1950 OPTICS LETTERS / Vol. 30, No. 15 / August 1, 2005

Polarization gratings in twisted-nematic liquid-crystal composites doped with azobenzene dye

Hiroshi Ono, Tomoyuki Sasaki, and Akira EmotoDepartment of Electrical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Japan

Nobuhiro Kawatsuki and Emi UchidaDepartment of Material Science and Chemistry, University of Hyogo, 2167 Shosha, Himeji 671-2201, Japan

Received February 8, 2005

Highly efficient and functionalized polarization gratings have been recorded in azobenzene-containing me-sogenic composites with twisted nematic cell configurations. The polarization gratings formed inazobenzene-containing mesogenic composites show a high diffraction efficiency of more than 45% and con-vert the polarization state of light at the same time. The polarization direction of the diffracted laser beamscan be controlled by the twisted angle of the nematic cell. These characteristics of the polarization gratingsare well explained by means of Jones calculus. © 2005 Optical Society of America

OCIS codes: 160.3710, 160.2900.

In recent years azobenzene-containing organic mate-rials have been the subject of intensive research dueto their potential applications in photonics.1–9 Bire-fringence and holographic gratings can be opticallyinduced in various forms of these materials, such aspolymer matrices doped with azo dyes, liquid-crystalline azopolymers,1,6,7 and amorphous azopoly-mers. It is known that linearly polarized light in-duces a reorientation of azobenzene groupsperpendicular to the polarization direction of light.Liquid crystals possess an abundance of useful mate-rial characteristics, including large birefringence,easy fabrication over large areas, high sensitivity toapplied fields, and structural flexibility.1,6,7,10–13 Po-larization gratings using functionalized mesogenicmaterials can diffract the laser beam and convert thepolarization state at the same time.12–21 These desir-able functions are expected to be applied to variouskinds of photonics application.

Holographic recording properties connected withreorientation of liquid-crystalline molecules are ex-pected to be strongly dependent on molecular ar-rangement and therefore to be dependent on theliquid-crystalline cell configuration. In this Letter wetheoretically and (or) experimentally investigate theinfluence of the initial cell orientation on the diffrac-tion properties in the polarization gratings generatedin azobenzene-containing mesogenic composites.

Our investigations of polarization holographicrecording were performed on a mesogenicorganic composite based on a side-chainliquid-crystalline polymer (SLCP; see Fig. 1), a low-molar-mass nematic mixture (E7), and an azoben-zene dye {4-[N-(2-hydroxyethyl)-N-ethyl]amino-4�-nitroazobenzene; DR1}. Poly(vinyl alcohol) (PVA) wasused as a rubbed alignment layer. We prepared theazobenzene-containing mesogenic composite by mix-ing E7, SLCP, and DR1 �59.5:39.5:1.0 wt. % � at�100 °C. The cell was mounted with twisted geom-etry 10 �m thick polyester films. We controlled thetwisted angle ���, which is defined as the angle be-

0146-9592/05/151950-3/$15.00 ©

tween the rubbing directions of the two substrates,by the rubbing direction of the two PVA-coated glasssubstrates. The twisted angle was set to be 30°, 60°,or 90°. Figure 2 shows a schematic of the sample.

Polarization gratings were written by use of two or-thogonal linearly polarized, mutually coherentfrequency-doubled Nd:YAG laser beams. The laseremits cw 532 nm wavelength light, with a power of8.0 mW for each beam incident on the sample. Thetwo writing beams with equal intensities crossing atan angle of �=3.0° impinge upon azobenzene-containing mesogenic films. The diffraction efficiencyof the first-order diffracted beam from the recordedgratings in transmission mode was defined as the in-tensity ratio of the diffracted beam to the incidentprobe beam and was probed with a linearly polarizedHe–Ne laser �633 nm� beam, which was incident nor-mally to the sample surface. The polarization state ofthe diffracted beam was characterized by Glan–Thompson polarizing prisms.

Once the writing beams were turned on, a diffrac-tion process was effective and, a result in a far fieldafter the sample the first-order diffraction spots ap-peared. Higher-order diffraction was almost invisiblein the samples studied. The diffraction spots werestable during irradiation by the light and rapidly dis-appeared after the writing beams were turned off. Inthis study, SLCP was dissolved into the mesogeniccomposite to improve the diffraction efficiency. Weconfirmed that the diffraction spots were not ob-served from the azobenzene-containing E7 film with-out SLCP under our experimental conditions. The in-dex matrix in a coordinate system related to theoptical axis is13–22

Fig. 1. Chemical structure of the SLCP.

2005 Optical Society of America

August 1, 2005 / Vol. 30, No. 15 / OPTICS LETTERS 1951

�n� = � �nlin cos � − i�ncir sin �

i�ncir sin � − �nlin cos �� . �1�

Here �nlin=ne−no, where ne and no are the laser-induced principal refractive indices in the absence ofoptical activity, and �ncir=nleft−nright, where nleft andnright are the refractive indices for the left- and right-hand-side circular components, respectively. Thephase difference between the two incident writingwaves, �=2�x /�, is a function of position x and ofgrating spacing �. The Jones matrix that describesthe transmission of the recorded holograms has theform

T� = exp�i2�

��n�d� �2�

for the phase recording, where d is the film’s thick-ness and � is the wavelength of the probe beam. Un-der our experimental conditions, the absolute valueof �lin���nlind /� and �cir���ncird /� is less thanunity. Therefore nonzero components in the matrixare expanded, and the Jones matrix for the first-order diffracted beam is obtained as follows:

T±1� = � i�lin cos � �cir sin �

− �cir sin � − i�lin cos �� , �3�

where the suffix of each transmission matrix is thediffraction order. Considering the coordinate trans-formation, we can obtain the transmission matrix asfollows:

T±1 = �cos − sin

sin cos �T±1�� cos sin

− sin cos �

� R�− �T±1�R��. �4�

Azimuth is defined as the angle between the opticaxis of the induced birefringence and the laboratoryaxis and, under our experimental conditions, =� /4,because the principal axis of the polarization ellip-soid of the interfered light is always slanted � /4 fromthe laboratory axis.13–22 To transform transmissionmatrix T±1 into a the diagonal matrix, consideringthe coordinate transformation, we can obtain the di-

Fig. 2. Schematic of the holographic recording medium.

agonal transmission matrix as follows:

T±1� = R�−�

2�T±1

=1

2��lin � �cir 0

0 − �lin � �cir� . �5�

In this Letter the propagation and diffraction of lightthrough a slowly twisting anisotropic medium as

Fig. 3. Summary of the characteristics of polarizationgratings formed in azobenzene-containing mesogenic com-posites with twisted nematic cell configurations. Twistedangle � was set to be (a) 30°, (b) 60°, and (c) 90°. The polarplots of the probe, �first-order �+1st� and first-order�−1st� diffracted beams appear in the figure. Circles, ex-perimental observation; solid curves, theoretical calcula-tion. The diffraction efficiency, which is defined as the in-tensity ratio of the diffracted beam to the incident probe

beam, appears at the bottom of each polar plot.

1952 OPTICS LETTERS / Vol. 30, No. 15 / August 1, 2005

shown in Fig. 2 have to be described by the Jones ma-trix method. The Jones matrix method can still beused, provided that we subdivide the medium into alarge number of thin plates such that each of the thinplates can be treated approximately as a homoge-neous medium. To derive the Jones matrix we dividethe medium into N equally thin plates. The Jonesmatrix for each plate can be written as

t±1 =1

21/N���lin � �cir�1/N 0

0 �− �lin � �cir�1/N� .

�6�

The plates are oriented at azimuth angles� ,2� ,3� , . . ., �N−1��, N�, with �=� /N. The overallJones matrix for these N plates is given by

W±1 = m=1

N

R�− m��t±1R�m��. �7�

Considering the transformation of the axis to x–y co-ordinates, the �first-order diffracted fields are

E±1 = R�−�

2�W±1Ep, �8�

where Ep is the electric field of the probe beam. Ac-cording to Eq. (8), intensities and polarization statesof diffracted beams are numerically calculated in thelimit when N tends to infinity. The polar plots dis-played in Fig. 3 represent experimental results andpolarization analysis when the twisted angle wasvaried. The polarization directions are rotated whenthe laser beam is diffracted in the medium, and therotation angle can be controlled by the twisted angleof sample cells. These characteristics are well ex-plained by means of the theory mentioned above. Thepolarization holographic gratings formed in ourazobenzene-containing mesogenic composite showhigh diffraction efficiencies of more than 45% becauseof the exceptional index change originating in coop-erative reorientation of the mesogenic molecules. Themaximum value of the anisotropy of the refractive-index change can be estimated to �1.4�10−2.

In conclusion, we have demonstrated holographicgrating recording in an azobenzene-containing me-sogenic composite with a twisted nematic cell con-

figuration. The gratings are recorded by a polariza-tion holographic technique, and the recordedpolarization gratings can diffract the laser beam andconvert the polarization states at the same time. Inaddition, the polarization directions are rotated whenthe laser beam is diffracted in the medium, and therotation angle can be controlled by the twisted angleof the sample cells.

H. Ono’s e-mail address is onoh@nagaokaut.ac.jp.References

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