Chapter 5 Diffraction Effect of the LCOS Devices
5.2 The influence of the pixel pitch to the light efficiency
From the derivation in Chap.2, the field components of reflective waves can be obtained using the extended beam propagation method. It is important to further investigate the angular distribution of the light intensity, which is called the intensity angular spectrum.
By using the Fourier transform, the amplitude angular spectra, , ( ) λ
where λ is the light wavelength in the propagating medium and α represents the cosine of the beam propagating direction depicted in Fig.4.1.
-θ
Finally, the output intensity angular spectrum is expressed as:
2
Equation (4.2) represents the spectrum of the light at the end of the propagation which is prior to enter the cover glass. When considering the spectrum of the light exits from the LC panel, the refraction at the interfaces of the cover glass and the air must be taken into consideration. As a consequence, the final propagating angle, θ , is given as follows:
Fig. 5.1 Schematic representation of angle definitions and mirror image of reflective LCOS device.
)) sin(cos (
sin 1 1α
θp = − neffr × − (5.3)
where the nreff represents the effective refractive index at the end of propagation in the LC layer. We then define the light efficiency of the LCOS optical system as, η, as follows:
in p
I
a I
∫
−a=
θ
θ λ
θ
η ( ), (5.4)
where Iin is the intensity of the incident light and θa represents the acceptance angle of the optical system which is related to the f-number (F#) of the projection lenses:
2 ) ( 1 tan
# 1 a F
= −
θ (5.5)
Figure 5.2 sketches the acceptance angle of the projection lenses.
Projection lenses
LCOS panel θa
θa f
Projection lenses
LCOS panel θa
θa f
Here we focus on two specific LC operation modes, VA and finger-on-plane (FOP) modes.
FOP mode was first developed byElectronics Research & Service Organization (ERSO), Industrial Technology Research Institute (ITRI) [8,9]. The main characteristic of this mode is its tiny common electrodes fabricated on top of the pixel electrodes. Using this specific structure, it can effectively eliminate the fringing-field effect of LCOS panel. However, the tiny common electrodes are found contributive to the diffraction effect and result in a poor l,ight efficiency as will be discussed in the following.
Fig. 5.2 Sketch of the acceptance angle θa of the light waves propagating from the LCOS panel to the projection lens.
Figure 5.3 shows the cell structures used for the 2D simulations of the LC director distributions and the light efficiencies. The d∆n equals 207.5 nm for the FOP mode and 190.9 nm for the VA mode. The LC parameters used for simulations are based on the commercial material MLC-6608.
Al (Rp) Al (Rp) Al (Rp)
Glass
Silicon Substrate
Al (Rp) Al (Rp) Al (Rp)
Glass
Silicon substrate (a)
(b)
ITO
Rg Rg
Al (Vcommon)
LC layer
LC layer
Isolation layer di
Al (Rp) Al (Rp) Al (Rp)
Glass
Silicon Substrate
Al (Rp) Al (Rp) Al (Rp)
Glass
Silicon substrate (a)
(b)
ITO
Rg Rg
Al (Vcommon)
LC layer
LC layer
Isolation layer di
The LCOS panels are both illuminated by a normally incident linearly polarized light.
The angles between the direction of polarization and the LC rubbing direction on the top glass are 0° and 45° for the FOP mode and the VA mode, respectively. In our optical engine, we assume F#= 2.8, which indicates θa~10˚ from Eq. (5.5). In order to investigate the influence of the pixel pitch (P) to the light efficiency, we varied the P/λ value from 30 to 2.5 with a fixed inter-pixel gap (0.7 µm). The LC layer is divided as a grid with the spatial step
∆x=100 nm and ∆z=50 nm during the numerical analyses. In simulations, we assume Rp=90% and Rg=0% for the pixelated aluminum electrodes and absorptive black matrices underneath the interpixel regions, respectively.
Figures 5.4 plots the calculated light efficiencies (θa=10°) of the LCOS devices with
Fig. 5.3 Cell structures used for 2D computer simulations of (a) FOP mode (b) VA mode.
respect to the P/λ value when all the pixels are turned off for the FOP. The results calculated by the Jones matrix method are also included in the figures. From Fig. 5.4, the light efficiencies predicted by the BPM are much lower than those given by the Jones matrix method. In reality, the comb-like common electrodes on the bottom substrate of the FOP device are acting as a phase grating. The light waves encountered these electrodes will be scattered and diffracted to various angles. The light waves propagating outside the acceptance angle of the projection lens are wasted. Thus, the overall light efficiency is decreased. It is well known that from the grating formula, mλ =gsinθ (where m is the order of diffraction, g is the grating pitch, and θ is the diffraction angle), the diffraction angle gets larger as the pitch becomes smaller [10]. Therefore, a smaller pixel pitch generally gives a lower light efficiency in LCOS devices. However, some exceptions may occur. For example, when P/λ=5 in Fig. 5.4, the diffraction angle of the first order light exceeds the critical angle of the total internal reflection at the glass-air interface. Hence, the energy will not escape from the device leading to a higher light efficiency than the larger P/λ case.
0 20 40 60 80 100
0 5 10 15 20 25 30 35
P/λ
Light Efficiency (%)
BPM Jones Matrix
We have shown that the BPM describes reasonably well the optical behavior of the FOP device. The Jones matrix results maintain almost identical for different pixel pitch and
Fig. 5.4 Computer simulated light efficiencies (θa=10°) with respect to P/λ value of FOP-LCOS devices at voltage-off state by extended BPM and Jones matrix method.
are much higher than those obtained from BPM. Basically, the Jones matrix method treats the bottom substrate only as a specular reflector. Figure 5.5 shows the intensity angular spectrum calculated by both methods with P=7.7 µm and λ=540 nm. It can be easily seen that without considering the diffraction effect, the signal light waves mainly propagate along the normal direction, which will cause an unbearable error in the real system.
pixel pitch=7.7µm
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-40 -20 0 20 40
Angle of Propagation (deg.)
Normalized Intensity
BPM Jones Matrix
In the case of VA mode, an absorption material (black matrix) is employed underneath the inter-pixel gaps. In the voltage-off state, the device is acting as a slit grating. The calculated light efficiencies from the BPM and the Jones matrix method are almost the same as shown in Figs. 5.6 (a) and (b). The light efficiency calculated by Jones Matrix depends on P/λ because of the influence of the dark inter-pixel gaps. These dark gaps act as slits and generate periodic intensity profiles of the signal light. Therefore, the diffraction effect induced by these gaps can still be analyzed via the angular spectrum even though the fields are calculated by the Jones matrix method. However, when the voltages between the adjacent pixels are different, which is common seen when an image is displayed, the diffraction and scattering induced by phase difference and the variation of LC directors are not included by using the Jones matrix method. Therefore, we simulated the extreme case in which one pixel is on and its adjacent pixels are off, i.e. the off-on-off configuration.
Fig. 5.5 Simulated intensity angular spectrum with P=7.7 µm and λ=540 nm for FOP mode.
30
Light Efficiency (%)
BPM
Angle of Propagation (deg.)
Normalized Intensity
Light Efficiency (%)
BPM
Angle of Propagation (deg.)
Normalized Intensity
Light Efficiency (%)
BPM
Angle of Propagation (deg.)
Normalized Intensity
BPM Jones Matrix
(a) (b)
Figure 5.7 (a) shows the calculated light efficiencies of the VA device as a function of P/λ. Although this figure still shows almost identical results between the two methods, the optical behaviors are very different. Figure 5.7 (b) shows the calculated intensity angular spectra with P=7.7 µm and λ=540 nm. As shown in the figure, the intensities of the signal light near the normal direction calculated by the BPM are much lower than those by the Jones matrix method. The intensity of the zeroth order diffracted light, I0, is also calculated with respect to the P/λ value as shown in Fig. 5.7 (c). The I0 calculated by the BPM is always lower due to the light scattering and diffraction by the various LC orientations around the pixel edges. These results are especially important for designing a projection display, because accurately predicting the angular distribution of the light intensity can prevent many unwanted image aberrations in the optical system.
Fig. 5.6 (a) Simulated light efficiencies with respect to P/λ value of VA-LCOS devices at voltage-off state by extended BPM and Jones matrix method, and (b) simulated intensity angular spectrum with P=7.7 µm and λ=540 nm.
(a)
Normalized Zeroth Order Intensity
BPM
Angle of Propagation (deg.)
Normalized Intensity
Light Efficiency (%)
BPM
Normalized Zeroth Order Intensity
BPM
Angle of Propagation (deg.)
Normalized Intensity
Light Efficiency (%)
BPM Jones Matrix
Fig. 5.7 Computer simulated results of VA mode with off-on-off pixel configuration by extended BPM and Jones matrix method: (a) light efficiencies (θa=10°) of LCOS devices with respect to P/λ value, (b) intensity angular spectrum with P=7.7 µm and λ=540 nm, and (c) the intensity of zeroth-order diffracted light, I0, calculated with respect to P/λ value.