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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 7979–7991
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Electro-optic effect in crystalline films of transverse planar octupolar symmetry

Mi-Yun Jeong, Sophie Brasselet, Bong Rae Cho, and Tong-Kun Lim  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 7979-7991 (2011)
http://dx.doi.org/10.1364/OE.19.007979


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Abstract

We present theoretical and experimental demonstrations of the electro-optic activity in crystalline molecular thin films with octupolar D 3 h 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 [1

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]

4

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]

]. 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

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

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]

]. 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

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]

]. This molecule has shown recently its ability to produce crystalline domains in polymer thin films with large multipolar SHG responses [4

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]

]. 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

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

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]

] with progressing performances [9

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]

], the octupolar structures based on crystalline thin films have been rarely studied [10

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]

]. Moreover, although many investigations have been carried-out in multipolar biaxial bulk crystals [11

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]

13

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]

], 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
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.
), which is suitable to the fabricated crystalline TTB thin films where molecules naturally form stacks perpendicular to the sample substrate [4

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]

]. 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

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]

,3

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]

], it is still expected to benefit from a non-centrosymmetric arrangement, as well as from a high nonlinear efficiency.

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

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]

], the corresponding electro–optic tensor in the crystal unit cell frame (U1,U2,U3) exhibits only three non-vanishing components: r11=-r21=-r62.

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
(5)
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)
(6)
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
(7)
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
(8)

Figure 3
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).
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
(9)
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.

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

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]

]. 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)
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.
) or longitudinal (Z) direction (Fig. 4(b)).

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

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]

].

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
(10)
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
(11)
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

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.

]. The crystallinity of these structures could be confirmed by X-rd measurement (Fig. 5(a)
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).
). 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

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.

], 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.

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

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.

]. The PI/ITO substrates were employed as transparent electrodes.

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)
(12)
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]
(13)
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)]
(14)
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)
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.
. 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.

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.

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.

OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 22, 2011
Revised Manuscript: March 17, 2011
Manuscript Accepted: April 1, 2011
Published: April 11, 2011

Citation
Mi-Yun Jeong, Sophie Brasselet, Bong Rae Cho, and Tong-Kun Lim, "Electro-optic effect in crystalline films of transverse planar octupolar symmetry," Opt. Express 19, 7979-7991 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-7979


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References

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  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.
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