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Photonics meets excitonics: natural and artificial molecular aggregates

Semion K. Saikin,1, 2, ∗ Alexander Eisfeld,3, † Stephanie Valleau,1 and Alan Aspuru-Guzik1, ‡

1Department of Chemistry and Chemical Biology,Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA

2Department of Physics, Kazan Federal University,18 Kremlyovskaya Street, Kazan 420008, Russian Federation

3Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Str. 38, D-01187 Dresden, Germany

Organic molecules store the energy of absorbed light in the form of charge-neutral molecularexcitations – Frenkel excitons. Usually, in amorphous organic materials, excitons are viewed asquasiparticles, localized on single molecules, which diffuse randomly through the structure. How-ever, the picture of incoherent hopping is not applicable to some classes of molecular aggregates –assemblies of molecules that have strong near field interaction between electronic excitations in theindividual subunits. Molecular aggregates can be found in nature, in photosynthetic complexes ofplants and bacteria, and they can also be produced artificially in various forms including quasi-onedimensional chains, two-dimensional films, tubes, etc. In these structures light is absorbed collec-tively by many molecules and the following dynamics of molecular excitation possesses coherentproperties. This energy transfer mechanism, mediated by the coherent exciton dynamics, resemblesthe propagation of electromagnetic waves through a structured medium on the nanometer scale.The absorbed energy can be transferred resonantly over distances of hundreds of nanometers beforeexciton relaxation occurs. Furthermore, the spatial and energetic landscape of molecular aggregatescan enable the funneling of the exciton energy to a small number of molecules either within oroutside the aggregate. In this review we establish a bridge between the fields of photonics andexcitonics by describing the present understanding of exciton dynamics in molecular aggregates.

I. INTRODUCTION

Advances in nanotechnology supported by our under-standing of material properties on the microscopic levelpersistently drive the field of photonics to the nanome-ter scale. With the development of photonic crystals1,2

and semiconductor optical cavities3,4 the size of opticaldevices, usually limited by light diffraction in free space,can been scaled down to hundreds of nanometers just byexploiting the material’s dielectric constant. Advancesin the design of plasmonic metamaterials5–7 permittedthis limit to be pushed even further down to the orderof tens of nanometers. The natural question which arisesis: what will be the next limit and how can it be ap-proached?

In this review we consider one of possible pathwaystowards reaching the goal of optical devices on thenanometer scale: using molecular aggregates as photonprocessing elements on the true nanometer scale, seeFig. 1. Molecular aggregates are assemblies of moleculesheld in place by non-covalent interactions. These sin-gle molecules mostly keep their nuclear and electronicstructure. Examples are molecular crystals as well asnanoscale self-assembled structures, molecular films andlight harvesting systems in photosynthesis. If the lowestallowed electronic transitions in the composing moleculesare within the visible part of the optical spectrum andif the molecules have large absorption and fluorescencecross-sections, the interaction between molecular elec-tronic transitions is strong enough to transfer the lightabsorbed from one molecule to the others, via a resonantde-excitation/excitation process.

This mechanism is closely related to the near-field en-

ergy transfer between classical dipoles (antennas)8–13.In this sense, the exciton dynamics in molecular aggre-gates resembles the propagation of light in a metamate-rial where dye molecules play the role of functional ele-ments. In contrast to excitons in inorganic semiconduc-tors, where free charge carrier mobility determines theexciton transport, in aggregates, electrons remain local-ized on molecules while the excitation is transferred.

A canonical example of molecular aggregates that pos-sess coherent exciton properties are J-aggregates. Theseare aggregates of fluorescent molecules, discovered about80 years ago independently by Scheibe14,15 and Jelley16.They observed that the formation of aggregates is ac-companied by drastic changes in the optical properties.The broad absorption line corresponding to the molec-ular excitation is shifted to the red side of the spec-

FIG. 1: Schematic illustration of the length scales character-izing the different physical phenomena present the differentfields discussed in this review.

2

trum and becomes much narrower. Later, these typesof molecular aggregates were named J-aggregates afterJelley. J-aggregates represent only one class of molecu-lar aggregates. For instance, there exist aggregates wherethe absorption line is blue-shifted, so called H-aggregates.Some aggregates exhibit several J-bands17 and some haveboth J-and H-bands18. In aggregates that consist of non-equivalent monomers even more complicated absorptionstructures can be found19.

Molecular aggregates also appear as functional units innature. For instance, they form the absorbing and energytransferring parts of light-harvesting complexes in plantsand some types of bacteria and algae19. In these com-plexes the exciton absorbed by the antenna aggregate hasto be funnelled to the reaction center – the part wherethe exciton energy is used to create free charges to beemployed in a chemical reaction. The efficiency and ro-bustness of light absorption and exciton transfer in lightharvesting complexes may be crucial for the survival ofphotosynthetic organisms under evolutionary pressure.

Shortly after the discovery of the self-assembled or-ganic dye aggregates the close connection of these arti-ficial structures to the natural light harvesting systemswas recognized20,21 and the exciton model of Frenkel9,22

has been used to explain the observed changes in op-tical properties and the transfer of energy along theaggregate21.

In Frenkel’s exciton theory, which is based on theclassical resonance interaction theory of Holtsmark8, theelectronic excitation in the aggregate is not confined toa single monomer, but it is coherently delocalized overmany monomers in the form of “excitation waves”. Fromsuperpositions of these excitation waves “excitation pack-ets” can be formed, which describe the coherent motionof (localized) excitations22. Already in these early worksit was established that coupling to internal and externalvibrational modes, imperfections of the aggregates anddisorder induced by the environment strongly influencesthe “coherence size” of the exciton waves and modifiesthe optical and transport properties.

When the interaction with the environment (internalvibrations, solvent, etc.) is much stronger than theresonant excitation transfer interaction, the excitationbecomes more or less localized on one monomer andthe transfer is no longer described by coherent excitonmotion but it becomes an incoherent hopping process.Forster derived an elegant formula for the rate constantsfor transport of excitation from one monomer to theother23,24. This rate is proportional to the overlap ofthe donor emission spectrum and the absorption spec-trum of the acceptor molecule and depends on the inversesixth power of the distance between donor and acceptor.Typically, in molecular aggregates, one is in a regimein-between these two extreme cases, i.e. the transport isneither fully coherent nor incoherent. This complicatesthe theoretical modeling and the interpretation of exper-iments.

The remarkable optical and transport properties of

molecular aggregates have led to a variety of appli-cations. Right from the beginning, molecular aggre-gates were employed as wavelength selective sensitiz-ers in photography25,26. Recent applications includethe measurement of membrane potentials27 or the de-sign of colorants28. Some molecular aggregates formself-assembled supramolecular flexible fluorescent fibers29

which may have applications in thin-film optical andoptoelectronic devices, for example by employing opti-cal bistability of J-aggregates30. Molecular aggregatescan be also utilized for sensing applications. For in-stance, it has been demonstrated that a large absorptioncross section combined with fast exciton diffusion maybe used to enhance fluorescence from a small numberof dye molecules adsorbed or embedded in an aggregatefilm31,32. Due to fast exciton diffusion within the aggre-gate the excitons explore the aggregate. Once they finda molecule with an electronic transition close to the J-band the exciton can be transferred inelastically to theadsorbed molecule. Moreover, dye aggregates might playan important role in the development of efficient, low-costartificial light harvesting units (like organic solar cells)33.This review gives a brief, yet by no means complete,

overview of our experimental and theoretical understand-ing of excitons in molecular aggregates. Most of the as-pects in this work are covered at the advanced intro-ductory level, and for a deeper understanding we referto more detailed studies such as19,34–38. The review isstructured as follows: In Sec. II, we describe basic ex-citonic properties of molecular aggregates starting withsingle molecules and molecular dimers and then introduc-ing several examples of artificial and natural molecularaggregates. In Sec. III, we overview the main experimen-tal techniques that allow for probing the structural prop-erties of molecular aggregates and excitation dynamics.Section IV introduces the main theoretical approachesutilized for modeling of excitons in aggregates. SectionV shows how molecular aggregates can be combined withphotonic and plasmonic structures. Finally, we concludethe review in Section VI.

II. BASIC PROPERTIES OF MOLECULARAGGREGATES

A. Properties of monomers

Molecules in the aggregates largely retain their elec-tronic and nuclear structure. Thus, it is natural to startour discussion with individual molecules interacting withlight. The interaction of a single molecule with light isschematically illustrated in Fig. 2. If the molecule has anoptically allowed electronic transitions within the photonspectrum it can be excited by absorbing light at the cor-responding frequency. The transition time between theground and excited state of the molecule is of the order oftens of attoseconds – the time that a single photon inter-acts with a molecule. During this short time interval the

3

Nuclear coordinate

En

erg

y

g

e

FluorescenceAbsorption

Non-radiative relaxation

Vibrational

relaxation

FIG. 2: Excitation/de-excitation processes in a singlemolecule illustrated on a two-level molecular energy diagram.The parabolic surfaces correspond to the ground state |g〉 andthe first excited |e〉 electronic states of the molecule. The hor-izontal axis indicates the displacements of nuclei from theirequilibrium positions. The molecule, initially in the groundelectronic and vibrational states, is excited by absorbing light– blue arrow. During the absorption process the positions ofthe nuclei are not changed. The light absorption also inducesmolecular vibrations. Due to the interaction with the en-vironment the molecular vibrations are equilibrated and themolecule relaxes to the bottom of the excited electronic state– orange wavy arrow. Finally, the molecule relaxes down tothe ground electronic state by emitting a photon – red arrow(fluorescence), or without photon emission – green dashed ar-row (non-radiative process). In the ground state the inducedvibrations are also equilibrated due to interaction with theenvironment.

positions of the nuclei in the molecule are not changed.Initially the molecule is in its ground state geometry, i.e.in a minimum of the electronic ground state potential |g〉indicated by the blue wave-packet in Fig 2. The equi-librium positions of atoms for the excited states, usu-ally, are different from those of the ground state. There-fore, after the transition to the state |e〉 the molecule isin a transient non-equilibrium state where molecular vi-brational modes are also excited (green wave-packet inFig 2). Then, due to the interaction of the moleculewith its environment the molecule relaxes towards theenergetic minimum of the excited state, i.e. the excitedvibrational modes are relaxed (wavy arrow and orangewavepacket in Fig 2). This relaxation of the molecu-lar geometry can also be accompanied by a rearrange-ment of the environmental molecules to a configurationwith lower total energy. At ambient conditions this pro-cess occurs over a timescale of hundreds of femtosecondsto several picoseconds. Finally, on timescales of tens ofpicoseconds to nanoseconds the molecule relaxes to itselectronic ground state either emitting a photon (fluo-rescence) or transferring energy to other degrees of free-dom, for instance vibrations (non-radiative relaxation39).

Usually, the absorption and emission spectra exhibit aprogression of peaks stemming from the coupling to vi-brational modes with high energy (∼150 meV). Thesepeaks are broadened by the same order of magnitude,due to coupling to a multitude of low energy modes ofthe molecule and the surroundings. Emission takes placefrom the thermally relaxed excited state, which is typ-ically located in the low energy wing of the absorptionspectrum. The relaxation energy is related to the en-ergy difference between the maxima of the absorptionand emission spectra, the so-called Stokes shift.The absorption efficiency of a particular electronic

transition can often be characterized by the correspond-ing transition dipole - a matrix element of a dipole opera-tor between the ground and the excited molecular states

~d = 〈e|q · ~r|g〉. (1)

Here and in the following we use an arrow symbol to indi-cate three-dimensional vectors in real space. The dipoleoperator is characterized by its charge q and the positionoperator ~r. The transition dipole is not a measurablevalue and is defined up to a complex phase factor (ifmagnetic interactions can be neglected, which is oftenthe case, then the wavefunction can be chosen real and~d becomes a real vector). The absorption and emissionstrengths of the respective transition are proportional to

|~d|2. In the absorption spectra the transition frequency isdetermined by the energy difference ε between the groundand excited state.Structures and optical spectra of representative

molecules are shown in Figs. 3 and 4. In Fig. 3 weshow a TDBC molecule, which can be used as an illustra-tive example for a broader class of cyanine dyes. Besidethe monomeric absorption and fluorescence spectra (insolution), spectra of aggregates formed on a glass sub-strate are also shown. The lowest electronic transitionin TDBC is characterized by a large transition dipole

of the order of |~d| ≈ 10 Debye (Debye units are com-monly used for molecular dipoles, 1 Debye ≈ 0.208 e·Awhere e denotes the electron charge), which is alignedwith the backbone of the molecule. The higher excitedstates in TDBC are well separated from the lowest one,which indicates that, for low intensity optical absorp-tion and exciton dynamics it is sufficient to take onlytwo electronic states into account. The absorption spec-trum of the molecule in a solution shows a broad linein the green part of the spectrum with a partially re-solved vibronic structure. Note also that the emissionfrom a monomer is roughly a mirror-image of the ab-sorption, where the maximum is shifted to lower ener-gies. This is the Stokes shift, which is caused by therelaxation/reorganisation after an electronic transition.The mirror image of absorption and fluorescence indi-cates that the vibrational frequencies and their couplingto electronic transitions are very similar in the electronicground and excited state. Upon aggregation the absorp-tion and fluorescence lines become much narrower withno structure and are shifted to the orange-red color. The

4

FIG. 3: TDBC fluorescent dye that forms 1D and 2D molec-ular aggregates. (a) Molecular structure, grey and whitespheres represent carbons and hydrogens respectively. (b)Normalized absorption and fluorescence spectra of TDBCmolecules taken in a solution (solid lines) and in a 2D ag-gregated form (dashed lines).

Stokes shift in the aggregated form is also much smaller,which indicates a reduced coupling to the environment.Aggregates composed of TDBC have, for example, beenproduced in solution17 and on surfaces40. By changingthe side groups different geometrical arrangements canbe achieved17.

Another representative example of molecules formingaggregates is the bacteriochlorophyll (Bchl)– a pigmentmolecule, which is a functional element of photosyntheticsystems in phototrophic bacteria, see Fig. 4(a). Thestructure of Bchl is similar to that of chlorophyll - thephotosynthetic pigment in plants. Both are derivativesof porphyrin, compelexed with Mg2+. The lowest elec-tronic transition, which is involved in the energy transfer,is the so called Qy-band. The corresponding transitiondipole lies in the plane of the porphyrin ring and is about

|~d| ≈ 5 Debye. The transition dipole corresponding tothe next electronic state is denoted as Qx. It is perpen-dicular to the Qy dipole, and the associated transitionstrength is much smaller. The Soret band which lies inthe ultraviolet has stronger absorption but is usually notinvolved in the energy transfer. As in the case of TDBCthe emission occurs from the lowest excited state and

FIG. 4: (a) Bacteriochlorophyll (Bchl) molecule - light ab-sorbing pigment that is a basic structural element of light-harvesting complexes in phototrophic bacteria. Its struc-ture is similar to chlorophyll - the photosynthetic pigmentin plants.; (b) Absorption and fluorescent spectra of Bchlmolecules.

the emission spectrum is roughly a mirror image of theabsorption band corresponding to this state.

B. The aggregate

Organic dye molecules can self-aggregate in differenttypes of structures. Sometimes the aggregation is drivenby electrostatic forces pushing molecules to adsorb on asurface; sometimes hydrophobic parts of the moleculesrepel the water and tend to collect together such as insynthetic tube aggregates17.

A specific property of molecular aggregates with stronginter-monomer couplings is that the absorption and flu-orescent spectra substantially differ from the spectra ofthe molecules which form the aggregates while the elec-tronic structure of the molecules is not modified. Theintermolecular distance in an aggregate is large enoughthat the electron tunneling between different moleculescan be neglected. Therefore, only the Coulomb interac-tion between the electronic transitions in monomers isresponsible for the spectral modifications and the inter-

5

molecular energy transfer. This interaction is similar tothe non-radiative near-field coupling between plasmonicstructures, which is mediated by virtual photons. It turnsout that the major contribution of the Coulomb interac-tion in the spectra of aggregates is from the excitationtransfer via resonant transitions. We will refer to thismain interaction term between the monomers as Forstercoupling. The Forster coupling, to a good approxima-tion, can be described by restricting to dipole transitionsonly (see below Eq. 2). The interaction is visualized inFig. 5 for a situation in which initially monomer 1 iselectronically excited and monomer 2 is in the electronicground state. Then, in a resonant process molecule 1 isdeexcited and simultaneously the second monomer is ex-cited. While this time-ordered discrete picture is easy forvisualisation in reality the exciton energy is transferredcoherently. For large distances between the monomers

monomer 1 monomer 2

ener

gy

e e

g g

FIG. 5: Illustration of the excitation transfer due to resonantnear-field interaction between the state |e〉|g〉 and |g〉|e〉.

the interaction between monomers 1 and 2 can be ap-proximated by the dipole-dipole term

V12 =1

R312

(

~d1 · ~d2 − 3(~d1 · R12)(~d2 · R12))

, (2)

where R12 denotes the distance between the monomers,R12 is the corresponding direction vector, and the vectors~dn are the transition dipoles introduced in Eq. (1).If the intermolecular distance is comparable with the

size of the molecules, then the interaction between thetwo monomers can no longer be described adequately us-ing the point dipole-dipole interaction of Eq. (2). Often,it is then sufficient to replace the point-dipoles in Eq. (2)by extended dipoles41. For even higher accuracy moreelaborate schemes have been developed (see e.g.42).

1. The dimer

Before discussing general molecular aggregates, let usdescribe some basic results for the case of two coupled

identical monomers, ignoring nuclear degrees of free-dom for the moment. The eigenstates of the uncou-pled monomers can be taken as a basis. These statesare |g〉|g〉, |e〉|g〉, |g〉|e〉, |e〉|e〉. While the states |g〉|g〉and |e〉|e〉 are still suitable to describe the ground stateand the doubly excited state of the dimer, respectively,the two degenerate single exciton states |e〉|g〉 and |g〉|e〉are no longer eigenstates of the coupled system, becauseof the resonant transfer interaction. The correspond-ing Hamiltonian is written as H = ε1|1〉〈1| + ε2|2〉〈2| +V12(|1〉〈2|+ |2〉〈1|) (we choose the energy of the monomerground state as zero), where we have introduced theshorthand notation |1〉 ≡ |e〉|g〉 and |2〉 ≡ |g〉|e〉 or equiv-alently in a matrix representation

H =

(

ε1 V12

V12 ε2

)

. (3)

For identical energies of excited states ε1 = ε2 ≡ εthe eigenstates of the dimer are superpositions |±〉 =1√2

(

|e〉|g〉 ± |e〉|g〉)

where the electronic excitation is co-

herently delocalized over both monomers. The corre-sponding eigenenergies are ǫ± = ε ± V12. Note that themagnitude and sign of the interaction depends sensitivelyon the distance and orientation of the two monomers.Fig. 6 illustrates how the relative orientations of molec-ular transition dipoles change the frequency of electronicexcitations in a dimer. If the transition frequencies of theinvolved monomers are equal and the transition dipolesare parallel, only the transition between the ground andthe |+〉 state is optically allowed. It is detuned by theenergy V12 from that of the non-interacting monomers.From Eq. (2) one can see that for case (a), where thetransition dipoles are orthogonal to the distance vectorbetween the monomers one has positive V12 ∼ |d|2/R3

12.For the case (b) the interaction is negative with V12 ∼−2|d|2/R3

12. Therefore, the alinement of the moleculesshown in Fig. 6 (a) and (b) will be seen as a blue and redshift of the absorption line, respectively. As it has beennoted before, the states with only one excited monomersuch as |g〉|e〉 and |e〉|g〉 are not eigenstates of the sys-tem anymore. Thus, if one of these state is populatedinitially, the energy will oscillate between them back andforth coherently.Let us briefly mention that the dimer often appears

as a first step of aggregation43 and thus has been inves-tigated intensively (see e.g.44–49) . This interest in thedimer is also due to the fact that many of the more re-alistic models for aggregates where the environment andthe internal vibrations are included can only be solvedefficiently for the dimer.

2. Arbitrary aggregates

The theoretical description of the dimer can easily beextended to arbitrarily arranged monomers. As in thecase of the dimer the total ground state is taken as a

6

(a)ge

gg

eg

+

−

−

dr

dr

12R ε

3

12

2

12 /|| RdV =

(b)

+

−

dr

dr

12R

3

12

2

12 /||2 RdV −=

FIG. 6: Interaction between electronic transitions dipoles(blue arrows) of two molecules. The directions of the ar-rows reflect the relative phase of the transition dipoles. Forthe considered molecular alignments only one of the opticaltransitions is allowed for the dimer (green arrows). (a) Theoptically allowed transition of the dimer is shifted to the bluepart of the spectrum, which is similar to H-aggregation; (b)the optically allowed transition is shifted to the red, whichcorrespond to J-aggregation.

product of states where all monomers are in the groundstate | gaggel 〉 = | g 〉1 · · · | g 〉N . We are interested in theproperties of aggregates in the linear absorption regime.Therefore, it is sufficient to take into account only thestates with at most one electronic excitation on the ag-gregate, such as

|n 〉 ≡ | g 〉1 · · · | e 〉n · · · | g 〉N , (4)

in which monomer n is electronically excited and all othermonomers are in their electronic ground state. In thisone-exciton manifold approximation the Hamiltonian canbe written as

He =

N∑

n=1

εn|n 〉〈n |+∑

nm

Vnm|n 〉〈m | (5)

where Vnm is the Coulomb dipole-dipole interaction, seeEq. 2, which transfers excitation from monomer n to m.

Examples of commonly discussed 1D and 2D planarstructures are shown in Fig. 7. While 1D models arewell studied theoretically (see e.g. Refs.50–58) and are fre-quently used to characterize excitons in self-assembledmolecular aggregates, it is not clear whether ideal 1Dmolecular chains are formed in experiments34. Usually,they are subsystems of higher dimensional structuressuch as films or crystals.

The 1D model of molecular aggregates is convenientbecause many results can be obtained analytically19,59.For a perfect very long chain with N molecules the eigen-

states are well described by “exciton waves”

|φj 〉 =1√N

N∑

n=1

ei2π

Njn|n 〉 (6)

with the corresponding eigenenergies

Ej = ǫ+ 2V cos(2πj

N

)

. (7)

In the last equation, for the sake of simplicity, we haveconsidered the interactions between nearest neighborsonly, which are denoted by V . A discussion of finite one-dimensional aggregates can be found e.g. in Refs.19,59.

For the perfect linear chain with parallel monomers,the largest transition dipole correspond to the excita-tion of the state with a minimal number of nodes. Inthe case of J-aggregation, Fig. 7(a), this state is at thebottom of the exciton spectrum shifted by about sev-eral hundreds of meV from the monomer transition whilefor H-aggregates, Fig. 7(b), this shift is to the blue partof the spectrum. In reality, to compare exciton transi-tions in aggregates with excitations in single moleculesone also has to include Van der Waals interaction withoff-resonant excitations19,47 and the vibronic structureof molecular excitation19,47,60. However, the simplifiedmodel presented above qualitatively describes the exci-ton states in aggregates.

2D molecular aggregates can be formed, for instance,as Langmuir-Blodgett films61, deposited molecule-by-molecule on a surface40,62, or by spin coating63. Thestructure of the aggregate is determined by the molecularproperties such as their shape, charge, etc., and the as-sembly method. For instance, for cyanine dyes64 (TDBCis one example of the class of molecules) some commonlyassumed aggregation structures are brickstone, Fig. 7(c),and herringbone, Fig. 7(d).

3D molecular aggregates with translational symmetryare usually known as molecular crystals. Frequently, inthese structures is possible to identify lower dimensionalsubsystems with a preferred interaction between molec-ular transition dipoles65. These directions would deter-mine anisotropy of exciton transport. While on averagethe exciton transport in a crystal can be incoherent onemay expect specific directions with large coherent excitondelocalization.

The above mentioned structures are only very simpleexamples of molecular aggregates. For instance, whendriven by hydrophobic and hydrophilic forces moleculescan aggregate in two-layer tubes of about 10 nanometersin diameter17,66 or one can use templates like polypep-tides or DNA to induce helical structures67,68.

Because of the huge variety of organic dyes that can ag-gregate it is possible to create narrow J-band absorptionwithin an arbitrary part of visible and near IR spectrum,see Fig 8.

7

(a) (b)

(c) (d)

FIG. 7: Illustrations of 1D and 2D planar molecular aggre-gates. Each block corresponds to a monomer forming theaggregate. (a) - staircase and (b) - ladder models for 1Dpacking; (c) - brickstone and (d) - herringbone 2D packingmodels.

FIG. 8: Absorption spectra of four different cyanine dyes inmonomeric and aggregated forms illustrating the variabilityin the aggregate optical properties. Adapted with permissionfrom Ref.69. Copyright 2011 American Chemical Society.

C. Natural aggregates

In nature, photosynthetic complexes of plants, pho-totrophic bacteria and algae are composed of molecularaggregates that efficiently transfer excitons. As an ex-

FIG. 9: Schematic structure of light-harvesting complex ingreen sulfur bacteria. The solar light is absorbed by chloro-some antenna aggregates of Bchl molecules. Then, the energyin the form of excitons is transferred through the baseplateand Fenna-Matthews-Olson (FMO) protein complexes to thereaction center, where the charge separation occurs.

ample, in Fig. 9 we sketch the energy transfer along thelight harvesting system of green sulfur bacteria (GSB).These GSB can be found e.g. in deep sea. By develop-ing a sophisticated light-harvesting antennae structurethese organisms adapted to survive at very low lightintensities70,71. Energy absorption and transfer in GSBgoes through a network of Bchl molecules, Fig. 4, aggre-gated in several types of functional structures – chloro-some antenna, baseplate, Fenna-Matthews-Olson proteincomplex (FMO), and the reaction center.The photons are absorbed by the chlorosome – an or-

ganelle which is bound to the bacterial membrane andhas a size of several hundreds of nanometers. The chloro-some contains a disordered array of cylindrical or ellip-soidal molecular aggregates – antennas. While differ-ent types of geometrical and structural disorders compli-cate the molecular structure characterization of naturalaggregates, recent NMR analysis of mutant chlorosomeantennas72 suggested that Bchl molecules in them arearranged in an array of concentric helical structures il-lustrated in Fig. 10(a). The Forster coupling betweennearest-neighbor Bchl molecules in the chlorosome an-tenna complexes is of the order of 100 meV and the pro-posed molecular arrangement of the mutant should resultin the formation of a J-band. Both experimental73 andtheoretical studies74, show that the exciton spreads overa single antennae on the timescale of hundreds of fem-toseconds.Another functional element of GSB light-harvesting

structure, is the Fenna-Matthews-Olson (FMO) complex,a protein which is depicted in Fig. 10(c). FMO playsthe role of a molecular wire transferring energy from thechlorosome to the reaction center. It is a trimer con-taining 8 Bchl molecules in each subunit. Unlike in thechlorosome antenna, Bchl molecules in FMO are held to-gether by a protein cage, and also the Forster coupling

8

FIG. 10: Examples of molecular aggregates in the light-harvesting complex of green sulfur bacteria. (a) Chlorosomeantenna complex – a cylindrical or ellipsoidal aggregate ofBchl molecules, several concentric aggregates are enclosed;(b) A Bchl dimer – a unit block of the antenna complex72;(c) Fenna-Matthews-Olson (FMO) protein complex – an ex-citonic “wire”; (d) organization of Bchls in a monomer unitof FMO complex78

between the molecules is several times weaker. However,from the multiple experimental and theoretical studies itis suggested that the exciton states in FMO are partlydelocalized75–77.

III. EXPERIMENTAL CHARACTERIZATIONOF EXCITONIC SYSTEMS

Much effort is devoted to obtain the microscopic struc-ture of the various aggregates (which in turn are neededfor theoretical models), including the arrangement of themonomers, their spacial and energetic disorder, etc. Be-side these conformational aspects there is also large inter-est in the dynamic properties of excitons such as excitonrelaxation and dephasing rates, diffusion coefficients, etc.X-ray crystallography can be used to obtain lattice

properties of molecular aggregates, if the latter eitherpossess an intrinsically long-range order (like molecularcrystals or two-dimensional monolayers on substrate79)or can be crystallized. For instance, crystallization ofphotosynthetic light-harvesting complexes80 had a largeimpact on the understanding of natural photosynthesis19.However, most molecular aggregates cannot be crystal-lized. In recent years Cryo-Transmission electron mi-croscopy has provided valuable information on the ge-ometrical structure of many aggregates66,81–83.The classical way to obtain information on the geome-

try of the aggregate is by optical spectroscopy (in partic-

ular absorption, linear dichroism and circular dichroism)combined with theoretical modeling. For instance, thepositions, intensities, polarizations and shapes of the ag-gregate absorption bands provide information about thestrength of intermolecular coupling as well as relative ori-entations of the monomers19,47,82. Circular dichroismspectra can be used to analyze chirality of the struc-tures, for instance, in studies of J-aggregate helices andtubes18,84–87. Similarly, the emission spectra can be usedto obtain information on the aggregate structure. Theseoptical experiments are often performed under varyingenvironmental conditions like solvent, temperature, con-centration of monomers, alignment of the aggregates orpressure88–90. More detailed information including sep-aration of homogeneous and inhomogeneous line widthsand femtosecond exciton dynamics can be obtained fromnon-linear 2D spectra73,91. Beside optical spectroscopyof electronic excitations a multitude of various experi-mental techniques is used to characterize aggregates, e.g.electroabsorption92, Fourier transform infrared (FTIR)spectroscopy93, nuclear magnetic resonance NMR94 andRaman spectroscopy95.With optical spectroscopy one probes the structure of

energetic levels in the aggregate and phase relations be-tween corresponding electronic transitions, from whichone can infer the excitation dynamics in the aggregate.This might be a viable way for small systems, where theexciton is delocalized along the aggregate. However, onewould like to follow the dynamics of the exciton also inreal space, that means to measure the time-dependentprobability to find excitation on a certain monomer. Herein particular, diffusion constants are of interest, whichcharacterize the spreading of the exciton after the initialcoherences have died out. Exciton diffusion coefficientscannot be measured directly using existing experimentaltechniques. The indirect methods include quenching ofphotoluminescence96,97, photocurrent response98, tran-sient grating99 and exciton-exciton annihilation100–103.Among the state-of-the-art techniques one could men-tion the recently developed coherent nanoscopy104, whichwould allow for spatial resolution comparable with theexciton diffusion length.

IV. MODELS OF EXCITON DYNAMICS

While the simple electronic model from Section II (seein particular Eq. (5)) already allows us to understand ba-sic properties of molecular aggregates (for instance, theposition of the J-band) it is not sufficient to describe im-portant features such as the narrowing of the J-band (inparticular in contrast to the broad H-band with vibronicstructure). Also, many transport properties, e.g. depen-dence on temperature105, cannot be explained. To thisend it is necessary to include vibrational modes and theinfluence of the environment into the description. Thiscan be done in various ways and there exists a multitudeof theoretical models in the literature where each is best

9

suited for a particular question and/or situation. Forexample, the Forster rate theory24 works well when thetimescale of the transfer is very long compared to deco-herence and vibrational relaxation of the excitation. Inthis Section we review the most common models.

A. Static disorder

Since usually the experiments are performed on en-sembles of aggregates where each aggregate experiencesa slightly different environment, it is common to averageover different “configurations” of the aggregate. Mostoften the influence of the environment is treated simplyas inducing random shifts of the transition frequenciesof the monomers. For early works see e.g.54,106,107. Of-ten, it is assumed that each monomer sees “its own” localenvironment and the shifts induced by this local environ-ment are uncorrelated from the shifts of the neighboringmonomers and disorder of the coupling is ignored. Thisassumption could be called “uncorrelated diagonal disor-der”. Sometimes also the positions or couplings of themonomers are treated as random variables (off-diagonaldisorder)107,108. For each disorder realisation the excitonstates are typically no longer delocalized over the full ag-gregate as in a perfect chain. This localisation becomesstronger for larger values of disorder54,107,109. In the lit-erature, the influence of various forms of correlations hasbeen discussed, see e.g.54,110,111. To account for tem-perature a variant of the open system model describedbelow is adapted112–114, where the environment of thedisordered chain can lead to scattering and relaxationbetween the localized exciton states. Such a model hasbeen successfully used to describe optical and transferproperties of some aggregates113,115,116. In particular atlow temperatures the increase of mobility with increasingtemperature could be explained.In the above formulation the influence of internal vi-

brations of the monomers is neglected. This seems tobe a good approximation for the J-band where one canshow that the electronic excitation is to a large extenddecoupled from vibrational modes55,111,117.

B. Dynamic disorder, Haken-Strobel-Reinekermodel

Fluctuations of the monomer transition frequencies orthe intermolecular couplings that are fast compared tothe exciton transfer time-scale are usually referred to asdynamic disorder. Dynamical fluctuations play a dualrole in exciton transport118–120. In structures with largestatic disorder excitons are localized. Dynamic fluctu-ations in this case remove localization. However, if thefluctuations are strong this results in the dynamical local-ization of the exciton. A seminal model to treat these fastfluctuations is due to Haken, Strobl and Reineker121–123,where the dynamical fluctuations are described by real

stochastic processes, εn(t) and Vnm(t) and modeled usingthe density matrix121 or stochastic Schrodinger124 equa-tions. In the original work the stochastic processes havebeen chosen as white noise, i.e. delta-correlated in time.This model has been shown to capture coherent and inco-herent excitation transfer on the same footing. Moreover,one should notice that the equation describing Haken-Strobel-Reineker (HRS) model for 1D systems is equiva-lent to telegrapher’s equation, which further reflects thesimilarity between the exciton propagation in molecularaggregates and a wave propagation in a medium.The Haken-Strobl-Reineker model, with several exten-

sions, has been utilized to study exciton dynamics in nat-ural and artificial molecular aggregates120,123–127. Thedrawback of this model is that the exciton populationdoes not relax to thermal equilibrium. There have beenmany investigations and extensions which have includedcolored noise and tried to cure the thermalization is-sue, e.g.128,129. The original model also does not in-clude the effect of strongly coupled high frequency modesof the monomers which is essential to describe the vi-bronic structure present in many H-aggregates. The re-cent development of so called quantum state diffusionmethods130,131 can be considered as an extension of theHSR model which cures these deficiencies at the cost ofcolored complex noise.Fig. 11(a) illustrates how the HRS model can be ap-

plied to exciton propagation on a brickstone lattice ofTDBC dyes at ambient conditions124. The second mo-ment of the exciton wavefunction, Fig. 11(b) shows thatthe initial propagation on the time scale of 20 − 30 fsis ballistic or wave-like, which is associated with thequadratic dependence of the second moment on time. Forthe longer timescale the time dependence is linear, whichcharacterizes a diffusive motion.

C. The vibronic model

Let us first consider a single monomer, where only thetwo lowest electronic states are taken into account, seeFig. 2. In the Born-Oppenheimer approximation132 wewrite the nuclear Hamiltonian of the electronic groundand excited states as

Hg/en =

1

2

∑

j

(P 2nj + Ug/e

n (Qnj)) (8)

where Qnj are the (mass-scaled) nuclear coordinates ofmonomer n and Pnj are the corresponding momenta.

Ug/e(Qnj) is the Born-Oppenheimer potential in the elec-tronic ground/excited state (see Fig. 2).Then, for a molecular aggregate the Hamiltonian

in the electronic ground state is given by Hg =(

∑Nn=1 H

gn

)

| gel 〉〈 gel |. We denote by Vnm the transi-

tion dipole-dipole interaction between monomer n andm, which, for simplicity, is taken to be independent of

10

FIG. 11: (a) Time dynamics of exciton wave function on a 2D lattice of TDBC molecules subject to static disorder (linewidthσ = 70meV) and dynamic fluctuations (linewidth Γ = 30meV) of molecular electronic transitions. At time zero the exciton islocalized in the center of the lattice. The contour plots show the population of lattice sites at four different times. (b)Secondmoments of the wave function corresponding to the exciton dynamics shown in (a). Two different transport regimes can be

observed: the ballistic or a wave-like propagation on timescales of 20 − 30 fs (M (2) ∼ t2) and the diffusive motion (M (2) ∼ t)at longer times. Reprinted with permission from Ref.124. Copyright 2012, American Institute of Physics.

nuclear coordinates. The Hamiltonian in the one-excitonmanifold, Eq. (4), is then given by

He =

N∑

n=1

Wn|n 〉〈n |+N∑

n,m=1

Vnm|n 〉〈m |. (9)

with the “collective” Born-Oppenheimer surfaces Wn =

Hen +

∑Nm 6=n H

gm. Note that the structure of Eq. (9) is

very similar to the purely electronic Hamiltonian (5).The only difference is that now the energies ǫn are re-placed by operators for the nuclear motion. Upon trans-fer of excitation the nuclear wavepacket, according toFig. 2, is no longer in its equilibrium position. Thusthe excitation transfer is linked to excitation of nuclearmotion. This vibrational model is sometimes combinedwith the static disorder approach111,133,134. The vibra-tional model offers a clear idea regarding why the J-banddoes not exhibit vibrational structure and the H-banddoes.The coupling to vibrations usually slows down the

propagation of the exciton, however, it can help to over-come energetic barriers caused by differences in the elec-tronic transition energies. In this way efficient directedtransport along a biased chain can be achieved.Often it is justified to approximate the Born-

Oppenheimer potentials, Eq. (8), as harmonic potentialswhere the surface of the electronically excited state is justshifted relative to that of the ground electronic state, i.e.

we have Hgn = 1

2

∑Mj=1(P

2nj + ω2

njQ2nj) and for the ex-

cited electronic state Hen = ǫn+

12

∑Mj=1

(

P 2nj+ω2

nj(Qnj−∆Qnj)

2)

where ǫn denotes the energy difference betweenthe minima of the upper and lower potential energy sur-face and the vibrational frequency of mode j is denotedby ωnj and the shift between the minima of the excitedand ground state harmonic potential is denoted by ∆Qnj .

The potential surfaces are sketched in Fig. 2 for the caseof one mode. This harmonic approximation is widelyemployed in the literature, e.g.46,55,134–138.

D. Open system approaches

Open system approaches are closely related to the vi-bronic model discussed in the previous subsection. Inthese approaches one typically considers an infinite set ofharmonic oscillators forming the bath. It is easy to seethat the Hamiltonian (9) can be written as He = Hsys +Hsys−bath+Hbath withHsys given by the purely electronicpart (5) with transition energies εn that already includestatic overall shifts induced by the environment. Thebath is taken as Hbath =

∑

n Hgn and the system-bath

coupling is described by a linear coupling of the elec-tronic excitation of a monomer to the set of vibrationalmodes, i.e.Hsys−bath =

∑

n |πn 〉〈πm |⊗∑

j κnjQnj . Thecoupling constant κnj describes the coupling of the ex-citation on monomer n to the harmonic oscillator withfrequency ωnj. Typically, the frequency spectrum ofbath oscillators is taken to be continuous so that thecoupling constant becomes a continuous function of fre-quency. The open system approaches have been usedto describe optical and transfer properties of light har-vesting systems139,140 and can also be applied to explainproperties of organic dye aggregates141. We note thatthe HRS model can be considered as a special case of theopen system models for which the bath is Markovian (i.e.memoryless).

11

E. Mixed QM/MM

With the increase of computer capabilities, in recentyears it has become possible to simulate aggregates start-ing from a microscopic description142–145. Since a fullquantum mechanical treatment is still out of reach, oneuses mixed quantum classical approaches. In these ap-proaches usually the nuclei are propagated classically inthe electronic ground state using molecular dynamics.Along these nuclear trajectories one calculates the (time-dependent) transition energies using quantum chemistrymethods. These time-dependent transition energies canthen be used to obtain input parameters for open systemmodels or to use them directly as the energy fluctuationsin HSR model. However, both approaches have theirproblems, since one is restricted to a classical propaga-tion in the electronic ground state.

F. Semi-empirical approach based onpolarizabilities

While the approaches discussed above start from a mi-croscopic description of the exciton-phonon coupling andthe environment, in the semi-empirical approaches onecan take the standpoint that all the relevant informationof the coupling of an electronic transition to other de-grees of freedom is already contained in the shape of theabsorption spectrum. The absorption spectrum in turnis linked to the polarizabilities of the monomers.The induced electric moment of a monomer depends

on the local field at that monomer, which is producedby the electric moments of all the other monomers andthe external field. This leads to a set of coupled equa-tions from which one can extract, for a given arrange-ment of the monomers, the polarizability of the aggregateand thus the optical properties. Such equations havebeen derived using classical treatments10 or quantumapproaches117,146. This method implicitly assumes thatthe frequency dependent polarizability does not change(beside an overall shift in energy) when going from themonomer to the aggregate. Recently, it has been demon-strated that using measured monomer spectra as inputone can accurately describe the band-shape of J- and H-aggregates60,147. This approach also gives an intuitiveexplanation of the vibrational structure and the broad-enings of the absorption bands of the aggregate.

G. Beyond the single-exciton approximation

Photonic device applications may require structuresoperating in a nonlinear response regime, where interac-tions between excitons cannot be neglected. For example,thin J-aggregate films switches based on optical bistabil-ity have been suggested in30. At higher intensities, how-ever, an additional loss-channel – exciton-exciton annihi-lation – appears. The underlying physical process is sim-

Spacer

J-aggregate

Spacer

Ag mirror

λ/2

(a) (b)

Substrate

Distributed

Bragg reflector

FIG. 12: (a) Structure of a planar λ/2 organic microcavitywith a thin layer of J-aggregates embedded. (b) An exampleof a cavity photon and a J-aggregate exciton energy level anti-crossing. Reprinted with permission from Ref.102. Copyright2010 by the American Physical Society.

ilar to the Auger effect, followed by a fast non-radiativeenergy conversion. Within an approximate picture thiscan be viewed as a process by which two excitons local-ized on neighboring molecules are combined into a higher-energy electronic excitation of a single molecule. Then,the resulting excitation quickly decays to the lowest ex-cited state or ground state dissipating the exceeding en-ergy through vibrations. A detailed kinematic model forthe exciton-exciton annihilation in molecular crystals ofdifferent dimensions has been introduced by Suna in148,and a similar master equation approach for exciton anni-hilation dynamics in natural photosynthetic complexeshas been suggested in149. While the microscopic ap-proaches discussed above are still valid, the molecularHamiltonian (5) should be extended to account for atleast two excited states per each monomer38,150.

V. HYBRID EXCITONIC STRUCTURES

In this section we specifically focus on J-aggregates.Their large absorption and fluorescence cross-sectionscombined with a narrow line width and a small Stokesshift allow for a coherent coupling between excitonsand photons in optical cavities or excitons and plasmonmodes in metal structures. This property can be uti-lized as an interface between photonic, plasmonic andexcitonic circuits.

A. Exciton-polariton structures

Most of the studies of strong coupling between exci-tons in J-aggreagtes and photons have been done usingorganic microcavities151–154. A schematic illustration ofan organic microcavity – a planar λ/2 cavity with a J-aggregate layer embedded in it – is shown in Fig. 12(a).Strong coupling of cavity photons with excitons in a J-aggregate result in formation of exciton-polariton modes.

12

This is associated with the splitting of a cavity mode –vacuum Rabi splitting, see Fig. 12(b).Within a simple model assuming only one exciton state

and a single photon mode the value of the Rabi splitting,ΩR, is just

ΩR = ~dX · ~Evac, (10)

where ~dX is the transition dipole of the narrow exciton

transition, ~Evac is the vacuum field in the position wherethe J-aggregate is located, and we assume that the vac-uum field does not vary substantially on the scale of theaggregate. In J-aggregates the value of the exciton tran-sition dipole scales with the number N∗ of coherently

coupled molecules involved as ~dX ∼√N∗. The value

of N∗ is usually much smaller than N - the total num-ber of molecules in the aggregate, since the environmentleads to localisation of the exciton states. The valueof the Rabi splitting observed for J-aggregates stronglycoupled with optical cavities ranges from several tens ofmeV151,152 to several hundreds of meV102,153,154 depend-ing on the disorder present in the aggregate and the de-sign of the cavity. Therefore, the splitting can be ob-served even at room temperatures. The photolumines-cence in these structures is usually observed from thelower polariton branch only, due to fast relaxation of po-laritons. By detunning the frequency of the cavity modefrom the exciton resonance transition one could controlthe mixture of the exciton and photon and therefore mod-ify its coherence properties making it more photon-likeor exciton-like. Electroluminescence from a polaritonmode has been demonstrated using a light-emitting-diodestructure with a J-aggregate layer154. Moreover, lasingfrom exciton-polariton mode has been shown for cavitieswith single anthracene crystals155 and some preliminaryresults were reported on lasing from cavities with cyaninedye J-aggregates156. Large interest has been attracted tothe idea of polariton Bose-Einstein condensation (BEC)in organic cavities. This may bring the rich and con-troversial quantum physics of non-equilibrium polaritoncondensates157–160 observed at low temperatures in inor-ganic systems161–163 up to room temperatures. However,to the best of our knowledge no confirmed observationsof BEC in organic cavities have been reported yet.

B. Plexciton structures

A strong coupling of excitons in molecular aggregateswith plasmons in noble metals has been demonstrated forboth propagating plasmon modes in films164 as well aslocalized modes in various types of nanostructures165,166

and nanostructure arrays167.The hybrid plasmon-excitonmodes were also named plexcitons166. The observed val-ues of the splitting between the plexciton modes are ofthe order of several hundreds of meV. The linewidthof plasmon modes is usually sufficiently larger than thelinewidth of excitons in molecular aggregates (plasmonlifetime is about tens of femtoseconds as compared to pi-cosecond exciton lifetime in J-aggregates). Therefore, theinteraction between the exciton and the plasmon modescan frequently be considered as the coupling of a singlemode (exciton) to a broader continuum (plasmon). Thisresults in the formation of a Fano resonance168,169. It isinteresting to notice that in the case of a strong opticalpumping of plexcitonic structures non-linear Fano effectscan be observed170

VI. CONCLUSIONS

Aggregates of organic molecules – supramolecular as-semblies with strong resonant near-field interactions be-tween electronic transitions – could be exploited in thedesign of nanophotonic devices at the true nanometerscale. The molecules, forming the aggregates, interactcollectively with optical fields, and the absorbed energyis transferred in the form of excitons on a sub-micronscale. The exciton transport within the aggregates pos-sesses coherent properties even at room temperatures,similar to the electromagnetic wave propagation througha medium. Moreover, molecular aggregates can be cou-pled coherently to photonic and plasmonic structures.While at the present stage there is a sufficient gap be-tween the research communities studying excitonics andphotonics, this review calls for merging the knowledgefrom the two fields.

Acknowledgments

The authors thank Gleb Akselrod and Brian Walkerfor providing experimental spectra. We also appreciatecomments from Alex Govorov on hybrid structures. TheHarvard contribution of this work was supported by theDefense Threat Reduction Agency under Contract NoHDTRA1-10-1-0046. S. V. acknowledges support fromthe Center for Excitonics, an Energy Frontier ResearchCenter funded by the U.S. Department of Energy, Of-fice of Science and Office of Basic Energy Sciences un-der Award Number de-sc0001088 as well as support fromthe Defense Advanced Research Projects Agency underaward number N66001-10-1-4060.

∗ Electronic address: saykin@fas.harvard.edu† Electronic address: eisfeld@mpipks-dresden.mpg.de

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