Non-reciprocal Light-harvesting NanoantennaeMade by Nature

Julian Juhi-Lian Ting∗

De-Font Research Institute, Taichung 40344, Taiwan, R.O.C.(Dated: March 26, 2019)

Most of our current understanding of mechanisms of photosynthesis comes from spectroscopy.However, classical definition of radio-antenna can be extended to optical regime to discuss thefunction of light-harvesting antennae. Further to our previously proposed model of a loop antennawe provide several more physical explanations on considering the non-reciprocal properties of thelight harvesters of bacteria. We explained the function of the non-heme iron at the reaction center,and presented reasons for each module of the light harvester being composed of one carotenoid, twoshort α-helical polypeptides and three bacteriochlorophylls; we explained also the toroidal shape ofthe light harvester, the upper bound of the characteristic length of the light harvester, the functionalrole played by the long-lasting spectrometric signal observed, and the photon anti-bunching observed.Based on these analyses, two mechanisms might be used by radiation-durable bacteria, Deinococcusradiodurans; and the non-reciprocity of an archaeon, Haloquadratum walsbyi, are analyzed. Thephysical lessons involved are useful for designing artificial light harvesters, optical sensors, wirelesspower chargers, passive super-Planckian heat radiators, photocatalytic hydrogen generators, andradiation protective cloaks. In particular it can predict what kind of particles should be used toseparate sunlight into a photovoltaically and thermally useful range to enhance the efficiency ofsolar cells.

I. INTRODUCTION

There are three plus one types of photo-autotrophson earth, i.e. plants, algae and bacteria plus archaea.Archaea use a photosynthetic mechanism quite differentfrom the others. The photosynthesis units of plants andalgae are much more complicate than bacteria, whichis a subject traditionally studied by chemists and bio-chemists [1, 2]. A major task in this field was tryingto understand the molecular structures. Because of theinadequate instrumental resolution, people struggled fordecades to know the structure of the light-harvesting an-tenna. Without precise structures, investigators tried toguess the content within the black box.

Since about 1995, satisfactory pictures of the bacte-rial light-harvesting (LH) systems have been obtained [3].Both the inner antenna (LH1) and the outer antenna(LH2) have a toroidal shape and are composed of thesame modules. Each module contains one carotenoid twoshort α-helical polypeptides, and three bacteriochloro-phylls. The exact numbers of modules involved forboth complexes are variable, as shown in Table I. Theouter antenna, LH2, is smaller and consists of nineunits for Rhodopseudomonas acidophila (1NKZ) [4] ; theinner antenna, LH1, is larger, as it contains the re-action center (RC), and has 17 units, for Blastochlo-ris viridis (6ET5) [5]. The exact dimension of eachmolecule can be read by software such as Jmol or Py-MOL from a .cif or .pdb files in the PDB (protein databank http://www.rcsb.org/pdb/). Symmetries are no-tably unaltered even under strained conditions for LH3,i.e., a variant of LH2 [6], which indicate their importance.

∗ http://amazon.com/author/julianting; juhilian@gmail.com

protein PDB ID symmetry cartoon

LH1-RC from Blastochloris viridis[5]

6ET5 C17

LH1-RC from Rhodopseudomonaspalustris [11]

1PYH C2

LH2 B800-850 from Rhodopseu-domonas acidophila [4]

1NKZ C9

LH2 B800-850 from Rhodospirillummolischianum [12]

1LGH C8

TABLE I. Various light harvesters with structural symmetry.

Two further subtleties in the structure of LH1 are im-portant. First, the RC contained in the LH1 has a non-heme iron. Second, for some species the ring of the LH1-RC complex has an opening, perhaps with a polypeptidetermed PufX or W present over that region [7, 8].

Molecular data show that photosystems I/II of algaeand plants likely evolved from the photosystems of green-sulfur bacteria; there are hence many analogous functionsand similar structures, except with more sophisticatedmaterial such as not only non-heme iron but even man-ganese (Mn) are presented at their RC [9, 10].

On the other hand, we do not know much aboutthe structure of archaea photosynthetic unit yet, whichwere classified as separate to bacteria only in the 1970s.

arX

iv:1

702.

0667

1v4

[ph

ysic

s.bi

o-ph

] 2

4 M

ar 2

019

2

Amongst them Haloquadratum walsbyi (Hqr. in genus ab-breviation) inhabiting in hypersaline environments wasdiscovered by Anthony Walsby in 1980 [13, 14]. It growsby using simple carbon-containing compounds leakedfrom other microbes in the salty lakes as energy sources,but can also convert light into usable energy. Its cell,which is the basic photosynthetic unit in compare to theLH of bacteria, is square-like shape with sharp cornersand edges measure about 2− 5 µm while its thickness isonly around 0.1 − 0.2 µm, unlike the spherical or cylin-drical shape of many other organisms, with a cross-shapedark line on its surface. The cell wall consists of bacteri-orhodopsin and surface layer (S-layer) glycoproteins [15].

Several kinds of bacteriorhodopsin have been analyzedwith x-ray crystallography. 5ITE, 5ITC, 5KKH, and4QI1 are in trimeric form, whereas 4QID, 4WAV are indimeric form. They occupy up to 50% area of the cellsurface of the archaea. These bacteriorhodopsins forma hexagonal lattice composed of three identical proteinchains, each rotated by 120 degrees relative to the oth-ers. They are used as light-gated proton pump to con-vert captured solar energy into ATP, which is differentfrom all other phototrophic systems in bacteria, algae,and plants that use chlorophylls or bacteriochlorophylls.Three alternative bacteriorhodopsins carry out photosyn-thetic growth; two are proton pumps and the other is achloride pump. The absorption spectrum has a peak ataround 568 nm, which is at the green light range and witha photon energy of about 2.18 eV in vacuum [16, 17]. Ac-cordingly to Walsby, the shape of the cell is determinedby the pattern in which the cell envelope particles assem-bled.

Even after a knowledge of the structure, questions re-main. Why has a light harvester of bacteria the form ofa tambourine-like shape instead of a spherical shape or aserpentine shape, for instance? Is the number of modulesinvolved important? What does these numbers implied?Why does each module contains one carotenoid two shortα-helical polypeptides, and three bacteriochlorophylls?Are these numbers important? Why is the surface areato volume ratio of Hqr. so large? Is the characteristiclength of the cell important? Could we grow a largercell? How and why does the cell had a square shape?

The standard explanations for photosynthesis are givenin terms of chemistry [1, 2], partly because the methodused to study the paths and time scales of transfer of exci-tation energy is, in general, spectrometry. There are fewphysical explanations, as defined by Gruner et al. [18];people tried to mimic the nature from chemical points ofview. For instances, Harriman proposed an artificial lightharvester design at molecular level based upon chemicalrequirements [19]. A theoretical energy model is con-structed and calibrated against spectroscopic data [20],which is more or less a kind of data fitting. We tried toincorporate structural information in a model by calcu-lating a simplified LH1 model based upon the chemicalrate equations for the shape acquired, but advanced nofurther than others [21].

a=9.2nm

(a)

a=9.2nm

(b)

FIG. 1. Antennae of two simplified shapes. (a) is called a(split-ring) loop antenna whereas (b) is called a loop antennawith line feed. The radius marked is a typical average of innerdiameter and outer diameter measured. Although resemblingthe special pair in the RC, the feed line modifies the resonantfrequency only slightly. To adjust the resonance frequency,the opening can be filled with other dielectric.

But physical explanations are possible as we extendedclassical definition of radio-antenna to optical regime [22,23]. In two previous papers, we explained the reasons for

• the function of the notch at the light harvester,

• the function of the PufX/W presented at the notch,

• the function of the special pair,

• the dimerization mechanism under intensive light,

• the shape of the light harvester must not be spheri-cal and the cross section of the light harvester mustnot be circular,

• the use of dielectrics instead of conductors to makethe light harvester,

• a mechanism to prevent damage from excess sun-light,

• a mechanism to achieve dual-band radiation spec-trum, and

• reasons for the modular design of the light har-vester.

In the present paper, we consider the non-reciprocity ofthe bacteria light-harvesting antennae, which can furtherexplain the function of the non-heme iron at the reactioncenter, the toroidal shape of the light harvester, somespectrometric observations and much more. After ana-lyzing its reciprocity we extend our analysis to archaea insection IV, and list out some possible applications alongwith two interpretations for a radio durable bacteria insection V. We begin with a review of the loop antennamodel:

3

II. LOOP ANTENNAE

How should we model the light harvester? We wantthe simplest model which captures all, if possible, essen-tial future instead of including every atoms. But whatare the essential details of the light harvester that wecannot ignore? The most important parameter of an an-tenna is its geometry; the material properties are imma-terial. The ring shape is apparently one of the essentialfutures. Symmetry as indicated is part of that. Therehave indeed such shaped antennae considered in classicalradio frequency antenna theories. Figure 1 (a) is typicallysolved analytically, whereas figure 1 (b), although resem-bling LH1 better, has a resonant frequency only slightlymodified from that of figure 1 (a). We hence consideronly figure 1 (a). The notch is essential for LH1, as thereceived energy must be taken from some point. TheRhodopseudomonas palustris molecule (1PYH), shown inthe table, clearly also has a notch; while the opening forBlastochloris viridis (6ET5) is less obvious. The open-ing can be filled with other material to adjust the reso-nant frequency in engineering [24], for which purpose apolypeptide called PufX/W is present in LH1 [25]. Thephysical origins of PufX/W and of the notch differ; onedoes not imply the other.

Loop antennae are classified into two categories: If theantenna has a radius larger than the wavelength of oper-ation, it is called a resonant-loop antenna; otherwise it iscalled a small-loop antenna [26]. Because the length scaleof free radiation, 850 nm, is much larger than the charac-teristic size of the antenna, 9.2 nm, the light-harvestingantennae belong to the category of small-loop antennae,which have small radiation resistances than their loss re-sistances and serve mainly as receivers. Similar argu-ments lead to the small cross-section for the generation ofexcitons which is a fundamental process for solar energyconversion. Such dimension is also much smaller thanthe thermal wavelength, ~c/kBT ≈ 7.5 µm at room tem-perature, hence fulfill the requirement of super-Planckianradiation [27]. A small-loop antenna is equivalent to aninfinitesimal magnetic dipole whose axis is perpendicularto the plane of the loop [28].

To arrive at the electromagnetic properties of such anantenna there are a simple way and a complete way. Webegin with the complete way.

Let the radius of the loop located at the origin be a,and the plane of the loop be x − y; let the angle fromthe x−axis be φ. If current I around the loop is uniformand in phase, the only component of the vector potentialis Aφ, as shown in Figure 2 (a). The infinitesimal valueof Aφ at a point distant r away from the loop caused bytwo diametrically opposed infinitesimal dipoles is

dAφ =µdM

4πr, (1)

in which dM = 2j[I]a cosφ[sin(2πa cosφ sin θ/λ)] dφ, θis the angle relative to the vertical axis through the cen-ter of the loop, and [I] = I0 exp {jω[t− (r/c)]} is the

To observer P

in xz plane

(a)

4

Square

Loop

(b)

FIG. 2. The coordinate system uses.

retarded current on the loop with I0 being its maximumvalue. After integration we obtain

Aφ =jµ[I]a

2rJ1(

2πa sin θ

λ) , (2)

in which J1 is a Bessel function of first order.We consider the far-field effects as the source of sun-

light is remote. The far electric field of the loop has onlya φ-component Eφ = −jωAφ that is in the plane of theloop. Therefore,

Eφ =120π2a[I]

λrJ1(

2πa sin θ

λ) . (3)

The corresponding magnetic field in free space reads

Hθ =πa[I]

λrJ1(

2πa sin θ

λ) . (4)

Four short linear dipoles suffice to approximate theloop whilst still preserving the symmetry of the problem,which is the second method.

Let the length of the dipoles be d, and the area of theantenna, which is commonly called the aperture of theantenna, be A, as shown in Figure 2 (b). Hence

d2 = πa2 ≡ A (5)

At the far field

Eφ =120π2[I] sin θ

r

A

λ2. (6)

A/λ2 is called the dimensionless aperture. The magneticfield is obtained on dividing by the intrinsic impedanceof the medium, i.e.

Hθ =Eφ

120π=π[I] sin θ

r

A

λ2(7)

in a vacuum. Eq. (7) is a special case of Eq. (4), justas Eq. (6) is a special case of Eq. (3), as for smallarguments, J1(x) ≈ x/2.

4

The (radiation or receiving) resistance at the loop ter-minals can be obtained from

P =I202R (8)

in which I0 is the maximum current on the loop and Ris the resistance. Integrating the Poynting vector

S =1

2|H|2 ReZ (9)

over a large sphere, in which Z is the impedance of themedium, the total power, P , is obtained. The resistancefor a small-loop antenna is therefore proportional to 1/λ4.

The analyses above are direct consequences ofMaxwell’s equations (in vacuum) that imply no restric-tion on the range of frequency applicable [29]. Symmetrybreaking of the electric field in space facilitates the an-tenna to radiate [30], which is the third reason for theopening at the LH1-RC complex and explaining the non-circular shape of the cross section observed. We did notassume material property, such as polarizabilities, unlikeprevious authors [31]. Penetration depth is not an issue,as people working in optical nanoantennae considered,because the wire of our idealized antnnae is infinitesi-mally thin [32]. An experiment is proposed based uponthe above analyses [22].

III. NON-RECIPROCAL ANTENNAE

A regular antenna both receives and emits, becauseMaxwell’s equations are symmetric with respect to timereversal [33], but a light harvester that functions solelyas a receiver must receive much better than it emits.What we seek is more than an antenna working withdiodes, which is artificial and is known as rectenna since1960s [34], but an optical counterpart of a duckbill checkvalve in fluid dynamics, which is a naturally designedpassive device that exists in a human heart.

As no modal or polarization properties of sunlight areknown, we require mechanisms to break the (Lorentz)time-reversal symmetry [35]. There are several possibili-ties to make such an optical check valve:

• Faraday rotator [36, 37];

• duplexer [38–40];

• nonlinearity (metamaterial) [41–46]; and

• anapole (toroidal dipole) [47, 48].

All four mechanisms are well known to the scientific andengineering communities.

• The first mechanism, gyrotropic materials whichuse Faraday effect, requires an externally ap-plied magnetic field. All LH1-RC complexes areequipped with a non-heme iron at the RC, whichcould provide the required field. The iron is not

bound to any protein and can be exchanged withzinc (Zn2+) or manganese (Mn2+), just like a pearlin a mussel’s mouth that chemists call ”coordi-nated” [49]. The promising perovskite material forsolar cells also have a lead ion (Pb2+) at its cen-ter [50]. The role played by the non-heme ironhas long been questioned, if not unknown to bio-chemists [51]. Biologists know that it serves as asource or sink of electrons during electron transferor redox (reduction-oxidation) chemistry [52], with-out recognizing the implication of magnetic fields.The fact that the non-heme iron can be exchangedconfirms our prediction about the role played bythe iron. The effect is, however, typically smalland decreases proportionally to the inverse squareof the wavelength in an organic material, althoughthere are isolated reports of large Faraday rota-tion [53, 54].

• Duplexer (or multiplexer) is the term used in com-munication engineering, whereas physicists use thedescriptor time-dependent material and its com-mon name is switch, which might function togetherwith other mechanisms, in particular the afore-mentioned Faraday effect. Biochemists know that,when a (bacterio)chlorophyll pigment absorbs light,it loses an electron to the RC, which already signi-fies duplexing [2]; when the RC received an elec-tron its Fe3+ becomes Fe2+ with the magnetismchanged. Although the magnetic field generatedby Fe3+ is tiny, the subtlety of a switch is that asmall change can control an entire device; in pho-tosynthesis it can lock the incoming electron. Theinternal states of the non-heme iron at the RC canserve to control the direction of the light propaga-tion [55].

In terms of mechanics, the photon received mightcause the α-helical polypeptides/ carotenoid/ bac-teriochlorophyll complex to alter its shape or ori-entation, hence rendering impracticable the flowof the electromagnetic wave in the other direction.Theorists have previously remarked that the FMOcomplex might work as a rectifier for unidirectionalenergy flow without specifying how that action pro-ceeds [56]. Such conformation change is also ob-served in retinal molecules [57]. With this mecha-nism the near unity quantum efficiency of conver-sion is not peculiar because the electron has beenlocked in [58].

The wave-like energy transfer or the coherence atroom temperature observed by previous authorssimply signifies a collective motion (mechanicalmovement) instead of quantum coherence [59], aslight at this wavelength, relative to the size of theantenna, would be better considered as wave in-stead of particle; as the authors also reached similarconclusion latter [60]. The functional role played bythe persistent spectrometric signal observed simply

5

mean duplexing as discussed here. The bacteri-ochlorophylls move in unison with the light wave asseaweed moves with the tides. A recent finding ofphoton anti-bunching from LH supports such a sce-nario, although no further reason for the physics be-hind conformational change was provided [61, 62].

Current methods of imaging with a microscope notonly are limited by the wavelength used but also re-quire harsh conditions or direct mechanical interac-tion with the samples, hence becoming inappropri-ate for living cells. Cyro-electron microscopy cancertainly be employed [63]. A newly invented imag-ing method using phonons (acoustic waves) of sub-optical wavelength or a photonic crystal-enhancedmicroscope might enable one to observe the routethat a photon takes on entering and leaving LH, todiscover how the LH alters its conformation [64, 65].

• Thirdly, matamaterial are using sub-wavelengthstructure, in particular a notched ring [66], toachieve non-reciprocity, of which the most notice-able future is chirality. Ullah et al. use asymmet-ric particles to achieve chirality of their nanoan-tenna [67], while each module of the bacteria lightharvester composed of one carotenoid two short α-helical polypeptides, and three bacteriochlorophyllsto achieve chirality. If the notched ring is further di-vided into sub-units the interleaving inductors willguide the flow of displacement current better [68].

• The shape of the light harvesters is toroidal as re-quired for anapole radiation. Toroidal structurescan support exotic high-frequency electromagneticexcitations that are neither electric nor magneticmultipoles, called toroidal moments, which can en-hance inter-molecular interaction and energy trans-fer.

The above statements have not excluded a sphericalshape, which occurs on evoking the Poincare-Brouwertheorem [69]. This theorem was originally proven byPoincare and is sometimes called the hairy-ball theorem;it states that there exists at least one point on the surfaceof a sphere at which vectors of electric and magnetic fieldsbecome equal to zero. The Poynting vector is also zeroat this point. This theorem indicates a toroidal shape in-stead of a spherical circulator, which is the second lessonfrom nature about solar light harvesting mentioned byprevious authors [70] and is consistent with the require-ment of anapole radiation, but is not honoured in manydesigns of bio-inspired optical antennae [71]. The non-spherical requirement is depicted not only at the scalefor the light-harvesting complex discussed but also ona larger scale as in chromatophores [72], although thelater authors describe the shape of the chromatophoresof Rhodobacter sphaeroides as spherical in their abstractbut as vesicles later in the content of their paper.

IV. NON-RECIPROCITY OF HQR.

It is natural to ask whether the proposed mechanismscould be equally applicable to archaea? The answershould be affirmative because anything that mediates be-tween an electromagnetic field and a final sink of the en-ergy can be considered as an antenna; the only differenceis their performance. There are two other hints indicat-ing that the antenna theory is applicable:

• Recently optical antennae configuration with four-fold (C4v) symmetry, a cross-shape antenna con-sisting of two perpendicular dipole antennae witha common feed gap, has been considered [73].

• When the cells grow and divide, they do not alwaysseparate from each other, and form two dimen-sional arrays of ten or more units like un-separatedpostage stamps.

The cross-shape dark lines on the surface of Hqr. confirmthe first point, while our previously proposed physicalmechanism for the bacteria light harvester to coalesceseems to confirm the second point [22]. The cross-shapeantenna if made from gold with complex permittivity ε =−26.64 + 1.66i and illuminated with 800 nm circularlypolarized light will have best performance at a side lengtharound 170 nm [73]. This is close to our requirement thatHqr. can survive under UV frequency. The question ishow? And, is it a good antenna? What kind of designdoes the nature employed to increase the light-harvestingefficiency? The key to uncover the answer should still inits non-reciprocity.

The light harvesting unit larger than the bacteri-orhodopsin is the whole cell for this microbe, unlike thebacteria had light harvesters LH1/LH2 inside its cell.There is no reaction center, and no ion at the reac-tion center, which appears in bacteria light harvestersand is responsible for making the light harvesters non-reciprocal. But the physics still requires a mechanism tomake the antenna non-reciprocal.

How could the cell makes the antenna non-reciprocal aspreviously proposed? The nonlinearity mechanism pro-posed seems to be able to serve this purpose:

• Mahmoud et al. proposed to manufacture a non-reciprocal artificial metastructure by divide its sur-face into nano-cells with neighbouring areas in dis-parate chirality [42]. The cross shape appears onthe cell wall divide the square into four smallersquares.

• Some bacteriorhodopsins might form modules tocreate chirality [67].

• Since there have been at least two types of bacteri-orhodopsin discovered, they might also have differ-ent chirality and located at different division of thecell-wall of the archaea, i.e. the trimer might havechirality while the dimer not.

6

These three points indicate that Hqr. is a naturally exist-ing metamaterial [74], a material that owes its propertiesto a sub-wavelength structure rather than to its chem-ical composition [75]. The bacteriorhodopsin structuresanalyzed so far are all obtained under non-physiologicalconditions that have mixed the molecules.

We hence need a study of the structure of Hqr. in situ,which can be done using a cryo-electron (transmission)microscope, and which involves a series of experimen-tal steps followed by some software analysis that doesnot require the sample to be crystalized and is particularsuitable for biological molecules.

Because Hqr. is very thin, it can be accommodatedwithin a slice of the sample prepared, and cool downrapidly by plunge-freezing to be embedded in amorphousice [76]. A bacteriorhodopsin structure, 1BRD, has beensolved using cryo-electron microscope [77], with a resolu-tion of 3.5 A in a direction parallel to the membraneplane but lower than this in the perpendicular direc-tion. A single-particle cryo-electron microscope coversfrom particles of mass 20 kDa up to several megadal-tons [78]. The larger is the molecule, the better is theimage after averaging. The images obtained can be ana-lyzed by SPIDER or RELION [79]. The software will firstsort the two-dimensional images into classes accordingto their orientation then reconstruct a three-dimensionalstructure.

V. APPLICATION

As the geometry is known, we interpret its physicalmechanisms that might be useful for the design and pro-duction of artificial light-harvesting systems [70, 80, 81],optical sensors, wireless power chargers, passive heat ra-diators, and photocatalytic hydrogen generators:

• An immediate application is to predict what kindof particles should be use to separate sunlight intoa photovoltaic useful range and thermally usefulrange to enhance the efficiency of solar cells [82, 83].The nanoparticles that Hjerrild et al. consid-ered are disk-shaped metallic particles of diame-ter roughly 100 nm, which exploit plasmon reso-nances. We have shown that the optimal shapeof the particles should be toroidal instead of dis-cotic (or nanorods for the infrared range). Hjerrildet al. attributed the geometry dependence to therole of dipole moments in the plasmon resonance,while we have shown geometry is itself important.They wrote that, to avoid scattering, the size of theparticles should be limited to 50 nm, whereas thenaturally designed light harvester that we consid-ered has a size about 10 nm. They further pointedout that silver is the best material to use, but thatis quite expensive. They considered the materialused to be important for the frequencies of absorp-tion, and mentioned that the ratio of surface to

volume of these nanoparticles makes the particlessusceptible to damage from high power. Such argu-ments are generally based upon the band-gap the-ory [84]. But that is for the case of single atom.For bulk material time-lag (spatial dispersion) be-tween atoms become important. Hence we came tothe world of nanoantennae. Our work shows thata dielectric can be used to avoid such high-powerdamage, which is actually the best material at ascale of 10 nm, and that the frequency of absorp-tion can be tailored with the radius of the toroidalparticle [23]. As those authors coated their metal-lic disk with dielectric, there is no need for a metalat all. Such nano-particles are also directly used insolar cells for light trapping [85].

• Secondly, we can make optical sensors which are de-vices that must interact with light strongly. (Bac-terio)rhodopsin and (bacterio)chlorophyll are twomolecules in biology that can serve this purpose.Most animals use rhodopsin, while most plantsand bacteria use chlorophyll, except archaea. Asa receiver nanoantennae concentrate light fromfar-field, enlarging the effective cross section ofmolecules. Most bio-mimetic or bio-inspired op-tical sensors are related to animals [86]. Plant andvirus which surely come to the earth earlier thananimals are not discussed yet.

• Wireless power transfers, presently, works notonly under microwave frequencies, if not radiofrequencies, but also only under designed (non-physiological) condition [87–89]. They are at mostseparable transformers, whose coils are not consid-ered as antennae. However, medical applicationsrequire the power chargers to work under flexiblephysiological condition [88]. The next generationwireless power transfer based upon our design prin-ciples will use incoherent light as the nature use,which is sustainable, renewable, and working un-der physiological condition.

• Thermodynamics told us that there are three typesof heat transfer, i.e., conduction, convection, andradiation. There are situations we have to rely onradiative cooling, such as devices operate in vac-uum and fanless notebook computers. Radiation isa kind of electromagnetic wave. If a system emitsmore electromagnetic waves than it absorbs, it willbe cooled down. Heat radiators normally operatewith wavelength between 0.1 to 100 µm [90].

There are two kinds of radiative heat transfer the-ory discussed in the literature. The near-field en-ergy transmission, correspond to the Forster effectin the photosynthesis community, contains photontunneling other than wave interference when theseparation distance is less than the thermal wave-length [91]. Such energy transfer is important inphotosynthesis because the light received by LH2

7

needs to find an LH1 to reach the RC and the en-ergy need to migrate from module to module withinthe antenna to the RC, but is of less importancein radiative-cooling because every radiator, whichis equivalent to LH2, can function independently.On the other hand, the far-field effects are gener-ally considered using Mie theory, which describethe particles only as spheres [92, 93]. The radiator,according to the nature design of light harvester,radiate more than Planck’s law predicted becauseits characteristic length is smaller than the thermalwavelength [94].

• It can also enhance the efficiency photocatalytic hy-drogen generation [95].

• Radiation protective cloaks [96]: Deinococcus ra-diodurans that is one of the most radiation-resistantorganisms known, apparently uses two passivemechanisms, other than active DNA repair nor-mally attributed, discussed above [97]. Each cellhas two perpendicular furrows that result in atetrad morphology, which closely resembles Hqr.Cells of dimer, tetramer and even multimer mor-phologies can also be obtained. Such a mechanismhas been discussed as forming electromagnetic mul-tipoles to diminish the excess radiation [22]. ItsS-layer is a nature made metamaterial.

VI. SUMMARY

In this perspective, we sought physical interpreta-tions/mechanisms to consider a light-harvesting antennaas a device to receive electromagnetic waves. Althoughtheories for light-harvesting in photosynthesis based onclassical electrodynamics have been proposed and appliedbefore [31, 98], antenna theory has never been used to ex-plain light harvesters, even though they have been calledantennae for decades [99]. A major theme of the presentperspective is that the geometry is more important thanthe material property, which is consistent with what hasbeen found for metamaterials, even though our startingpoint is antenna theory. We have shown in this paperthat nature uses a metamaterial design in several places.

Our model from classical electrodynamics has thestructural information enforced. We thereby provide ex-planations for

1. the function of the notch,

2. the function of PufX/W,

3. the function of the special pair,

4. the function of the non-heme iron at the LH1-RCcomplex,

5. the shape of the LH must not be spherical,6. the cross section of the light harvester must not be

circular,

7. preferring a toroidal shape,

8. an upper-bound for the characteristic length of anefficient light harvester,

9. the usage of dielectric as an antenna,

10. a mechanism to prevent damages from excess sun-light,

11. the dimerization mechanism under intensive light,

12. a mechanism to achieve dual-band radiation spec-trum,

13. the wave-like energy transfer observed,

14. the physics behind photon anti-bunching,

15. reasons for the modular design of the light har-vester, and

16. the reason why each module of the light harvesteris composed of one carotenoid two short α-helicalpolypeptides, and three bacteriochlorophylls.

We have discovered also the number of modules involvedin each light harvester can be explained by the languageof fractal [100]. The connectivity matrix thus derivedis what we obtained years ago from chemical rate equa-tions [21]. We show that not only chemistry but alsophysics illuminate the problem of photosynthesis.

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