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Organic fluorinated materials demonstrate their excellent electro-optic properties and versatility for technological applications. The partial substitution of hydrogen with fluorine in carbon-halides bounds allows the reduction of absorption losses at the telecommunication wavelengths. In these interesting compounds, the electro-optic coefficient was typically induced by a poling procedure. The magnitude and the time stability of the coefficient is an important issue to be investigated in order to compare copolymer species. Here, a review of different measurement techniques (such as nonlinear ellipsometry, second harmonic generation, temperature scanning and isothermal relaxation) was shown and applied to a variety of fluorinated and non-fluorinated electro-optic compounds.

Organic conjugated polymers were thoroughly investigated in recent years due to their interesting and peculiar physical properties, granted by electron delocalization of the π-bonds. Moreover, the extraordinary physical properties shown by organics can be easily tuned by appropriate synthesis processes [

Nowadays, organic materials have emerged from academic research to become useful building blocks of integrated optical devices for light emission, modulation and switching [

The large-scale introduction of optical technologies in communication networks has become a reality with an enormous impact on the bandwidth and quality of communication services offered, on the economy of the industrialized countries and also on interpersonal and social relations. Fiber optics has enabled high bit-rate transmission capacity in the core network. Broad-band access, however, is limited because of the high costs of the hardware needed for distributing, routing and switching and eventually generation and detection of the optical signals. Guided by the situation in the field of electronics, the solution should be found in large-scale integration of optical functions in compact optical circuitries. The conversion of source data that are mainly in the electrical domain to optical bits and the dynamical functionality in optical networks require electro-optic or other active optical materials. Hybrid integration of passive wave-guiding structures with these active materials is a route to low-cost, high-performance modules. In this context, progress in organic materials demonstrates the excellent electro-optic properties and versatility for technological applications, for example a polymeric electro-optic modulation, based on a Mach-Zehnder integrated interferometer (MZI) operating at over 200 GHz was demonstrated [

Among other advantages of organic materials, we can point out the compatibility with a variety of substrates, such as Si, GaAs, or plastics (a high-performance electro-optic polymer modulator on a flexible substrate was fabricated [

Here we show a review of the characterization technique used in order to retrieve the magnitude and the thermostability of the electro-optic properties of different species of fluorinated and non-fluorinated polymers.

In the

In the

In the

In many applications and in a more realistic description of the electromagnetic interaction, the response of a medium immersed in an electromagnetic field cannot be described as a linear response:

(

Such dependence can be expanded in a power series of the electric field, and in a general case the electric polarization vector can be written as [

where the nonlinear susceptivities ^{(n)} are used (the ^{(1)} term is responsible for the linear refractive index). In centrosymmetric materials are present only the even term of Equation (3), otherwise in non-centrosymmetric materials the second order term ^{(2)} can be dominant with respect to the other nonlinear terms.

We limit our attention only at the second order term that is responsible of the linear electro-optic (EO) effect (or Pockels effect) as well as other interesting phenomena and applications such as second harmonic generation (SHG), frequency mixing, photorefractivity [

In Equation (3) if we consider that the driving field oscillates at one frequency

If the exciting field is composed by an electromagnetic field oscillating at _{1}_{2} = 0), the resulting polarization ^{(1)}, but the linear term responsible for the refractive index is modified by the presence of the static field:

This phenomenon is the EO effect of our interest.

Organic conjugated molecules and polymers show interesting and peculiar physical properties, given by electron delocalization of the π-bonds [_{6}H_{6}), it shows complete delocalization of π-electrons on the aromatic ring (

(

If we substitute some hydrogen atoms with an electron acceptor A (for example NO_{2}) or electron donor group D (for example NH_{2}) (

For a general molecule, using a description similar to that used in the previous paragraph for macroscopic nonlinear media, we can write down the expression of the induced dipole moment as:

where _{0i} are the static electric dipole moment components, _{ij}_{ijk}_{ijkl}_{i}^{ω}

The local field factor in the range of the optical frequencies is given by the Lorenz-Lorentz formula:

where

where _{r}_{0} is the static relative dielectric constant and _{r}_{∞} is the relative dielectric constant in the range of optical frequencies [

One of the best known electro-optic chromophore used in applications is the 4-[

(

The main characteristics are reported in

Characteristic data of the Disperse Red 1 (DR1) molecule.

Chromophore | λ_{max} (nm, CHCl_{3}) |
μ_{0} (Debye) |
β_{0} (10^{−3}^{0} esu) |
β_{1.9μm} (10^{−3}^{0} esu) |
μ_{0}β_{ 1.9μm} (10^{−48} esu) |
---|---|---|---|---|---|

DR1 | 480 (497) | 7.7 (8.7) | 40 | 5,046 | 580 |

Up to now, we described the nonlinear optical properties of a single molecule. However we are generally interested to the nonlinear optical response of bulk macroscopic materials made out of a large number of such molecules.

In order to evaluate the nonlinear response of the whole macroscopic material it is not sufficient to know the nonlinear properties of the single molecule, but we need to consider the number of chromophores per volume unit and their orientation inside the macroscopic structure. In particular, the macroscopic nonlinear optical properties increase with the density of oriented chromophores. Considering a system constituted by molecules with large ^{(2)} is zero because the material, as a whole, is centrosymmetric.

Since we are interested in electro-optic applications, we need to achieve a high ^{(2)} value and consequently we need to fabricate a structure in which the nonlinear molecules are oriented in a polar order. One way is to realize a solid solution of highly nonlinear molecules in a high optical quality passive polymer matrix. The matrix, in order not to interfere with the optical properties of the chromophore, is in general transparent in the wavelength used for applications and can be considered as optically linear; it is just a host material that gives mechanical stability to the ensemble of nonlinear molecules. One of the most used polymer matrices is the poly-methyl-metha-acrylate (PMMA) [

There are several ways of introducing nonlinear optical chromophores into the polymer matrix. The two most common methods are dissolving (guest-host systems) and covalently attaching (functionalized system) the chromophores to the polymer.

In the guest-host system, nonlinear optic (NLO) chromophores are dissolved, in the polymer host. The principal disadvantages of such a structure are: (i) low nonlinear activity, that it is due to the dopant maximum solubility (largest concentration is about 10% of the host weight), because greater concentrations can lead to chromophores’ aggregation or crystallization; (ii) the presence of optical losses due to scattering originated by the non homogeneity of the structure; (iii) the thermal and temporal instability, in fact, the chromophores are not attached at the polymer matrix and they can move with a higher degree of freedom. In the functionalized systems, the chromophores are attached to the polymer matrix, and the relative dopant concentration can be much higher than in guest-host systems. Moreover functionalized systems are more stable since their orientational mobility is significantly hindered and the order of such systems therefore relaxes more slowly.

In the functionalized systems nonlinear optical chromophores can be incorporated in the polymer matrix by chemically attaching them into the polymer main-chain (or backbone) or as a pendant side-group. In the side-chain systems, the chromophores can rotate around the attaching point and it is easier to orient them in the poling procedure. Nevertheless, the orientation is maintained longer than in the guest-host systems. For all these reasons, side-chain copolymers are widely used in optical application but also guest-host systems are used because of the relatively easy fabrication process.

In order to induce non-centrosymmetry after the films deposition, several poling techniques can be used. The most common ones are:

_{0}, due to their rod shape with donor and acceptor at the opposite sides. As a result, it is possible to use a large static electric field to orient these polar molecules along the field and thus induce an asymmetric configuration. For contact poling, the sample must be prepared by spinning the polymeric solution on a substrate that was previously covered by an electrode. Then, after spinning and drying, the polymeric film must be topped with another electrode, via sputtering deposition or other techniques, in order to obtain a sandwich structure with the copolymer sandwiched between the two electrodes. Then, the sample is ready for the poling procedure; the temperature of the sample is increased to the glass transition one (_{g}

_{g}

The method is, however, the subject of criticism for material characterization purposes: in fact, the real effective poling field remains unknown and it is not well reproducible.

_{g}

Photoassisted poling.

In all the three cases described above, the electro-optic coefficient induced by poling will relax on a long-time scale, because the chromophores’ orientational mobility is not zero, even at room temperature.

In this paragraph, we show a theoretical model describing the nonlinear optical response of a medium constituted by nonlinear units (chromophores) dispersed in a linear matrix and oriented along a preferential axis [

Relationship between the molecular axes 1,2,3 and laboratory axes x,y,z.

The second order nonlinear dipole moment results in:

Considering the cylindrical and elongated shape of the chromophores, we can assume that the only nonvanishing component of _{ijk}_{333}.

The macroscopic electro-optic polarization induced by an external dc field

where

and cos(

In order to find another component of the macroscopic nonlinear optical susceptibility, we consider the case where the external dc field is along the

From the above relations we obtain the following relations for the macroscopic electro-optic susceptibility:

During poling, two competing mechanisms determine the final steady-state equilibrium distribution. The electric dipole interaction of the molecular dipoles with the dc field favors the alignment of molecular dipoles along the

This expression allows to estimate directly the second order susceptibility terms from Equations (13) and (14):

The Equation (15) give, also, a first order approximation of the ratio

By applying the relation between the electro-optic tensor with the

The calculations previously exposed neglect the chromophore–chromophore intermolecular electrostatic interactions. In this regime the electro-optic coefficient will increase in a linear manner with chromophore number density _{0}, they will interact, thereby minimizing their energy and forming an anti-ferroelectric state, where neighbouring chromophores are preferentially oriented in opposite directions, leading to a decrease of the effective electro-optic coefficient [_{0}, it is not possible to align them using the standard poling procedure shown previously. A more complicated all-optical poling was proposed [

At the end of the poling procedure, when temperature has been lowered to the ambient one and the poling field has been turned off, the orientational distribution

In order to describe these time-dependent phenomena, we introduce the rotational diffusion equation (Smoluchowski-Einstein) for a molecular dipole [

where

However the behavior expected from the model showed above is not always in strong agreement with experimental data, because in the model, it is assumed that the material homogeneously acts on the mobility of the chromophores via a determined diffusion constant _{i}

where _{zz}_{zz}_{p}_{p}

Where

where Γ(

The average time constant <

For temperature above or equal to _{0}, a characteristic temperature of the material that is close to, but lower than, the glass transition, the matrix is in a quasi-fluid state and the chromophores can move easily. In this case, the time constant follows the Vogel-Fulcher-Tamann-Hesse (VFTH) or Williams-Landel-Ferry (WLF) law that is typical of semi-fluid glassy systems:

where

For temperatures below _{0}, the average time constant follows an Arrhenius behavior:

where _{a}_{B}N_{a}^{−1}·K^{−1}).

Also

Where _{0}, _{β}

Nonlinear ellipsometry (NLE) is based on a single wavelength reflection configuration proposed, independently, by Teng and Man [^{(2)} applications, the two electrodes are used either to pole the film or to apply a modulating voltage on the polymer film itself in order to measure the ^{(2)} values. As the TMT is based on the measurement of the electric field induced change of the optical phase difference experienced by the s (perpendicular to the incidence plane) and p (parallel to the incidence plane) components of a laser which propagates through the polymer film, at least one (reflection operation) of the electrodes must be transparent to the probe light.

Usually, a semiconductive transparent oxide thin layer, deposited on a glass substrate is used as transparent electrode. A polymer film is then deposited by spin coating it and then coating it with a metal electrode. Some researchers used polymer films sandwiched between two transparent electrodes and performed the experiments in a transmittance configuration [

The experimental configuration in reflection mode for TMT is usually composed by a cw laser that impinges on the sample at an incident angle α after passing through a polarizer, which sets its polarization at 45° with respect to the incidence plane, and a phase compensating device that changes the relative phase between the s and p components of the laser beam by an amount _{c}_{p}

The optical power at the output of the whole system is modulated, due to the response of the polymer film, both at Ω and 2Ω through the linear ^{(2)} and quadratic ^{(}^{3}^{)} electro-optic response.

The average output power can be written as:

where _{0} is the input beam power after the first polarizer, _{ps}_{c}

where and _{p}_{s}

In the low birefringence approximation, with the assumption of Δ|_{s}^{2} ≈ 0, the amplitude of the _{ac}

with

By varying the phase difference _{c}

There are two working points (labeled 1 and 2) where the _{dc}_{ps}_{c}

By using a lock-in amplifier, it is possible to measure the effective _{ac}

We point out that the measurements in the two working points 1 and 2 are faster than the measurement based on the sampling of the whole ellipse, but suffer from lower accuracy. The faster measurements can be usefully adopted in monitoring the time decay of the electro-optic coefficient, as we will show later.

Usually, when analyzing experimental data in an ellipsometric measurement, one makes the assumption that the laser beam is passing just twice through the polymer layer. However, if the reflectance of the semiconductor electrode is not negligible at the measurement wavelength, the electrodes system can behave as a Fabry-Perot resonator and the evaluation of the electro-optic coefficient obtained via the application of the simplified single pass model is wrong [

Since the EO coefficient ^{(2)} (see Equation (14)) it is possible to evaluate it by measuring the efficiency of the second harmonic generation process in polymeric films. Second harmonic generation was the first all-optical phenomenon shown in an experiment in nonlinear optics [^{(2)} coefficient is present only in non-centrosymmetric materials, SHG was widely used in order to study symmetry properties of bulk materials, thin films [

Usually, the polymeric samples used in SHG measurements are film deposited by spin coating on glass substrates. In order to prevent influencing the measurement, the substrate was an amorphous glass slide (no ^{(2)} contribution) without electrodes on the polymeric film. Since, after deposition, the orientation of the nonlinear chromophores is isotropic, the material must be poled before measurement. In this case, the poling technique used is the corona poling, as it does not require any contact electrode. An alternative poling procedure is the in-plane poling or lateral poling [

A standard technique used in order to measure the electro-optic coefficient by SHG from poled samples is the Maker fringes scheme [

where _{2}_{ω}_{ω}_{ω}_{ω}_{2}_{ω}_{eff}

In the Equation (30), _{eff}^{(2)} tensor by the relation

The expression for _{eff}_{33} and _{31} = _{32} = _{24} = _{15}. Depending on the polarization of both fundamental and generated beams, it is possible to retrieve separately the value of these components. The _{31} component can be directly evaluated from SHG measurements obtained in the _{ω}p_{2}_{ω}_{eff}

Where _{ω}_{33} coefficient can be obtained from a _{ω}p_{2}_{ω}_{31} evaluated with an independent _{ω}p_{2}_{ω}_{eff}_{ω}p_{2}_{ω}

Where _{2}_{ω}

The previous procedure can be used to find the susceptibility coefficient

where the field factors Equations (7) and (8) are present. We point out that in the two-index simplified notation, _{ij}_{ji}_{31} and _{33}, so the technique can be used to check the ratio _{33 }≈ 3_{13}, used in the nonlinear ellipsometric technique is valid. By continuously measuring the SHG signal, it is possible to perform faster measurements that can be usefully used in monitoring the time decay of the electro-optic coefficient as we will show later.

In order to retrieve preliminary information on the stability of the induced electro-optic coefficient, temperature scanning measurements were performed. This type of measurement consists of the continuous measurement of the electro-optic coefficient of a poled sample while the temperature is increased from room temperature up to temperatures above _{g}

During the temperature scanning procedure, the polymer electro-optic coefficient quickly relaxes and it is not stable enough to allow the use of the complete ellipsometric technique or the complete Maker fringe technique. In this case, the faster measurements shown previously (at the end of the _{g}_{33} is evaluated as a function of the temperature. Typical graphs are given by normalizing the _{33} value with respect to the _{33} coefficient measured at the beginning in room temperature condition. As an example, _{g}_{dep}_{33} gets half of the initial maximum value at room temperature. In this case, _{dep}

It is evident that it is possible to compare different polymer types with this technique only if all the measurements are performed under the same conditions,

Temperature scanning measurement on HFIP-DR1AF. Reprinted with permission from [

A more reliable and useful measurement technique to probe stability of the EO properties is the series of isothermal relaxation measurements. In this technique, the sample must be poled, as usual, at the poling temperature T_{p} for a time interval ∆t_{p} with an applied poling voltage V_{p}, then the sample is cooled down to the measurement temperature T_{m} maintaining the applied poling field. As soon as the T_{m} is reached, the poling field is switched off and the EO coefficient is continuously monitored by using either fast TMT or fast SHG measurements. In this case, the value of r_{33} is evaluated as a function of time for the given temperature T_{m}. As an example,

Isothermal relaxation measurements on HFIP-DR1AF. Reprinted with permission from [

Aligning the behaviour of the EO coefficient with the Kohlrausch-Williams-Watts (KWW) stretched exponential law Equation (20), it is possible to obtain the value of the time constant τ, of the stretching constant β and, from Equation (21), the value of the average time constant <τ> at a given temperature.

By comparing the curves for different temperatures, it is possible to retrieve the dependence of βand <τ> as a function of temperature. The β dependence is usually described by the Equation (24), while <τ> is well described by the Equation (22) for temperatures close or greater than T_{0}, and by the Equation (23) for temperatures below T_{0}. In

Plot of the average relaxation-time constant retrieved from the measurements similar to the one reported in

For temperatures below T_{0} ≈ 110 °C, (1/T × 1,000 > 2.6 K^{−1}), the average time constant follows an Arrhenius behaviour Equation (23). The Arrhenius behavior is described by a straight line in such type of plot. an activation energy _{a}

We point out that, for this purpose, it is necessary to be sure that the measurements are performed in the Arrhenius regime and not in the VFTH regime. This last observation shows that it is not possible to perform relaxation measurements at high temperatures, near _{g}_{a}^{1yr}

Here we show the results of the measurements described above on different fluorinated and non fluorinated electro-optic polymer species that are present in literature. The first four cases regard EO fluorinated polymers that can be used directly in the fabrication of active waveguides, meanwhile the other cases, here presented, are very stable crosslinkable EO polymers that can be used in EO modulators coupled with passive fluorinated waveguides [

The copolymer described here is a fluorinated side-chain copolymer, the HFIP-DR1AF [

(

The synthesis of the copolymers was carried out with the hexafluoroisopropyl alphafluoroacrylate monomer (HFIPAF) and the alphafluoroacrylate monomer bearing the Disperse Red 1 (DR1) chromophore (DR1AF). The polymer present 46 % of DR1 substituted group, the electro-optic coefficient of the sample was measured at _{33} = (4.6 ± 0.5) pm/V, for a poling field of _{p}

Thermal stability of the poling induced electro-optic coefficient was measured by means of both temperature scanning and isothermal relaxation measurements as shown in _{g}_{dep}_{g}

We then performed isothermal relaxation measurements (_{A}

The copolymer described here is a fluorinated side-chain copolymer, the FATRIFE-DR1AF [_{g}_{3})_{2} is substituted by the side group –CH_{2}CF_{3}. It is an evolution of DR1PMMA, with structure shown in _{33} = (4.7 ± 0.5) pm/V, for a poling field of _{p}

Thermal stability of the poling induced electro-optic coefficient was measured by means of both temperature scanning and isothermal relaxation measurements [_{g}_{dep}_{g}

We then performed isothermal relaxation measurements for different temperatures ranging between 60 °C and 110 °C. The retrieved activation energy is _{A}

The copolymer described here is a fluorinated side-chain copolymer, the ADAMANTANE-DR1AF [_{g}_{2}-C_{10}H_{15}), and a molar fraction y = 27% of the α-fluoroacrylate monomer bearing the Disperse Red 1 (DR1) chromophore (DR1AF). The general structure is given in

(

The electro-optic coefficient of the sample fabricated with ADAMANTANE-DR1AF was measured at _{33} = (2.8 ± 0.3) pm/V, for a poling field of _{p}

Thermal stability of the poling induced electro-optic coefficient was measured by means of both temperature scanning and isothermal relaxation measurements [

We scanned the temperature from the ambient one up to 150 °C, above the _{g}_{dep}_{g}

Temperature scanning measurements on ADAMANTANE-DR1AF. Reprinted with permission from [

We then performed isothermal relaxation measurements on the ADAMANTANE-DR1AF sample for different temperatures ranging between 110 °C and 140 °C. In _{33}(_{33}(0), for the three different fluorinated compounds presented so far, performed at the same temperatures _{m}

Isothermal relaxation measurements at _{m}

In _{A}_{A}_{A}_{dep}

Arrhenius plot of the average relaxation time constants retrieved from the isothermal relaxation measurements performed on the ADAMANTANE-DR1AF copolymer at different temperatures. Reprinted with permission from [

The copolymer described here [_{g}

The electro-optic coefficient of a sample fabricated with Polyimides-EHNT was measured at _{33} = 18 pm/V, after a corona poling procedure of one hour with an applied voltage of 8.5 kV at 190 °C.

Thermal stability of the poling induced electro-optic coefficient was measured by means of isothermal relaxation measurements performed at 80 °C and 120 °C, showing that at 120 °C the poled polymer maintains the 84% of its original _{33} value after 200 h [

In [_{g}

The electro-optic coefficient of the P2/C3 sample is the highest one with a value of _{33} = 126 pm/V (measured at

Thermal stability of the poling induced electro-optic coefficient was measured by means of TMT isothermal relaxation measurements performed at 150 °C, showing that the poled polymer maintains 88% of its original _{33} value after 500 h [

The polymer described in [_{g}_{33} value after 500 h.

Electro-optic fluorinated copolymers are very useful materials for technological applications in the telecommunication domain. The presence of fluorine reduces optical losses at the telecom wavelength of 1,550 nm. Meanwhile, the electro-optic coefficient can be optimized by using suitable nonlinear chromophores, as appeared here as an example with the well-known Disperse Red 1 (DR1) and also the hetarylazo EHNT chromophore that presents a larger electro-optic coefficient and other chromophores. In this context, the time stability of the externally induced electro-optic coefficient is an important issue in technological design and can be optimized by developing a crosslinkable high-Tg polymers host. Here, we have shown different measurement techniques that can be utilized in the characterization of the time stability of the EO coefficient. A review of the application of these techniques to different copolymer species was given, showing the high potentiality of the fluorinated EO copolymers in this field of application.

The author grateful acknowledge F. Michelotti for his teachings and for his support.

_{12}SiO

_{20}crystals