^{1}

^{*}

^{2}

^{2}

^{1}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

We report a simplified reflection mode Fabry-Perot interferometry method for determination of electro-optic (EO) coefficients of poled polymer thin films. Rather than fitting the detailed shape of the Fabry-Perot resonance curve, our simplification involves a technique to experimentally determine the voltage-induced shift in the angular position of the resonance minimum. Rigorous analysis based on optical properties of individual layers of the multilayer structure is not necessary in the data analysis. Although angle scans are involved, the experimental setup does not require a

Second-order nonlinear polymers have been widely studied because of their potential applications in high-speed communication and signal processing [

Using a reflective sample structure as one of the mirrors, Mach-Zehnder interferometry [_{13} and _{33}, the Michelson method can only measure _{13} and a separate experimental technique must be used to get _{33}. The modified attenuated total reflection (ATR) method [_{13} and _{33} separately, without an assumption for the value of the ratio _{13}/_{33} as required in both the simple and rigorous Teng-Man reflection methods [

A spectroscopic Fabry-Perot (FP) method was introduced by Uchiki

In this paper, we present a somewhat simplified experimental setup not requiring a

Angle-dependent reflectivity and voltage-modulated reflectivity data are collected using the experimental setup shown in

In order to analyze the experimental data for determination of the two independent EO coefficients _{13} and _{33} of poled polymer thin films, we consider the phase condition for reflection minima for two different FP resonator structures shown in

The reflection coefficient for the simple three-layer FP resonator can be obtained using Airy's formula [_{o} and _{e} are ordinary and extraordinary indices of refraction of the nonlinear poled organic thin film belonging to the point group symmetry ∞_{∞}_{v}_{o}^{(}^{γ}^{)} =_{γ} change simultaneously. In terms of the exterior angle of incidence _{s}_{o}_{p}_{γ}

From the angular shift Δ_{s}_{p}_{o}_{s}_{e}_{p}_{o}_{e}

Experimentally, direct observation of the angular shift of reflectivity minima under an applied voltage

The modulated reflectivity _{γ} is measured by lock-in amplifier at incident angles around the reflectivity minima where the voltage-modulated reflectivity is in the linear regime for validation of a Taylor expansion to first order. These angles can be found where the reflectivity has the largest gradient, _{γ}_{o}_{p}_{13} and _{33} are obtained using
_{o}_{e}_{3} are the separately measured anisotropic indices and thickness of the NLOP film.

_{13} and _{33} in this simplified model. In the next section, we explore the validity of using

A practical poled polymer thin film sample is a multilayer structure glass/(TCO or metal)/NLOP/metal as shown in ^{(}^{γ}^{)} at the reflectivity minima can still be expressed as ^{(}^{γ}^{)} =

_{13} and _{33} with varying wavelengths of 1,300 nm–1,550 nm for one of the many parameter combinations we explored We assumed a 4 μm thick NLOP film with dispersive anisotropic indices and EO coefficients (_{o} = 1.73, _{e} = 1.75, _{13}_{33} = 150 pm/V at 1,550 nm) on 30 nm thick gold layer and calculated the angular shift of the reflection minima obtained from _{13} and _{33} in the telecommunication wavelength range fall under ∼3%, indicating that

In principle, one should multiply the reflection coefficient in

Error in the EO coefficients can also result from the uncertainty in the film thickness and anisotropic indices, _{o}_{e}_{o}_{e}_{o}_{e}_{13} and _{33} caused only by the uncertainty in refractive indices are about 1.8% and 3.5%, respectively. In order to minimize these errors, the film thickness and anisotropic indices should be measured more precisely by prism coupling or other techniques, such as ellipsometry, after collection of the reflection FP data and removal of the metal layer. Although removal of the metal layer is also required for the ATR measurement technique, the data analysis is more straightforward in our simplified FP method.

We investigated the suitability of both ITO and a thin gold layer as the transparent electrode to determine which type of electrode is appropriate for reliable estimation of EO coefficients. Numerical simulation has been performed based on the equations described in Section 2. We simulated three different cases using 30 nm thick gold and two different ITOs as the transparent electrode. The complex index of refraction, ^{®} as shown in

_{e} and Δ_{p}_{e}, which is directly proportional to the EO coefficient _{33}, is within about 5% at the angle of incidence corresponding to the highest reflectivity modulation. Note that higher accuracy (less than 2% error) was achieved from the sample containing the 30 nm thick gold layer. Typical indices of refraction for NLOPs range from 1.5 to 2 at telecommunication wavelengths. In this range of refractive index and at the wavelengths of 1,300 nm and 1,550 nm, numerical simulations indicate that less than 4% error is expected to be obtained with the 30 nm gold layer, whereas the DT ITO gave less than 6% error with varying thickness and refractive index. For

The sample containing the TFD ITO layer, however, may give an error higher than 50% because of its low finesse resulting from relatively low reflectivity of the TFD ITO. Therefore, careful selection of a transparent conducting oxide should be made in order to make a higher Q resonator structure and reduce the error from using the simplified analysis. Once a highly reflective (absorptive) transparent conducting layer such as DT ITO or thin Au layer is employed in the sample,

In this simulation, we ignored any inverse piezoelectric contribution, but it can be characterized as described in the Appendix. According to [_{33} < ∼2 pm/V. A _{33} less than ∼1 pm/V was reported for the materials investigated in [_{13} and _{33}, respectively.

For characterization at telecommunication wavelengths, the nonlinear film must have appropriate thickness in order to have a reflectivity dip within a range of angle of incidence from about 30–60°. This is also true for the previous reflective FP method introduced in [_{3}>3.7_{3}<3.7

_{e}_{o}

A nonlinear polymer thin film was prepared with 30 wt.% of AJLZ53, in an amorphous polycarbonate (APC) host as shown in

The poled anisotropic indices and thickness can be obtained precisely using the prism coupling technique. In our case, the gold layer was subsequently etched in order to perform an attenuated total reflection (ATR) experiment using a modified prism coupling setup [_{13} and _{33}, respectively, using the simplified FP analysis, which showed good agreement (within ∼5%) with the values of 16 pm/V and 52 pm/V for _{13} and _{33} obtained using the ATR method.

We have presented a simplified reflection-mode Fabry-Perot method for estimation of EO coefficients of poled polymer thin films using a highly reflective transparent electrode layer. In the simple Teng-Man reflective method [_{13} and _{33} separately within an error of 8–10% without a complete analysis of the multilayer structure. Rigorous analysis of the multilayer structure based on _{33} of ∼50 pm/V at 1,550 nm. The EO response of the chromophore AJLZ53 yielded higher _{33} values measured independently elsewhere [

Schematic of Fabry-Perot (FP) experimental setup (

Schematics of two Fabry-Perot structures: (

Representative reflective curves without bias

Simulated errors of _{13} (blue) and _{33} (red) with varying wavelengths from the calculated angular shift of the reflection minima.

Complex index of refraction (

(

Simulated Δ_{e} (solid curves) and Δ_{p}_{o} and _{e}. Gray region shows ±5% error bound of Δ_{e}, directly corresponding to the error bound of an EO coefficient _{33}.

Existence maps of reflection minima in the angle of incidence range 30–60° as a function of unpoled index and film thickness using 20 nm thick gold as the transparent electrode: (

Molecular structures of AJLZ53 chromophore (

Experimental results from AJLZ53/APC. The measured reflectivities (Rs and Rp: left axis) and modulated reflectivities (Rs and Rp: right axis) as a function of angle.

Dong Hun Park and Warren N. Herman thank Victor Yun for assistance in construction of a Fabry-Perot experimental setup.

Here, we describe a technique to determine the inverse piezoelectric coefficient of a poled polymer thin film when two or more reflection minima are observed in a reflectivity curve. Taking the derivative of _{1} and Δ_{2}, we obtain

Using the reverse of this 2 × 2 matrix gives
_{33}_{33} using