- Email: [email protected]
Optimization of twisted nematic liquid crystal panels for spatial light phase modulation
1 March 1995
OPTICS COMMUNICATIONS Optics Communications 115( 1995) 19-25
Optimization of twisted nematic liquid crystal panels for spatial light phase modulation Makoto Yamauchi, Tomoaki Eiju Optical Engineering Division, Mechanical Engineering Laboratory, Namiki l-2, Tsukuba, Ibaraki 305, Japan
Received 18 July 1994
Abstract To optimize a twisted nematic liquid crystal panel for large phase modulation, it is necessary to optimize the angles of the polarizer and analyzer. We determine the Jones matrix of a panel and find these optimum angles by computer simulations. They compare well to the experimental results.
1. Introduction
Recently liquid crystal panels (LCPs) have been used in many applications, such as optical information processing [ l-5 1, optical interconnections [ 68 1, real-time holography [9-l 11, etc. In these applications LCPs are used for both intensity and phase modulation. Twisted nematic (TN) type LCPs are good for intensity modulation and homogenous type (parallel aligned) LCPs are suitable for phase modulation. Unfortunately homogenous type LC panels are very hard to obtain because there are no commercial suppliers, while TN LCPs are easily available because they are mass produced for LCTVs. That is why much effort has been made to use TN LCPs as spatial light phase modulators [ 12,131, despite their inability to achieve a phase modulation of more than 2n with very high spatial resolution. Phase modulation characteristics of TN LCPs have been studied [ 14-181. TN LCPs change the polarization state of input light, when a TN LCP is sandwiched by a polarizer and an analyzer, both intensity and phase of the input light are simultaneously modulated. Intensity-only modulation is rather easy to
obtain, however phase-only modulation is only possible when the panel is used in binary operation [ 19 ] or below the optical threshold [ 201. In addition to the unavoidable accompanying intensity modulation, the lack of phase modulation range is also a problem. This problem is especially serious when we use TN LCPs with very high spatial resolution because these LCPs are thinner, and the phase modulation is proportional to the thickness of the panel. To solve these problems optimization of the optical setup has to be considered. For thin LCPs the setup in which the polarizer angle equals the director angle of the input plane of the panel is not the best choice. Arranging the angles of polarizer and analyzer is very important, though most people set the angles to be either parallel to the director angle or perpendicular to it. A commercially available LCTV was used to experimentally obtain the optimum angles. The Jones matrix of one of the LCPs was determined from intensity transmittance measurements, and the optimum angles of polarizer and analyzer were indicated by computer simulation using Jones calculus. Experimental results coincided well with the simulation,
0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOO30-4018(94)00654-7
20
M. Yamauchi, T. Egu /Optics Communicatrons 115 (1995) 19-25
and we succeeded in attaining K phase modulation with small intensity modulation.
(3) 1
cos2B
sin28
n:(e) =n,Z + n, 2
2. Theory Fig. 1 shows a schematic diagram of a TN LCP whose directors in the input and output planes are aligned with 19sand 0, (measured from x-axis), respectively. If we set parameters as listed in Table 1, the Jones matrix of the panel is expressed as follows:
J=cexp[-i(@0+8)1
f-ig
(
f+ig
h_G
(5)
g= $sinycos(&+B,),
(6)
(1)
,
1
eE-es -sinyc0s(OE-8S) Y
+cosysin(O,-8,))
where c represents intensity loss caused by surface reflections etc., i is the imaginary unit and
(4)
e,-es. f=---y smysin($-e~)+COsyCOS(eE-e~),
h=_
--h-G
'
(7)
j= ;Psinysin($f&)
,
y=Jp2+(eE-ess)2.
(8) (9)
It should be noticed that y+
Input Plane
,
f 2+g2+h2+j2= det(J) =c2 .
Fig. 1. Schematic diagram of a TN LCP structure. Right handed coordinate system is used for the calculation of a Jones matrix. Table 1 Parameters of TN LCPs A d n0
4 I3 4 0, 2s
Wavelength Thickness of the panel Ordinary refractive index of the liquid crystal Extraordinary refractive index of the liquid crystal Tilt angle of the liquid crystal molecules caused by applied voltage Director angle of input plane of the panel with respect to x-axis Director angle of output plane of the panel with respect to x-axis Retardation of the panel
1
(10) (11)
Because we are able to control only the applied voltage on the panel, J is regarded as a function of just one parameter /I [ 15 1. However, to determine J, we have to know three other parameters c, 0s and &; that are thought to be constants with respect to the applied voltage. As shown later, we can determine c, f; g, and h from experiments. (&-es) and y are solved using Eqs. (5) and (7), consequently B is also derived from Eq. (9). Then (0, + 0,) is calculated by Eq. (6), and all parameters but @,,are determined. One possible way to determine c, f; g, and h is to measure intensity transmittances with four different optical setups. If a TN LCP is sandwiched by a polarizer and an analyzer whose azimuth angles are vp and t,uA,respectively, and illuminated by an input beam denoted by Jones vector xin
( Yin13 the output beam X0”, ( YOU,>> is
calculated to be
M. Yamauchi. T. Eiju /Optics Communications 115 (I 995) 19-B
Xout
Table 2 Specifications of the TN LCP used in the experiments (Epson VPJ-2000 Video Projector)
(>
(>
=P(Y*) JP(YP) ;
YO”t
I”
=cew[-i(h++P)l X
(xin
COSV/P+
Yin
21
Type
( >
sinV/P) ~vp,vA “,yiK ,
Control
(12)
Panel size
=fcos(yA-t[/p)+hsin(yA-yp) %NA
-i{gcos(WA+y/,)+jsin(yA+yp)i,
Number of pixels Pixel pitch
(13)
Twisted nematic transmission Electrically addressed TFT active matrix 1.32 inches (diagonal) 26.9 mm (H)x20.2 mm (V) 480 (H)x440 (V) 56pm (H)X46pm (V)
where P(v) is the Jones matrix of a polarizer with azimuth angle t,u,namely P(w)=
cos=w ( sin v cos v
sin w cos w sin2y/ ) ’
Intensity transmittance setup is
6wp,yIA = 8-
/
Tvp,vA of the panel in this
T ,,,=C21XinCOSWp+Yi”sinWp12
and phase delay S,,,,
(14)
I~~p.lyA12~ (15)
caused by this panel is
arg( TYp.cuA 1
(16)
ignoring terms independent of applied voltage.
Personal Computer Fig. 2. Optical system to measure the intensity transmittance of a TN LCP. Azimuth angles of the polarizer and the analyzer are vp and V/A,respectively. Intensity of the input beam was measured between the polarizer and the LCP.
3. Experiments and results Experiments were conducted to determine the Jones matrix of a panel with several applied voltages. Using these results, computer simulations were carried out to find setups for which the panel generated a large phase modulation with small intensity modulation. Experiments to check the theory were also carried out. A TN LCP from a video projector (Epson VPJ2000) was used in the following experiments. The projector has three LCPs (R, G and B), we used the red panel. Specifications of the panels are shown in Table 2. Each panel has 480 horizontal by 440 vertical pixels. Thin film transistors are used and each pixel is addressed by the active matrix method. We used the original electronics to drive the panel, so the projector is controlled by NTSC video signals which are generated by a personal computer equipped with a video board. Intensity transmittance of the panel was measured using the optical system shown in Fig. 2. A HeNe laser
beam (wavelength is 633 nm) was expanded and collimated to be incident on a polarizer whose azimuth angle was vp. To obtain a constant intensity output beam after the rotated polarizer, a quarter wave plate was inserted in the optical system. The output beam from the polarizer went through the LCP and an analyzer whose azimuth angle was vA. Experiments were made with polarizer-analyzer setups ( yp, v/A) equal (OD,OD), (00, 90”), (30”, 60”) and (45”, -45”) at states when the input video signals were 0, 64, 128, 192 and 255. Intensity transmittance was also measured when the video projector was switched off. Maximum voltage is applied to the panel electrodes when the video signal is 0, while minimum voltage is applied when it is 255. For convenience, we measured the input beam intensity between the polarizer and the panel as indicated in the figure. The output beam intensity was measured after the beam passed through the analyzer. In this case we can neglect (Xi”cos v/p+yi, sin v,) terms in Eqs. (12) and (15).
22
M. Yamauchi, T. Eiju / Optics ~ommu~~cat~ons1I5 (I 995) i9-25
Overall
intensity
transmittance,
namely
c* =
Twp,vA+Tw,yA+l(,2was about 14.5% in all (VP, v/A)
pairs. The Jones matrix of each state was calculated and is shown in Table 3. The calculation is explained in the Appendix. /_Iand y are also shown in Table 3. Because it is difficult to solve (19,- 0,) and y from Eqs. ( 5 ) and ( 7 ) , they are calculated numerically by the Newton-Raphson method. 6s and 0, were determined using the values f and h at the switched off state, which were found to be 83.4” and -4.3”, respectively, this indicates the twist angle (t9a- 0s) equals 87.7”. A computer simulation was carried out to find the best setup for high phase modulation, with low intensity modulation, using Eqs. ( 15 ) and ( 16). TvBwAand 6wp,wI\ were calculated for every 5 degrees of v/Pand VA.From the simulation we found: (i)when(~p,~A)=(-50,850),namelyinputlight is aligned to the director angle, phase modulation is about 0.9 n and intensity modulation is almost loo%, (ii) maximum phase modulation is about 1.4 n and there are some setups to attain that, however intensity modulation is always very large in these setups, (iii) under the condition that phase modulation is larger than n, we found that ( vpvp, VA)= (30”, 85”) gave the minimum intensity modulation. Figs. 3a and 3b respectively show the simulated intensity transmittance and difference in phase delay, versus video signal in each case. To examine the interesting situation in case 3, in
detail, we did experiments setting the polarizer angle to 30” and changing the analyzer angle. Fig. 4a shows the intensity transmittance. Symbols denote the experimental results and lines show the simulation for each level of video signal. They coincide very well. Intensity modulation takes a minimum value near vA= 85”. Computer simulation of phase delay were also carried out on the same condition, and results are shown in Fig. 4b. When the video signal is 0 and vA= 120”, the phase delay jumps from 0 to n. However, physical difficulty caused by this singularity is avoided because no transmitting light is expected by Fig. 4a. Phase modulation capability is the maximum difference in phase delay caused by the video signal modulation, that is also shown in Fig. 4b, by a solid line. From the figure, we can expect more than Kphase modulation between VA=700 and v/A= 120”. In the setup ( I,u~,VA) = (30”, 85’)) phase modulation versus video signal, was measured using a phase shifting Mach-Zehnder interferometer shown in Fig. 5. A stripe pattern was written on the panel. Interference fringes were imaged on to the CCD TV camera. The phase of several points on the pattern was calculated using the three step phase shifting method. The result is shown in Fig. 6, along with the experimental result of intensity transmittance measurements. We achieved n phase modulation with 25.8% intensity modulation.
Table 3 Jones matrix of a TN LCP for several states Video signal
B (rad)
Y (rad)
Jones matrix
0
0.000 x
0.48 1 IT
J,,=O.380
64
0.147 x
0.508 R
J,,=O,381
128
0.329 K
0.587 n
J,**=O.38,
192
0.445 R
0.660 x
255
0.518 II
0.999 e-l*
-0.019-0.041%
0.019-0.0415i 0.976-0.0563i
)
e-‘teo+0-=9”) ( -0.306-0.4531
0.835+0.0563i
)
J,9,=0.381
e-‘(@+“-“5x)
o’50~.~~~550i)
0.711 n
~~~~=0.382
e-i(Oo+O-slsn) ( -0.639-0.5581
0.726 IT
5,,=0.3*2
( _o,5~~~~.550i 0.528-0.0427i
Off Power
0.538 II
) 0.0665-0.2011 0.976+0.05631 0.306-0.453i
e-it*+o.14W
( -0.0665-0.2Oli 0.835-0.0563i
0.999
0.639-0.558i 0.528+0.04271
)
e -i(go+0.53ar) -0.672-0.5541 0.481-0.107i
0.48l+O.l07i 0.672-0.5541
)
M. Yamauchi, T. E& /Optics Communications 1IS (1995) 19-25
23 Polarizer Sohd
= 30”
Line
: Simulation -l
0 .64 128
“-
0
50
100
150
200
250
Video Signal
J "0
80
40
120
160
Analyzer Angle (degree) ’
(b)
I’
”
1
”
”
Video Signal
1.5
Video Signal
Fig. 3. Computer simulation of (a) the intensity transmittance T and (b) difference in phase delay 6 of three special cases. Case 1: polarizer is aligned to the director; (vr, vA) = ( - 5”, 85”). Case 2: maximum phase modulation is attained; (yr, vA) = ( W, I 15”). Case 3: phase modulation is larger than R and intensity modulation is minimum; (v/p, vA) = (30”, 85”).
4. Discussion In general, it is accepted that when linearly polarized light aligned with the director angle is input on a TN LCP, the angle of polarization changes along the twisted molecules by a waveguide effect and the output light remains in its linear polarization state. However the output light is no longer linearly polarized when the retardation of the panel is small, even if the input light is linearly polarized and aligned with the director angle [ 2 I]. In that case the maximum phase modulation does not occur when the input light is aligned with director angle. TN LCPs should not be considered as optical elements for changing the polarization angle but for changing the polarization state. It should also be mentioned that TN type LCPs
Analyzer
Angle
(Degree)
Fig. 4. (a) Intensity transmittance T. (b) Computer simulation of phase delay 6, when the polarizer angle is fixed at 30” and the analyzer angle is changed. Solid line in (b) shows difference in phase delay between the video signal 0 and 255.
were thought to have less capability for phase modulation than homogenous type (parallel aligned) LCPs [ 20 1. Phase modulation capability of homogenous type LCPs equals their retardation, namely somewhat less than (2n/l)(n,-n,)d [22]. However,we showed that TN LCPs are able to modulate more than their retardation. For example, in our case retardation of the panel was 1.04a while the maximum phase modulation exceeded 1.4~. We could not give a clear
24
M. Yamauchi, MlCKWXJpe ObJeCtWe
T. Eiju / Optics Communications
Half Mmar \
He-Ne Laser
Half Mm
LUlS
CCD Camera
OX I I PersonalComputer
I15 (I 995) 19-25
shown the procedure to determine the Jones matrix of a TN LCP from intensity transmittance measurements. Changing the angles of polarizer and analyzer, we succeeded in obtaining the best setup for n phase modulation, with the smallest intensity modulation. We also found an interesting phenomenon; the phase modulation capability of an LCP exceeds its retardation.
/Dnverlu PersonalComputer
Fig. 5. Phase shifting Mach-Zehnder interferometer to measure the phase modulation of a LCP.
Acknowledgements This work was done under a cooperative research agreement with Heriot-Watt Univ., Edinburgh, UK. Authors wish to thank to Dr. H. Ichikawa, Dr. N. McArdle, and Dr. M. Taghizadeh of the University for helpful suggestions, and to Dr. I. Khandaker of Mechanical Engineering Laboratory for checking the manuscript.
Appendix
0 t&4, 0
From Eqs. ( 13) and ( 15 ) the intensity transmittance of (VP, VA/A) setup is
/
,I
, 50
100
T Wp.V,=c2[Gfcos(~~-~P)+hsin(~~-~P)j2
0
150
200
+(gcos(W,+Y/p)+jsinlW,+WP))‘l.
250
Vldeo Stgnal
Fig. 6. Experimental results of the phase modulation and the intensity transmittance of a TN LCP at the best setup for R phase modulation (VP,v,) = (30”, 85”).
explanation of this physically discrepant phenomenon yet. Further study is needed to analyze it. The short-coming in TN LCPs compared to homogenous type LCPs, is that the intensity modulation always accompanies phase modulation.
(A.11
Taking account of Eq. (lo), this equation consists four variables, c, fl h and g. However we can only determine square of each variable from four independent measurements of T. The sign of each variable is determined another way. c is easily solved. Namely c2 = To, + c
To.90
.
(A.2)
is positive by definition. If we set 2
IA= G
T T30,60+ D,o +
3T457-45
4
1
5. Conclusion
u= z” (T4,,-,,-Toso) >
Optimum setup of TN LCPs, for optical spatial phase modulators, was studied. Polarization states of light propagating through a thin TN LCP are sufficiently complex to require analysis using Jones matrices and computer simulations. The best setup for this purpose is obtained by simulation. We have
we have h*=
v+JZG
2
c2 )>
(A.3)
4
(A.4)
, f*=h*-v,
(A.51
A4. Yamauchi. T. Eiju /Optics Communications 115 (1995) 19-25
If we assume 1&-&I E 90” and /3z 0 (i.e. higher voltage is applied),fis always positive. Then the sign of h is determined from the value of U, because u equals hJ: The sign of &- 0s is also determined from the sign of U. If we know t9s= o”, we can determine the sign ofgand j. Otherwise it cannot be determined from intensity measurements, but can be from measurements of phase delay.
References [ 1 ] T.H. Barnes, K. Matsuda, T. Eiju, K. Matsumoto and F. Johnson, Jpn. J. Appl. Phys. 29 (1990) 1293. [2]T.H. Barnes, F.T.J. Johnson, T. Eiju, T.G. Haskell, K. Matsuda and S. Kokaji, Opt. Eng. 31 (1992) 1936. [3] A. Ogiwara, H. Sakai and J. Ohtsubo, Optics Comm. 86 (1991) 513. [4] A. Ogiwara and J. Ohtsubo, Optics Comm. 93 (1992) 234. [ 51H. Sakai and J. Ohtsubo, Appl. Optics 31 (1992) 6852. [6]T.H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M.R. Taghizadeh and J. Turunen, Appl. Optics 3 1 ( 1992) 5527.
25
[7] T.H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda and N. Ooyama, J. Mod. Optics 37 (1990) 1849. [ 8 ] H. Ichikawa, T.H. Barnes, M.R. Taghizadeh, J. Turunen, T. Eiju and K. Matsuda, Optics Comm. 93 ( 1992) 145. [9] F. Mok, J. Diep, H. Liu and D. Psaltis, Optics Lett. 11 ( 1986) 748. [IO] J. Amako and T. Sonehara, Jpn. J. Appl. Phys. 29 ( 1990) 1533. [ II] J. Amako and T. Sonehara, Appl. Optics 30 ( 1991) 4622. [ 121 D.A. Yocky, T.H. Barnes, K. Matsumoto, N. Ooyama and K. Matsuda, Optik 84 ( 1990) 140. [ 131 K. Ohkubo and J. Ohtsubo, Optics Comm. 102 ( 193) 116. [ 141 A. Yariv and P. Yeh, Optical waves in Crystals (Wiley, New York, 1984) ch. 5. [ 151 K. Lu and B.E.A. Saleh, Opt. Eng. 29 ( 1990) 240. [ 161 K. Lu and B.E.A. Saleh, Appl. Optics 30 (1991) 2354. [ 171 J.C. Kirsch, D.A. Gregory, M.W. Thie and B.K. Jones, Opt. Eng. 31 (1992) 963. [ 181 C. Soutar, S.E. Monroe Jr. and Jerome Knopp, Opt. Eng. 33 (1994) 1061. [ 191 T.H. Barnes, T. Eiju, K. Matsuda and N. Ooyama, Appl. Optics 28 (1989) 4845. [20] N. Konforti and E. Marom, Optics Lett. 13 (1988) 251. [2l]C.H.GoochandH.A.Tarry,J.Phys.D8 (1975) 1575. [22] ST. Wu and U. Efron, Appl. Phys. Lett. 48 (1986) 624.
OPTICS COMMUNICATIONS Optics Communications 115( 1995) 19-25
Optimization of twisted nematic liquid crystal panels for spatial light phase modulation Makoto Yamauchi, Tomoaki Eiju Optical Engineering Division, Mechanical Engineering Laboratory, Namiki l-2, Tsukuba, Ibaraki 305, Japan
Received 18 July 1994
Abstract To optimize a twisted nematic liquid crystal panel for large phase modulation, it is necessary to optimize the angles of the polarizer and analyzer. We determine the Jones matrix of a panel and find these optimum angles by computer simulations. They compare well to the experimental results.
1. Introduction
Recently liquid crystal panels (LCPs) have been used in many applications, such as optical information processing [ l-5 1, optical interconnections [ 68 1, real-time holography [9-l 11, etc. In these applications LCPs are used for both intensity and phase modulation. Twisted nematic (TN) type LCPs are good for intensity modulation and homogenous type (parallel aligned) LCPs are suitable for phase modulation. Unfortunately homogenous type LC panels are very hard to obtain because there are no commercial suppliers, while TN LCPs are easily available because they are mass produced for LCTVs. That is why much effort has been made to use TN LCPs as spatial light phase modulators [ 12,131, despite their inability to achieve a phase modulation of more than 2n with very high spatial resolution. Phase modulation characteristics of TN LCPs have been studied [ 14-181. TN LCPs change the polarization state of input light, when a TN LCP is sandwiched by a polarizer and an analyzer, both intensity and phase of the input light are simultaneously modulated. Intensity-only modulation is rather easy to
obtain, however phase-only modulation is only possible when the panel is used in binary operation [ 19 ] or below the optical threshold [ 201. In addition to the unavoidable accompanying intensity modulation, the lack of phase modulation range is also a problem. This problem is especially serious when we use TN LCPs with very high spatial resolution because these LCPs are thinner, and the phase modulation is proportional to the thickness of the panel. To solve these problems optimization of the optical setup has to be considered. For thin LCPs the setup in which the polarizer angle equals the director angle of the input plane of the panel is not the best choice. Arranging the angles of polarizer and analyzer is very important, though most people set the angles to be either parallel to the director angle or perpendicular to it. A commercially available LCTV was used to experimentally obtain the optimum angles. The Jones matrix of one of the LCPs was determined from intensity transmittance measurements, and the optimum angles of polarizer and analyzer were indicated by computer simulation using Jones calculus. Experimental results coincided well with the simulation,
0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOO30-4018(94)00654-7
20
M. Yamauchi, T. Egu /Optics Communicatrons 115 (1995) 19-25
and we succeeded in attaining K phase modulation with small intensity modulation.
(3) 1
cos2B
sin28
n:(e) =n,Z + n, 2
2. Theory Fig. 1 shows a schematic diagram of a TN LCP whose directors in the input and output planes are aligned with 19sand 0, (measured from x-axis), respectively. If we set parameters as listed in Table 1, the Jones matrix of the panel is expressed as follows:
J=cexp[-i(@0+8)1
f-ig
(
f+ig
h_G
(5)
g= $sinycos(&+B,),
(6)
(1)
,
1
eE-es -sinyc0s(OE-8S) Y
+cosysin(O,-8,))
where c represents intensity loss caused by surface reflections etc., i is the imaginary unit and
(4)
e,-es. f=---y smysin($-e~)+COsyCOS(eE-e~),
h=_
--h-G
'
(7)
j= ;Psinysin($f&)
,
y=Jp2+(eE-ess)2.
(8) (9)
It should be noticed that y+
Input Plane
,
f 2+g2+h2+j2= det(J) =c2 .
Fig. 1. Schematic diagram of a TN LCP structure. Right handed coordinate system is used for the calculation of a Jones matrix. Table 1 Parameters of TN LCPs A d n0
4 I3 4 0, 2s
Wavelength Thickness of the panel Ordinary refractive index of the liquid crystal Extraordinary refractive index of the liquid crystal Tilt angle of the liquid crystal molecules caused by applied voltage Director angle of input plane of the panel with respect to x-axis Director angle of output plane of the panel with respect to x-axis Retardation of the panel
1
(10) (11)
Because we are able to control only the applied voltage on the panel, J is regarded as a function of just one parameter /I [ 15 1. However, to determine J, we have to know three other parameters c, 0s and &; that are thought to be constants with respect to the applied voltage. As shown later, we can determine c, f; g, and h from experiments. (&-es) and y are solved using Eqs. (5) and (7), consequently B is also derived from Eq. (9). Then (0, + 0,) is calculated by Eq. (6), and all parameters but @,,are determined. One possible way to determine c, f; g, and h is to measure intensity transmittances with four different optical setups. If a TN LCP is sandwiched by a polarizer and an analyzer whose azimuth angles are vp and t,uA,respectively, and illuminated by an input beam denoted by Jones vector xin
( Yin13 the output beam X0”, ( YOU,>> is
calculated to be
M. Yamauchi. T. Eiju /Optics Communications 115 (I 995) 19-B
Xout
Table 2 Specifications of the TN LCP used in the experiments (Epson VPJ-2000 Video Projector)
(>
(>
=P(Y*) JP(YP) ;
YO”t
I”
=cew[-i(h++P)l X
(xin
COSV/P+
Yin
21
Type
( >
sinV/P) ~vp,vA “,yiK ,
Control
(12)
Panel size
=fcos(yA-t[/p)+hsin(yA-yp) %NA
-i{gcos(WA+y/,)+jsin(yA+yp)i,
Number of pixels Pixel pitch
(13)
Twisted nematic transmission Electrically addressed TFT active matrix 1.32 inches (diagonal) 26.9 mm (H)x20.2 mm (V) 480 (H)x440 (V) 56pm (H)X46pm (V)
where P(v) is the Jones matrix of a polarizer with azimuth angle t,u,namely P(w)=
cos=w ( sin v cos v
sin w cos w sin2y/ ) ’
Intensity transmittance setup is
6wp,yIA = 8-
/
Tvp,vA of the panel in this
T ,,,=C21XinCOSWp+Yi”sinWp12
and phase delay S,,,,
(14)
I~~p.lyA12~ (15)
caused by this panel is
arg( TYp.cuA 1
(16)
ignoring terms independent of applied voltage.
Personal Computer Fig. 2. Optical system to measure the intensity transmittance of a TN LCP. Azimuth angles of the polarizer and the analyzer are vp and V/A,respectively. Intensity of the input beam was measured between the polarizer and the LCP.
3. Experiments and results Experiments were conducted to determine the Jones matrix of a panel with several applied voltages. Using these results, computer simulations were carried out to find setups for which the panel generated a large phase modulation with small intensity modulation. Experiments to check the theory were also carried out. A TN LCP from a video projector (Epson VPJ2000) was used in the following experiments. The projector has three LCPs (R, G and B), we used the red panel. Specifications of the panels are shown in Table 2. Each panel has 480 horizontal by 440 vertical pixels. Thin film transistors are used and each pixel is addressed by the active matrix method. We used the original electronics to drive the panel, so the projector is controlled by NTSC video signals which are generated by a personal computer equipped with a video board. Intensity transmittance of the panel was measured using the optical system shown in Fig. 2. A HeNe laser
beam (wavelength is 633 nm) was expanded and collimated to be incident on a polarizer whose azimuth angle was vp. To obtain a constant intensity output beam after the rotated polarizer, a quarter wave plate was inserted in the optical system. The output beam from the polarizer went through the LCP and an analyzer whose azimuth angle was vA. Experiments were made with polarizer-analyzer setups ( yp, v/A) equal (OD,OD), (00, 90”), (30”, 60”) and (45”, -45”) at states when the input video signals were 0, 64, 128, 192 and 255. Intensity transmittance was also measured when the video projector was switched off. Maximum voltage is applied to the panel electrodes when the video signal is 0, while minimum voltage is applied when it is 255. For convenience, we measured the input beam intensity between the polarizer and the panel as indicated in the figure. The output beam intensity was measured after the beam passed through the analyzer. In this case we can neglect (Xi”cos v/p+yi, sin v,) terms in Eqs. (12) and (15).
22
M. Yamauchi, T. Eiju / Optics ~ommu~~cat~ons1I5 (I 995) i9-25
Overall
intensity
transmittance,
namely
c* =
Twp,vA+Tw,yA+l(,2was about 14.5% in all (VP, v/A)
pairs. The Jones matrix of each state was calculated and is shown in Table 3. The calculation is explained in the Appendix. /_Iand y are also shown in Table 3. Because it is difficult to solve (19,- 0,) and y from Eqs. ( 5 ) and ( 7 ) , they are calculated numerically by the Newton-Raphson method. 6s and 0, were determined using the values f and h at the switched off state, which were found to be 83.4” and -4.3”, respectively, this indicates the twist angle (t9a- 0s) equals 87.7”. A computer simulation was carried out to find the best setup for high phase modulation, with low intensity modulation, using Eqs. ( 15 ) and ( 16). TvBwAand 6wp,wI\ were calculated for every 5 degrees of v/Pand VA.From the simulation we found: (i)when(~p,~A)=(-50,850),namelyinputlight is aligned to the director angle, phase modulation is about 0.9 n and intensity modulation is almost loo%, (ii) maximum phase modulation is about 1.4 n and there are some setups to attain that, however intensity modulation is always very large in these setups, (iii) under the condition that phase modulation is larger than n, we found that ( vpvp, VA)= (30”, 85”) gave the minimum intensity modulation. Figs. 3a and 3b respectively show the simulated intensity transmittance and difference in phase delay, versus video signal in each case. To examine the interesting situation in case 3, in
detail, we did experiments setting the polarizer angle to 30” and changing the analyzer angle. Fig. 4a shows the intensity transmittance. Symbols denote the experimental results and lines show the simulation for each level of video signal. They coincide very well. Intensity modulation takes a minimum value near vA= 85”. Computer simulation of phase delay were also carried out on the same condition, and results are shown in Fig. 4b. When the video signal is 0 and vA= 120”, the phase delay jumps from 0 to n. However, physical difficulty caused by this singularity is avoided because no transmitting light is expected by Fig. 4a. Phase modulation capability is the maximum difference in phase delay caused by the video signal modulation, that is also shown in Fig. 4b, by a solid line. From the figure, we can expect more than Kphase modulation between VA=700 and v/A= 120”. In the setup ( I,u~,VA) = (30”, 85’)) phase modulation versus video signal, was measured using a phase shifting Mach-Zehnder interferometer shown in Fig. 5. A stripe pattern was written on the panel. Interference fringes were imaged on to the CCD TV camera. The phase of several points on the pattern was calculated using the three step phase shifting method. The result is shown in Fig. 6, along with the experimental result of intensity transmittance measurements. We achieved n phase modulation with 25.8% intensity modulation.
Table 3 Jones matrix of a TN LCP for several states Video signal
B (rad)
Y (rad)
Jones matrix
0
0.000 x
0.48 1 IT
J,,=O.380
64
0.147 x
0.508 R
J,,=O,381
128
0.329 K
0.587 n
J,**=O.38,
192
0.445 R
0.660 x
255
0.518 II
0.999 e-l*
-0.019-0.041%
0.019-0.0415i 0.976-0.0563i
)
e-‘teo+0-=9”) ( -0.306-0.4531
0.835+0.0563i
)
J,9,=0.381
e-‘(@+“-“5x)
o’50~.~~~550i)
0.711 n
~~~~=0.382
e-i(Oo+O-slsn) ( -0.639-0.5581
0.726 IT
5,,=0.3*2
( _o,5~~~~.550i 0.528-0.0427i
Off Power
0.538 II
) 0.0665-0.2011 0.976+0.05631 0.306-0.453i
e-it*+o.14W
( -0.0665-0.2Oli 0.835-0.0563i
0.999
0.639-0.558i 0.528+0.04271
)
e -i(go+0.53ar) -0.672-0.5541 0.481-0.107i
0.48l+O.l07i 0.672-0.5541
)
M. Yamauchi, T. E& /Optics Communications 1IS (1995) 19-25
23 Polarizer Sohd
= 30”
Line
: Simulation -l
0 .64 128
“-
0
50
100
150
200
250
Video Signal
J "0
80
40
120
160
Analyzer Angle (degree) ’
(b)
I’
”
1
”
”
Video Signal
1.5
Video Signal
Fig. 3. Computer simulation of (a) the intensity transmittance T and (b) difference in phase delay 6 of three special cases. Case 1: polarizer is aligned to the director; (vr, vA) = ( - 5”, 85”). Case 2: maximum phase modulation is attained; (yr, vA) = ( W, I 15”). Case 3: phase modulation is larger than R and intensity modulation is minimum; (v/p, vA) = (30”, 85”).
4. Discussion In general, it is accepted that when linearly polarized light aligned with the director angle is input on a TN LCP, the angle of polarization changes along the twisted molecules by a waveguide effect and the output light remains in its linear polarization state. However the output light is no longer linearly polarized when the retardation of the panel is small, even if the input light is linearly polarized and aligned with the director angle [ 2 I]. In that case the maximum phase modulation does not occur when the input light is aligned with director angle. TN LCPs should not be considered as optical elements for changing the polarization angle but for changing the polarization state. It should also be mentioned that TN type LCPs
Analyzer
Angle
(Degree)
Fig. 4. (a) Intensity transmittance T. (b) Computer simulation of phase delay 6, when the polarizer angle is fixed at 30” and the analyzer angle is changed. Solid line in (b) shows difference in phase delay between the video signal 0 and 255.
were thought to have less capability for phase modulation than homogenous type (parallel aligned) LCPs [ 20 1. Phase modulation capability of homogenous type LCPs equals their retardation, namely somewhat less than (2n/l)(n,-n,)d [22]. However,we showed that TN LCPs are able to modulate more than their retardation. For example, in our case retardation of the panel was 1.04a while the maximum phase modulation exceeded 1.4~. We could not give a clear
24
M. Yamauchi, MlCKWXJpe ObJeCtWe
T. Eiju / Optics Communications
Half Mmar \
He-Ne Laser
Half Mm
LUlS
CCD Camera
OX I I PersonalComputer
I15 (I 995) 19-25
shown the procedure to determine the Jones matrix of a TN LCP from intensity transmittance measurements. Changing the angles of polarizer and analyzer, we succeeded in obtaining the best setup for n phase modulation, with the smallest intensity modulation. We also found an interesting phenomenon; the phase modulation capability of an LCP exceeds its retardation.
/Dnverlu PersonalComputer
Fig. 5. Phase shifting Mach-Zehnder interferometer to measure the phase modulation of a LCP.
Acknowledgements This work was done under a cooperative research agreement with Heriot-Watt Univ., Edinburgh, UK. Authors wish to thank to Dr. H. Ichikawa, Dr. N. McArdle, and Dr. M. Taghizadeh of the University for helpful suggestions, and to Dr. I. Khandaker of Mechanical Engineering Laboratory for checking the manuscript.
Appendix
0 t&4, 0
From Eqs. ( 13) and ( 15 ) the intensity transmittance of (VP, VA/A) setup is
/
,I
, 50
100
T Wp.V,=c2[Gfcos(~~-~P)+hsin(~~-~P)j2
0
150
200
+(gcos(W,+Y/p)+jsinlW,+WP))‘l.
250
Vldeo Stgnal
Fig. 6. Experimental results of the phase modulation and the intensity transmittance of a TN LCP at the best setup for R phase modulation (VP,v,) = (30”, 85”).
explanation of this physically discrepant phenomenon yet. Further study is needed to analyze it. The short-coming in TN LCPs compared to homogenous type LCPs, is that the intensity modulation always accompanies phase modulation.
(A.11
Taking account of Eq. (lo), this equation consists four variables, c, fl h and g. However we can only determine square of each variable from four independent measurements of T. The sign of each variable is determined another way. c is easily solved. Namely c2 = To, + c
To.90
.
(A.2)
is positive by definition. If we set 2
IA= G
T T30,60+ D,o +
3T457-45
4
1
5. Conclusion
u= z” (T4,,-,,-Toso) >
Optimum setup of TN LCPs, for optical spatial phase modulators, was studied. Polarization states of light propagating through a thin TN LCP are sufficiently complex to require analysis using Jones matrices and computer simulations. The best setup for this purpose is obtained by simulation. We have
we have h*=
v+JZG
2
c2 )>
(A.3)
4
(A.4)
, f*=h*-v,
(A.51
A4. Yamauchi. T. Eiju /Optics Communications 115 (1995) 19-25
If we assume 1&-&I E 90” and /3z 0 (i.e. higher voltage is applied),fis always positive. Then the sign of h is determined from the value of U, because u equals hJ: The sign of &- 0s is also determined from the sign of U. If we know t9s= o”, we can determine the sign ofgand j. Otherwise it cannot be determined from intensity measurements, but can be from measurements of phase delay.
References [ 1 ] T.H. Barnes, K. Matsuda, T. Eiju, K. Matsumoto and F. Johnson, Jpn. J. Appl. Phys. 29 (1990) 1293. [2]T.H. Barnes, F.T.J. Johnson, T. Eiju, T.G. Haskell, K. Matsuda and S. Kokaji, Opt. Eng. 31 (1992) 1936. [3] A. Ogiwara, H. Sakai and J. Ohtsubo, Optics Comm. 86 (1991) 513. [4] A. Ogiwara and J. Ohtsubo, Optics Comm. 93 (1992) 234. [ 51H. Sakai and J. Ohtsubo, Appl. Optics 31 (1992) 6852. [6]T.H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M.R. Taghizadeh and J. Turunen, Appl. Optics 3 1 ( 1992) 5527.
25
[7] T.H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda and N. Ooyama, J. Mod. Optics 37 (1990) 1849. [ 8 ] H. Ichikawa, T.H. Barnes, M.R. Taghizadeh, J. Turunen, T. Eiju and K. Matsuda, Optics Comm. 93 ( 1992) 145. [9] F. Mok, J. Diep, H. Liu and D. Psaltis, Optics Lett. 11 ( 1986) 748. [IO] J. Amako and T. Sonehara, Jpn. J. Appl. Phys. 29 ( 1990) 1533. [ II] J. Amako and T. Sonehara, Appl. Optics 30 ( 1991) 4622. [ 121 D.A. Yocky, T.H. Barnes, K. Matsumoto, N. Ooyama and K. Matsuda, Optik 84 ( 1990) 140. [ 131 K. Ohkubo and J. Ohtsubo, Optics Comm. 102 ( 193) 116. [ 141 A. Yariv and P. Yeh, Optical waves in Crystals (Wiley, New York, 1984) ch. 5. [ 151 K. Lu and B.E.A. Saleh, Opt. Eng. 29 ( 1990) 240. [ 161 K. Lu and B.E.A. Saleh, Appl. Optics 30 (1991) 2354. [ 171 J.C. Kirsch, D.A. Gregory, M.W. Thie and B.K. Jones, Opt. Eng. 31 (1992) 963. [ 181 C. Soutar, S.E. Monroe Jr. and Jerome Knopp, Opt. Eng. 33 (1994) 1061. [ 191 T.H. Barnes, T. Eiju, K. Matsuda and N. Ooyama, Appl. Optics 28 (1989) 4845. [20] N. Konforti and E. Marom, Optics Lett. 13 (1988) 251. [2l]C.H.GoochandH.A.Tarry,J.Phys.D8 (1975) 1575. [22] ST. Wu and U. Efron, Appl. Phys. Lett. 48 (1986) 624.