1. Introduction

A dichroic polarizer film is a highly oriented, linear anisotropic material with a periodic structure; these films are employed to adjust the light intensity of several light sources, transforming the polarization direction vector as function of the film polarizing axis angle. In this context, polymeric dichroic polarizers are of great importance in standard optical and optoelectronic applications. For example, such polarizers can act as light-modulating passive optical elements in Liquid Crystal Displays (LCD) and low-power laser devices, among others [1]. The polarizer’s quality can be determined by the well-known optical Malus’ law. This expression describes the light intensity output as function of the angle between two consecutive linear polarizers. This optical test can be directly performed with a polarized light source and a standard optical power-meter, obtaining the well-known and representative quadratic sinusoidal transmission curve.

On the other hand, the PLPA-technique, takes advantage of the excitation of a material with a pulsed laser source which produces among other physical effects, acoustic signals on the lattice of the material. The acoustic waves (in this particular case, the ultrasonic waves), are produced within the illuminated material volume due to thermal processes such as a non-radiative response of the absorbed light; thus the PLPA-signal’s amplitude can be considered to be a directly proportional measurement of the energy absorption of the electromagnetic wave. In a typical PLPA-experiment the acoustic waves travel at the characteristic sound speed of the material under study reaching a PZT (PbZrTiO₃ ceramic) detector/microphone which allows the analysis of the PLPA-data via numerical correlation and RMS-processes. The PLPA-technique has emerged as an effective and accurate tool for the evaluation of thermal- (phase transitions) [2, 3] and optical- (optical absorption coefficients in solids) [4, 5, 6] processes occurring in different materials such as semiconductors, polymers, organic and inorganic crystals, etc [7, 8, 9, 10]. In short, several structural material characteristics can be accurately studied by PLPA-technique and the adequate analysis of the obtained data.

Most common experimental techniques applied in order to determine the optical absorption properties in materials are indirect procedures. Most of these techniques use direct optical transmission spectra and mathematical processing to obtain the complementary optical absorption data. In this work, we first show the reconstruction of the optical Malus’s law from the absolute absorption point of view via the photoacoustic signal analysis. Concretely, an organic linear polarizer film is excited at normal incidence by a pulsed laser beam and the generated photoacoustic signals are monitored as function of the polarizer axis angle while rotating the sample. It was observed that the obtained experimental curve is complementary and exhibits reciprocal symmetry to the sinusoidal optical Malus’s law. Moreover, we also demonstrate that a complete RMS- and CA-analysis of the photoacoustic signals as function of the polarizer axis angle permits monitoring of the morphological structure of the dichroic polymer film within the linear optical regime. This brings the possibility to derive, at first instance, the macroscopic structural properties of materials, such as the molecular order and anisotropy, which represent an important advantage particularly for low transparent materials where the analyses of purely optical measurements represent a difficult task.

2. Experimental section

2.1 Materials: iodine-impregnated polyvinyl alcohol

In this work, we have implemented a ~600 µm thick commercial linear polarizer film (Kenko, IN2170) which is commonly used in photographic studios, optical laboratories and as substrate support in the liquid crystal display industry, among other low optical power applications. This polarizer is built-up from a micro-structured dichroic sheet sandwiched between two strain-free glass plates. This specific kind of polarizer is commonly designed for visible (380–780 nm) applications. The polymer dichroic film is also known as a Polaroid-H sheet, which is an iodine-impregnated polyvinyl alcohol (PVA) sheet. PVA is a well oriented polymer containing hydroxyl groups that give rise to intermolecular and intramolecular hydrogen bondings. PVA is classified into three different types: isotactic, atactic, and syndiotactic, according to the stereoregularity of its hydroxyl groups. Physical properties of PVA are highly dependent on the degree of syndiotacticity, which is primarily determined by the choice of the vinyl ester monomers [11, 12, 13].

To manufacture Polaroid-H films, a sheet of PVA is heated and stretched in one direction while softened, this procedure induces the alignment of the long polymeric molecules along the stretch direction. When dipping the stretched PVA-film in an iodine solution, the iodine atoms attach themselves to the aligned polymeric chains, providing electrons to the film structure; as a consequence high electronic mobility along the aligned chains is possible, but not in the perpendicular direction. Therefore, optical waves traveling across the organic film with electric fields parallel to the polymeric chains (low transmission optical axes) are strongly absorbed due to dissipative effects produced by the allowed electron mobility. Thus, the respective perpendicular film direction of the PVA-chains can be considered as the “transparent” optical axis, since electrons cannot freely move to absorb energy. This kind of polarizer looks neutral in color when viewed under unpolarized light and is remarkably free of light scattering due to the tiny dichromophore molecular dimensions [11].

2.2 Detection of the photoacoustic signals

The experimental setup for the PLPA-signal detection is schematically shown in Fig. 1. The sample is illuminated by a p-polarized Q-switched frequency-doubled Nd:YAG laser system (Minilite II from Continuum, USA) along the z-direction, the laser system generates light pulses of ~7 ns and operates at a repetition rate of 10 Hz with maximum output energy of ~5.0 mJ per pulse at a wavelength of 532 nm. The beam is not focused in order to avoid lateral diffusion of heat or sample damage. A fast photodiode detector (Thorlabs Inc. model 201/579–7227) with a rise time <1 ns is implemented to receive part of the laser beam triggering a digital oscilloscope in order to monitor the acoustic signals. The iodine-PVA sample is mounted on a manual rotation stage (RSP1, THORLABS, accuracy: 1°). A 500 KHz cylindrical PZT piezoelectric transducer (10.0 mm in diameter) is attached to the center of the sample (on its rotation axis), in order to preserve the same Δy-path from the light excitation point (acoustic source) to the PZT-detector, while rotating the PVA-film sample a given θ-angle within the x-y-plane. The microphone transforms the generated photoacoustic wave signals to electronic ones which are then visualized and analyzed on a 500 MHz digital oscilloscope (Tektronik TDS5040). These signals were processed in a PC via several RMS and correlation numerical processes encoded in MatLab. On the other hand, the purely transmitted laser beam is captured by a quartz optical fiber (600 µm core aperture), the corresponding optical signals were recorded by an optical spectrometer (Ocean Optics, HR4000 UV-vis-NIR) in order to verify the traditional Maluś law at 532 nm.

 

Fig. 1. Schematic diagram of the photoacoustic experimental setup implemented for the simultaneous PLPA and optical transmission measurements as function of the linear polarizer θ-angle film rotation.

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3. Results and discussions

3.1 UV-Vis absorption spectra

UV-Vis Absorption spectra were obtained with non-polarized light at room conditions from a double beam Shimadzu-260 UV-Vis spectrophotometer using air as reference in the second window. In Fig. 2, the absorption spectra from the linear polarizer and a 1.5 cm thickness corning glass window used as a control sample, are presented. At 532 nm the light absorption of the linear polarizer is more significant; in this way, the photoacoustic signal from this polarizer should be considerably stronger than that obtained from the amorphous glass window, including those signals arriving from the constituting sandwiching glass plates of the commercial polarizer sample.

 

Fig. 2. UV-Vis absorption spectra of a commercial linear polarizer film and a common glass window plate implemented as control sample. The linear polarizer presents stronger absorption in the visible range; thus strong photoacoustic signals are expected at 532 nm for this sample.

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3.2 PLPA signals

Figure 3 shows an example of two unprocessed PLPA-signals taken at θ=256.0° and θ=166.0°, corresponding to the minimum and maximum optical transmission axis of the film, respectively (θ is referenced from the y-coordinate in Fig. 1). These directions correspond to the orthogonal polarizing states. The PLPA-signals present oscillations with a multitude of amplitudes which decay as the acoustic wave loses energy. Differences in the relative phases and changes in the frequency components are also possible. The observed amplitude variations on the PLPA-signals are directly related to the optical absorption, while phase and frequency changes are primly connected to the optical reemission and optical impedance of the material at the implemented wavelength. Consequently, a systematic study of all PLPA-signals generated within the 0–360° θ-interval may reveal fundamental information regarding the structure and anisotropies existing within the polymer film. In fact, such studies, if feasible, may give rise to alternative calibration and testing experimental procedures, which could be very useful in nontransparent film systems.

 

Fig. 3. Two unprocessed photoacoustic signals obtained from a commercial linear polarizer at θ angles of 166.0° and 256.0° (corresponding to the minimum and maximum optical absorption, respectively).

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3.3 Photoacoustic Maluś law via RMS and PLPA analysis

Figure 4 shows the pure optical laser transmission curve obtained as a function of the linear polarizer θ-angle, this curve was measured using the spectrometer in order to monitor, as reference and calibration measurement, the traditional optical Maluś law. Data were fitted by a simple cubic spline method. In general, the degree of polarization is a dimensionless quantity, and can be defined as follows [14]:

where I_M and I_m are the maximum and minimum values of the optical transmission curve, respectively. For the commercial polarizer sample, the obtained degree of polarization is given by P=0.7621. Thus, according to Malus’s law [14], the optical transmission I_A can be described as:

where θ is the angle of incidence. In this work, symmetry directions were experimentally located within a full θ-cycle (360°) measurement at: 81.5° (minimum), 172.0° (maximum), 262.5° (minimum) and 350.5° (maximum) from the starting θ=0° (y-axis) reference coordinate. In this case, a phase shift of ~8° between the maxima/minima measured data and the mechanically located 0°-position was observed. This experimental error produced when locating the high transmission axis of the polarizer at the θ=0° position arise from the fact that the polarizer film does not present a polarizing axis mark, thus the position of this axis was not well determined as the film was attached to the rotation stage (aligned to the 0°-axis). This 8° mismatch is actually meaningless, since the reproducibility of the optical Malus law can be accurately verified as the polarizer is rotated in a full 360°-cycle, no matter what the starting position is. In fact, it can be observed from Fig. 4 that the difference between well established maxima/minima is ~90°, which agrees well with the Malus-law, establishing the relative positions of maxima/minima optical transmittance.

 

Fig. 4. Pure optical laser transmission observed at 532 nm through the studied organic polarizer film: an excellent concordance with the traditional optical Malus’s law can be observed.

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On the other hand, as explained before and shown in Fig. 3, the photoacoustic signals present numerous peaks in a time interval for each individual measurement. An examination of only one of these peaks would be insufficient to study the structural properties of the film sample. However a complete study of the photoacoustic signals (considering all amplitudes in each signal), allows the extraction of more accurate information concerning the macroscopic structural properties of the material. For example, the RMS analysis represents the absolute amplitude average of the whole signal, hence all amplitude changes detected in each signal are considered with this kind of numerical processing. In this way, Fig. 5 shows the normalized RMS analysis of the PLPA-signals; data were fitted with the optical Maluś law Eq.(2) with a shift of 98.0° in order to be compared with the previous results obtained for the pure optical experiment. As can be seen in Fig. 5, RMS data obtained from the experimental PLPA-signals show again a well defined contrast corresponding to the main symmetry directions of the organic film (maximum/minimum optical absorptions). In this case, the processed RMS-data exhibit maximal/minimal responses at: 76° (maximum), 166° (minimum), 256° (maximum), and 346° (minimum), these angles were obtained after the spline fitting procedure defining the material symmetry directions and anisotropy. We found an outstanding correlation between the curves of Fig. 4 and Fig. 5, since the maxima and minima are remarkably traded-off, in such a way that maxima/minima from the optical experiment correspond to minima/maxima from the PLPA-experiment, producing a clear phase shift of nearly 90°. It should be stated that scattering effects, which may contribute to the phase differences, are neglected under the present approach. On the other hand, since at normal incidence the reflection is constant, then an increase of the optical absorption leads to an increment on the PLPA-signal amplitude, this occurs in opposition to the optical experiment where an absorption increment provokes a decrease of the transmission signal. When comparing minima/maxima between the PLPA and optical experiments, only a small difference of ~6° can be determined for corresponding angles. The contrast (maxima/minima definition, see Eq.(1) observed in the degree of polarization via the PLPA-experiment is given by the normalized data (taking I_M=1, I_m=0.338) to P=0.4948.

As illustrated from Fig. 4 and Fig. 5, the RMS analysis of the PLPA-signals permits an adequate reconstruction of the optical Malus’s law and the accurate identification of the optical axes, evidencing the anisotropy of the system.

 

Fig. 5. RMS-analysis of the PLPA-signals: the RMS-numerical processing permits an average of the PLPA-acoustic signals which is directly proportional to the optical absorption. This kind of analysis provides a reconstruction of an alternative opto-acoustical Malus’s law from the absorption point of view.

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3.4 Structural properties using correlation analysis of the PLPA-signals

RMS analyses mainly provide information concerning the amplitude of the PLPA-signals; but correlation analyses primarily bring information about the constituting phase and frequency components of the PLPA-signals. These additional studies also provide a close connection with the structural properties of the studied material [2], in particular with the macroscopic morphology and arrangement of the polymer film. In the present study, this mathematical analysis consists of the correlation of the PLPA-signals (u_m) at an incidence θ_i-angle with the immediately subsequent u_m+1 signal corresponding to the θ_i+1-angle:

In the implemented experimental design, the θ_i-angle is the only experimental variable; thus differences between consecutive correlated PLPA-signals can represent structural changes within the film. In the case that these CA-signals do not show any marked difference, the resulting data present only a flat distribution; for instance the PLPA-signal produced from an amorphous sample, where no particular symmetry directions can be found, the CA-signals remains practically unchanged from one CA-process to another. In Fig. 6, the CA-processing of the PLPA-signals obtained from the polarizer film is presented (CA-data were fitted by a cubic spline interpolation process: continuous line). In order to find material symmetries in the film sample, an averaging was carried out in the sloped zones to evidence the symmetry directions. In increasing order, these directions were found at: 72.5° (maximum), 165.5° (minimum), 252.5° (maximum) and 340.0° (minimum). In this case, the obtained splined-curve again shows a similar trend of absolute maxima/minima comparable to that of the RMS-analysis; the CA-curve is indicative of the corresponding structural film changes observed on rotating the sample (in this case the macroscopic molecular order or material anisotropy are the main structural properties detectable at a given and fixed room conditions). The full curve exhibits truncated maximal/minimal peaks, where the absorption/transmission strongly dominates the optical process. Since the PLPA-technique and the corresponding RMS and CA have proven to be an extremely sensible methodology to detect thermally induced structural material transformations [2], material constitution or, as proven in this work, orientational molecular order; it could be possible that although the iodine molecules are highly aligned perpendicular to the transmission polarizer axis, the polymer could itself adopt a twisted distribution along this axis, for instance, in a helix-like organization, or even other more complicate geometries. In such a case, the induced acoustic waves can transit in many directions with respect to the polymer axis and the full PLPA-signal arriving at the acoustic detector would be diminished, provoking the reduced and not well defined absolute maxima/minima peaks observed in Fig. 6.

 

Fig. 6. Correlation analysis of the PLPA-signals: The study of the macroscopic film structure can be performed by the analysis of the numerical correlation of consecutive the PLPA signals. Hence, the correlation processing reveals a periodic structure, where the structural anisotropy exposes basically the same main directions as in the RMS case.

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In Table 1 the established symmetry directions (SD) found by the different optical and PLPA-data processing methodologies used in this work, are summarized. The sample is a dichroic polymer film; hence it is possible to find the orthogonal polarization axes within the anisotropic material. Hence, in the first row of Table 1, the optical transmission results are presented. The minimum optical transmission axis is sequentially localized, within the measured range, at 81.5° and 262.5° ± 0.5°; whereas the maximum optical transmission axis, which lies practically orthogonally to the previous one, is again sequentially localized at 172.0° and 350.5° within the obtained experimental data. The optical Malus’s law is a well- known optical experiment, thus once the film optical axes are defined by this law, they can be utilized as reference for the PLPA-experiments and its respective analyses. In the latter cases, the established axes (see second and third rows on Table 1) obtained from the RMS- and CA-analyses, reveal maximum acoustic amplitude signals (low optical transmission axis) at 76o/72.5° and 256°/252.5° for the RMS/CA-methodologies, respectively. Here, the relative percentage errors with respect to the optical result are in the order of 6.8% and 2.5% for the RMS case at the two corresponding comparative maxima/minima points, whereas for the CA-data processing these errors are accordingly in the order of 11.0% and 3.8%. Finally, the presence of minimal acoustic amplitude signals (high optical transmission axis), confirm the symmetry of the film structure, these minima are located at 166/165.5o and 346o/340o for the RMS/CA-methodologies, respectively. In this case, the relative percentage errors with respect to the optical result are in the order of 3.9% and 1.3% for the RMS analysis at the two comparative minima/maxima points; under the CA processing, these errors are correspondingly in the order of 2.8% and 3.0% In fact, as shown in this work, the correspondence between the RMS- and CA-analyses is outstanding, in both cases, the maximal/minimal transmission axes are found to be nearly perpendicular to each other; therefore, the PLPA-technique reveals the presence of the orthonormal polarization axes with concordance to the optical analysis.

Table 1. Symmetry directions (SD) observed in the linear polarizer sample by the optical transmission, RMS and CA-methodologies: SD1 and SD3 correspond to the minimum optical transmission axis (maximum acoustic transmission), and SD2 and SD4 correspond to the maxima optical transmission axis (minimum acoustic transmission). The three different analyses actually reveal the same anisotropy and point out to the orthogonality of the main symmetry axes

View Table

4. Conclusions

Classical absorption measurements are not direct measurements since these quantities are derived from purely optical experiments, namely the transmittance spectra, where absorbance is obtained from the difference between the incident and the transmitted energy via the Beer-Lambert law, thus alternative experimental methodologies have been applied in order to investigate absorption effects and its consequences in the interaction of light with matter in more detail. One of these techniques is the photoacoustic analysis, which can be considered as a direct absorption measurement as the measured quantity is directly proportional to this photophysical effect and the related physical phenomenon occurs as a direct result of the amount of absorbed light. Under this framework, the sample heating produced by light which produces the PLPA-signals is directly related to the absorbed electromagnetic energy, and contrary to conventional transmission spectroscopic measurements, neither scattered nor reflected light considerably alters the PLPA-signals [4]. The PLPA-technique can then provide a more accurate perspective of the different photophysical processes occurring within the studied material structures at an electronic-lattice level. In fact, as shown in this work, the correspondence between the traditional optical Maluśs law and the RMS/CA-analyses applied to the PLPA-signals shows the possibility to precisely identify symmetry directions in polymeric film structures. In addition, from the RMS-study, it is shown that the full reconstruction of Malus’s law (from the opto-acoustic absorption point the view), is possible. In this case, the optical transmission data was itself used as control experiment to consistently confirm the PLPA-results.

In general, the PLPA-method is a low cost, easy to apply technique, whose analysis reveals important and complementary information concerning the macroscopic material structure. The success in the studies carried out in this work allowed the accurate characterization of the absorption distribution in a common anisotropic material, which opens new and potential possibilities for the PLPA-method, including for instance the characterizations of anisotropic linear and nonlinear optical materials and plastic stress determination. In particular, in the research of novel materials or in industrial control processes, the implementation of PLPA-experimental methodologies and RMS/CA-data processing thereof may provide practical, highly efficient alternatives, in order to characterize non-transparent oriented materials and in general, anisotropic structures. These are from our point of view, plausible new application proposed for the PLPA-technique, allowing in principle, the determination of preferential/induced directions and/or macroscopic orientational order distributions within the material network.