APPLIED PHYSICS LETTERS 91, 181104 共2007兲
Electrically controllable and polarization-independent Fresnel zone
plate in a circularly symmetric hybrid-aligned liquid crystal film
with a photoconductive polymer layer
K.-C. Lo, J.-D. Wang, and C.-R. Leea兲
Institute of Electro-Optical Science and Engineering, National Cheng Kung University, Tainan, Taiwan 701,
Republic of China
T.-S. Mo
Department of Electronic Engineering, Kun Shan University of Technology, Tainan, Taiwan 710,
Republic of China
共Received 30 July 2007; accepted 5 October 2007; published online 30 October 2007兲
This work reports a Fresnel zone plate in a circularly symmetric hybrid-aligned liquid crystal 共LC兲
film with a photoconductive polymer layer. An ultraviolet-induced electrodelike pattern of polymer
layer under a zone plate photomask results in alternating major and minor portions of external
voltage dropping on LC layer in conductive and nonconductive regions, respectively. These effects
cause the discrepancy in LC reorientation between adjacent zones, generating a Fresnel zone plate.
The focusing of the zone plate is electrically controllable and polarization independent.
Additionally, the zone plate has advantages of a zero focusing in the voltage-off state and a very
small operating dc field range from 0 to 0.3 V / ␮m. © 2007 American Institute of Physics.
关DOI: 10.1063/1.2802568兴
In recent years, numerous Fresnel zone plates have been
developed for various fields, including optical communication, photonics, space navigation, and optical imaging.1–5
Conventional Fresnel zone plates, fabricated by electronbeam writing or thin film deposition, have certain limitations, including static focusing. Controllable Fresnel zone
plates with programmable focusing, based on flexibly controllable liquid crystal 共LC兲 materials, have been, accordingly, comprehensively studied.6–11 The effective phase
difference between the incident light through the adjacent
odd and even zones in a binary-phase LC Fresnel zone plate
is electrically tunable. Diffraction may be maximized by setting the effective phase difference equal to an odd multiple
of ␲; no diffraction occurs when this difference is an even
multiple of ␲. Therefore, Fresnel zone plates can be adopted
as diffractive focusing elements.12
The polarization independence of the programmable
focusing feature of a LC Fresnel zone plate is very important. Two approaches have been employed to fabricate
polarization-independent LC Fresnel zone plate. They are
photolithographic9 and photoalignment techniques.10,11 Regardless of the method used, the LC structures are formed to
be mutually orthogonal in neighboring zones of the zone
plate, resulting in a nonzero but nonmaximal diffraction efficiency in the voltage-off state. This inherent ability in these
zone plates results in an inevitable detrimental higher power
consumption.10,11 Hence, this work presents a peculiar approach for generating a circularly symmetric hybrid-aligned
LC Fresnel zone plate with an UV-induced electrodelike pattern of the polymer layer. The low and high conductivities,
resulting in minor and major portions of external voltage
dropping on the LC layer in the nonconductive and conductive regions, respectively, cause a difference between LC reorientations in the adjacent zones, thus forming the LC
a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
Fresnel zone plate. The programmable focusing feature of
the formed zone plate is polarization independent and electrically controllable. Additionally, the LC Fresnel zone plate
has the advantage of a very low operating dc voltage range
共0 – 2.4 V兲 in a cell with a thickness of 8 ␮m and a moderate
diffraction efficiency 共18%兲.
Figure 1 schematically presents the procedure for fabricating the Fresnel zone plate in a circularly symmetric
hybrid-aligned LC cell with a photoconductive polymer
layer. The zone plate photomask has a key role in this work;
it has transparent odd zones and opaque even zones, as
shown in Fig. 1共a兲. The used photomask with 80 concentric
rings within a diameter of 1 cm was formed by etching a
chromium oxide layer using electron-beam lithography. The
related information about the photomask used herein can be
found in Ref. 13.
In Fig. 1共a兲, a nonpolarized UV light 共from a 7.5 W Hg
lamp兲 with an intensity of 9.2 mW/ cm2 selectively illuminates a photoconductive polymer film 关poly共N-vinyl carbazole兲 共PVK兲兴 that is precoated over an indium-tin-oxide
共ITO兲 glass substrate using a zone plate photomask. The
photomask is in contact with the PVK film during irradiation
FIG. 1. Schematic diagram of fabrication procedure of LC Fresnel zone
plate in a circularly symmetric hybrid-aligned LC cell with a photoconductive polymer layer. Two substrates with a PVA-PVK-ITO film and a
DMOAP-ITO film are combined to produce an empty cell. The PVA film is
rubbed in the direction of ê␾ on xy plane.
0003-6951/2007/91共18兲/181104/3/$23.00
91, 181104-1
© 2007 American Institute of Physics
Downloaded 30 Oct 2007 to 140.116.210.6. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
181104-2
Appl. Phys. Lett. 91, 181104 共2007兲
Lo et al.
FIG. 2. Experimental setup for examining the focusing properties of the LC
Fresnel zone plate. P polarizer; D1 and D2 diaphragms.
with UV light. The thickness of the PVK film is measured to
be ⬃0.25 ␮m. In 6 h, permanently conductive odd and nonconductive even regions are formed in the PVK layer, corresponding to the transparent odd zones and opaque even
zones of the zone plate, respectively. The PVK electrodelike pattern with concentric rings is then generated over
the ITO glass substrate. A poly共vinyl alcohol兲 共PVA兲 film
with a thin thickness of ⬃50 nm is then coated over
the PVK-ITO substrate and rubbed in the circular direction
共represented by the azimuthal unit vector 共ê␾兲 on xy plane兲,
as plotted in Fig. 1共b兲. At the same time, another ITO
substrate is coated with a homeotropically aligned film
of N , N-dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl
chloride 共DMOAP兲. Such substrates with a PVA-PVK-ITO
film and a DMOAP-ITO film are combined to produce an
empty cell.
Then, the LCs 共E7, Merck, no = 1.5216, ne = 1.7462兲 are
injected into the empty cell and oriented themselves as a
circularly symmetric hybrid structure, forming a LC Fresnel
zone plate, as displayed in Fig. 1共b兲. The thickness of the
plastic spacer of the cell is 8 ␮m. As presented in Fig. 4共a兲,
the LC molecules in the formed Fresnel zone plate are verified to be aligned closely in the ê␾ direction by observation
under a POM with crossed polarizers in both the odd and the
even zones. The transmission axis of the polarizer 共analyzer兲
is set along x 共y兲 axis.
Figure 2 presents the experimental setup for examining
the programmable focusing features of the formed LC
Fresnel zone plate. The incident randomly polarized He–Ne
laser beam 共␭ = 633 nm兲 is expanded and collimated via an
expander with a magnifying power of 10 and then passes
through a diaphragm 共D1兲 with a 1 cm diameter aperture and
the LC Fresnel zone plate with an external applied dc voltage
共V兲. The polarization of the incident light is maintained linear or random by passing or not passing the light through or
not the polarizer 共P兲. A photodiode with a 1.1 cm active diameter, linked to a computer, is placed at a distance of
⬃40 cm from the LC Fresnel zone plate to measure the total
transmission intensity and the first-order focusing diffracted
intensity, in which another diaphragm D2 with a 1 mm diameter aperture is inserted in front of and close to the photodiode when the latter is measured.
Figure 3 plots the variations in the first-order focusing
diffraction efficiency with the applied dc voltage for the
incident light with various linear polarizations, at ␣ = 0°
共triangle兲, 45° 共circle兲, and 90° 共square兲, and random polarization 共rhombus兲. The first-order focusing diffraction efficiency is defined as the ratio of the first-order diffraction
FIG. 3. Measurement of polarization-independent programmable focusing
feature of the LC Fresnel zone plate: variation of first-order focusing diffraction efficiency through LC Fresnel zone plate under applied external dc
voltage for incident light with various linear polarizations, at polarizing
angles of 0° 共triangle兲, 45° 共circle兲, and 90° 共square兲, and random polarization 共rhombus兲.
intensity to the total transmission intensity through the LC
Fresnel zone plate. Figure 3 indicates that the electrically
controllable first-order focusing diffraction efficiency from
the LC Fresnel zone plate is entirely independent of the direction of the polarization of the incident beam including
random polarization. This result is certainly reasonable because the LC structures in the zone plate are always circularly symmetric at any applied dc voltage.
Notably, Fig. 1共b兲 indicates that the LC structures in
the even and the odd zones are equal in the voltage-off state,
and no focusing effect is evident. This feature is independent
of the cell thickness and the birefringence 共⌬n兲 of LCs and
differs from that in all developed polarization-independent
LC Fresnel zone plates.9–11 Its advantage is that it reduces
the range of operating voltage in a certain cell thickness.
As presented in Fig. 3, as the applied dc voltage increases
from 0 to 2.4 V, the first-order focusing diffraction efficiency from the LC Fresnel zone plate increases; it declines
as the voltage increases over 2.4 V. When an external dc
voltage is applied to the LC cell with PVK layers, the voltage on the LC layer 共VLC兲 in the steady-state regime can be
written as14
VLC =
V
,
1 + 共dPVK␴LC兲/共dLC␴PVK兲
共1兲
where dPVK 共␴PVK兲 and dLC 共␴LC兲 are the thicknesses 共conductivities兲 of LC and PVK layers, respectively. Equation 共1兲
shows that the voltage dropping on the LC layer is dependent
on the ratio of ␴LC to ␴PVK. If the PVK film is conductive
共␴PVK Ⰷ ␴LC兲, the external voltage will drop mostly on the
LC layer. If the PVK film is nonconductive 共␴PVK ⬍ ␴LC兲,
only minor fraction of external voltage will drop on the LC
layer. In this work, when the external dc voltage is applied
to the LC Fresnel zone plate, the conductivity in the conductive 共nonconductive兲 regions of the UV-induced PVK
electrodelike pattern is high 共low兲, resulting in a major
共minor兲 fraction of external voltage dropping on the LC
layer. These mechanisms may cause a discrepancy between
LC reorientations and interference between the light rays that
pass through each pair of adjacent odd and even zones, resulting in the programmable focusing effect. By comparing
Fig. 4共a兲 共at V = 0 V兲, Fig. 4共b兲 共at V = 2.4 V兲, and Fig. 4共c兲
Downloaded 30 Oct 2007 to 140.116.210.6. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
181104-3
Appl. Phys. Lett. 91, 181104 共2007兲
Lo et al.
Dm =
冕
2A1
Eoute−i2m␲共A/2A1兲dA
0
2A1
−im␲
=
E0共1 − e
2␲mi
+
FIG. 4. Central part of observed images of LC Fresnel zone plate under a
POM with crossed polarizers at 共a兲 0, 共b兲 2.4, and 共c兲 10 V. The transmission axis of the polarizer is parallel to the x axis.
共at V = 10 V兲, it indicates that the LCs in the nonconductive
regions cannot reorient in the range of operating voltages
共0 – 2.4 V兲, but can reorient as exceeding this range, because
the voltage on the LC layer in these regions is small enough
共lower than the threshold voltage兲 at 0 – 2.4 V, but not at
V ⬎ 2.4 V. However, in the conductive regions, a major portion of the external voltage drops on the LC layer such that
the LCs can reorient at a small voltage 共larger than the
threshold voltage兲 at 0 – 2.4 V.
In this experiment, the incident light field Ein, with a
linear polarization at a polarizing angle of ␣ with respect to
x axis in the xy-coordinate system, is given by
Ein = E0
冋 册
cos ␣
sin ␣
共2兲
.
The circularly symmetric distribution of the LCs on the plane
of the zone plate is such that the x⬘y ⬘-coordinate system,
which is a principal axis coordinate system, in Fig. 1共b兲 is
established to make an included angle of ␾ with respect to
xy-coordinate system, in which x⬘ and y ⬘ axes are parallel
and perpendicular to the short axis of the LC director, respectively. Through transforming Ein into the x⬘y ⬘-coordinate
system by introducing the mutually orthogonal field components along x⬘ and y ⬘ axes, the individual phase retardation
via the LC layer and then transforms the outgoing field 共in
the x⬘y ⬘-coordinate system兲 back into the xy-coordinate system; the outgoing field Eout through the LC zone plate in the
xy-coordinate system is given by
冉 冋册
Eout = E0 cos ␣
a
b
+ sin ␣
冋 册冊
b
a
,
共3兲
where a and b represent the terms cos2 ␾ exp共i2␲dno / ␭兲
+ sin2 ␾ exp共i2␲dneff / ␭兲 and cos ␾ sin ␾ exp共i2␲dno / ␭兲
+ exp共i2␲dneff / ␭兲, respectively. no 共neff兲 is the ordinary
共effective extraordinary兲 refractive index of LCs that is
experienced by the component of the light field parallel
共perpendicular兲 to the short axis of the LC director. Since
the conductivities are different in the even and odd zones
at V ⫽ 0, neff varies with voltage as given by neff共even兲共V兲
and neff共odd兲共V兲 in these two zones. Substituting the result of
Eq. 共3兲 into the mth-order diffracted light field Dm, which can
be determined by the mth Fourier component of the outgoing
light field, yields11
兲
冋
ei共2␲dno/␭兲 + ei共2␲dneff共odd兲/␭兲
共ei共2␲dno/␭兲 + ei共2␲dneff共even兲/␭兲兲
eim␲
册冋 册
cos ␣
sin ␣
,
共4兲
where r1 and A1 denote the radius and the area of the first
odd zone of the zone plate, respectively. The diffraction efficiency of the first-order 共m = ± 1兲 diffracted beams is therefore given by
兩D±1兩2 1
2␲
d⌬neff ,
␩±1 ⬅
共5兲
2 = 2 1 − cos
兩Ein兩
␲
␭
冋 冉
冊册
where ⌬neff equals neff共even兲 − neff共odd兲. From Eq. 共5兲, the firstorder efficiency of diffraction from the zone plate is independent of the direction of polarization of the incident beam,
confirming the results that are plotted in Fig. 3. The even
orders of the diffraction light all vanish according to Eq. 共4兲.
When the phase difference, 2␲d⌬neff / ␭, in Eq. 共5兲 equals ␲,
the maximum first-order diffraction efficiency of ⬃20%,
which approaches the experimental value of ⬃18%, can be
obtained.
In summary, this work elucidates a Fresnel zone plate
based on a circularly symmetric hybrid-aligned LC film with
a photoconductive polymer layer. Experimental results reveal
that the focusing feature of the LC Fresnel zone plate is
polarization independent and electrically controllable. Additionally, the LC zone plate provides advantages of a zero
focusing in the voltage-off state, a low operating dc field
range from 0 to 0.3 V / ␮m, and a moderate diffraction efficiency 共⬃18% 兲.
The authors would like to thank the National Science
Council of the Republic of China, Taiwan, for financially
supporting this research under Contract No. NSC 95-2112M-006-020-MY2.
1
M. Makowski, G. Mikula, M. Sypek, A. Kolodziejczyk, and C.
Prokopowicz, Proc. SPIE 5484, 475 共2004兲.
2
E. Marom, E. Ben-Eliezer, L. P. Yaroslavsky, and Z. Zalevsky, Proc. SPIE
5227, 8 共2004兲.
3
X. Ren, S. Liu, and X. Zhang, Proc. SPIE 5456, 391 共2004兲.
4
S. C. Kim, S. E. Lee, and E. S. Kim, Proc. SPIE 5443, 250 共2004兲.
5
J. T. Early and R. Hyde, Proc. SPIE 5166, 148 共2004兲.
6
H. Ren, Y.-H. Fan, and S.-T. Wu, Appl. Phys. Lett. 83, 1515 共2003兲.
7
Y.-H. Fan, H. Ren, and S.-T. Wu, Opt. Express 13, 4141 共2005兲.
8
T.-H. Lin, Y. Huang, A. Y.-G. Fuh, and S.-T. Wu, Opt. Express 14, 2359
共2006兲.
9
G. Williams, N. J. Powell, A. Purvis, and M. G. Clark, Proc. SPIE 1168,
352 共1989兲.
10
D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, Appl. Phys.
Lett. 88, 203505 共2006兲.
11
L.-C. Lin, H.-C. Jau, T.-H. Lin, and A. Y.-G. Fuh, Opt. Express 15, 2900
共2007兲.
12
E. Hecht, Optics, 4th ed. 共Addison Wesley, San Francisco, 2002兲,
Chap. 10, p. 495.
13
K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, and
R. E. Nahory, Appl. Opt. 30, 1347 共1991兲.
14
F. L. Vladimirov, A. N. Chaika, I. E. Morichev, N. I. Pletneva, A. F.
Naumov, and M. Yu. Loktev, J. Opt. Technol. 67, 712 共2000兲.
Downloaded 30 Oct 2007 to 140.116.210.6. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp