A reflection-type Fabry-Perot interferometer (FPI) with a large tunability has been demonstrated on relaxor ferroelectric poly(vinylidenefluoride-chlorotrifluoroethylene-trifluoroethylene) [P(VDF-CTFE-TrFE)] 78.9/13.9/7.2 mol% with a thickness of 9.2 µm. The optical path length of the FPI is modulated by the electrostrictive strain of the terpolymer under electric field, where the low-loss distributed Bragg reflector and aluminium film are employed as the mirrors in the FPI. A positive strain of 20% has been achieved in the terpolymer film under a field of 30 MV/m, which leads to the FPI with a tunable range of more than 200 nm at wavelengths around 680 nm.
© 2008 Optical Society of America
The development of new electro-optical (EO) modulators and optical filters for wavelength division multiplexing (WDM) communication systems has drawn increasing attention recently, because these optical interconnections are regarded as one of the best solutions that overcome the disadvantages of electrical interconnections . The Fabry-Perot interferometer (FPI), which makes use of multiple reflections between two closely spaced surfaces to create interference patterns, has been used extensively in high resolution spectroscopy as EO modulators and tunable filters [2–7]. The shift of resonant wavelength in FPI is usually realized via the change of refractive index of etalons and/or space between two reflective mirrors in response to the applied field. Compared with inorganic crystals and liquid crystals, polymeric materials posses many processing advantages such as flexibility, compatibility with “soft” technologies of lithography, and ability to be deposited into intricate shapes. Some polymers exhibit high EO coefficients relative to their inorganic counterparts, but a significant change of refractive index requires extremely large EO coefficients[8,9], it is thereby challenging to fabricate high-performance FPIs solely based on the EO effect in the polymers [10,11].
As well-known ferroelectric polymers, poly(vinylidene fluoride) (PVDF) and its copolymers with trifluoroethylene [P(VDF-TrFE)] exhibit a high piezoelectric response and have consequently found their applications as a spacer to vary optical path length in electrical tunable FPIs . More recently, it has been found that the electromechanical properties of PVDF-based ferroelectric polymers can be significantly improved by introducing 1,1-chlorofluoroethylene (CFE) as crystalline defects into P(VDF-TrFE) [13–15]. A electrostrictive strain of more than 7% has been obtained in P(VDF-TrFE-CFE) with a composition of 68/32/9 mol%, which are orders of magnitude larger than those of P(VDF-TrFE) . Correspondingly, this terpolymer has been shown to generate a total -5.4% optical path length change including a refractive index change of -2.6 % from the Kerr effect under an electric field of 80 MV/m . The electrical tunable FPIs with a tunable range of 22.5 nm at wavelengths near 1.5 µm have also been demonstrated in the P(VDF-TrFE-CFE) terpolymer sandwiched by silver films .
In this letter, we report a new reflection FPI based on a poly(vinylidenefluoride-chlorotrifluoroethylene-trifluoroethylene) (PVDF-CTFE-TrFE) terpolymer. The presence of bulky chlorotrifluoroethylene (CTFE) unit in the terpolymer induces a complete transformation to the relaxor ferroelectric phase from the normal ferroelectric phase in P(VDF-TrFE), and consequently a high electromechanical response .
The P(VDF-CTFE-TrFE) terpolymer with a composition of 78.9/13.9/7.2 mol% was synthesized by a newly developed approach, including the copolymerization of VDF and CTFE and a subsequent hydrogenation reaction . Compared with the polymers prepared via the conventional direct ter-polymerization, the terpolymers synthesized by this two-step method possess a higher percentage of regiodefects, giving rise to a high dielectric constant and a lower elastic modulus, and thus a high electrostrictive strain .
The reflection FPI used in our work is focused on studying the electromechanical effect of the PVDF terpolymer, the schematic of it is shown in Fig. 1. The terpolymer was deposited onto ITO substrate using the solution-cast method with dimethyformamide (DMF) as the solvent. After the solvent was evaporated under vacuum at 80°C for 20 h, the film was annealed at a temperature near 70 °C for ~12 h to improve the crystallinity. Reflection spectra of the film and FPI were recorded on an Olympus USPM-RU spectral reflectivity measurement system from 560 to 720 nm. Normal incidence was adopted in the reflection measurement. If the incident angle increases, the interference peak wavelengths blue-shift and the acutance of the interference fringes decrease because of the deceasing of the reflectivity of two reflectors, so the normal incidence is the best choose. Aluminium (Al) was evaporated onto the terpolymer film to serve as both electrode and reflection mirror. Low-loss distributed Bragg reflector (DBR) forms the top mirror of the FPI. The distance between the two mirrors was horizontally aligned by the glass particles with the uniform diameter and then fixed using UV curable epoxy. In this configuration, the air gap space in the FPI etalon is modulated by the field-induced longitudinal strain of the terpolymer film. In order to reduce the experimental error, all the tests are focused on the center of the mirrors or polymer film.
3. Results and discussion
The reflection spectrum of the terpolymer film on ITO substrate is presented in Fig. 2(a). When a homogeneous thin film is deposited on a substrate, the characteristic matrix of the film can be defined by 
where N=n-ik and Ns=ns-iks are the complex refractive indices of the film and substrate, respectively. The dispersion of substrate material was calculated directly from the reflection spectrum of the bare substrate during the fitting. Δ(2πNd/λ) is the phase thickness of the film, where d is the physical thickness. Therefore, the reflection of the thin film follows the formula
where n 0=1 when the incident medium is air. Since n, k and d can not be obtained from Eq. (2), an additional dispersion equation as a function of wavelength was introduced to fit the reflection values. For the transparent polymer with the extinction coefficient close to zero over the whole spectrum, the Cauchy dispersion [Eq. (3)] was used to extract the optical constants of the film [22–24],
where An, Bn, Cn, Ak, Bk are the Cauchy parameters, and the n(λ) expression is ended after the first two terms in most cases. The thickness of terpolymer film 9.2 µm obtained from the model is in good agreement with the value obtained by surface profiler.
As also shown in Fig. 2(a), the extracted refractive indices of the terpolymer film monotonically decrease from 1.47 to 1.40 as wavelength shifts from 560 to 720 nm. The structure of the DBR mirror is air/(HL)˄2H/glass, where H is TiO2 layer with a refractive index of 2.18 and L is SiO2 layer with a refractive index of 1.45, and the optical thicknesses of these layers are quarter wave of the central wavelength (670 nm). As shown in Fig. 2(b), the reflectance between two mirrors matches reasonably well from 560 to 720 nm. The cavity finesse F is defined as F=4R/(1-R)2, where R is the reflectivity of the mirror. The reflectivity of Al mirror evaporated onto the terpolymer film is not high, which decreased the cavity finesse. Moreover, the reflectivity and roughness of Al mirror determined the extinction ratio of the FPI (Fig. 3). The further work will be focused on modifying conditions of Al and polymer film fabrication to improve the reflectivity of Al mirror on the polymer film or using other metal mirror to replace Al.
Figure 3 shows the reflection spectra of the FPI at the applied voltages. It has been found that the resonant wavelength continuously shifts to short wavelength with the increase of voltage, which indicates the air gap space of the FPI has shrunk under the applied field. It is noted that obvious decrease in the interference orders of the FPI occurs when the applied voltage is higher than 200 V. For the valleys of the resonant wave, the interference order m can thus be expressed as
Because of the normal incidence (θ=0) and air gap space (n=1), Eq. (4) can be rewritten as m=2d/λ. In order to clearly show the interference orders change, the interference fringes were labeled by their order number at the different applied voltages in Fig. 3.
The air gap space (l) at different applied voltages can be calculated from the interference curve [Eq. (5)], λ1, λ2 are the adjacent valleys of the resonant wave.
The calculated air gap spaces are 5.04 and 3.10 µm at 0 and 300 V, respectively. In the current scheme, the terpolymer film is not directly used as the cavity of the etalon. Thereby, the change in optical path length is due to the longitudinal strain of the terpolymer film without the influence from the EO effect. The tunability Δλ can thus be expressed as
As Δl/l reaches 0.385 at 300 V, a wide tunable range of more than 200 nm has been obtained for the resonant wavelength at 684 nm.
The large tunable range demonstrated in the FPI results from a high electric field-induced longitudinal strain in the terpolymer film. The longitudinal strain (S=Δl/d) of the terpolymer film as a function of electric field is shown in Fig. 4. Under a field of 30 MV/m, a thickness strain of 20% has been obtained, which is among the highest electrostriction reported in the PVDF based ferroelectric polymers. The electromechanical response is generally composed of the linear piezoelectric effect and the electrostriction where the strain is proportional to the square of the applied field . In our work, the modulation of the FPI is found to be independent of the sign of the electric field, indicating that the inverse piezoelectric effect has little contribution to the strain under the applied field. Moreover, the nearly linear relationship between the strain and the square of the electric field confirms that the high strain mainly comes from the electrostriction effect.
The terpolymer P(VDF-TrFE-CTFE) 78.9/7.2/13.9 mol% is a relaxor ferroelectric polymer with the TC of only 22.8 °C. The crystalline structure of the terpolymer was examined in wide-angle X-ray diffraction (WAXD) measurements, which shows a diffraction peak at a 2θ angle of ~18° arising from the (002) reflection of the non-polar γ phase. Consistent with the WAXD result, the FTIR spectrum of the terpolymer displays an absorption band associated with the tttg+tttg- conformation at 505 cm-1. On the other hand, the peak corresponding to all-trans chain conformation of the ferroelectric β-phase is absent, further confirming tttg+tttg- conformation in stead of all-trans conformation becomes the domination of ferroelectric phase in the terpolymer , so the observed giant electrostriction in this polymer is likely to come from the nonpolar γ-phase reorientation under the applied field [18,26].
In summary, a high performance reflection FPI has been fabricated based on relaxor ferroelectric P(VDF-CTFE-TrFE) terpolymer. The large electrostrictive strain of the terpolymer has been accounted for a wide tunable range (>200 nm at ~680 nm) demonstrated in the FPI. The results suggest that the large electromechanical response in these electroactive polymers can be utilized effectively for electro-optical devices.
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