Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

Colorant, Nonlinear Optical

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_184



Light is composed of an electromagnetic field that can interact with the elementary charges in matter, whose response can in turn influence the behavior of the other light waves. When light passes through any material, its electric field induces changes in the polarization of the material’s molecules. In “linear” materials the degree of electron displacement, characterized by the linear polarizability α, is proportional to the strength of the applied electric field.

The distinguishing characteristic of nonlinear optical colorants is that their polarization response to optical waves depends nonlinearly on the applied electric field strength. This can result in the emission of new radiation fields which are altered in phase, frequency, polarization, or amplitude relative to the incident optical radiation. Many of these effects are sensitive to specific characteristics of the local optical properties and interfaces. Multi-photonic absorption can also result in electronic excitations that for a given incident light beam are more strongly localized in space than those resulting from linear absorption processes.

Nonlinear optical materials continue to attract the interest of both industrial and academic researchers due to their many versatile applications in the domain of optoelectronics and photonics.

Historical Background

Over the past decades, a variety of materials have been investigated for their nonlinear optical properties, including inorganic materials, coordination and organometallic compounds, liquid crystals, organic molecules, and polymers [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Nonlinear optics was born in 1875 when John Kerr discovered that the refractive index of glass and organic liquids could be altered by an applied electric field with the induced changes being proportional to the square of the applied field strength. Kerr measured, for the first time, the third-order nonlinear susceptibility, or what is today called the Kerr effect or the electro-optical effect. This discovery was shortly followed in 1883 by the observation of a similar but linear electric field effect in quartz; this latter process now referred to the Pockels effect. These nonlinear effects had limited use until the invention of the laser in 1960 by Maiman and, in the following year, the observation by Franken et al. of second harmonic generation in quartz. Following these events, the field of nonlinear optics developed explosively throughout the 1960s, highlighted by the work of Bloembergen and coworkers in exploring the full range of nonlinear optical responses of material systems and that of Buckingham and colleagues in exploring nonlinear processes in atoms and molecules of interest to chemists [11].

Initially, optical communications technology used components almost exclusively based on inorganic NLO materials. At the time it was thought that these compounds were more suitable than organic compounds due to their greater chemical, photochemical, and physical stability and ease of processing. The two main classes of materials investigated were inorganic crystals of lithium niobate (LiNbO3) and barium titanate (BaTiO3) or semiconductors such as gallium arsenide (GaAs) or zinc selenide (ZnSe). Electro-optical devices that use lithium niobate have been on the market for several decades. However, these crystals have several drawbacks: high-quality single crystals are difficult to grow, are expensive, and are not easy to incorporate into electronic devices. During the 1980s it became clear that organic materials might be a better choice for use in nonlinear optical applications. A lot of organic compounds exhibit extremely high and fast nonlinearities, much better than those observed in inorganic crystals. In addition, due to the versatility of organic synthesis, their nonlinear optical properties can be modified depending on the desired application. Furthermore, organic chromophores can be incorporated into a variety of macroscopic structures such as crystals, Langmuir-Blodgett (LB) films, self-assembled films, poled polymers [1, 2, 8, 9], zeolites [12], and nanofibers [13].

At present, several organic systems (molecular as well macroscopic) with sufficiently high nonlinearities have been developed. The focus of the research in this area seems to be shifting to the optimization of a variety of other parameters, i.e., thermal and chemical stability and optical loss. Also, new approaches to design efficient nonlinear optical materials have lately emerged [7, 9].

Principles and Origin of Nonlinear Optical (NLO) Effects

In “linear” materials the degree of electron displacement, characterized by the linear polarizability α, is proportional to the strength of the applied electric field. Nonlinear optical effects arise from the interaction of electromagnetic fields in various dielectric media to produce new fields altered in phase, frequency, amplitude, or other propagation characteristics relative to the incident optical fields with a response that depends nonlinearly on the applied electric field strength. When a beam of light propagates through a material, the electric field associated with the incident beam can provoke small displacements of the electrons within the material. This results in an induced dipole moment (μind) which, at low electric field strengths, is linearly proportional to the amplitude of the applied electric field E, the proportionality factor being the first-order polarizability α. However, at high electric field strengths, higher-order terms become significant, and the induced dipole moment can be expanded in a Taylor series in powers of the applied electric fields (Eq. 1):
$$ {\mu}_{\mathrm{ind}}=\alpha E+\beta {E}^2+\gamma {E}^3+\dots $$
in which β represents the second-order polarizability or first-order hyperpolarizability and γ the third-order polarizability or second-order hyperpolarizability. This description may be expanded to the macroscopic regime of the bulk media with the first-order susceptibility and the second- and third-order nonlinear susceptibility, respectively (Eq. 2):
$$ {P}_{\mathrm{ind} = }{\upchi}^{(1)}E+{\chi}^{(2)}{E}^2+{\chi}^{(3)}{E}^3+\dots $$
When the polarization of the incident and induced fields is taken in account, the above relations taken on a matrix form with the first and second hyperpolarizabilities (or equivalently the second- and third-order susceptibilities) being three and four rank tensors.

For practical applications, organic second-order NLO materials can be considered to be dipolar molecules organized into noncentrosymmetric lattices. Therefore, high β values are a necessary but not sufficient condition in order to obtain efficient NLO second-order materials [5, 8, 9].

Nonlinear Optical Effects and Their Practical Applications

The main NLO effects associated with linear and nonlinear susceptibilities are [1, 7, 9, 14, 15, 16]:
  • First-order susceptibility χ (1) : Refraction is the change in direction of a light wave due to a change in its phase velocity. This phenomenon is the foundation of most geometric optical effects and has applications in optical fibers and lenses.

  • Second-order susceptibility χ (2) :
    1. (i)

      Optical second harmonic generation (SHG) is the nonlinear conversion of two photons of frequency ω into a single photon of frequency 2ω (ω + ω → 2ω) which, in the electric dipole approximation, requires a noncentrosymmetric medium. This effect was first demonstrated by Franken et al. [14] in 1961 and has applications in the frequency doubling of lasers. More recently, SHG-imaging has developed through the last decade as a progressively popular analytical technique especially for high-resolution optical microscopy for biological imaging. In fact nonlinear optical imaging has revolutionized microscopy for the life sciences due to the capacity of this technique to produce high-resolution images from deep inside biological tissues [15].

    2. (ii)

      Frequency mixing: an NLO material may be used to add frequencies of two input waves to produce a single wave, whose frequency is their sum: ω1 + ω2 → ω3 – or difference: ω1 − ω2 → ω3. This effect has application in the frequency conversion of lasers and various nonlinear spectroscopic techniques.

    3. (iii)

      Parametric amplification: an NLO material may transmit two light waves of different frequencies, with one light wave leaving the material amplified at the expense of the other. This effect allows the production coherent light at wavelengths for which no lasers are available and is frequently used in high-resolution spectroscopy.

    4. (iv)

      Linear electro-optical effect (Pockels effect) is the change of refractive index of an NLO material which occurs on the application of an electric field, the extent of the change being related to the strength of the field (ω + 0 → ω). This effect has application in waveguides and electro-optical modulators.

  • Third-order susceptibility χ (3) :
    1. (i)

      Kerr effect is a change in the refractive index of a material in response to an applied electric field. This effect has applications in optical transistors and image processing.

    2. (ii)

      Third harmonic generation: light of frequency ω enters the material and leaves with frequency 3ω, (ω + ω + ω → 3ω). This effect has applications in optical image processing and scanning microscopy [7].

    3. (iii)

      Two-photon absorption is the induced electronic transition provoked by the near simultaneous absorption of two incident photons. This effect was first studied theoretically by Maria Goeppert-Mayer already in the 1931 and is often used in nonlinear microscopy to allow deeper penetration of the incident light, avoid photobleaching, and increase spatial resolution [16].


Nonlinear Optical Materials: Classes, Advantages, and Limitations

The search for novel chromophores for optoelectronics and nonlinear optics (NLO) is one of the main goals of modern materials science and physics. Their practical applications require not only an appropriate design but also the relevant macroscopic properties of newly established materials. The even susceptibilities χ2, χ4, etc., are only nonzero in materials lacking a center of symmetry. Therefore, the arrangements of the molecules on a macroscopic level are vitally important to NLO activity. For example, if a crystalline material with a large value of β crystallizes in a centrosymmetric structure, the nonlinear responses of the individual molecules will cancel each other out, and there will be no resultant NLO activity. The same applies to an organic compound with an amorphous structure. If there is no order in the molecule at all, the statistical average of the NLO responses of the molecules will be zero or nearly zero, and again, the material will be not be an active NLO material. Thus to use the strong hyperpolarizabilities often found in organic molecules in a bulk phase, the constituent molecules must be somehow noncentrosymmetrically ordered. The main types of ordered assemblies that have been investigated for use in NLO materials are the following [5, 8, 9, 10, 11, 12, 13].


These materials were the first to be studied since the observation by Franken et al. [14] of second harmonic generation in quartz. Several ionic crystals such as potassium dihydrogen phosphate (KDF=KH2PO4), lithium niobate LiNbO3, barium sodium niobate (Ba2NaNb5O15), and β-barium borate (BBO=BaB2O4) were developed and are currently used for several optical applications such as frequency converters, electro-optical modulators, and optical switches. The main advantages of inorganic materials are their high stability, high mechanical strength, and high nonlinear optical susceptibilities. However, the growth of these crystals is time consuming (frequently requiring 1–8 weeks) and the crystals tend to be hygroscopic, and expensive, somewhat difficult to integrate into electronic devices and are often limited by the low response speeds.

Coordination and Organometallic Complexes

In the last decade, organometallic and coordination metal complexes have occupied a relevant role in the area of NLO chromophores due to an additional flexibility, when compared to organic chromophores, owing to the presence of metal-ligand charge transfer (MLCT) transitions usually at relatively low energy and of high intensity, tunable by virtue of the nature, oxidation state, and coordination sphere of the metal center. The main classes of SHG NLO coordination and organometallic complexes include derivatives with monodentate nitrogen donor ligands (amines, stilbazoles, pyridines), chelating ligands (Schiff bases, bipyridines, phenanthrolines, terpyridines), alkenyl, vinylidene and cyclometallated ligands, macrocyclic ligands (porphyrins and phthalocyanines), metallocene derivatives, and chromophores with two metal centers (Fig. 1) [11].
Colorant, Nonlinear Optical, Fig. 1

Structure of several SHG organometallic and coordination metal complexes [11]


Dipolar and octopolar organic NLO chromophores (Fig. 2) have several advantages when compared to inorganic materials: (i) ultrafast response times, low dielectric constants, better tailorability and processability, as well as large NLO responses, due to the high electronic polarization of the π electrons of the molecules instead of the distortions of the atoms in the crystal lattice; (ii) easy synthesis and functionalization, allowing the optimization of their structural characteristics leading to the maximization of their NLO properties; and (iii) can be used as monocrystals and films or incorporated into liquid crystals, zeolites, or fibers. On the other hand, they have also several disadvantages such as (i) lower mechanical strength, (ii) lower photochemical stability, (iii) the propensity to acquire defects during crystal growth, and (iv) a somewhat limited working temperature range. Over the past three decades, great progress has been made in the development of new organic donor-acceptor π-conjugated systems [5, 8, 9] being driven by their chemical and thermal stability as well as the ease of synthesis and functionalization which lead to facile optical property tuning. Dipolar push-pull (d-π-A) organic chromophores are constituted by a π-bridge (aromatic or heteroaromatic) substituted with strong electron donors D (e.g., NR2 or OR groups) and strong electron acceptor A groups (e.g., CN, NO2, etc.). This d-π-A arrangement guarantees efficient intramolecular charge transfer (ICT) between the donor and acceptor groups and generates a dipolar push-pull system featuring low-energy and intense CT absorption (Fig. 2a). The polarizability and the corresponding NLO properties, namely, the SHG of these systems, depend mainly on their chemical structure, particularly the strength of the attached donors and acceptors groups as well as the electronic nature and length of the π-conjugated bridge. However, dipolar chromophores have the tendency for unfavorable aggregation at high concentrations, and it is rare that they undergo noncentrosymmetric crystallization. One way of circumventing these disadvantages is the use of octopolar molecules.
Colorant, Nonlinear Optical, Fig. 2

Schematic representations of (a) a dipolar organic d-π-A system featuring ICT and (b) octopolar chromophores

Octopolar NLO chromophores are not so commonly investigated compared to dipolar ones. Nevertheless, their advantage is that they show the same optical transparency as their linear analogues but their second-order response is higher. Due to the fact that they possess zero overall dipole moment, they can often be oriented in the bulk phase in a manner that their molecular polarizability is additive. On the other hand, not possessing a permanent dipole moment invalidates their use in some electro-optical applications. The usual way to design SHG octopolar molecules consists in the synthesis of substituted trigonal or tetrahedral π-conjugated systems that allows an efficient charge transfer from periphery to the center of the molecule (Fig. 2b).

Several one-dimensional charge transfer systems with good SHG properties were developed during the 1980s. Typical examples of such molecules are p-nitroaniline (pNA) and N,N-dimethylaminostilbene (DANS) (Fig. 3); both are still being used as standards to evaluate SHG of other molecules.
Colorant, Nonlinear Optical, Fig. 3

Structure of p-nitroaniline (p-NA) and N,N-dimethylaminostilbene (DANS)

Chromophores with other types of conjugated spacers have been also investigated (e.g., substituted benzenes, biphenyls, stilbenes, and azostilbenes). All these systems have a predominantly aromatic ground state and a corresponding charge transfer state that is quinoidal in nature. More recently, the investigation by several groups has led to the development of highly advanced SHG organic chromophores. The results of these studies suggest that optimal β values could be obtained through two different but complementary methodologies: the optimization of the π-bridge structure for particular donor and acceptor pairs and optimization of donor and acceptor groups for a given π-bridge. Novel highly efficient donor-acceptor pairs have been developed such as alkyl and arylamine electron donors (Fig. 4a) and tricyanofuran-based electron acceptors, for example, 2-dicyanomethylene-3-cyano-4,5,5-trimethyl-2,5-dihydrofuran (TCF1), 2-dicyanomethylene-3-cyano-4,5-dimethyl-5-trifluoromethyl-2,5-dihydrofuran (TCF4), and the tricyanopyrroline (TCP) electron acceptor (Fig. 4b). This arrangement of donor-acceptor pairs combines high chemical, thermal, and photostability [5, 8, 9]. In recent years the enhancement of β values by using ever stronger electron donor or acceptor groups has tended to reach its limit. A versatile methodology to overcome this problem was the optimization of the π-bridge. Therefore, several experimental and theoretical studies have confirmed that substitution of the benzene ring of a chromophore bridge with easily delocalizable heterocycles (e.g., thiophene, pyrrole, furan, and thiazole) (Fig. 4c) results in improved molecular hyperpolarizability of push-pull systems. Due to their electronic nature and low aromaticity, they can act efficiently as π-bridges as well as auxiliary donors (electron-rich heterocycles: thiophene, pyrrole, furan) or as auxiliary acceptors (electron-deficient heterocycles: thiazole, oxazole, imidazole). In fact, the increase or decrease of the molecular nonlinear activity of these heteroaromatic systems depends not only on the electronic nature of the aromatic rings but also on the location of these heterocycles in the system. Additionally, these heterocyclic systems are also thermally and photochemically stable [8, 9, 17, 18, 19, 20].
Colorant, Nonlinear Optical, Fig. 4

Structures of (a) aryl amines as examples of strong electron donor groups, (b) electron acceptor groups belonging to the general TCF and TCP classes, and (c) heterocyclic compounds as π-bridges/auxiliary donor or auxiliary acceptor groups [8]

Concurrently, multidimensional charge transfer (e.g., X-shaped and higher-order symmetry) and twisted intramolecular charge transfer (TICT) chromophores (Fig. 5) have been explored as alternative approaches to improve hyperpolarizability [9].
Colorant, Nonlinear Optical, Fig. 5

Structures of twisted intramolecular charge transfer molecular (TICT) chromophores [9]

The easiest method to impose order on the molecules of a compound is to assemble them into a crystalline matrix. Crystals have several advantages such as their high optical quality and high laser damage thresholds. On the other hand, they have several serious drawbacks; a major one is the fact that most of the promising molecules have significant ground state dipole moments, which tend to make them crystallize centrosymmetrically. For example, 4-nitroaniline (pNA) packs centrosymmetrically and exhibits no appreciable SHG in crystalline form, while the analogous 2-methyl-4-nitroaniline (MNA) packs in an almost perfect head-to-tail arrangement and has a large χ2 value. There are some examples of noncentrosymmetric small molecules such as derivatives of nitroanilines and nitropyridines or enantiomers of an optically active component. For example, MMONS (3-methyl-4-methoxy-4′-nitrostilbene) has a very high powder SHG value (1,250 times that of urea) and POM (3-methyl-4-nitropyridine-N-oxide) is the only commercially available organic crystal for SHG, other than urea (Fig. 6).
Colorant, Nonlinear Optical, Fig. 6

Structure of selected organic NLO crystals [1, 4, 5, 9]


Oriented Guest-Host Polymers

Second-order NLO applications that require crystalline materials limit the scope of molecule types that can be employed to those that crystallize in acentric space groups. To achieve good device functionality, the NLO chromophore must simultaneously possess high microscopic molecular nonlinearity, good thermal stability, good photostability, low optical absorption, and weak intermolecular electrostatic interactions in a given host matrix. Polymeric materials are attractive because they are compatible with manufacturing methods practiced in industry and can provide durability, environmental protection, and packing advantages not provided by crystalline materials. Nonlinear optical chromophores can be incorporated into a macroscopic polymeric environment in a variety of ways. Probably the most important and most widely used is the incorporation of dipolar chromophores into a polymer host. In this approach, the active species (the guest) is dissolved in a polymeric host, which is processed to give a thin film. At this stage the molecular dipoles are randomly orientated with respect to each other. The polymer is heated above its glass transition temperature (Tg) allowing the guest molecules to became freely mobile. A strong external electric field is then applied, aligning the dipoles along one direction. With the field still applied, the polymer is cooled below its Tg again, freezing the alignment of the NLO molecules. This approach is successful in obtaining highly oriented NLO materials showing large bulk susceptibilities. The main disadvantages are (i) gradual disordering of the dipoles, (ii) limited solubility of the active species in the host polymer which limits the attainable NLO activity, and (iii) dielectrically induced breakdown of the NLO species during poling. The advantages of the poled polymer approach are the relative ease of thin film making by spin coating and its compatibility with existing semiconductor technology. Figure 7 shows the structures of some examples of organic chromophores used as guests in guest-hosts polymeric systems.
Colorant, Nonlinear Optical, Fig. 7

Structure of selected organic chromophores used in guest-host polymers [8, 9]

Oriented Side-Chain and Main-Chain Polymers

Nonlinear optical chromophores can be also incorporated into a polymer by covalently attaching the chromophores to a polymeric backbone as part of the side chain (side-chain polymers) or by incorporation of the chromophores into the backbone of the polymer (main-chain polymers).

Langmuir-Blodgett Films

Another approach to organize molecules has been to incorporate organic NLO chromophores into noncentrosymmetric Langmuir-Blodgett films. The Langmuir-Blodgett film technique is used to build up ordered assemblies of molecules onto a substrate from a floating monolayer on a liquid, usually water. The molecule must be amphiphilic, that is, hydrophilic at one end and hydrophobic at the other, so that the molecules in the monolayer at the water’s surface have uniform orientation. This approach offers the advantage of much greater chromophore alignment and chromophore density. However, these films often have poor optical quality and poor temporal stability and are often very fragile.


Zeolites and the related mesoporous materials have been also tested as the hosts for aligned inclusion of dipolar organic NLO dyes as a possible means to overcome the problems arising from the use of polymer matrices. The first dyes tested were p-nitroaniline (pNA), 2-methyl-4-nitroaniline (MNA), and 2-amino-4-nitropyridine which have low molecular second-order hyperpolarizability values, and the zeolites have been mostly limited to powders that bear limited practical applicability. More recently hemicyanine dyes (Fig. 8) exhibiting higher β values and a high degree of uniform orientation were introduced into transparent zeolite films with uniformly oriented channels. These second-order NLO dye-incorporating films have shown higher thermal and mechanical stability without any notable loss of activity with time. They have a strong potential to be practically applied in industry [12].
Colorant, Nonlinear Optical, Fig. 8

Structure of second harmonic generator compounds that have been incorporated into zeolite hosts [12]


Very recently, nanofibers of poly(L-lactic) acid (PLLA) produced by the electrospinning technique, in which donor-acceptor organic compounds such as 2-methyl-4-nitroaniline, urea, and β-glycine were imbedded, exhibit a permanent nonvanishing quadratic nonlinear susceptibility. The nonlinear optical properties displayed indicate that a noncentrosymmetric polar state was achieved and maintained a long time, allowing the use of otherwise centrosymmetric organic materials. Moreover, it was proved that the SHG efficiency of these fibers strongly depends on the diameter of the nanofibers and can be increased up to an order of magnitude by controlling the electrospinning processing parameters [13].

As most of the donor-acceptor organic molecules with large hyperpolarizabilities tend to crystallize in centrosymmetric structures which invalidate their use in quadratic nonlinear optical applications, the inclusion of these molecules in electrospun nanofibers may provide a means of overcoming this limitation for any donor-acceptor organic molecules with delocalized π electrons. The results of this work could have a direct impact on the design of novel nanodevices for a variety of nanophotonic applications (e.g., electro-optical transducers, pyroelectric sensors, optical frequency converters).

Experimental Methods for the Determination of Second-Order Nonlinear Effects

The second-order polarizability β and the second-order susceptibility χ (2) are two parameters indicative of a second-order response [5, 9]. The first is a molecular parameter and is usually measured in solution, whereas the latter is typically measured by second harmonic generation from the solid state. Several experimental techniques can be used in order to study these parameters in solution or in solid state: solvatochromic method, Kurtz powder technique, Maker fringes, electric field-induced second harmonic (EFISH) technique, and the hyper-Rayleigh scattering (HRS) technique (Figs. 9 and 10). In solution, the two major techniques that are presently used are EFISH and HRS.
Colorant, Nonlinear Optical, Fig. 9

Scheme of assembly for measurements of diffusion hyper-Rayleigh. P polarizer, λ/2 half-wave plate, L lens, E mirror, PD disperser prism, F’ band-pass filter, F low-pass filter, FD photodetector, FM photomultiplier (Nonlinear Optics Laboratory of the Physics Center at the University of Minho) [19, 20]

Colorant, Nonlinear Optical, Fig. 10

Experimental setup for the determination of SHG through hyper-Rayleigh scattering technique (Nonlinear Optics Laboratory of the Physics Center at the University of Minho) [19, 20]

Future and Perspectives

From the proceeding description, it is clear that the molecular design of molecules with strong nonlinear optical responses has reached a high level of sophistication. Important advances are likely to come from breakthroughs in methods that are able to make use of these strong individual molecular responses by incorporating in restricted environments that break their tendency to aggregate in centrosymmetric forms. The future of organic nonlinear optical materials is undoubtedly a bright one.



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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of MinhoBragaPortugal