A polarization independent liquid crystal phase modulation adopting surface pinning
effect of polymer dispersed liquid crystals
Yi-Hsin Lin and Yu-Shih Tsou
Citation: Journal of Applied Physics 110, 114516 (2011); doi: 10.1063/1.3666053
View online: http://dx.doi.org/10.1063/1.3666053
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/110/11?ver=pdfcov Published by the AIP Publishing
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A polarization independent liquid crystal phase modulation adopting surface
pinning effect of polymer dispersed liquid crystals
Yi-Hsin Lina)and Yu-Shih Tsou
Department of Photonics, National Chiao Tung University, Hsinchu, Taiwan 30010
(Received 15 September 2011; accepted 9 November 2011; published online 8 December 2011) A polarization-independent liquid crystal (LC) phase modulation using the surface pinning effect of polymer dispersed liquid crystals (SP-PDLC) is demonstrated. In the bulk region of the SP-PDLC, the orientations of LC directors are randomly dispersed; thus, any polarization of incident light experiences the same averaged refractive index. In the regions near glass substrates, the LC droplets are pinned. The orientations of top and bottom droplets are orthogonal. Two eigen-polarizations of an incident light experience the same phase shift. As a result, the SP-PDLC is polarization independent. Polarizer-free microlens arrays of SP-PDLC are also demonstrated. The SP-PDLC has potential for application in spatial light modulators, laser beam steering, and electrically tunable microprisms.VC 2011 American Institute of Physics. [doi:10.1063/1.3666053]
I. INTRODUCTION
Liquid crystal (LC) phase-only modulations are useful for laser beam steering,1 tunable focus lenses,2electrically tunable gratings and prisms,3and spatial light modulators.4 The advantages of LC phase modulators are their low cost, light weight, low power consumption, and electrical controll-ability without mechanical moving parts. However, the use of polarizers greatly reduces the optical efficiency. There-fore, the development of a polarization independent LC phase modulator is necessary.5–7 Two main types of polar-ization independent LC phase modulators have been demon-strated. One is the residual phase type of LC phase modulations.5,6 The orientations of LC directors are ran-domly dispersed. As a result, any polarization of incident light experiences the same averaged refractive index, which is related to the same phase shift. However, the residual phase type suffers from a relatively small phase change. To enhance the phase change while maintaining polarization in-dependence, a double-layered type of LC phase modulations is demonstrated.5,7The structure is based on two homogene-ous LC layers with orthogonal rubbing directions. Each LC layer modulates one of the eigen-polarizations of an incident light. As a result, two eigen-polarizations of an incident light experience the same phase shift. Recently, the polarization independent phase modulation of polymer-stabilized blue phase liquid crystals (PSBP-LC) has been investigated as well, based on the optical isotropy of blue phase liquid crys-tals.8However, the stability of materials and the temperature range of PSBP-LC limited the applications. In the current work, we aim to develop a different type of polarization in-dependent LC phase modulator by mixing the residual phase type and the double-layered type. In 2005, the surface pin-ning effect of polymer dispersed liquid crystals (SP-PDLC), which can determine the morphologies of polymer dispersed liquid crystals, was studied.9 The LC droplets are pinned
near glass substrates and at random in the bulk region. Add-ing dye in to SP-PDLC can enable a high contrast polarizer-free display.10 Up to now, no related phase investigation of SP-PDLC has been studied. Here, we demonstrate a polariza-tion independent LC phase modulapolariza-tion based on SP-PDLC. The mechanism of such a LC phase modulation includes the residual phase type of LC phase modulation in the bulk region and the double-layered type of LC phase modulation in two layers near the glass substrates. The measured phase shift is around 0.28 rad. Polarizer-free LC microlens arrays using SP-PDLC are also demonstrated.
II. STRUCTURE AND OPERATING PRINCIPLES
Figures1(a)and1(b)illustrate the structure and operat-ing principles of the phase modulation usoperat-ing SP-PDLC. In Fig. 1(a), the LC droplets near the substrates are pinned owing to the surface pinning effect,9,10 and the orientations of LC directors are along the rubbing directions (y direction of the top alignment layer and x direction of the bottom alignment layer). In the bulk region of Fig.1(a), the averaged orientations of the rest of the LC droplets are randomly dis-persed in the polymer matrix. Without an applied voltage (V¼ 0), the SP-PDLC cell scatters the incoming light due to the refractive mismatch between polymer and liquid crystals, as shown in Fig. 1(a). As the applied voltage increases, LC directors are reoriented along the direction of the electric field (z direction), as shown in Fig.1(b). As a result, scatter-ing decreases and the SP-PDLC cell becomes more transpar-ent. When the voltage exceeds the saturation voltage (Vs),
the SP-PDLC is scatter-free and it is switched into a pure phase modulation that is polarization independent.
In the pure phase region (V > Vs), the mechanism of the
polarization-independent phase modulation of SP-PDLC can be proven as follows. Let us consider a randomly polarized and quasi-monochromatic light incident to a sample at a nor-mal angle. The electric field of the incident light consists of randomly polarized lights, and each polarized light can be
a)Electronic mail: [email protected].
decomposed as x- and y-linearly polarized lights. The elec-tric field of the incident light can be written as
~
Einputð~r; tÞ X j
ajð~r; tÞ A0xð~ r; tÞ ^xþ A0yð~r; tÞ ^yj
h i
;
(1)
whereA0xð~r; tÞ and A0yð~r; tÞ are two complex numbers that are functions of the position (~r) and the time (t). A0xð~r; tÞ and A0yð~r; tÞ satisfy the following relationship: A0xð~r; tÞ2 þ A0yð~r; tÞ2¼ 1. The coefficient ajð~r; tÞ is a complex weighting factor for the jth component, and ðA0xð~r; tÞ ^x þ A0yð~r; tÞ ^yÞj represents the polarization state of the jth component. When the incoming light passes through the SP-PDLC cell along theþz direction in Fig.1(a), thex and y components of the polarization of the incident light accumu-late phases. The total accumuaccumu-lated phase (d) is attributed to two parts. First, the orientations of LC droplets near the top and bottom glass substrates are orthogonal to each other at V¼ 0. The phase modulation is similar to the double-layered type of phase modulations.5,7 Thus, the phase of the two eigen-polarizations (x and y linear polarizations) is (k neff ðh; w þ p=2Þ d1þ k neffðh; wÞ d1), wherek is a wave number (k¼ 2p/k), d1is the radius of the droplet pinned on
the glass substrate, andneffðh; wÞ is the effective refractive index depending on the tilt angle h with respect to the z direction and the twist angle w of LC directors with respect to the x direction.neffðh; wÞ satisfies the following relation when w¼ 0: 1 n2 effðh; 0Þ ¼sin 2ðhÞ n2 e þcos 2ðhÞ n2 o ; (2)
andneffðh; wÞ ¼ no with arbitrary h when w¼ p=2 radians. Second, LC droplets in the middle layer are randomly dis-persed; therefore, it is similar to the residual phase type of phase modulations.5,6The phase is (k naveðhÞ d2), where d2is the diameter of the droplet in the middle layer of
SP-PDLC as depicted in Fig. 1, and the averaged refractive nave(h) depending on the tilt angle h of LC directors is
ðneffðh; 0Þ þ noÞ2. Thus, the total accumulated phase (d) can be expressed as
d¼ k neffðh; w þ p=2Þ d1þ k naveðhÞ d2 þ k neffðh; wÞ d1; (3) where w¼ 0 and p=2 radians for the x and y components of the polarization of the incident light, respectively. After light
passes through a SP-PDLC cell, the electric field of the out-put light is
~
Eoutputð~r;tÞ ¼X
j
fajð~r;tÞ½eiðkneffðh;wÞd1þknaveðhÞd2þkneffðh;wþp=2Þd1Þ
A0xð~r;tÞ ^xþeiðkneffðh;wþp=2Þd1þknaveðhÞd2þkneffðh;wÞd1Þ
A0yð~r;tÞ ^yjg: (4)
We can rearrange Eq.(4), and it can be expressed as
~
Eoutputð~r; tÞ ¼ eiðkneffðh;wþp=2Þd1þknaveðhÞd2þkneffðh;wÞd1Þ
~Einputð~r; tÞ: (5) In Eq. (5), the only difference between output and input lights is the phase shift. Therefore, SP-PDLC is polarization independent.
III. EXPERIMENTS AND DISCUSSIONS
To prepare a SP-PDLC sample, we mixed UV-curable monomer NOA65 (np¼ 1.524) in a nematic LC host (E48,
Dn¼ 0.231 at k ¼ 589 nm) at 30:70 wt. % ratios. We injected the LC/monomer mixture into an empty cell with an inner surface coated with indium-tin-oxide (ITO) and polyimide that was mechanically buffered in orthogonal directions in the isotropic state at T¼ 70C. The cell gap was 7.7 lm. The cell then exposed UV light with an intensity I¼ 60 mW/cm2for 15 min at T¼ 20C. We observed the phase separation morphology of the SP-PDLC sample under a polarizing optical microscope (POM) and a scanning elec-tron microscope (SEM) as shown in Figs. 2(a) and2(b). In Fig.2(a), the morphology of the SP-PDLC is uniform due to the surface pinning effect.9,10 In Fig.2(b), the side view of the SP-PDLC cell shows three layers. The thickness (or droplet size) near the top and bottom substrate is around 3 lm, and the thickness in the middle layer is around 1 lm. The droplet size or layer thickness can be adjusted by chang-ing the curchang-ing temperature and UV curchang-ing intensity.
Next, we measured the transmittance of the SP-PDLC cell. The light source was an unpolarized He-Ne laser (JDSU, model 1122, k¼ 633 nm). A large area photodiode detector (New Focus, model 2031) was placed 30 cm behind the SP-PDLC cell, corresponding to a2collection angle. A computer controlled LabVIEW data acquisition sys-tem was used to apply the voltage to the sample and record
FIG. 2. (Color online) (a) The top view POM morphology and (b) SEM side view image of SP-PDLC.
FIG. 1. (Color online) The structure and operating principles of SP-PDLC at (a) V¼ 0 and (b) V > Vs.
the transmittance at the same time. Figure3shows the meas-ured transmittance as a function of an applied voltage. At V¼ 0, the SP-PDLC has low transmittance because of scat-tering. When the voltage increases, the transmittance increases. The transmittance is high and remains almost unchanged after V > 20 Vrms. We define this voltage as the
saturation voltage (Vs). When V > Vs, SP-PDLC is operated
as a pure phase modulator.
In order to measure the phase as V > Vs, we adopted a
Mach-Zehnder interferometer. An unpolarized He-Ne laser (JDSU, model 1122, k¼ 633 nm) was split equally into two arms by a beam splitter, and then the two beams were re-combined again by the other beam splitter. The interfer-ence fringes can be observed when two beams overlap. Our sample was put in one arm of the interferometer. The fringes were recorded by a digital camera (SONY, DCR-HC40). By recording the shifted fringes between the high voltage and the saturation voltage, we can obtain the phase shift of the SP-PDLC cell. The saturation voltage is defined as the volt-age at a transmittance of 85% due to the clear interference fringes when the voltage is larger than the saturation voltage. Figure 3shows the phase shift as a function of an applied voltage as V > Vs. The total phase shift between 20 and
40 Vrmsis around 0.09 p or 0.28 rad. In fact, the interference
patterns were smeared at V < Vs due to the scattering of
SP-PDLC. In order to examine the polarization dependency, we measured the phase shift as we put a polarizer in front of the laser and rotated the polarizer. The phase shifts are almost the same at the different polarizations of the incident light, as shown in Fig. 3. That means SP-PDLC has pure phase modulation and is polarization independent as well. The total response time (rise time plus decay time) is around 12 ms when the SP-PDLC is given a square burst at f¼ 1 kHz between 0 and 40 Vrmsand around 3.8 ms when
the voltage is switched between 20 and 40 Vrms. The fast
response is because of the bias voltage effect and polymer networks.11
From Eq.(3), the total accumulated phases at Vsand at
high voltage (V Vs) for any polarized light can be
expressed as in Eq.(6)and Eq.(7).
dðVSÞ ¼ k neffðhÞ d1þ k naveðhÞ d2þ k no d1 (6) dðV VSÞ ¼ k no d1þ k no d2þ k no d1 (7) From Eqs.(6) and(7), the total phase shift (Dd) between V and Vs, defined as Dd dðV VsÞ dðVsÞ, turns out to be
Dd
j j ¼ k ðneffðhÞ noÞ d1þ k ðnaveðhÞ noÞ d2: (8)
In our experiments, no¼ 1.523, ne¼ 1.754, d1 3 lm, and
d2 1 lm. The values of d1 and d2 are obtained from
Fig. 2(b). The SP-PDLC cell is transparent when nave no
< 0.005.11The value of nave noequals ðneffðh; 0Þ noÞ
2, and then the calculated h is around 13 according to Eq.(2). The calculated Dd is then0.106 p radians, close to the measured result of 0.09 p radians. The phase shift of SP-PDLC (0.1 p radians) is larger than that of the residual phase type (0.016 p radians with an 8 lm cell gap) and smaller than that of the double layered type (5 p radians with an 8 lm cell gap).5–7To enlarge the phase shift, we can enlarge the domain size and cell gap. However, the polariza-tion dependency increases as the domain size gets too large. The surface pinning effect decreases when the cell gap is large.
To demonstrate a two-dimensional (2D) microlens arrays using SP-PDLC as an electro-optics medium, we pre-pared microlens arrays consisting of one ITO glass substrate, one glass substrate coating with an aluminum layer into which were etched hole-patterns 130 mm in diameter, and SP-PDLC, as shown in Fig. 4(a).12 The distance between hole-patterns was 120 mm. The cell gap was 8 mm. In order to characterize the focusing properties, a collimated unpolar-ized light at k¼ 532 nm was used to illuminate the SP-PDLC microlens arrays. The transmitted light was recorded by a charge-coupled device (CCD). The light inten-sities of a sub-microlens of SP-PDLC microlens arrays at different voltages are shown in Fig. 4(b). The CCD was placed 3 cm from the sample. The intensity in Fig. 4(b)
FIG. 3. (Color online) Voltage-dependent transmittance of SP-PDLC and voltage-dependent phase shift at rotational angles of the polarizer: 0(red squares), 45(blue triangles), and 90(green diamonds). Black dots
repre-sent instances when no polarizer was used.
FIG. 4. (Color online) (a) The structure of SP-PDLC microlens arrays. (b) The light intensity of a sub-microlens of SP-PDLC microlens arrays as a function of position at different voltages.
increases with the voltage. SP-PDLC microlens arrays showed clear focal spots at 100 Vrms. When we applied
dif-ferent voltages, the position of the CCD was changed so as to obtain a clear focal spot, and we recorded the distance between the CCD and the sample as the measured focal length. The measured focal length as a function of voltage is plotted in Fig.5. When the applied voltage is less than 40 V, the SP-PDLC microlens arrays are in the scattering state and are out of focus. As the applied voltage exceeds 40 V, the SP-PDLC microlens arrays become transmitted and focus the light. The tunable focal length was measured from14 cm at 40 Vrmsto1 cm at 200 Vrms. When we placed a
po-larizer in front of the microlens arrays, the measured focal length did not change with the rotation of the polarizer. Thus, the focal length of SP-PDLC microlens arrays is elec-trically tunable, and SP-PDLC microlens arrays are polariza-tion independent. To reduce the voltage, the droplet size can be increased and the dielectric constant of the polymer can be enlarged.
IV. CONCLUSION
We have demonstrated a polarization-independent LC phase modulation using SP-PDLC, as well as the microlens
arrays. The mechanism of polarization independence of the SP-PDLC phase modulation is a mixture of LC phase modu-lations that is a combination of two well-known types, the re-sidual phase type LC phase modulations in the bulk region and the double-layered type LC phase modulation near two substrates. The microlens arrays of SP-PDLC are in the scat-tering state at 0 < V < 40 Vrmsand in the pure phase state at
V > 40 Vrms. The focusing properties are polarization
inde-pendent. The focal length is electrically tunable from 14 cm to 1 cm. Such a polarization independent LC phase modula-tion is important in many applicamodula-tions, such as spatial light modulators, laser beam steering, e-lens, and microprisms.
ACKNOWLEDGMENTS
The authors are indebted to Professor Chyong-Hua Chen, Mr. Hung-Chun Lin, and Mr. Wei-Chih Lin for tech-nical assistance. This research was supported by the National Science Council (NSC) in Taiwan under Contract No. 98-2112-M-009-017-MY3.
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