# Electro-optic phase modulation in light induced self-written waveguides propagated in a 5CB doped photopolymer

A Jemal, M Ben Belgacem, S Kamoun, M Gargouri, Kokou Dorkenoo, Alberto Barsella, Loic Mager

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## To cite this version:

A Jemal, M Ben Belgacem, S Kamoun, M Gargouri, Kokou Dorkenoo, et al.. Electro-optic phase modulation in light induced self-written waveguides propagated in a 5CB doped photopolymer. Optics Express, 2013, 21 (2), pp.1541-1546. 10.1364/OE.21.001541 . hal-05258647

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Distributed under a Creative Commons Attribution 4.0 International License
Electro-optic phase modulation in light
induced self-written waveguides
propagated in a 5CB doped
photopolymer

Abdelmonem Jemal,¹ Mohamed Ben Belgacem,¹ Saber Kamoun,¹
Mohamed Gargouri,¹ Kokou D. (Honorat) Dorkenoo,² Alberto
Barsella,² and Loïc Mager²,*,

¹Laboratoire de l'État Solide, Groupe Télécommunication Optique, Faculté des Sciences de Sfax, B.P. 1171, 3000 Sfax, Tunisia

²Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), UMR7504,
CNRS-Université de Strasbourg, 23 rue du Loess, B.P. 43, 67034 Strasbourg CEDEX 2,
France

*loic.mager@ipcms.unistra.fr

**Abstract:** We present the inscription of a Light Induced Self-Written (LISW) waveguide in a 4-cyano-4'-pentylbipheny (5CB) doped photopolymer. The dynamic reorientation of the 5CB molecules in the material under applied electric field leads to birefringence in LISW waveguide and thus allows the control of the phase of the guided mode.

© 2013 Optical Society of America

**OCIS codes:** (160.4890) Organic materials; (190.6135) Spatial solitons; (230.2090) Electro-optical devices.

**References and links**

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**1. Introduction**

The propagation of a Gaussian beam in a photosensitive medium leads to the inscription of a self-written channel [1]. In this process, the propagating light beam initiates a localized photopolymerization of the medium. The resulting increase in refractive index counters the diffraction and leads to the dynamical inscription of a self-written waveguide. This process allows the fabrication of single mode waveguides without the use of complex microlithographic processes and ensures automatically their alignment with the optical fiber used to inject the light into the material. Light Induced Self-Written (LISW) waveguides are now prospects for different applications such as optical interconnections on Printed Circuit Boards (PCB) and integrated optical device fabrication [2]. Beside the possibilities to build optical waveguides without the use of complex processes and to achieve self-controlled interconnections, photopolymer-based LISW waveguides also allow the implementation of optical functions [3, 4]. For example, the demonstration of optical amplification has been made using fluorescent doped photopolymers [5, 6] and the addition of photochromic molecules has enabled the control of light transmission [7]. In this paper, we present our first attempt to induce electro-optical (EO) properties in LISW waveguides by doping them with optically active molecules prior to the inscription of the guide itself. Using these waveguides, we demonstrate the control of the phase of the guided mode.

**2. Material**

In organic materials, EO properties are generally induced through the addition of active non linear optical chromophores. These dipolar chromophores are aligned under applied electric field in order to break their centrosymmetrical arrangement and consequently to enable the EO effect. The great challenge for EO organics lies in the efficient freezing of the orientation of the chromophores. This is obtained through the preparation of specific materials (e.g. see L. Dalton et al., 2010 [8] and references therein) exhibiting very high viscosity. In the photopolymer used in this work, the orientational mobility of the molecules dispersed in the matrix remains very high, even after the full photopolymerization step. This is a desirable property here since we intend to induce a modulation of the refractive index of the material by adding dipolar molecules exhibiting linear polarizability anisotropy. As they remain free to orient in the matrix at room temperature, they can be dynamically aligned by an externally applied electric field. The apparition of the birefringence depends entirely on this alignment. When the electric field is switched off, the orientation of the molecules returns to the isotropic distribution and the birefringence vanishes. It is important to note that since this phenomenon involves the
re-orientation of molecules, it is completely different in nature from the Pockels effect, and it operates at larger timescales. In order to avoid any ambiguity, we will refer to this induced orientational birefringence as “electro-optical response” (EOR).

The molecule used in our sample to induce EOR is 4'-n-pentyl-4-cyanobiphenyl (5CB, Merck). 5CB is transparent in the visible part of the spectrum and does not inhibit the radical photopolymerization process of the chosen pentaerythritol triacrylate (PETA, Alpha Aesar) monomer. 5CB exhibits a high linear polarizability anisotropy and a 4.9 D permanent electric dipole [9]. Finally, it remains free to orient in the polymerized material. Published results on polymers doped with birefringent molecules can be used to predict the variation in refractive index under applied electric fields [10]. This variation can be extrapolated from the data of 5CB and PETA. When the light is polarized along the applied electric field direction the refractive index change is given by:

$$ \Delta n = \frac{2\pi}{n} \frac{4}{45} N f_{\infty} \Delta\alpha \left(\frac{f_0\mu}{k_B T}\right)^2 E^2 = \frac{1}{2} n^3 r E. \quad (1) $$

where $E = 10V \cdot \mu m^{-1}$ is the applied electric field, $n = 1.52$ is the refractive index, $f_{\infty} = (n^2 + 2)/3$ is the Lorentz-Lorenz local field factor, $\mu$ is the dipolar moment, $f_0 = \varepsilon(n^2 + 2)/(n^2 + 2\varepsilon)$ is the Onsager factor, $\varepsilon = 5$ is the relative dielectric permittivity, $\Delta\alpha = 1.5 \cdot 10^{-23}cm^{-3}$ is the linear polarizability anisotropy for the 5CB, $k_B$ is the Boltzmann constant $T = 300^\circ K$ is the temperature and $r$ is the electric field dependent EOR coefficient. For a 15 % wt. concentration of 5CB, translating into a molecular concentration of $N = 4 \cdot 10^{20} cm^{-3}$, this would lead to a change in refractive index of $\Delta n = 0.8 \cdot 10^{-5}$ which can be measured through an interferometric method.

### 3. Functionalized LISW waveguide fabrication

Following the above considerations, 5CB is incorporated at 15 % wt. in the trifunctional acrylate PETA, along with 0.5 % wt. of Bis(cyclopentadienyl)bis[2,6-difluoro-3-(1-pyrryl)phenyl]titanium (Irgacure 784, Ciba) used to initiate the photopolymerization in the blue/green part of the spectrum. These constituents are mixed without additional solvent. The proportion of 5CB remains within the solubility limit and no phase segregation is observed.

To write a single mode self-written channel, a prepolymerization step is needed to control the final refractive index contrast [11]. However, the addition of 5CB lowers the final refractive index change in the photopolymer, as the addition of any non reactive species does. Moreover, 5CB is partially expelled from the polymerized regions and its concentration shows a gradient [12]. As its average refractive index ($n_{5CB} = 1.61$) is higher than that of the matrix ($n_{PETA} = 1.52$), this gradient lowers the contrast in refractive index needed to insure the waveguide inscription. This feature increases the sensitivity of the propagation process to the prepolymerization step. Figure 1 illustrates the strong dependence of the guiding process on the initial exposure to a halogen lamp, providing 25 mW \cdot cm$^{-2}$ power density on the sample. For excessive prepolymerization times (> 2 minutes), no light confinement can be observed (Fig. 1(a)). We have found that a for a prepolymerization time of one minute (Fig. 1(b)) and an injected power of $10\mu W@514nm$, the LISW waveguide does propagate efficiently. Nevertheless, the addition of 5CB induces fluctuations in the diameter of the guide along the direction of propagation that damp out one millimeter from the injecting optical fiber. Beyond this length, the waveguide propagates steadily. No noticeable alteration of the properties of the guide are noticed over more than one month of experimentation.

A 125 µm thick cell, containing the doped photopolymer, is made from two $1 \times 2cm^2$ ITO glass plates that allow the observation of the LISW waveguide build-up and the application of the electric field. The light is injected into the polymer using a polarization maintaining single
<figure><img src="image_3.png" /><figcaption>Fig. 1. Built-up of the LISW. The injecting fiber is on the left of the pictures. a) with 5 min. prepolymerization, b) with 1 min. prepolymerization</figcaption></figure>

mode optical fiber. The orientation of the fiber is set to align the light polarization direction with that of the applied electric field. The LISW waveguide propagates from the fiber to an exit window placed at the output of the cell in order to avoid the introduction of aberrations on the exiting mode by an irregular air/photopolymer interface.

## 4. Electro-optical response measurement

To measure the EOR of the doped LISW waveguide a Mach-Zehnder interferometric arrangement (see Fig. 2) has been used. Two cells containing the LISW waveguides are connected to the polarization maintaining optical fibers (Nufern PM460-HP) and are inserted in the interferometer. We have checked that the polarization of the light is not altered by the propagation in the LISW. One cell (Active) is connected to the high voltage amplifier driven by a function generator, while the other one (Passive), prepared from a pure mixture of PETA and Irgacure, is only used to improve the matching of the interfering wavefronts. The interference pattern appears as a set of concentric rings. To determine the phase modulation, the inner ring is selected using a diaphragm and send to a photodiode. Both the variations of the applied electric field and of the light intensity are simultaneously monitored on a numerical oscilloscope.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Experimental setup. Light from the Ar+ laser is coupled into the fibers through x10 microscope objectives. Fibers are coupled with the LISW waveguide in each cell. The two beams at the exit of the two LISW waveguides interfere. The central part of the interference pattern is selected using a diaphragm and send to a photodiode. The active cell is connected to a high voltage amplifier driven by a function generator.</figcaption></figure>
## 5. Experimental results and discussion

The mechanical instabilities of the setup generate a slow drift of the phase (see Fig. 3). The amplitude of these slow erratic variations $\Delta I$ allows the determination of the maximum of the amplitude modulation which corresponds to the $\pi$ phase shift. When applying a square voltage modulation on the doped LISW, one clearly distinguishes modulations on the interference signal corresponding to the electrically induced birefringence introducing a phase shift, $\Delta\varphi = \pi\Delta i/\Delta I$, on the guided mode. The amplitude of the phase jumps (see Fig. 3) are averaged to improve the accuracy of the measurement from which the EOR of the doped LISW waveguide is calculated.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Signal of the time varying intensity of the inner ring of the interference pattern. Red: applied voltage. Black: intensity modulation measured by the photodiode.</figcaption></figure>

In order to ascertain that the EOR is indeed due to the doping molecule, we have verified that no modulation can be observed without 5CB in the photopolymerizable matrix. We define the coefficient $r$ for the EOR:

$$r = \frac{\lambda \Delta\varphi e}{\pi n^3 V d} \qquad (2)$$

Where $d = 8$ mm is the LISW waveguide length, $e = 125$ µm is the cell thickness, $V$ is the applied voltage and $n$ is the refractive index. For $V = 900$V, assuming a refractive index $n = 1.52$, the EO response coefficient is $r = 0.4$ pm $\cdot$ V$^{-1}$ for a 1 Hz modulation rate.

This value corresponds to a $\Delta n = 1.2 \cdot 10^{-5}$ that compares well with the expected value given by Equation 1. The measurements of the voltage dependency (see Fig. 4) clearly show an increase in EOR, as described by Eq. (1), and due to the improvement in orientation of the 5CB molecules with the amplitude of the applied electric field. Monitoring the frequency dependence of the EOR, one observes that the modulated signal begins to decrease at 5 Hz and completely vanishes for frequencies higher than 20 Hz. For all frequencies, the modulation signal is in phase with the applied electric field indicating that the re-orientation of the 5CB in the photopolymerized matrix remains mainly in the elastic domain. Nevertheless, the EOR threshold observed in the voltage dependent measurement and its diminution with increasing frequency gives evidence to a more complex interaction between the 5CB and the matrix [13, 14].

The current level of performances allows the application these doped LISW waveguide for optical circuit dynamic configurations or for the compensation of slow phase drift. Another
<figure><img src="image_6.png" /><figcaption>Fig. 4. Variation of the EO response with the applied voltage. The red line corresponds to a linear fit. The error bars are calculated from the Δφ measurement uncertainties.</figcaption></figure>

application is the dynamic control of the propagation mode polarization (TE-TM conversion) using patterned electrodes on the cell to control the electric field orientation in the material and therefore the direction of the induced birefringence [15]. Improvements in cut-off frequency can reasonably be expected from a modification of the mechanical properties of the matrix and/or by using other doping molecules such as a fluorinated cyano-tolane chromophores described by Herlocker et al. [16] who demonstrated a response time in the millisecond range. Higher modulation frequencies will require the synthesis of specific chromophores with high quadratic hyperpolarizability so as to enable an actual Pockels effect [17]. However, the absorption bands of nonlinear chromophore and of the photoinitiator should not overlap to allow the proper growth of the LISW. For this purpose, the construction of the LISW waveguide through the two-photon photopolymerization process may relax the restrictions on the absorptions bands [18]. The value of $V_π$ can be lowered by reducing the gap between the two electrodes. As the core diameter has been measured to be about 6 µm one can expect to gain one order of magnitude in applied electric field.

## 6. Conclusion

We have demonstrated the possibility to apply LISW waveguides to electro-optical phase control through the addition of birefringent molecules in the initial blend. This work shows that the self-propagated waveguides can be used in low frequency optical modulations, but other applications can be considered such as the control of the polarization of the propagating mode. Improvements to the response time will have to be achieved by using specific designed and synthesized molecules. Two different solutions are considered. The first one is to use more efficient anisotropic molecules that have already demonstrated millisecond response times. But the most promising one entails the doping with push-pull chromophores exhibiting quadratic hyperpolarizability. This second solution will bring about an effective Pockels effect and therefore reach high modulation rates. Finally, the connection of two single mode optical fibers via the functionnalized LISW will allow the fabrication of a fully integrated EO phase modulator.

## Acknowledgments

The work has been performed in the frame of the contract DGRS/CNRS 21819.