This paper reviews the work of my group over the last 20 years on the role of chirality in second-order nonlinear optics of molecular systems and new developments linking my research to magneto-optics and organic magnetism.
©2011 Optical Society of America
Ever since Francis Fukuyama published in 1992 the now famous book “The End of History and the Last Man” - based upon his 1989 essay in National Interest - tumultuous historical events have changed the modern world unrecognizably . This reminds me of those scientists in late 19th century who saw the end of science approaching, with only some small unresolved problems, such as black body radiation. Then in the first decades of the 20th century the new ideas about space and time and the rise of quantum physics overthrew all these feelings of the end of science and changed our scientific understanding of nature beyond recognition. It now appears that the Theory of Everything has to wait for - at least - another century…
Looking to the field of optics, the science of light, such an emergence of revolutionary changes is again striking. Mid 20th century the science of optics was well developed but was considered by many as not very exciting - few academic institutions worldwide had programs in optical sciences. Optics was often seen as an applied science of lenses and mirrors, of photography. But, 50 years ago, the laser came - a new source of light, coherent and intense, created by scientists. Over an extremely short period the properties of this laser light were used to develop new methods, techniques, devices… and companies, while young and bright students were flocking together in “laser-labs”. Central in these new developments was the recognition of the important role of materials, henceforth called optical materials, inviting many chemists to enter new innovative research on synthesis of new materials. Many of these new materials – and the research is now going on at an unabated pace - offer the stage for the photons to realize their full possibilities, and are basic to the new field of photonics.
I would preferably call this review a memoir since this paper will not give an exhaustive enumeration of all papers and relevant references but rather an indication of the important papers, previous papers inspiring us, the ideas generated, and results, some of them still poorly understood. It will be a memoir for me, looking back to all these bright associates, many of them now involved as professors, researchers, and business people, in the thriving field of photonics. Moreover, an extensive review has already been given elsewhere [2,3]. And rather than giving lists of references to papers and journals I prefer to indicate the names of the scientists involved. Indeed these days it is easy and straightforward to go to the Web of Science with their names – Author Finder – to obtain all information (sometimes surprising!) about the work/author(s) mentioned.
2. Non-linear optics – second order 
Here I give a short overview of second-order nonlinear optics as developed since the seminal, spotless paper of Peter Franken  and associates at the University of Michigan in 1961, hardly a year after the pulse ruby laser – then still called the optical maser – developed by Maiman . Peter Franken realized early the potential for generation of optical harmonics with this new intense light source which produces very large fields with focused pulses. At such field strengths, approaching interatomic field strengths, the (dielectric) polarization of a material is no longer linear with the electric field but we have to consider for the polarization a series expansion in the electric field - I entered the field of nonlinear optics from nonlinear dielectrics , my first encounter with David Buckingham :
The stringent requirement of noncentrosymmetry attracted the attention of chemists since they have easy access to noncentrosymmetric molecules and the polarizabilities of molecules were very well known. Since the polarizability of molecules is due to electrons molecules may present some advantages over the ionic polarizability of crystalline systems. So we saw in the 70’s of the previous century the emergence of a new field, partially grown out from dielectrics, investigating the nonlinear properties of molecules, polymers and molecular systems, the still thriving field of organic nonlinear optics .
On a microscopic, molecular level we write Eq. (1) as:
To develop nonlinear optical materials from these molecules the challenge was to organize the molecules in a noncentrosymmetric macroscopic arrangement to obtain a second-order susceptibility. The method of choice became the attachment of the molecules to a polymer chain – the nonlinear optical polymers – and the use of electric field poling of spin-coated films of these polymers on a solid substrate [10–12]. In this poling technique the film is heated above the glass transition temperature and a strong electric field orients the polar molecules in the polymer matrix. Subsequent cooling below the glass transition temperature, in the field, will freeze in this orientation and films are obtained with the required noncentrosymmetry (C∞v). These films have the drawback of being thermodynamically unstable and they tend to return to their isotropic state over time. A tremendous amount of research in this field has culminated in the development of stable, very fast electro-optical modulators by Larry Dalton and Alex Jen, who were able to develop synthetic methods for optical polymers with exceptional stability [13,14].
To summarize the problems encountered in organic nonlinear optics, we need materials, preferentially films for integrated optics, which should have a stable noncentrosymmetric structure, and if we are looking for materials for second harmonic generation then issues of phase matching become important.
These were the problems we discussed in our group beginning of the 90’s and in, often heated, discussions with the groups of Jean-Luc Bredas (then at Mons University), Bert Meijer (TUE), Roeland Nolte (University of Nijmegen), François Kajzar (then CEA), David Reinhoudt (TUT), Jo Zyss (then at CNET, Paris) – we even discussed spelling of words - Seth Marder (then at Caltech)… and out of these discussions slowly emerged the need of a thorough investigation of the basic requirements for nonlinear optical materials.
Strongly influenced by our Dutch colleagues we started focusing on the symmetry of chiral molecules. Such molecules comes in two mirror forms and show optical activity, e.g. polarization rotation and circular dichroism arising from the different interaction with left- and right-handed circular polarized light for the two enantiomers, the signature of their lack of reflection symmetry. Chiral molecules and chirality have been a central topic in chemistry research ever since Pasteur in 1849 linked the optical rotation to the presence of two mirror forms of tartaric acid, a molecule he isolated from wine lees – Pasteur was French. He showed that the chemically synthesized tartaric acid, an equal mixture of the two enantiomers, the racemic mixture, has no optical activity. The book of Laurence Barron is a beautiful introduction, and more, to the field of chirality  while Aklhlesh Lakhtakia gave a marvelous overview on the field of natural optical activity . Most important for us was the fact that these properties are observed in isotropic chiral materials. And since chiral molecules are noncentrosymmetric by necessity they should show second-order nonlinear optical response. Symmetry properties of molecules were described by Giordmaine where we could find that the susceptibility of chiral molecules with their lack of reflection symmetry had nonvanishing components . Most interesting to us was the experimental confirmation by Peter Rentzepis of sum-frequency generation (second harmonic is prohibited by permutation symmetry) in a solution – isotropic - of enantiomers of arabinose, a chiral sugar – unfortunately we could not reproduce the experiment .
Of great importance to motivate us further into research of chirality was the paper published by Janice Hicks and associates and showing convincingly the existence of optical acitivity in nonlinear optics . In a first approach we investigated biological systems , with their inherent chirality. However, after some discussion, we decided to investigate second-harmonic generation from thin molecular films of well-defined chiral polymers, abundantly available from Bert Meijer’s group in Eindhoven. Very thin films of such polymers could easily be made by Langmuir-Blodgett (LB) techniques, a technique which was well established in our group. Moreover, the thinness of the films would avoid problems with polarization effects due to the linear light propagation and the nonlinear response could be directly related to the components of the nonlinear susceptibility tensor. Also, considering the very thin film as a merely chiral surface we were adding the required noncentrosymmetry to have a second harmonic signal and we could obtain, in principle, the value of all components.
As our first polymer film we investigated a LB-film of a chiral polyisocyanide provided by Roeland Nolte from Nijmegen [21–23]. For the experiments a relatively simple set-up used a pulsed Nd-YAG laser, the workhorse of nonlinear optics in those days. The results obtained confronted us quickly with the fact that the basic noncentrosymmetry requirement actually should be stated, in a correct reading, as a requirement in the “electric-dipole approximation” where the interaction Hamiltonian between matter and electromagnetic field is described by:15].
For the nonlinear polarization we wrote now:
The results obtained from our investigation of SHG of the polyisocyanide LB-films clearly showed circular difference effects for the four measured, s- and p-polarized, reflected and transmitted (very thin films) second harmonic fields. Even more important was the fact that the SHG intensity pattern as function of the polarization of the fundamental beam could not be explained without invoking the xyz term of χeee, the chirality component in the electric dipole interaction, ànd the absolute need to invoke χeem components, being about 10% of the largest electric-dipole allowed term. These were very pleasing days when we saw chirality expressed in full in our measurements and magneto-optics entering our studies of organic nonlinear optics.
When discussing these exciting results we used extensively, and intuitively, the model of a left- or right-handed screw describing a chiral molecule spurred by the screwish, helical conformation of the polyisocyanide polymer. After all a box of, e.g. left-handed screws remains left-handed, whatever the distribution is. This helical model focused our thinking on the physical aspects of optical activity seeing the role of electric and magnetic dipoles, their phase relations, the importance of reflection symmetries… Amusingly, our simple figure of such a helical model was a great success at presentations and several colleagues asked me to send this illustration, see Fig. 1 .
An intuitive view of (the optical activity in) a helical molecule:The polarization and magnetization induced by the incoming field, forcing the electron to move in a helical path, are both the source of radiation with a field parallel with the electric dipole and a field perpendicular to the magnetic dipole - the beauty of Maxwell’s equations! Simply summing these vectors we obtain a rotation of the plane of polarization. This model indicates very clearly the essential role of magnetic effects in optical activity, the change of handedness changing only the sign of optical rotation, the phase relations between electric and magnetic effects… Later we analyzed with Jeff Maki this model more in depth and calculated the one-electron second-order optical activity of a helix .
Later we analyzed an 18 layer-film (thickness 35 nm) of a nonlinear polyisocyanide mixed with poly(-S-l-acetoxymethylethylisocyanide) . The results showed that the nonlinear response was determined largely by the zzz, zxx, and xxz components of the electric-dipole tensor. These achiral components are due to polar ordering along the substrate normal. However, certain components of the magnetic tensors χeem and χmee were also large with zzz components of the order of 25% of the largest zzz component of χeee, even larger than the chiral xyz component of χeee. The largest components of the magnetic tensors are thus associated with chirality, a result in agreement with the interpretation that large magnetic effects in chiral molecules are directly related to the structural asymmetry of the molecules. However, the chirality and nonlinear response in polyisocyanide LB-films is mainly associated with the helical backbone of this polymer while the nonlinear response resides in the NLO-active chromophore attached to the backbone. Our observations on these NLO properties indicated a strong coupling between backbone and chromophore, presumably due to the spatial phase differences the helical backbone imposes on the chromophore positions . However, it could be argued that the nonlinear chirality effects in polyisocyanide were of a secondary nature.
In order to possibly observe stronger chiral and magneto-optical effects we turned to chiral polythiophenes, abundantly available from Bert Meijer, these polymers being one of his important research topics - out of many. These conjugated polymers show extremely strong optical rotation in poor solvents and in the solid (film) state, with the displacement of the electrons along the helical conjugated backbone. Intuitively we felt, again using our pet-model that we should see strong magnetic effects - it would later prove that our intuition was even more correct than we ever expected. We indeed found for a 10-layer LB-film of a polythiophene that the electric and magnetic contributions were of the same order of magnitude, perhaps somewhat helped by the centrosymmetric arrangement of the monomer units suppressing the electric dipole interaction [26–28]
By the “diplomatic talents” of Seth Marder (now at GeorgiaTech) we obtained samples of the chiral helicenebisquinones from Tom Katz (Columbia) - which turned out to be a goldmine for research in nonlinear chiral optics. These helicenes in the nonracemic, enantiomeric pure state spontaneously aggregates in the appropriate solvents, e.g. dodecane, showing an enormous optical activity - we even measured the CD-spectrum from a LB-monolayer. Indeed these helicenes amazingly formed, rather easily, very stable LB-films. To our surprise SHG from LB-films made from the nonracemic helicenes was particularly strong, about 1000 times as intense as the SHG-signal from a racemic helicene film, hence a 30-fold increase in the susceptibility. Based upon a comparison of the polarization dependence for SHG from racemic and nonracemic LB-films we could conclude that the dominant part of the susceptibility in the nonracemic form was due to chirality. Oddly, in the analysis of the SHG-response no evidence was found of the presence of magnetic dipole interactions. This told us clearly that chirality and magneto-optical effects are different phenomena - why we see magnetic effects playing a role in the highly chiral polythiophene films while they are absent in the highly chiral helicene systems is still puzzling and may be an important issue for future development in optical materials. Other helicene films, spun-coat, were also investigated. The films from the nonracemic helicenes showed a SHG response in agreement with a D∞ symmetry and as the nonvanishing tensor component only χxyz present, with a magnitude of about 2 pm/V - too small for practical applications but illustrating convincingly the potential of chirality in nonlinear optical applications. Indeed these films will never relax to a more stable structure, they are the most stable structure showing excellent thermal stability - above the melting point of the film the SHG disappears, only to reappear, with the same intensity upon cooling, a definite proof of stability [29,30].
A beautiful experiment was carried out by Sonja Sioncke and clarified the role of tensor components, polar and apolar, in these helicene films. She investigated SHG from a binary mixture of two helicenes in dodecane forming a chiral discotic nematic phase. The polarization analysis of SHG signals from this sample in a LC cell showed that here again the symmetry was D∞ symmetry with χxyz the only tensor component present. But when an electric field was applied to the LC cell the symmetry changed to C∞ and several polar components appeared which could all be determined. It was also nice to see that upon reversal of the electric field the values of the polar susceptibility components changed sign - as expected - while the apolar component remained unchanged . This ability to reverse the sign of susceptibility components may have an application for quasi-phase matching.
But we could use chirality, with the susceptibility components of opposite sign for the two enantiomers in a much simpler way to realize quasi-phase matching. As said before phase matching is of great importance in SHG to build up a sufficient intensity for the SHG signal. Indeed, we see that in the NLO material the source polarization and the harmonic field will be out of phase after a given distance, the coherence length, - unless the indices of refraction for fundamental and harmonic are equal, not easy to realize. An alternative solution, quasi-phase matching, consists of reversing the sign of the nonlinear optical coefficients after every (or odd multiple) coherence length. In this way the nonlinear signal will grow continuously. This is just what we could realize with enantiomeric molecules and it would be sufficient to have a structure with alternate stacks of enantiomers, the stacks with a thickness of the (odd multiple) of the coherence length. This is what Bertrand Busson did by using the LB-technique to deposit stacks of molecular layers of the two enantiomers of the helicenebisquinone. For practical reasons the experiments were carried out in a reflection set-up since the coherence length is much shorter. This work beautifully illustrated the potential of chirality to realize quasi-phase matching .
Another interesting possibility of chiral materials we discussed extensively is their use, as isotropic materials, in electro-optical modulation (Pockels effect). Indeed, for the polarization we always can write:33]. Up to now this prediction, which is also challenged, is waiting for experimental confirmation, or refutation.
I want to mention a last item on the research on chirality. In our discussions in the group a question surfaced if it would be possible to put the chirality in the light beam and not in the molecule. Could this be realized by using Laguerre-Gaussian or so called twisted light beams? I was fortunate to have at the right time Fumito Araoka as a post-doc who surprised me, and every group member, by setting up such an experiment with LG-beams in a few days – I programmed 6 – 8 weeks! Fumito Araoka did a beautiful piece of work but we were all disappointed to see that the twisted light, although carrying orbital angular momentum, is not specific at all in its interaction with chiral matter- an important result in itself . But this story is not yet ended.
4. Faraday rotation
Looking back at the Pockels effect, the polarization described by Eqs (7) and (8), we started to think about the possibility of a “magnetic Pockels effect”. Indeed, writing the optical polarization taking now into account magnetic effects we have, in a complete analogy with the Pockels effect:
But now with an effective susceptibility which is dependent upon a low frequency magnetic field. How we should relate χeem(ω; ω, 0) to χeem(2ω; ω, ω), how we should take dispersion into account here is still a somewhat open question. This expected “magnetic Pockels” we quickly identified as the Faraday effect, the rotation of the plane of polarization when an linearly polarized light beam passes through a material in a magnetic field oriented parallel to the light beam. This effect was first observed by Michael Faraday in 1845 - September 13th, see his Diary) in a piece of glass [35,36]. This tells us that actually the Faraday effect is the oldest nonlinear effect and September 13th the birthday of nonlinear optics - few scientific fields can claim such an exact birthday.
The Faraday effect, or Faraday rotation, is described by the simple relation:37], using different definition for χ):
Therefore the imaginary part of χeem defines Faraday rotation - and in lossless media χeem is imaginary. Also, since all materials show Faraday rotation we measured V for some simple molecules, e.g. aromatics, and obtained the Verdet constant from a theoretical value for χeem in good agreement with these experimental values . The fact that all (isotropic) materials show Faraday rotation indicates also the presence of χeem (ω; ω, 0) in all materials – as said before. And since isotropic materials have only magnetic susceptibility components xyz only magnetic fields in the direction of light propagation will show an effect.
When we applied Eq. (12) to the values measured for the proper χeem components obtained in the investigation of SHG in polythiophene films, and neglecting dispersion, the corresponding Verdet constants seemed unreasonably large as compared with the known values for materials in current use for Faraday rotators. We therefore set out to measure the Faraday rotation in the polythiophene films we were also investigating for SHG. One polythiophene was highly regioregular poly(3-octyloxythiophene). Amazingly, when Palash Gangopadhyay measured the Verdet constant for this polymer it turned out to be orders of magnitude larger than the Verdet constant for a commercial material such as TGG (Terbium Gallium garnet) having a V = 0.077 105 deg T−1 m−1 at 633 nm while the poly(3-octyloxythiophene) film came with a Verdet constant of V = 2.5 106 deg T−1 m−1 at 800 nm, still V = 106 deg T−1 m−1 at 1549 nm, far out of resonance. Although we did not understand the underlying reason or mechanism of this giant Faraday rotation” - we still don’t - there was a lot of enthousiasm in the group and these effects were soon confirmed for many other polythiophenes, although - serendipity! - poly(3-octyloxythiophene) still hold the record value. Since these conjugated polymers are often prone to spurious oxidation effects it was gratifying to see that the Verdet constants measured were stable over months, even for films kept in air at room temperature. This way we entered the field of conjugated polymers by discovering rather unexpected optical properties. Suddenly our polythiophenes became basic materials for entirely new types of applications in compact, integrated optical devices. We were able to build magnetometers based upon these materials with a sensitivity approaching SQUID sensitivity. Motivated by these findings Guy Koeckelberghs, our synthetic wizard in the group, started a whole program synthesizing polythiophenes and measuring their Verdet constants in films. Soon we discovered the important role of the polymer structure and their behavior in films. The really large Verdet constant were only observed for highly regioregular polythiophenes while the supramolecular structure in the film seemed to play also an important role since the Faraday rotation is completely lost by heating the films - effects mirrored in the film structure as determined by X-rays and AFM [39–42].
Maybe we should stress here that the Faraday effect, observed in all materials, not necessarily chiral, is fundamentally different from the optical rotation in chiral molecules. Optical rotation is a linear optical effect while Faraday rotation is a second-order nonlinear effect described by a nonlinear magnetic susceptibility. Moreover due to the spatial orientation of the magnetic field the Faraday is a nonreciprocal effect – upon reflecting the light beam the rotation is doubled – as opposed to optical rotation. As a matter of fact this nonreciprocal behavior is the basis for using Faraday rotation in optical rotators.
Some difficult questions remain in the field. Why is the Faraday rotation in conjugated polymers, specifically the polythiophenes so large or, the same question, why polythiophene films show such remarkable strong magneto-optical effects, as opposed to films of other strongly chiral molecules, e.g. the helicenes? What are the requirements for a material to show magnetic susceptibilities – other groups observe also these magneto-optical effects but the relation with the molecular (super)structure remains unclear . This is one of the research topics of current research, also by former team members distributed over the globe – the group went global.
It was quite evident that there is now a vigorous research investigating the magnetic properties of polythiophenes, and other conjugated polymers. Here I just want to describe a property measured and, although confirmed by other groups now, still controversial, hotly debated and not yet published. We - the people at NIST - measured a hysteresis behavior in the magnetization of a sample of poly(3-dodecylthiophene) below 20 K. Such a ferromagnetic (?) transition is very hard to understand, especially since these polymers are free of spins as measured by ESR. Even more puzzling is the fact that these phenomenon could only be observed with a highly regioregular polymer – the regiorandom polymer showed, under identical experimental conditions, only a paramagnetic behavior. However, I am not any longer in the review/memoir format and just looking to the excitement of future research carried out by enthusiastic young scientists.
5. Where next?
Although a paragraph entitled “where next” should not be expected in a review/memoir I want to refrain from using the more conventional “Conclusion” with its inherent finality because the work presented here is far from finished. Indeed the research initiated in our group on nonlinear optics from chiral films still is a continuing journey and takes many unexpected new directions.
Experiments on SHG from chiral surfaces are still refined in the work of Martti Kauranen  now with his own active group in Finland. And it is a pleasure to see how Pierre-François Brevet in Lyon is also carrying out magneto-optic research on thin films . Departing from the more molecular approach Martti Kauranen started also looking at the intricate chirality aspects of nanoparticles and nanostructures using the new possibilities offered by nanotechnological techniques to make a whole array of these, also entering the field of nonlinear chiral imaging [45,46]. This is a road followed also by the group of Thierry Verbiest and Ventsi Valev – and I feel proud that this group is the successor of my former group – using very intricate “chiralized” nanostructured surfaces of gold or magnetic materials contributing to the important field of plasmonics [47–49]. I see that the links between nanophotonics, nanoelectronics and nanomagnetics are slowly emerging from these investigations. They try in this way to realize a long-standing goal of the group to realize metamaterials by making very special chiral nanostructures, still strongly inspired by the seminal paper of John Pendry on “a chiral route to negative refraction” .
We see also new and established researchers in the field of chirality. Ron Shen using his marvelous sum frequency generation techniques to probe chirality of many systems [51,52] while Franz Geiger [53,54] use these techniques to obtain new insights in the chirality of DNA. Ken Singer  analyzing the hyperpolarizabilities of chiral molecules, Marie-Claire Schanne-Klein [56,57] in Paris - a birthplace of chirality - investigating nonlinear circular dichroism, Gary Simpson  studying the chiral sensitivity of nonlinear optics… and a great pleasure to see David Buckingham still very active, also in the field of nonlinear chirality working on electro-optics [59,60]. It really was hilarious to see Ron Shen, David Buckingham and this author at the ACS symposium on the Physical Chemistry of Chirality, San Francsico, 2000, organized by Janice Hicks, all coming with the same talk (at least in title) on SHG in chiral media and chaired by… Peter Rentzepis who originally this experiment in 1966 [18,61]. Very new developments are also seen in the field of photonic materials where Martin Wegener is introducing optical activity and chirality in photonic crystals [62–64].
Chirality, that “simple” lack of mirror symmetry” is still a fascinating and absorbing concept with many questions and possibilities. Surprisingly we do not yet see effects of chirality, more generally magneto-optics, appearing in the now thriving field of organics photorefractivity, exemplified by the work of the group of Nasser Peyghambarian in Tucson .
I want to end with a word of thanks to all my co-travelers on the challenging and serendipitous road leading us from organic nonlinear optics, to chirality, to magneto-optics, to organic magnetism… from synthetic chemistry, to chemical physics, optics, and, sometimes, difficult physics. A road giving us also a preview to new aspects of nanoscience, plasmonics, molecular electronics, metamaterials…
Thanks to Thierry Verbiest, Martti Kauranen and Jeff Maki, travelers from the first hour. To Bertrand Busson, Sonja Sioncke, Palash Gangopadhyay, Fumito Araoka, Guy Koeckelberghs… and all post-docs and Ph.D. students who made the “chirality group” in Leuven such a place-to-be.
Most of our work discussed has been supported by the Katholieke Universiteit Leuven, FWO-Vlaanderen, the Belgian Government through their IUAP programs and the Flemish Government through their GOA and IWT programs. Support from European programs and EOARD is also acknowledged.
References and links
1. F. Fukuyama, The End of History and the Last Man (The Free Press, 1992).
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4. All serious students of nonlinear optics should have copies of the following books, in order of mathematical depth first editions given, but see subsequent editions also: G. C. Baldwin, An Introduction to Nonlinear Optics (Plenum Press, 1969); T. Verbiest, K. Clays, and V. Rodriguez, Second-Order Nonlinear Optical Characterization Techniques (CRC Press, 2009); P. N. Prasad and D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, 1991); D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic Press, 1987); R. W. Boyd, Nonlinear Optics (Academic Press, 1992); A. Yariv, Quantum Electronics (Wiley and Sons, 1967); Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984); N. Bloembergen, Nonlinear Optics (W. A. Benjamin, 1965).
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25. M. Kauranen, C. Boutton, T. Verbiest, M. N. Teerenstra, K. Clays, A. J. Schouten, R. J. M. Nolte, and A. Persoons, “Supramolecular second-order nonlinearity of polymers with orientationally correlated chromophores,” Science 270(5238), 966–969 (1995). [CrossRef]
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