Abstract

We present theoretical and experimental demonstrations of the electro-optic activity in crystalline molecular thin films with octupolar D3h symmetry. Applying a longitudinal electric field modulation within the molecular plane, we analyze the induced refractive index change relative to the orientation of the octupoles in their plane, and show that a maximum value is reached when one octupolar branch lies along the direction of the modulating field. These characteristics, as well as their electric field dependence, are drastically different from more traditional one-dimensional symmetry samples, bringing additional advantages related to electro-optic coupling possibilities.

© 2011 OSA

1. Introduction

In recent years, molecular crystals of octupolar symmetry having large second order optical properties have been the center of a large interest, first with theoretical developments and then experimental demonstrations [14]. The major advantage of octupolar molecules with three-fold symmetry is their potential to lead to non-centrosymmetric crystallization due to the lack of ground-state dipole moment, avoiding the frequent head-to-tail centrosymmetric conformation found in one-dimensional dipolar molecules [5,6]. One of the most promising octupolar molecule crystallizing in macroscopic size crystals is TTB (1,3,5-tricyano-2, 4,6-tris (p-diethylaminostyryl) benzene), leading to a D3h non-centrosymmetric structure with one of the largest Second Harmonic Generation (SHG) value reported among organic crystals [3]. This molecule has shown recently its ability to produce crystalline domains in polymer thin films with large multipolar SHG responses [4]. This achievement of octupolar crystalline thin films now brings the possibility to build electro-optic (EO) active devices from which large efficiencies are expected. While in the last decades, a large theoretical and experimental effort has been brought on EO integrated devices made of polymer thin films doped or grafted with immobilized dipolar molecules [7,8] with progressing performances [9], the octupolar structures based on crystalline thin films have been rarely studied [10]. Moreover, although many investigations have been carried-out in multipolar biaxial bulk crystals [1113], the study of EO effect in three-fold symmetry structures has not been reported so far, to the best of our knowledge.

In this paper, we derive a theoretical expression of the electro-optic effect in a D3h symmetry system, and apply it to the response of an octupolar crystalline thin film fabricated from the TTB molecule. In the geometry chosen here for practical reasons, the optical beam incident direction is set parallel to the molecular plane (Fig. 1 ), which is suitable to the fabricated crystalline TTB thin films where molecules naturally form stacks perpendicular to the sample substrate [4]. Although the resulting molecular-fields coupling geometry does not take full advantage of the polarization-independent efficiency possibilities of an illumination perpendicular to the molecular plane [1,3], it is still expected to benefit from a non-centrosymmetric arrangement, as well as from a high nonlinear efficiency.

 

Fig. 1 (a) Schematic drawing of a TTB molecule (3 branches) and its orientation by the Euler angles (θ,ϕ,ψ). The molecular coordinates are denoted (U1,U2,U3) in the laboratory coordinate (X,Y,Z). The (x,y,z) notations are used as intermediate axes to define the orientation of the (U1,U2)molecular plane in the laboratory frame. (b) Geometry of the electro-optic modulation in the octupolar thin film. (c) Euler angles used in this geometry: the octupolar plane is defined by (θ = π/2, ϕ = 0), and ψ defines the octupoles orientation in the (Y,Z) plane. (d) The molecular structure of TTB.

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2. Electro-optic effect in an octupolar system: theory

The studied sample is a few micrometers thick molecular crystalline film sandwiched between two planar transparent electrodes, traversed by the incident optical beam and undergoing a modulated electric field perpendicular to the sample plane (Fig. 1). The molecular orientation in the macroscopic frame is defined by the Euler angles (θ,ϕ,ψ) in the laboratory frame (X,Y,Z), with the corresponding molecular frame denoted (U1,U2,U3) (Fig. 1). From an optical point of view, the TTB crystal structure is uniaxial with its optical axis along U3. The refractive index in the (100) plane, independent of the polarization orientation, is defined by the ordinary index no, whereas the extraordinary index ne is associated to an incoming polarization along U3. From the geometrical selection rules governed by the D3h octupolar symmetry [1], the corresponding electro–optic tensor in the crystal unit cell frame (U1,U2,U3) exhibits only three non-vanishing components: r11=-r21=-r62.

From the system geometry depicted in Fig. 1, the molecular crystal plane (U1,U2) lies in (Y,Z) macroscopic plane, while the electrode planes are parallel to (X,Y). The incident light is polarized in the (X,Y) plane at 45° relative to X. When a modulated electric field Emis applied along the Z direction, the electric field components in the crystal frame (U1,U2) are given by E1=-Em×cosψ and E2=Em×sinψ. In this configuration, the index ellipsoid is defined by the equation [12,13]:

(1no2r11Emcosψ)U12+(1no2+r11Emcosψ)U222r11EmsinψU1U2+U32ne2=1
The system, initially uniaxial, becomes therefore biaxial upon the application of the electric field. Since the optical propagation is along the Z direction, the optical study can be performed in the (U1,U2) plane. Defining A=r11Emcosψ and B=r11Emsinψ, and the initially ordinary and extraordinary indexes nU1=n1=no and nU3=n2=ne, Eq. (1) can be written in a more synthetic formulation:
[U1U2]M[U1U2] =1,   with   M=  [(1no2A)              -B        -B               (1no2+A)] 
The resolution of the characteristic equation of this matrix |M-μI|=0 (with I the identity matrix) leads to the corresponding characteristic values: μ1=1no2r11Em and μ2=1no2+r11Em. In the new principal axes frame (U1', U2'), the index ellipsoid takes the form:
[U'1U'2][μ100μ2][U'1U'2] =1   or  U1'2n1'+U2'2n2'+U3'2n3'=1with  1n'12=1no2r11Em  and  1n'22=1no2+r11Em
After resolution of the eigenvector of the matrix M for the eigenvalues μ1,2, the new optical axes (U1', U2') of the system after application of the modulated field are seen to be related to the (U1, U2) frame by a rotation angle Θ with:
(U'1U'2)=(cosΘsinΘsinΘcosΘ)(U1U2)  and  Θ =ψ2
The modulation of an electric field in the Z direction therefore induces a rotation of the principal axes (U1, U2) by an angle Θ which is directly related to the Euler angle ψ, as depicted in Fig. 2 .

 

Fig. 2 Principal axes of the index ellipsoid (U1, U2) in the absence of an applied field and principal axes intersection of the index ellipsoid (U1', U2') in the presence of an applied field along the direction Z. The angles Θ, ψ and α are described in the text.

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As the input optical field polarization lies in the (X,Y) plane, a refractive index modulation will take place for the Y component of the polarization while the X component (perpendicular to the molecular stacks) is associated to a constant index ne. The calculation of the refractive index along Y, defined as nY, can be deduced from the interception of the new index ellipsoid with the Y direction. Using the physically realistic limit r11Em<<1 in Eq. (3), the new principal values of the refractive index are then given by:

n'1=no+12r11Emno3  and  n'2=no12r11Emno3
In the presence of a modulating electric field, the intersection of the index ellipsoid with the plane X=U3=0 (Fig. 2) is therefore given by the equation:
cosα2(no+12r11Emno3)2+sinα2(no12r11Emno3)2=1n2(α)
where α is the angle between the U'1 direction and the direction defining the current point on the ellipsoid (Fig. 2). Denoting nm=12r11Emno3, the corresponding index for this current point is then:
n(α)=no2nm2(nonm)2cosα2+(no+nm)2sinα2
The index nY is equal to nY=n (α=π2(ψ+Θ)) with Θ=ψ/2, therefore nY is a function of ψ with:

nY(ψ)=no2nm2(nonm)2sin(3ψ2)2+(no+nm)2cos(3ψ2)2

Figure 3 shows the influence of the octupoles orientation angle ψ on the induced refractive index change. The minimum index nY is obtained at ψ=0°, with nYmin=nonm and the maximum for ψ=60° with nYmax=no+nm. As expected, the maximum index change from its initial value |ΔnY(ψ)|=|nY(ψ)no| occurs for ψ = 0° with a π/3 periodicity, corresponding to one octupolar branch lying along the modulating field direction Z. At ψ=π/6 (with a π/3 periodicity), the index change is almost zero, corresponding to a situation where one octupolar branch is perpendicular to the modulating field. In the present geometry, an electro-optic experiment can access the EO efficiency of the sample by measuring the induced phase shift between the X and Y polarization components of a field propagating along Z and polarized at 45° with the X direction (Fig. 1), for a crystal length L. This phase shift is denoted Γ(ψ)=|nXnY(ψ)|L2π/λ, with λ the incident wavelength and nX=ne. Its maximum expected value is therefore:

Γmax=Γ(ψ=kπ/3)=2πλ|ne(nonm)|L
with nm=12r11Emno3, which is obtained for ψ=0° for instance. This phase shift can be written Γmax=Γ0+Γmmax, sum of a constant phase shift Γ0=2πλ(neno)L=2πλΔnL and a modulated contribution Γmmax=2πλnmL=πλr11Emno3L=πλr11Vmno3with the associated potential Vm=EmL. A π modulated phase change in this configuration can thus be obtained with the half voltage Vπ=λr11no3, from which r11 can be measured providing that ψ0° is known.

 

Fig. 3 Calculated ψ-dependence of nY(ψ) and |ΔnY(ψ)| supposing no=1.5 and r11Em=0.01. The corresponding orientations of the octupolar molecules in their plane are given for situations giving a maximum or minimum index change (k is an integer).

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For all other orientations ψ, the phase shift Γ(ψ) is no more a simple expression as a function of r11 and Em, in particular the dependence with respect to the modulating field amplitude is no more purely linear. For instance at ψ90° where the minimum effect is expected, the calculation of the induced refractive index leads to (ψ90°)=(no2nm2)/(no1+nm2no2)no3nm22no2 assuming nm4<<2no3. The corresponding phase shift is Γ(ψ90°)=2πλ|ne(no3nm22no)|L=Γ0+Γmmin, with Γmmin=2πλ.3nm22n0L=2πλ.38Lr112Vm2no5, which is quadratically dependent on the electric field modulation amplitude. A π modulated phase change in this configuration is obtained with the half voltage Vπ=4λL3r112no5, from which r11 can be measured providing that ψ90° is known.

3. Comparison with the electro-optic effect in a uni-dimensional symmetry system

In order to compare this situation to more traditional systems used in electro-optic devices based on organic materials, a similar calculation is undertaken in a system of non-centrosymmetric 1D symmetry. For comparison we consider that the molecular system lies along the U1 axis, therefore only one electro-optic coefficient r11 exists. This situation relates to crystals having a predominant nonlinear diagonal coefficient, or in a first approximation to Cv poled polymers neglecting the off-diagonal coefficient contributions [7]. In the case where the molecular symmetry axis (molecules main orientation direction) lies in the (Y, Z) plane, the applied electric modulation field Em can be either set in the transverse (Y) (Fig. 4(a) ) or longitudinal (Z) direction (Fig. 4(b)).

 

Fig. 4 Transverse (a) and longitudinal (b) electro-optic modulation geometries in 1D molecular systems. The angles and direction notations are the same as used for the octupolar systems.

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The transverse case (Fig. 4(a)) is naturally optimized if the molecules also lie along the Y direction, leading to an optimized modulated phase Γm=πλr11Vmno3L. This value is the same expression as obtained previously for octupoles in a longitudinal configuration. This transverse geometry would however lead to more delicate electrodes fabrication and fields application [14].

The case of a longitudinal field application along Z (Fig. 4(b)) leads to a modified index ellipsoid which is reduced to:

(1ne2+r11Emcosψ)U12+1no2U22=1
with ψ the angle between Z and the molecular direction U1. As the characteristic matrix of Eq. (10) is still diagonal, there is therefore no rotation of the index ellipsoid under a modulating field, the corresponding indexes being: n1(ψ)ne12no3r11Emcosψ, n2=no. The calculation of the nY index following the same procedure as above leads to:
nY=n(α=π2ψ)=n1(ψ)nono2sinψ2+n12(ψ)cosψ2
The minimum index nY is obtained at ψ=0° (with a π periodicity), with nYmin=no and the maximum for ψ=90° (with a π periodicity) with nYmax=ne. Such values are expected from situations where the molecules lie respectively along the Z and Y directions. The optimal case where the molecules lie along Y is however not favorable for electro-optic modulation since the corresponding index does not depend on the modulated field amplitude. The optimization of electro-optic coefficient coupling and field modulation are therefore antagonistic and cannot be combined in a common molecular orientation scheme. Obtaining an electro-optic modulation necessitates a compromise orientation such as ψ=45°, which leads to a loss of index change amplitude compared to the octupolar case.

This comparison shows overall that electro-optic modulation in octupolar systems is more flexible and can lead, with more amenable technology, to electro-optic modulation values as high (if not higher, depending on r11) as in transverse 1D molecular systems.

4. Experimental results

The sample is an evaporated crystalline thin film of TTB (20 wt %)–PMMA(80 wt %) in chlorobenzene made of micrometric to millimetric size columnar cylindrical structures which naturally form on a polyimide (800 Å thickness) / ITO (PI/ITO) substrate [15]. The crystallinity of these structures could be confirmed by X-rd measurement (Fig. 5(a) ). Further confirmation of both the sample crystalline behavior and the nature of the molecular orientation have been obtained by measuring the birefringence of the columnar structures. Figure 5(b) shows the transmission of a sample region of with 1 mm diameter illuminated by a circularly polarized 633 nm beam at normal incidence. The sample is sandwiched between two crossed polarizers which are rotated simultaneously. In this situation, a π/4 periodic response is expected if the sample is strongly birefringent with a privileged direction, which is observed in the case of the TTB sample. Therefore, from the results of X-rd, birefringence measurements, and second harmonic generation measurements [15], we could confirm that the columnar cylindrical structures of the TTB molecules on PI/ITO were developed as a single crystal. At last, the birefringence and SHG measurements performed on large crystalline area support the evidence that this mono-crystalline behavior occurs at the optical-measurement spatial scale. Therefore, we suppose that the sample symmetry and orientation are constant over the whole illumination area. Any molecular orientation disorder would lead to an underestimation of the nonlinear coefficients in the sample.

 

Fig. 5 (a) X-rd measurement. (b) The birefringence measurement of the cylinder TTB crystal, performed by measuring the transmission of a TTB sample region of 1mm size between two crossed polarizers rotating simultaneously (the polar angle in the polar graph is the polarizers rotation angle).

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The electro-optic modulation experiment is performed following the geometry depicted in Fig. 6(a) . The sample of columnar cylindrical structures was sandwiched between polyimide (800 Å thickness)/ITO (PI/ITO) substrates [15]. The PI/ITO substrates were employed as transparent electrodes.

 

Fig. 6 Experimental electro-optic effect in a TTB thin crystalline film. (a) Setup. P: linear polarizer, λ/2: half wave plate, S: crystal sample, λ/4: quarter waver plate, A: analyzer. (b) Measured modulated light intensity vs. input beam polarization angle (dots) and theoretical fit to Eq. (12) (continuous line). (c) Modulated light intensity (dots) vs. fast axis angle of λ/4plate. The continuous line is the theoretical fit to Eq. (13). The experimental and fit curves are normalized to their maximum. The data of (b) and (c) were measured at a fixed applied electric field modulation of 61 VPP at 4 kHz.

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The orientation of the columnar structures is set such as the molecular stacking direction is along X, with both electric field modulation at AC 4 kHz and optical incidence lying along Z, as described below. The incident beam from a 633nm HeNe laser with a few mWs power passes through an input linear polarizer, a λ/2 plate used to rotate the polarization of the input field, the sample, a λ/4 plate, and an analyzer (Fig. 6(a)). The polarizer and the analyzer are initially kept perpendicularly polarized at ±45° from the (X, Y) axes.

The optic field amplitude Eout and the output intensity Iout can be expressed using the Jones matrices of the each optical element.

In a first situation the input polarization and the analyzer are rotated simultaneously from their initial position indicated in Fig. 6(a), by an angle β relative to X. The other optical elements are fixed. The final output optical field Eout and output intensity passing through the analyzer is given by:

Eout=[sinβ2cosβsinβsinβcosβcosβ2][eiΓT200eiΓT2]Ein[cosβsinβ] Iout=EoutEout*=2Iinsinβ2cosβ2(1+sinΓ)
where  ΓT=π2+Γ is the total phase retardation induced by the λ/4 plate (π/2) and the sample (Γ). As shown above, the sample phase shift Γ is the sum of a constant phase shift Γ0=2πλΔn and the modulated contributionΓm. Figure 6(b) shows the experimental dependence of the modulated light intensity vs. the input beam polarization angle β, which is seen to be in good agreement with Eq. (12).

In a second situation the λ/4plate is rotated by an angle γ relative to X and the other optical elements are fixed, such as the input polarization is at +45 relative to X and the analyzer is crossed at 45. The optical field and the output intensity become:

Eout=12[1111]12[1+i(sinγ2cosγ2)2isinγcosγ2isinγcosγ1i(sinγ2cosγ2)][eiΓ200eiΓ2]Ein12[11] Iout=Iin[12[sinΓ2+cosΓ2(sinγ2cosγ2)]2+2sinΓ22sinγ2cosγ2]
Figure 6(c) shows the experimental dependence of the modulated light intensity vs. the fast axis γ angle of the plate, which is also seen to be in good agreement with Eq. (13).

The experiments corresponding to the two described situations have been used to determine the electro-optic efficiency of the TTB crystalline samples. When the direction of the input polarizer is +45 relative to X (β=45), and the slow-axis of the quarter wave plate is horizontal (γ=0), the direction of analyzer remaining 45 relative to X, then the above two expressions become a same equation:

Iout(Em, ψ)=Iin12[1+sinΓ(Em, ψ)]
As mentioned above, Γ(Em,ψ)=|nXnY(Em,ψ)|L2π/λ=Γ0+Γm(Em,ψ) is a complex function of the orientation of the octupolar molecules in their plane, with nY(Em,ψ) given in Eq. (8). Γm(Em,ψ) exhibits in particular either a linear or a nonlinear dependence relative to the electric field modulation amplitude Em, depending on the molecular orientation ψ. Examples of Iout(Em) dependences are shown in Fig. 7(a) . While the case ψ=0 shows a traditional sinusoidal behavior representative of a Γm(Em, ψ=0°)Em linear dependence, the case ψ90shows a modified behavior since in this situation Γm(Em,ψ90o)Em2, as described above. As can be observed in Fig. 7(b), this behavior has also been observed experimentally, where different responses can be measured in samples where different angles ψ are expected. This situation is primarily due to the complex fields-matter coupling occurring for not optimal molecular orientations.

 

Fig. 7 Experimental electro-optic responses in a TTB thin crystalline film. (a) Theoretical Iout(Vm) dependence, assuming the parameters L=1μm, no=1.5825, ne=1.59, r11=300pm/V (ψ=0° curve) and r11=1100pm/V (ψ=90° curve), λ=633nm. (b,c) Experimental Iexp(Vm) dependence measured on the modulation intensity for two different samples and the data of Fig. 7(b) and 7(c) were renormalized with maximum value.

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The experimental measurement of the EO coefficient r11 finally requires a preliminary knowledge of the molecular orientation ψ. Assuming an orientation ψ=0in the sample leads to an estimation of a the lower limit for r11, since this situation leads to optimal coupling.

Experimental data on TTB thin crystalline films are treated by measuring the Vπ voltage necessary to obtain a phase shift Γm=π, which corresponds to a cancellation of the modulated contribution of the output intensity. In the investigated samples, a modulated electric field of maximum amplitude 140V is applied between the electrodes distant by L=3.35μm, at a modulation frequency of 4 kHz. The sample ordinary index no=1.5825 is known from a separate measurement. ψ can be in principle determined from a Second Harmonic Generation measurement where both polarization and incidence angle are tuned [3,15]. Typical values of Vπ230V are measured in samples whose output intensity dependence Iout(Vm) resembles Fig. 6(b), for which one can consider that ψ is close to 0°. The knowledge of the exact molecules orientation in the crystal being however inaccurate, this Vπ measurement can nevertheless be used to estimate a range of possible values for the nonlinear coefficient r11 of the measured crystal. The previous equations given in Section 2 lead to an estimation of r11 from r11=λVπno3 (estimated for ψ=0°) to r11=4λL3Vπ2no5 (estimated for ψ=90°), which makes r11 falls in the range r116952300pm/V. This range of values is consistent with values of d1110001500pm/V previously measured in similar samples by Second Harmonic Generation [3,15,16]. Overall this order of magnitude of EO efficiencies of TTB crystalline thin films is high compared to more traditional molecular materials [7,10,17,18]. Note that in the most general case, r11 can also be deduced without the need to measure Vπ by further simplifying Eq. (14) using the preliminary assumption Γ0, Γm<<1. Then sinΓΓm+Γ0 and Iout=I0+Im is the sum between a constant intensity I0=Iin/2 (measured without electric field modulation) and the modulated contribution ImI0Γm. Under this assumption, r11 can be directly inferred from the measurement of Im/I0=Γm.

5. Conclusion

The electro-optic effect in crystalline films of octupolar symmetry has been studied theoretically and experimentally. Simple relations have been found between the molecular orientation in the sample plane and the expected electro-optic response, which show that a control of the octupoles orientation in their plane is essential to optimize the macroscopic response. The derived longitudinal electro-optic response, compared to the one from traditional 1D systems, shows that octupolar films can provide a flexible and efficient solution for electro-optic modulation where the compromise molecular orientation versus fields-molecular coupling is more readily obtained. The experimental data fit are shown to be in good agreement with the expected modulation, and provide an estimation of the order of magnitude of the EO efficiency in TTB crystalline thin films.

Acknowledgments

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-C00348 and 2009-0068755), the National Research Foundation (NRF) grant (No. 2010-0018921), and Priority Research Centers Program through the NRF funded by the Ministry of Education, Science and Technology (2010-0020209).

References and links

1. J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998). [CrossRef]  

2. M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

3. V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005). [CrossRef]  

4. M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007). [CrossRef]  

5. J. Zyss, “Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials,” J. Chem. Phys. 98(9), 6583–6599 (1993). [CrossRef]  

6. S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15(1), 257–288 (1998). [CrossRef]  

7. D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997). [CrossRef]  

8. T. Katchalski, G. Levy-Yurista, A. Friesem, G. Martin, R. Hierle, and J. Zyss, “Light modulation with electro-optic polymer-based resonant grating waveguide structures,” Opt. Express 13(12), 4645–4650 (2005). [CrossRef]   [PubMed]  

9. S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010). [CrossRef]  

10. A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004). [CrossRef]  

11. G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981). [CrossRef]  

12. S. Lochran, R. T. Bailey, F. R. Cruickshank, D. Pugh, and J. N. Sherwood, “Linear electro-optic effect in the organic crystal 4-aminobenzophenone,” Appl. Opt. 36(3), 613–616 (1997). [CrossRef]   [PubMed]  

13. M. J. Gunning and R. E. Raab, “Algebraic determination of the principal refractive indices and axes in the electro-optic effect,” Appl. Opt. 37(36), 8438–8447 (1998). [CrossRef]  

14. A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000). [CrossRef]  

15. Will be submitted elsewhere; M.-Y. Jeong, S. Brasselet, B. R. Cho, and T.-K. Lim, “Octupolar patterned films with large second harmonic generation and electro-optical effects,” This paper include more specific results of the EO and SHG for the octupolar crystal films.

16. H. S. Nalwa and S. Miyata, Nonlinear Optics of Organic Molecules and Polymers, (Crc Press, Tokyo University, 1996) p. 95, Chap. 4.

17. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990). [CrossRef]  

18. R. W. Boyd, Nonlinear Optics (Academic press, 1992) Chap. 10.

References

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  1. J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
    [CrossRef]
  2. M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).
  3. V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
    [CrossRef]
  4. M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
    [CrossRef]
  5. J. Zyss, “Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials,” J. Chem. Phys. 98(9), 6583–6599 (1993).
    [CrossRef]
  6. S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15(1), 257–288 (1998).
    [CrossRef]
  7. D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
    [CrossRef]
  8. T. Katchalski, G. Levy-Yurista, A. Friesem, G. Martin, R. Hierle, and J. Zyss, “Light modulation with electro-optic polymer-based resonant grating waveguide structures,” Opt. Express 13(12), 4645–4650 (2005).
    [CrossRef] [PubMed]
  9. S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
    [CrossRef]
  10. A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
    [CrossRef]
  11. G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
    [CrossRef]
  12. S. Lochran, R. T. Bailey, F. R. Cruickshank, D. Pugh, and J. N. Sherwood, “Linear electro-optic effect in the organic crystal 4-aminobenzophenone,” Appl. Opt. 36(3), 613–616 (1997).
    [CrossRef] [PubMed]
  13. M. J. Gunning and R. E. Raab, “Algebraic determination of the principal refractive indices and axes in the electro-optic effect,” Appl. Opt. 37(36), 8438–8447 (1998).
    [CrossRef]
  14. A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
    [CrossRef]
  15. Will be submitted elsewhere; M.-Y. Jeong, S. Brasselet, B. R. Cho, and T.-K. Lim, “Octupolar patterned films with large second harmonic generation and electro-optical effects,” This paper include more specific results of the EO and SHG for the octupolar crystal films.
  16. H. S. Nalwa and S. Miyata, Nonlinear Optics of Organic Molecules and Polymers, (Crc Press, Tokyo University, 1996) p. 95, Chap. 4.
  17. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990).
    [CrossRef]
  18. R. W. Boyd, Nonlinear Optics (Academic press, 1992) Chap. 10.

2010 (1)

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

2007 (1)

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

2005 (2)

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

T. Katchalski, G. Levy-Yurista, A. Friesem, G. Martin, R. Hierle, and J. Zyss, “Light modulation with electro-optic polymer-based resonant grating waveguide structures,” Opt. Express 13(12), 4645–4650 (2005).
[CrossRef] [PubMed]

2004 (1)

A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
[CrossRef]

2003 (1)

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

2000 (1)

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[CrossRef]

1998 (3)

1997 (2)

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

S. Lochran, R. T. Bailey, F. R. Cruickshank, D. Pugh, and J. N. Sherwood, “Linear electro-optic effect in the organic crystal 4-aminobenzophenone,” Appl. Opt. 36(3), 613–616 (1997).
[CrossRef] [PubMed]

1993 (1)

J. Zyss, “Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials,” J. Chem. Phys. 98(9), 6583–6599 (1993).
[CrossRef]

1990 (1)

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990).
[CrossRef]

1981 (1)

G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
[CrossRef]

Ahyi, A. C.

A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
[CrossRef]

Bailey, R. T.

Bhowmik, A. K.

A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
[CrossRef]

Brasselet, S.

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
[CrossRef]

S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15(1), 257–288 (1998).
[CrossRef]

Chen, A.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Chen, D.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Cho, B. R.

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Cho, M.

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

Cruickshank, F. R.

Dalton, L. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Desiraju, G. R.

J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
[CrossRef]

Donval, A.

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[CrossRef]

Fetterman, H. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Friesem, A.

Garito, A. F.

G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
[CrossRef]

Gunning, M. J.

Hau, S. K.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Hierle, R.

Huang, S.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Jen, A. K.-Y.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Jeon, S.-J.

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Jeong, M.-Y.

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Katchalski, T.

Kim, H. M.

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

Kim, T.-D.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Le Floc’h, V.

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

Lee, M. J.

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Lee, S. H.

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Levy-Yurista, G.

Lim, T. G.

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Lipscomb, G. F.

G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
[CrossRef]

Lochran, S.

Luo, J.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Man, H. T.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990).
[CrossRef]

Martin, G.

Min, K. S.

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

Narang, R. S.

G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
[CrossRef]

Piao, M.

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

Pugh, D.

Raab, R. E.

Sherwood, J. N.

Shi, Y.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Shi, Z.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Steier, W. H.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Suh, M. P.

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

Tan, S.

A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
[CrossRef]

Teng, C. C.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990).
[CrossRef]

Thalladi, V. R.

J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
[CrossRef]

Toussaere, E.

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[CrossRef]

Wang, W.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

Yip, H.-L.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Zhou, X.-H.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

Zyss, J.

T. Katchalski, G. Levy-Yurista, A. Friesem, G. Martin, R. Hierle, and J. Zyss, “Light modulation with electro-optic polymer-based resonant grating waveguide structures,” Opt. Express 13(12), 4645–4650 (2005).
[CrossRef] [PubMed]

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[CrossRef]

J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
[CrossRef]

S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15(1), 257–288 (1998).
[CrossRef]

J. Zyss, “Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials,” J. Chem. Phys. 98(9), 6583–6599 (1993).
[CrossRef]

Adv. Mater. (Deerfield Beach Fla.) (2)

V. Le Floc’h, S. Brasselet, J. Zyss, B. R. Cho, S. H. Lee, S.-J. Jeon, M. Cho, K. S. Min, and M. P. Suh, “High efficiency and quadratic nonlinear optical properties of a fully optimized 2D octupolar crystal characterized by nonlinear microscopy,” Adv. Mater. (Deerfield Beach Fla.) 17(2), 196–200 (2005).
[CrossRef]

M.-Y. Jeong, H. M. Kim, S.-J. Jeon, S. Brasselet, and B. R. Cho, “Octupolar films with significant second-harmonic generation,” Adv. Mater. (Deerfield Beach Fla.) 19(16), 2107–2111 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010).
[CrossRef]

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymer,” Appl. Phys. Lett. 56(18), 1734–1736 (1990).
[CrossRef]

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70(25), 3335–3337 (1997).
[CrossRef]

G. F. Lipscomb, A. F. Garito, and R. S. Narang, “A large linear electro-optic effect in a polar organic crystal 2-methyl-4-nitroaniline,” Appl. Phys. Lett. 38(9), 663–665 (1981).
[CrossRef]

J. Appl. Phys. (1)

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[CrossRef]

J. Chem. Phys. (2)

J. Zyss, S. Brasselet, V. R. Thalladi, and G. R. Desiraju, “Octupolar versus dipolar crystalline structures for nonlinear optics: a dual crystal and propagative engineering approach,” J. Chem. Phys. 109(2), 658–669 (1998).
[CrossRef]

J. Zyss, “Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials,” J. Chem. Phys. 98(9), 6583–6599 (1993).
[CrossRef]

J. Mater. Chem. (1)

M. J. Lee, M. Piao, M.-Y. Jeong, S. H. Lee, S.-J. Jeon, T. G. Lim, and B. R. Cho, “Novel azo octupoles with large first hyperpolarizabilities,” J. Mater. Chem. 13, 1030–1037 (2003).

J. Opt. Soc. Am. B (1)

J. Phys. D Appl. Phys. (1)

A. K. Bhowmik, S. Tan, and A. C. Ahyi, “On the electro-optic measurements in organic single-crystal films,” J. Phys. D Appl. Phys. 37(23), 3330–3336 (2004).
[CrossRef]

Opt. Express (1)

Other (3)

R. W. Boyd, Nonlinear Optics (Academic press, 1992) Chap. 10.

Will be submitted elsewhere; M.-Y. Jeong, S. Brasselet, B. R. Cho, and T.-K. Lim, “Octupolar patterned films with large second harmonic generation and electro-optical effects,” This paper include more specific results of the EO and SHG for the octupolar crystal films.

H. S. Nalwa and S. Miyata, Nonlinear Optics of Organic Molecules and Polymers, (Crc Press, Tokyo University, 1996) p. 95, Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic drawing of a TTB molecule (3 branches) and its orientation by the Euler angles (θ,ϕ,ψ). The molecular coordinates are denoted ( U 1 , U 2 , U 3 ) in the laboratory coordinate (X,Y,Z). The (x,y,z) notations are used as intermediate axes to define the orientation of the ( U 1 , U 2 ) molecular plane in the laboratory frame. (b) Geometry of the electro-optic modulation in the octupolar thin film. (c) Euler angles used in this geometry: the octupolar plane is defined by (θ = π/2, ϕ = 0), and ψ defines the octupoles orientation in the (Y,Z) plane. (d) The molecular structure of TTB.

Fig. 2
Fig. 2

Principal axes of the index ellipsoid ( U 1 ,   U 2 ) in the absence of an applied field and principal axes intersection of the index ellipsoid ( U 1 ' ,   U 2 ' ) in the presence of an applied field along the direction Z. The angles Θ, ψ and α are described in the text.

Fig. 3
Fig. 3

Calculated ψ-dependence of n Y ( ψ ) and | Δ n Y ( ψ ) | supposing n o = 1.5 and r 11 E m = 0.01 . The corresponding orientations of the octupolar molecules in their plane are given for situations giving a maximum or minimum index change (k is an integer).

Fig. 4
Fig. 4

Transverse (a) and longitudinal (b) electro-optic modulation geometries in 1D molecular systems. The angles and direction notations are the same as used for the octupolar systems.

Fig. 5
Fig. 5

(a) X-rd measurement. (b) The birefringence measurement of the cylinder TTB crystal, performed by measuring the transmission of a TTB sample region of 1mm size between two crossed polarizers rotating simultaneously (the polar angle in the polar graph is the polarizers rotation angle).

Fig. 6
Fig. 6

Experimental electro-optic effect in a TTB thin crystalline film. (a) Setup. P: linear polarizer, λ / 2 : half wave plate, S: crystal sample, λ / 4 : quarter waver plate, A: analyzer. (b) Measured modulated light intensity vs. input beam polarization angle (dots) and theoretical fit to Eq. (12) (continuous line). (c) Modulated light intensity (dots) vs. fast axis angle of λ / 4 plate. The continuous line is the theoretical fit to Eq. (13). The experimental and fit curves are normalized to their maximum. The data of (b) and (c) were measured at a fixed applied electric field modulation of 61 V P P at 4 kHz.

Fig. 7
Fig. 7

Experimental electro-optic responses in a TTB thin crystalline film. (a) Theoretical Iout(Vm) dependence, assuming the parameters L = 1 μ m , n o = 1.5825 , n e = 1.59 , r 11 = 300 p m / V ( ψ = 0 ° curve) and r 11 = 1100 p m / V ( ψ = 90 ° curve), λ = 633 n m . (b,c) Experimental Iexp(Vm) dependence measured on the modulation intensity for two different samples and the data of Fig. 7(b) and 7(c) were renormalized with maximum value.

Equations (14)

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( 1 n o 2 r 11 E m cos ψ ) U 1 2 + ( 1 n o 2 + r 11 E m cos ψ ) U 2 2 2 r 11 E m sin ψ U 1 U 2 + U 3 2 n e 2 = 1
[ U 1 U 2 ] M [ U 1 U 2 ]   = 1,   with   M =    [ ( 1 n o 2 A )               -B         -B                ( 1 n o 2 + A ) ]  
[ U ' 1 U ' 2 ] [ μ 1 0 0 μ 2 ] [ U ' 1 U ' 2 ]   = 1   or   U 1 ' 2 n 1 ' + U 2 ' 2 n 2 ' + U 3 ' 2 n 3 ' = 1 with   1 n ' 1 2 = 1 n o 2 r 11 E m   and   1 n ' 2 2 = 1 n o 2 + r 11 E m
( U ' 1 U ' 2 ) = ( cos Θ sin Θ sin Θ cos Θ ) ( U 1 U 2 )   and   Θ   = ψ 2
n ' 1 = n o + 1 2 r 11 E m n o 3   and   n ' 2 = n o 1 2 r 11 E m n o 3
cos α 2 ( n o + 1 2 r 11 E m n o 3 ) 2 + sin α 2 ( n o 1 2 r 11 E m n o 3 ) 2 = 1 n 2 ( α )
n ( α ) = n o 2 n m 2 ( n o n m ) 2 cos α 2 + ( n o + n m ) 2 sin α 2
n Y ( ψ ) = n o 2 n m 2 ( n o n m ) 2 sin ( 3 ψ 2 ) 2 + ( n o + n m ) 2 cos ( 3 ψ 2 ) 2
Γ max = Γ ( ψ = k π / 3 ) = 2 π λ | n e ( n o n m ) | L
( 1 n e 2 + r 11 E m cos ψ ) U 1 2 + 1 n o 2 U 2 2 = 1
n Y = n ( α = π 2 ψ ) = n 1 ( ψ ) n o n o 2 sin ψ 2 + n 1 2 ( ψ ) cos ψ 2
E o u t = [ sin β 2 cos β sin β sin β cos β cos β 2 ] [ e i Γ T 2 0 0 e i Γ T 2 ] E i n [ cos β sin β ]   I o u t = E o u t E o u t * = 2 I i n sin β 2 cos β 2 ( 1 + sin Γ )
E o u t = 1 2 [ 1 1 1 1 ] 1 2 [ 1 + i ( sin γ 2 cos γ 2 ) 2 i sin γ cos γ 2 i sin γ cos γ 1 i ( sin γ 2 cos γ 2 ) ] [ e i Γ 2 0 0 e i Γ 2 ] E i n 1 2 [ 1 1 ]   I o u t = I i n [ 1 2 [ sin Γ 2 + cos Γ 2 ( sin γ 2 cos γ 2 ) ] 2 + 2 sin Γ 2 2 sin γ 2 cos γ 2 ]
I o u t ( E m ,   ψ ) = I i n 1 2 [ 1 + sin Γ ( E m ,   ψ ) ]

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