) can be expressed inthe form [39]an(x; nr) =An(x; nr)An(x; nr) + i Cn(x; nr)andbn(x; nr) =Bn(x; nr)Bn(x; nr) + iDn(x; nr):(5)The pairs of functions An, Cnand Bn, Dnare deter-mined by the Mie scattering problem [40] and resonancestructure in scattering spectra can be expected when thereal part of anor bnreaches its maximum value of 1 andthe imaginary part passes through 0 from the positive tothe negative side. In other words, the resonances in the Miescattering characteristics occur when Cn= 0 or Dn= 0,which gives the following mathematical condition for aresonancenrn(x) 0n(nrx) n(nrx) 0n(x) = 0 (6)ornrn(x) 0n(nrx) n(nrx) 0n(x) = 0 : (7)Note, that for given n and m, these equations have in-finitely many solutions at discrete values of x for TM andTE WGMs respectively. Also, Eqs. (6) and (7) are inde-pendent of the azimuthal mode numberm because of thespherical symmetry implying that them-modes are wave-length degenerate. The RiccatiBessel functions of the firstand second kind can be introduced as:n(z) = zjn(z) =rz2Jn+12(z) ;andn(z) = zyn(z) =rz2Yn+12(z) ;(8)where J(z) and Y (z) are the cylindrical Bessel functionsof the first and second kind, respectively. The use of Besselfunctions for systems with cylindrical symmetry 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim182 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculeswith the reccurence relation 0n(z) = nzn(z)+ n1(z)enables us to reduce Eqs. (6) and (7) to a form convenientfor practical calculation of the position of the WGMs. Thus,if the refractive index is real (no absorption) the TM andTE resonances can be taken in the form:1xnnr nrnJn+1=2(x)Jn+1=2(nrx)+nrJn+1=2(nrx)Jn1=2(x)Jn+1=2(x)Jn1=2(nrx) = 0 ; (9)nrYn+1=2(x)Jn1=2(nrx)Jn+1=2(nrx)Yn1=2(x) = 0 : (10)These conditions are transcendental equations, which canbe solved for the size parameter x (position of a resonance)for given values of refractive index and for given angularquantum number n. Thus, comparing the calculated resultswith the spectral positions of the WGM in the experimentalphotoluminescence (PL) or emission spectra of the micro-sphere we can identify the indexes n and l for each modeand estimate the size of the sphere. Additionally, absorptivelosses can be accounted for by taking into consideration animaginary part of the refraction index.The algorithm for the mode assignment can be de-scribed as follows. 1) The resonant wavelengths corre-sponding to the WGM resonances expi(i = 1; 2: : :; N )are determined from a PL spectrum of a single microsphere.2) We assume an approximate value of the microsphereradius based on the technical specification within the dis-tribution of sizes that are specified by the manufacturer.3) Theoretical resonance positions theoriare then calcu-lated using Eqs. (8) and (9). 4) The two lists are comparedand for each value of expi, the closest value theoriis sug-gested and the difference between them iis calculated.5) Taking into account the spectral resolution , the cor-relation S = 1NNP1(1 + i=)1 is then maximized byadjusting only one fitting parameter, namely the size ofthe microsphere. Fig. 4 shows a result of WGM identifica-tion in the PL spectra of QDs attached to two spheres ofdifferent sizes.Among all the factors that cause the modification in thePL emission pattern due to the spatial photon confinementin spherical microcavities, the nature of the polarization ofthe WGM plays an important role because of the potentialfor their use in all-optical switches and logical devices [41].Direct experimental identification of the polarization stateof WGMs can be provided by inserting a polarizer into theoptical beam path in front of the detection system. In thiscase the polarizer selects only signals from WGMs thatemit components of the electromagnetic field parallel to theorientation of the polarizer axis.For a focal spot on the top rim of a microsphere (Fig. 5,inset), the emission spectrum detected with the polarizerorientation parallel to the polarization plane of the laseris shown (Fig. 5a). Due to the higher excitation efficiencyFigure 4 Micro-PL spectra of two single microspheres witha monolayer of CdTe QDs, with diameters of 1.98 m a) and3.06 m b) with modes identified from Eqs. (8) and (9).Figure 5 Micro-PL spectra of a single microsphere with a mono-layer of CdTe NCs with the polarizer orientation parallel to the po-larization plane of the Ar+ laser a), and with the polarizer rotatedby 90 b). The inset shows a microscope image of the microcavitywith the crosshairs indicating the excitation-detection position.of transverse electric modes provided by this experimentalscheme [42] the dominant spectral features in this case areWGMs of TE polarization. Rotation of the polarizer by 90leads to a similar WGM structure but with TM peaks domi-nating in the PL spectrum (Fig. 5b). This result confirms thepolarization nature of the WGM resonances; the two adja-cent peaks representing TE and TM modes of a microcavityhave orthogonal polarization states. The experimental con-cept of polarization-sensitive mode analysis represents aconvenient tool for determining the polarization properties, 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.orgLaser & Photon. Rev. 4, No. 2 (2010) 183in particular for larger microspheres, without performingextensive numerical calculations.Figs. 4 and 5 also demonstrate two important featuresthat can contribute to the understanding and interpretationof experimental results and to further applications. First,from experiment, the spectral spacing between two reso-nances of successive modes with the same order and po-larization strongly depends on the size of the sphericalmicrocavity. If the refractive index of the microsphere isconstant and unchanged during the measurement, this spec-tral spacing can be expressed in terms of the size parameteras [43]x = xn+1 xn=tan1(n2r 1)1=2n2r 1; (11)for resonances with xn;l 1, n 1, and xn;l n.In small sphere limit, when jx nj 1=2, the follow-ing relation applies [39]x = xn+1 xn=xntan1(nrxn=n)2 11=2n [(nrxn=n)2 1]1=2: (12)Since the experimental resonant spectrum can be preciselyfitted using Mie theory, it was shown that the differencebetween the mode spacing obtained by Eqs. (11) or Eq. (2)and by experiment is 1%.For example, from the resonant spectrum in Fig. 4b,the mode spacing between resonances TE124and TE123measured in terms of wavelength is 21.8 nm, hence theexperimental mode spacing can be fitted by the asymptoticformulae above with an accuracy within 1%, i.e. deviation< 0.22 nm, when a suitable sphere size, refractive indexand mode number are chosen. This simplified approachis of considerable current use in the analysis of a WGMstructure especially for large values of the size parameterwhen use of the full Mie scattering theory is cumbersomealgebraically or even computationally.The second phenomenon clearly seen in Figs. 4 and 5is the significant broadening of WGM peaks in the spec-trum of the microsphere of smaller size as compared to thespectrum of bigger microcavities, which reflects the lowerquality factor Q of the smaller microspheres. Due to thefact that WGM are in fact leaky modes, the quality factorof a resonance is defined as [44]Q =Stored energyEnergy lost per cycle: (13)Also, the Q-factor is the number of cycles required for thestored energy to decrease to e times of its original value.A high quality factor is the basis for the interest in most ofthe suggested applications for microsphere resonators.Near a WGM, the electric field of a resonant modeinside the microcavity varies asE(t) = E0expi!0!02Qt; (14)where !0is the resonant frequency. The distribution of theenergy of a near-resonant mode in a microcavity jE(t)j2,is therefore proportional to the Lorentzian function1(! !0)2+!02Q2: (15)The spectral width between two points at which the energyis half of its maximum value is! =!0Q; (16)which also defines the average lifetime of the photon inresonant mode as =1!0=Q!0: (17)Aside from diffractive losses, the actual Q of a microcav-ity is determined by various factors like radiative losses,losses or gain attributable to absorption or emission by thematerial of the cavity, refractive-index inhomogeneity orshape deformation. Also, a strong decrease in the value ofthe Q-factor is expected when the radius of curvature of themicrosphere is comparable (within an order of magnitude)to the resonant wavelength of the WGM. This effect is ac-companied by broadening of the corresponding spectralpeaks (Figs. 4a and b).Much of the work being done on WGM microcavitieshas been to achieve the ultimate quality factors [45, 46]required for investigations of cavity quantum electrody-namics [23], quantum informatics applications [4749]and nonlinear optics [50, 51] in a regime of strong cou-pling. The typical value of Q-factor for composite CdTeQDs/microcavity of 3 m size is 3500, which corre-sponds to the value of average photon storage time 1 ps.Decreasing the size of microspheres down to 2 m resultsin a Q value of 800 and a corresponding reduction ofthe photon storage lifetime.3. Applications of photonic atoms3.1. LasingA QDs/microsphere structure is a very promising object todesign an optically pumped QD-based microlaser emittingin the visible spectral range at room temperature. SinceKlimov et al. [52] first reported the amplified spontaneousemission (ASE) in Cd(SSe) QDs, ASE and lasing fromcolloidal semiconductor QDs have been realized with avariety of photonic structures including spherical microcav-ities [25,5356]. Laser emission in spherical resonators is adirect result of light trapping in the WGMs [57]. As light cir-culates inside the photonic atom, the electric field strengthincreases exponentially as a result of stimulated emissionfrom an inverted QDs population. The key feature when us-ing colloidal QDs for lasing applications is that entering 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim184 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculesFigure 6 (online color at: of the WGM biosensor. a) Resonanceis identified at a specific wavelength from a dipin the transmission spectrum acquired with atunable laser. The resonance wavelength, r,is measured by locating the minimum of thetransmission dip within its linewidth (arrows).A resonance shift associated with molecularbinding, ris indicated by the dashed arrow.b) WGM in a dielectric sphere driven by evanes-cent coupling to a tapered optical fiber. Thelight wave (red) circumnavigates the surface ofthe glass sphere (green) where binding of ana-lyte molecules (purple) to immobilized antibod-ies (blue) is detected from a shift of the reso-nance wavelength. c) Binding of analyte is iden-tified from a shiftrof resonance wavelength.(Adopted from [68].)strong confinement regime (i.e. QDs sizes < 10 nm, wherethe spacing between the electronic states is larger than thethermal energy of the carriers at room temperature) createsnew loss mechanisms that hinder the buildup of lasing. Onemajor loss factor is Auger recombination, which is intrinsi-cally connected with the biexcitonic population inversionnecessary for optical gain [58]. Numerous reports on lasingin QDs coupled to a microresonator [5963] imply that themicrocavity can provide optical feedback sufficiently highto overcome this problem.3.2. BiosensingSpherical WGM microcavities offer unprecedented sensi-tivity for detection of labeled and unlabeled biomolecules(Fig. 6). The resonant internal field of the microsphere is notfully confined and an evanescent field extends into the sur-roundings, being extremely sensitive to the changes of thedielectric function in the intimate vicinity of the cavity. Itwas recently recognized that this evanescent field can facil-itate the fabrication of highly sensitive microscopic biosen-sors, where either the shift in the resonant position [15]or the change in Q-factor [64] due to bioanalyte absorp-tion on the cavity surface can be detected with a masssensitivity of up to 6 pg/mm2 [16] or absolute amountsof bound analyte, down to 0.25 fmol [65]. In pilot exper-iments the quantitative use of the WGM biosensors wasdemonstrated for detection of proteins [15, 16, 66], DNAand a single-nucleotide polymorphism [16,67]. Due to theirspherical symmetry, the spectral response of microspheresensors can be analyzed using Mie scattering theory (seeSect. 2), and simple equations can be obtained to calcu-late the shift of whispering-gallery resonances dependingon the surface density of absorbed biomolecules and theirpolarizability [16]. Although all these experiments havedemonstrated the large potential of using WGM as a sens-ing technique, the concept of high-Q sensing is hinderedby several impediments, particularly in terms of minitur-ization, multiplexing, and simplicity of use. Most of theabove-mentioned experiments have been carried out us-ing high-Q microspheres with diameters of some hundredsof micrometers. The reason behind this is the demand fora sufficiently high Q-factor when sensing take place in abiological environment. The Q-factor can be higher than1010 in air, and greater than 109 in a variety of solvents,including methanol, H2O and phosphate-buffered saline(PBS) [64]. The presence of dyes in the evanescent zonethat absorb on the wavelength of the WG excitation cancause this Q value to drop by almost 3 orders of magni-tude. Silanization of the surface with mercapto-terminalsilanes is compatible with high Q (> 109), but chemicalcrosslinking of streptavidin reduces the Q to 105106 dueto build-up of a thick, irregular layer of protein [64].On the other hand, the evanescent field in spheres of thissize (> 100 m) propagates into the surrounding for onlyhundreds or even tens of nanometers [69], which requiressophisticated experimental approaches to couple excitationlight into the sphere and collect the emitted signal. In the ba-sic configuration light from a tunable distributed feedbacklaser is coupled into a WGM of the sphere from an erodedoptical fiber, while resonant modes are detected as dips inthe transmission spectrum through the fiber [16]. As thistakes place, the distance between the source of the evanes-cent field excitation and microsphere surface must be con-trolled with nanometer precision. The large size of spheresand the complexity of the coupling system restrict the im-plementation of miniature user-friendly WGM biosensors.Another drawback of using big microspheres for biosens-ing is the complexity of the spectra when identification 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.orgLaser & Photon. Rev. 4, No. 2 (2010) 185of the WGMs as discussed in Sect. 2 is impossible, thuscomplicating the process of tracing of any changes in theenvironment. In contrast, microspheres in the small sizeregime (< 10 m) show well-resolved WGM that can beeasily identified in terms of mode numbers and polariza-tion (Figs. 4 and 5). Due to the small microsphere size theevanescent field propagation length is up to a couple ofmicrometers, which simplifies the applicability of the ex-perimental system. One of the serious drawbacks of smallWGM cavities in terms of biosensing is their moderate Q-factor: 103105 for microspheres of 36 m size [23,70,71].For smaller sphere sizes (2 m) the Q-factor drops downto Q 102 [72]. Such a low Q-factor strongly reducesthe resolving power of the system, so that microspheres of2 m or less have not been considered for biosensing appli-cations so far. The feasibility of small WGM microcavitiesfor applications in optical biosensing was demonstratedrecently for the absorption of bovine serum albumin witha mass sensitivity limit of 3 fg [66]. In another report thefirst application of QD-encoded microspheres of 3 m sizein clinical proteomics was demonstrated by multiplexed de-tection of circulating auto-antibodies, markers of systemicsclerosis [73]. Although in the last study the advantagesof WGMs in small microspheres have not been used, thisstudy paves the way to remote in-vivo WGM biosensing inthe future.3.3. Photonic nanojetsIt was recently demonstrated that spherical dielectric parti-cles with sizes between 2 and 10 m are able to concentratevisible light when illuminated by a plane wave (Fig. 7). De-pending on the refractive index the focus position can beinside or outside the microsphere. When the focus point isjust outside the microsphere the beam waist stays in sub-wavelength regime along a distance of propagation up toFigure 7 (online color at: Distribution ofintensity in nanojet region obtained for a 5-m sphere a) and a3-m sphere b). (Adopted from [75].)2 m in a regime of extremely low divergence. This beamhas been called a photonic nanojet [74] because of the anal-ogy between the high-speed gradient that is characteristicof a jet in fluid mechanics and the observed high light fluxgradient. In contrast to diffraction-limited microlensing,the nanojet phenomenon is a near-field effect due to theproximity of the focus position and the microsphere surface.Also, because of the nanoscale beam waist, the photonicnanojets can reach a very high intensity (Fig. 7).Although they do not involve evanescent fields, pho-tonic nanojets may provide a new means to detect andimage nanoparticles of size well below the diffractionlimit [76]. The high detection contrast afforded by the pho-tonic nanojet could potentially yield significant increasesin data density and throughput relative to current commer-cial optical data-storage systems, while retaining the basicgeometry of the storage medium [77]. This could also yielda potential novel ultramicroscopy technique using visiblelight for detecting proteins, viral particles, and even singlemolecules; and monitoring molecular synthesis and aggre-gation processes of importance in many areas of biology,chemistry, material sciences, and tissue engineering [74].4. From photonic atoms towardsphotonic moleculesAs discussed in Sect. 3, the resonant internal field of a spher-ical cavity is not completely confined to the interior of themicrosphere. Depending on the size of the microsphere, theevanescent field can extend into the surroundings up to acouple of micrometers. It was recently recognized that thepartial delocalization of Mie resonance states is of greatimportance because it suggests the possibility for coher-ent coupling between WGMs of two adjacent sphericalparticles with closely matched sizes. Such a system of co-herently coupled photonic atoms may be called a photonicmolecule (PM) [31, 78] and can be employed in orderto manipulate photons in the micrometer length scale. Inanalogy to the formation of molecular electronic orbits, thetight-binding approximation provides two combinationsfor the electromagnetic field in a system of interacting mi-crospheres: bonding (BN) and antibonding (ABN) states(Fig. 8) [71, 78].Experimentally, the coupling of the photon modes ofindividual microspheres in the PM can cause narrow reso-nance of a photonic atom to split into two modes of lowerQ-factor [79]. This phenomenon has been demonstrated ina system of two square, photonic dots coupled by a narrowchannel [78], in a dye-stained bisphere system [71, 80, 81],in photonic dots with semiconductor QDs [70, 82] and inchains of polymer-blend microparticles [83]. However, re-cent theoretical considerations [84] and experimental stud-ies [70, 72] reveal a complex internal distribution of thedensity of photonic states of the PM originating from lift-ing of the degeneracy of PM modes with respect to theazimuthal 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim186 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculesFigure 8 (online color at: Schematic of thesplitting of the energy levels of hydrogen atoms a). By analogy, theWGMs with the same resonant frequency split into two coupledmodes of the photonic molecule b).Recent proposals for coupled resonator optical waveg-uides [85], high-order optical filters [86], and optical delayelements [87, 88] stimulated further interest in systemsof optically coupled microspheres such as linear chains,two-dimensional arrays or three-dimensional crystal struc-tures [18, 83]. In these systems a photon-hopping trans-port between adjacent spheres should occur at the frequen-cies of the WGMs, providing the possibility of manipu-lating light paths as well as light dispersion on a micro-scopic scale.4.1. Confined optical modes in small photonicmolecules with semiconductor nanocrystals inthe strong-coupling regimeTheoretical considerations [71, 79, 84] show that the inter-sphere coupling is expected to be maximum for the pairof modes whose orbitals include the contact point betweenmicrospheres and lie in the same plane. Taking this into ac-count, the PL intensity of the coupled modes is anticipatedto be a maximum in the direction parallel to the PM axisand the signal from the coupled intersphere modes shouldbe more pronounced in the parallel configuration than inthe perpendicular one.Recently, a new approach to control the alignmentof the spheres constituting the PM have been devel-oped [70, 72] utilizing a polystyrene substrate containinga three-dimensionally ordered array of pores of 5 min size prepared through a thermocapillary convection pro-cess [89]. The ordered structures are formed by evaporatingsolutions of polystyrene in a volatile solvent, in the pres-ence of moisture with forced airflow across the solutionsurface. An hexagonally packed array of holes (microwells)of 35 m depth then forms on the surface of the polymer(Fig. 9a). Only one pair of the 3-m microspheres can beFigure 9 Polystyrene filmwith an hexagonally orderedarray of air holes with di-ameters of about 5 m a),and experimental geometryfor off-axis excitation and de-tection b).accommodated within each microwell, and the axis of thePM is close to the surface normal (Fig. 9b).Fig. 10 shows the PL spectrum of a PM accommodatedin a microwell and the spectra of the individual micro-spheres prior to being manipulated into the microwell. Thepronounced doublet structure in the spectrum presentedin Fig. 9a, coinciding with the spectral positions of theWGM of individual microspheres (Fig. 10b), is a result ofthe overlap of uncoupled modes of the two spheres. Theshift in position of the WGM, which can be clearly seen inFigs. 10a and b, is a result of a difference in the size of thetwo microspheres of only 25 nm. However, in contrast tothe spectrum in Fig. 9a, this doublet is accompanied by twoextra relatively broad peaks (indicated by arrows in Fig. 9b,which are indicative of strong mode coupling in the PM).The appearance of these two satellites can be interpretedas a result of the formation of BN and ABN orbitals inthe PM [78] with the ABN peak observed at lower wave-length than the BN one. In terms of cooperative scatteringtheory the observed satellites originate from the removalof the WGM degeneracy with respect to them index [79].The line shape of the satellite lines reflects the energy dis-tribution among the coupled modes, because modes withdifferent combinations ofm can contribute to the PL spec-tra. The observation of a broader ABN peak, relative to theBN peak, reflects the decrease of the quality factor of thePM when compared with that of a single sphere presumablydue to the interaction with more dissipative modes of lower 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.orgLaser & Photon. Rev. 4, No. 2 (2010) 187Figure 10 PL spectrum of a PM accommodated ina microwell a). Arrows indicate the coupled modes.b) PL spectra of noninteracting microspheres. Inset:microscope image of the PM in the microwell. Thedark cross indicates the excitation position.l [71]. The deconvolution of the lineshape of resonances be-longing to TE122WGM (Figs. 10a and b) using Lorentzianfunctions shows that the quality factors of PM peaks are 8 times smaller than the Q-factors of noninteractingmicrospheres.4.2. Optical modes in photonic molecules formedfrom spherical microcavitiesPhotonic states in the PM can be described using a linearcombination of the Mie resonance states of each micro-sphere [79] or using a more general phenomenologicaltight-binding model [84] that also been used recently toreproduce the band structure of two-dimensional photonicbandgap lattices composed of cylinders [28]. The linearcombination model predicts that the electromagnetic cou-pling between spheres causes the narrow Mie resonancesto split into relatively broad peaks (BN and ABN modes).However, detailed consideration of coherent mode couplingin PMs using the tight-binding approach shows that in factthe BN and ABN branches consist of a number of verynarrow peaks, which are due to the presence of m 6= 1components. The total number of these sharp peaks, orig-inating from a certain mode n; is governed by the actualdegeneracy of the Mie resonances that in the approach ofthe normal mode concept is 2n+1. (Due to the dependenceof the mode coupling on the orbital plane orientation, theinteraction is limited between modes of only the samem,no degeneracy is removed betweenm and m and the newdegeneracy of PM modes is now n + 1 with m runningfrom 0 to n).In calculations within the SMTB model, the splittingswere estimated as a spectral distance between outer peaksassigned to modes withm = 1, which do not correspondto the maximum of envelope of the PM modes and thereforethis may cause a discrepancy between the estimated and ob-served values of the mode splitting. The fine structure of BNand ABN modes of the PM is of great interest to the experi-mentalists because it suggests a manifold of applicationsparticularly in the field of information processing. However,in order to observe this phenomenon two conditions shouldbe met. First, the spacing betweenm-resonances formingthe BN and ABN modes of the PM strongly depends on theangle of incidence of the electromagnetic wave [71, 84].For = 0, when the incident light propagates parallelto the longitudinal axis of the PM, the incident wave canpreferentially excitem = 1 modes. The interaction withother dissipative modes of lower l causes the broadening ofBN and ABN peaks and decreases the Q-factor relative tothat of single spheres, as was observed in a number of pa-pers [7072, 79]. In the perpendicular configuration, when = 90, the intermode coupling and spacing betweenm-resonances are expected to be minimal. In other words, inthe case of perpendicular orientation of the PM with respectto excitation, allm-modes would merge into broad BN andABN features and their fine structure would not be easilyrecognized. An intermediate regime can be reached only foroff-axis excitation with 0 < < 90. Secondly, in orderto reveal them 6= 1 components, the interacting cavitiesshould not only have similar size, but also similar Q-factors.If the resonances of the two cavities are of greatly differentwidth, the coherent coupling is disturbed and therefore thefine structure of PM modes will be difficult to detect.Fig. 11a shows PL spectra of a PM formed by two al-most identical microspheres with sizes of 3.0168 m and3.0189 m measured for excitation (and signal collection)at the right edge of the upper microsphere providing off-axis excitation (inset, Fig. 11a). The presented PL spectraclearly reveal major features unique to strong coherent cou-pling between the photonic states of the two microspheresforming the PM. One can clearly see a number of narrowpeaks grouping on both sides arising from TE and TM 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim188 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculesFigure 11 PL spectra of the PM formed by twoalmost identical microspheres with off-axis excita-tion and detection a), and PL spectra of noninter-acting microspheres b). Inset: microscope image ofthe PM in the microwell. The dark cross indicatesthe excitation position.nances of the individual spheres and forming BN and ABNmodes of the PM. The origin of this fine structure of the BNand ABN modes lies in the lifting of the mode degeneracyin the PM [70, 84] and therefore this multipeak structurewould not be radically altered in scattering spectra or evenin lasing, or stimulated Raman scattering in the same waythat in a semiconductor laser the lasing does not alter thecavity resonances.It is noteworthy that the number of experimentally re-solved peaks increases with the angular mode number bothfor TE and TM modes, and is very close to the n value,although never in excess of n. Indeed, 19 peaks have beenobserved in the spectral region of TE120(19 peaks for TE120),21 peaks around the TE121resonance (20 peaks for TM121),21 peaks in the region of the TE122resonance (21 peaksfor TM122), 22 peaks for TE123(22 peaks for TM123) and23 peaks around the TE124resonance. Note that the spec-tral region occupied by a set of these narrow resonances ismuch wider than the linewidth of WGMs of noninteractingmicrospheres (Fig. 10b).The deconvolution of the lineshape of them-resonancesof the PM using Lorentzian functions shows that m-resonances of the BN branch are always sharper than thatof the ABN one, providing a higher quality factor Q valuefor these modes and therefore a higher photon lifetime inthe resonant modes. However, the most remarkable experi-mental fact is that the Q-factor of them-resonances in thespectra of the PM exceeds theQ value of single noninteract-ing microspheres, suggesting the respective modificationof photon lifetime in the PM (PM) relative to the pho-ton storage time in a single spherical microcavity beforecontact (SS). These two facts along with the estimatedvalue of BN/ABN splitting ( 57 nm) implies the possi-bility for development of a new PM-based photonic devicesuch as an optical delay line with controllable spectral andtemporal tunability [87].Fig. 12 shows spectral distribution of the ratio betweenphoton lifetime ofm-modes of PM and photon storage timein WGMs of a single sphere calculated from the correspond-ing values of mode linewidth in the region of TE121andTM120resonances demonstrating a threefold photon-storageenhancement in the PM. It is evident from Fig. 12b that theinteraction between spherical microcavities results in peri-odic group delay spectra with peaks occurring at each of them-resonant frequencies with longer delay times for higherm values, which implies that the spectral components nearthesem-resonance have a longer lifetime within the PM.In all the experiments described here, the strong cou-pling phenomenon in the spectra of the PM was investi-gated in the visible and near-infrared spectral regions. How-ever, recent achievements in the development of infrared-emitting colloidal QDs can meet the first basic requirementfor PM devices operating at such wavelengths, i.e. matchingthe basic communication spectral windows near 1300 nmand 1550 nm.Based on theoretical considerations of the internalfield in the PM and a number of experimental stud-ies [71, 81, 82, 87] it is anticipated that the size of inter-acting microcavities is probably not the only parameter thatallows us to control the spacing between split modes anddistribution of photon storage times. First, the efficiencyof coupling between spherical microcavities forming thePM strongly depends on the spacing between microspheres:the splitting of the BN and ABN modes decreases exponen-tially with increasing separation [84, 87].The next possibility to control the spacing betweenchannels emerges from the strong dependence of the split-ting parameters of the PM modes on the angle of incidenceof electromagnetic wave . For = 0, when the incidentlight propagates parallel to the longitudinal axis of the PM,the incident wave can only excitem = 1 modes [71, 84].Interaction with other dissipative modes of lower n causes 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.orgLaser & Photon. Rev. 4, No. 2 (2010) 189Figure 12 (online color at: a) PL spectra of the PM (solidline) formed by two almost identical micro-spheres with off-axis excitation and detec-tion. Dashed lines show the PL spectra ofnoninteracting microspheres. b) Ratio be-tween the photon lifetime of the m-modesof the photonic molecule and that of singlespheres. The solid lines are the result of alinear fit.the broadening of BN and ABN peaks and their Q-factoris lower than that of single spheres, as was observed in anumber of studies [7072]. In the perpendicular configu-ration, when = 90 intermode coupling is expected tobe minimal and the fine structure of PM modes can not beeasily resolved. In that case, however, the Q-factor of BNand ABN modes can be at least comparable to that of non-interacting microspheres, presumably due to disappearanceof one wing of these PM branches. The bandpass spectrumwas demonstrated to be much more complicated for off-axisexcitation with 0 < < 90, showing a number of tinypeaks between upper lower peaks ofm = 1 [7072]. Al-though further investigations need to be done on the angulardependence of the fine structure of the PM modes, recentinvestigations point clearly to the last configuration as thebasis for the development of a PM-based optical delay de-vice with controllable spectral and temporal tunability.Finally, it remains to be noted that the parameters ofthe intercavity coupling in the PM can be governed also bydetuning of the microsphere sizes [71]. Forming PM frompairs of microspheres of slightly different sizes one canmanipulate the spectral position of BN and ABN modescontrolling the symmetry of the splitting.Microsphere resonators can be explored as buildingblocks for a number of other devices like coupled-resonatoroptical waveguides (CROWs) in which delayed signals aretransmitted via photon hopping [18, 85]. The small groupvelocity of the CROW band can result in a large opticalfield with only a modest amount of power flux causingstrong enhancement of the efficiency of nonlinear opticalprocesses (for example, second-harmonic generation). Inthis respect, highly desirable functionality may be the possi-bility to control of the Q dynamically, as has been recentlydemonstrated in silicon microring resonators or photoniccrystal nanocavities [9092].5. ConclusionsProgress in the field of manipulation with modes of pho-tonic atoms and molecules is extremely rapid. The studyof microcavity/QDs structures demonstrated here, revealsmany fascinating insights that appear when merging twomajor concepts of solid-state physics, complete 3D elec-tronic and photonic confinement, in one structure. The de-pendence of WGM parameters on the characteristics ofboth interacting and noninteracting microcavities suggestsa manifold of photonic applications, in particular in thefields of biosensing and quantum information processing.Acknowledgements This work was supported by Science Founda-tion Ireland under Grant Nos. 02/IN.1/I47, 00/PI.1/C077A.2, and07/IN.1/B1862.Yury Rakovich received his diplomain physics from the Belarusian StateUniversity and his Ph. D. in physicsfrom the National Academy of Sci-ences of Belarus in 1995. He workedas a lecturer in Physics at the BrestState Technical University until 1997and moved to the University ofMinho (Portugal) in 1998. He joinedthe School of Physics in Trinity College Dublin in 2001,where he works now as a senior research fellow in theCentre for Research on Adaptive Nanostructures andNanodevices (CRANN). His current research focuseson optics of microcavities and photonic molecules, pho-tonic nanojets, semiconductor nanocrystals and 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim190 Y. P. Rakovich and J. F. Donegan: Photonic atoms and moleculesJohn F. Donegan received B. Sc. andPh. D. degrees from the National Uni-versity of Ireland, Galway. He hadpostdoctoral periods at Lehigh Uni-versity and the Max Planck Institutefor Solid State Research, Stuttgart.He was appointed to the academicstaff in Trinity College Dublin in1993. He leads the SemiconductorPhotonics Group and is Head of the School of Physics.He is also a principal investigator at the CRANN re-search institute in Trinity College Dublin. 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