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Abstract
This paper demonstrates a phase-only liquid crystal on silicon (LCOS) device with improved total optical efficiency. A multi-layer dielectric mirror coating was carefully designed with an aim to maximise its reflectance and fabrication tolerance while minimising its thickness. The coated backplane improves the reflectance of the LCOS device from ∼80% to >96%. Although the dielectric mirror may lead to an enhanced fringing field effect and therefore a reduction in the diffraction efficiency, a straightforward optimisation on the driving waveform has been demonstrated to maintain the diffraction efficiency at a similar level. As a result, the total optical efficiency of the LCOS device with the coated silicon backplane is 12%–18% higher than that of the standard LCOS device, for different beam steering angles.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystal on silicon (LCOS) technology [1–3] has been developed over many years, mainly for information display applications. Due to its unique capability of spatially modulating the wavefront of an optical beam, it has been widely used in ultra-high definition (UHD) projectors [4,5], augmented reality (AR) [6–8] and virtual reality (VR) [9] devices. In the past ten years, it has also been commercially used in telecommunications networks as the optical engine for wavelength selective switches (WSSs) [10,11].
A typical LCOS device consists of a liquid crystal (LC) layer sandwiched between a glass coverplate and a silicon backplane, based on the complementary metal-oxide-semiconductor (CMOS) technology. The silicon backplane has millions of individually addressable reflective electrodes, i.e. pixels, each of which is able to apply a voltage level across the LC layer. Since the birefringence of the LC material [12] can be controlled electrically, the LCOS device is able to spatially modulate the wavefront of the optical beam, either in phase [13] or amplitude [14], depending on the configuration of the LC layer.
When the LC layer is configured using a homogeneously-aligned nematic LC material [15], the LC molecule will tilt at different angles in response to the voltage level across the pixel. Therefore, its effective refractive index is changed according to the linearly polarised beam [16], whose polarisation direction is parallel to the LC alignment direction. As a result, the LCOS device is able to spatially modulate the phase of the incoming beam, while its amplitude remains unchanged. This type of LCOS device is often referred to as a phase-only LCOS device. Phase-only LCOS devices are highly efficient as there is almost no light absorption within the LC layer. Phase-only modulation has been proven capable of flexible and complex holographic beam manipulation [17–19].
However, there is still strong demand to further increase the total optical efficiency of the phase-only LCOS device [20]. Optical loss in the LCOS device can be attributed to the reflectance of the silicon backplane and the diffraction efficiency of the hologram. The reflectance of the silicon backplane is dependent on the reflectance of the pixels as well as the inter-pixel regions, i.e. dead space. Although the reflectance of each pixel has been enhanced with an aluminium coating, it is still challenging to coat the dead space without causing inter-pixel interference. As a result, the overall reflectance of the silicon backplane is reduced. Diffraction loss is due to the intrinsic inability of an LCOS device to display large phase discontinuity between neighbouring pixels [21–23]. This may blur the designed phase pattern and result in poor diffraction efficiency.
This paper analyses the optical loss from the silicon backplane and proposes a dielectric mirror coating structure that is able to significantly improve the reflectance. Although the additional mirror layer may further blur the displayed hologram and reduce the diffraction efficiency, the voltage range of the driving waveform has been optimised to maintain the diffraction efficiency at a similar level. The improved optical efficiency can simplify the heat management in UHD projector application, prolong the lifetime of AR/VR applications, and improve the performance and scale in optical switching applications.
2. Dielectric mirror for the silicon backplane
This section analysis in detail the loss from the LCOS silicon backplane. In order to address this problem, a dielectric mirror structure is designed and toleranced against the incident angles and fabrication errors. The optical and electrical properties of the fabricated dielectric mirror structure are then investigated.
2.1 Loss from the LCOS silicon backplane
A JD2552 SP55 silicon backplane [24] was selected for this work. This backplane has 1920 × 1080 pixels in total, with a pixel pitch of 6.4 µm and an inter-pixel gap of 0.2 µm. This translates to an aperture ratio of 93%. The coated aluminium is measured to have a reflectance of 94% between 1400 nm and 2000nm wavelength.
Based on this information, it is tempting to assume that the overall reflectance of the silicon backplane is 0.94×0.93 = 87.4%. However, this is actually more complicated since the dead space has a different reflectivity value from the pixels. In addition, as shown in Fig. 1 the backplane might not be even on the same plane as the pixels. Therefore, the silicon backplane carries out a spatial phase and amplitude modulation for the incoming beam, which could further reduce its reflectance.
The optical system shown in Fig. 2(a) is a simple way to verify this effect. A collimated laser beam with a size of 2 mm passes through an aperture, whose diameter is slightly larger than the beam. The LCOS device is aligned perpendicular to the incoming beam. The reflected beam, i.e. 0th order, passes through the aperture again, while the diffracted beam, if any, is blocked by the aperture. Figure 2(b) shows the beam patterns on the rear side of the aperture. This confirms that the pixelated structure of the silicon backplane does cause diffraction and reduces the 0th order reflectance.
A simulation based on the Fourier optics theory [25] was carried out to evaluate the effect of the pixel reflectance, r, and the depth difference between the pixel and substrate, φ, on the reflectance of the silicon backplane. The results are plotted in Fig. 3. It can be seen that both values can lead to a large change in the reflectance of the silicon backplane.
2.2 Dielectric mirror design
The key requirement of the dielectric mirror design is high reflectance over the wavelength range of interest, which in this specific case is 1530 nm to 1565 nm. The overall thickness of the dielectric mirror needs to be as small as possible since a thick dielectric mirror would distort the electrical field distribution across the LC layer. This will enhance the fringing field effect and adversely affect the optical performance of the LCOS device. In addition, a thin dielectric mirror is normally associated with relatively low resistivity, which can ensure that the majority of the voltage drop occurs across the LC layer instead of the dielectric mirror itself. This helps to reduce the maximum voltage level required for the silicon backplane.
The standard dielectric mirror design based on a (0.5H L 0.5H) stack was picked in this work mainly due to its simplicity of fabrication. Figure 4(a) shows the structure of a basic (0.5H L 0.5H) element. It has a sandwiched structure that consists of two different materials. The refractive index of the one material is higher than the other. The light will experience 0.125λ phase delay passing through the 0.5H layer, which has the higher refractive index. It will experience 0.25λ phase delay passing through the L layer made of the lower refractive index material. A highly reflective dielectric mirror can be constructed by stacking multiple such basic element in a way shown in Fig. 4(b). The specific example shown in Fig. 4(b) consists of four repetitions of the (0.5H L 0.5H) element. In its equivalent drawing Fig. 4(c), this dielectric mirror consists of 9 layers in total. ZrO2 was chosen as the higher refractive index material while SiO2 was chosen as the lower refractive index material. Their refractive index values are 2.11 and 1.44, respectively, over the wavelength range of interest. Both materials have very low optical absorbance and have been previously used in the telecommunication application over the same wavelength range.
Fig. 4. The dielectric mirror coating structure based on (0.5H L 0.5H) stack: (a) a single (0.5H L 0.5H) element; (b) 4-repetition (0.5H L 0.5H) stack; (c) the equivalent 9-layer drawing.
The reflectance of the optical coatings based on the (0.5H L 0.5H) stack repetition design increases with the number of stack repetitions in the design. Figure 5 shows the relationship between the dielectric mirror’s theoretical reflectance at 1550 nm and the number of stack repetitions, when the coating is applied to a silicon substrate and an aluminium substrate, respectively. Normal incidence is assumed in this figure. It can be seen that the reflectance increased rapidly with respect to the number of stack repetitions for the silicon substrate. The reflectance of the aluminium substrate is already high even without the coating. Therefore, the gain in the reflectance is marginal. As the number of repetitions reached 7, the reflectance for both substrates converged to a very high level, at >98%. The difference between the aluminium and silicon substrates was only ∼1%. In other words, this dielectric mirror is able to have similar reflectance on the pixel area and the inter-pixel gap. As a result, an excellent spatial uniformity in the reflectance can be expected across the backplane surface. It should be noted that the reflectance could be further increased to >99.99% by increasing the number of stack repetitions. As mentioned in the introduction, however, thicker dielectric mirror structure will introduce stronger fringing field effect in the LCOS device. This could negatively affect the diffraction performance and offset any further improvement in the reflectance in overall. Therefore, this 7-repetition design was picked in this work. Its details are listed in the first three columns in Table 1. The values in the last column of Table 1 will be explained in the next section.
Fig. 5. The relationship between the reflectance and the number of (0.5H L 0.5H) stack repetitions in the dielectric mirror for the silicon and aluminium substrates.
Table 1. The 7-repetition stack design and the fitted layer thickness based on the ellipsometry
This design has a total thickness of 3.16 µm. This is lower than the thickness of the liquid crystal layer for the 1550 nm wavelength, which is normally between 5 µm and 6 µm. The resistivity of the dielectric mirror will be characterised and analysed in the later part of this paper. As mentioned previously, one of the considerations in the design process is to make the dielectric mirror as thin as possible.
Figure 6 shows that the design also has an excellent consistency across the test wavelength range from 1530 nm to 1565 nm. The variation of the reflectance is negligible across the wavelength range for the silicon substrate.
Fig. 6. The reflectance of the dielectric mirror across the test wavelength range for the silicon substrate.
This dielectric mirror is designed for a beam with a normal incident angle. In many applications, however, the LCOS device will be slightly tilted with respect to the incident beam. Therefore, it is important to test this design’s tolerance against the incident angle. Figure 7 shows the change of the reflectance at 1550 nm with respect to the incident angles, when the coating is applied to a silicon substrate and an aluminium substrate, respectively. Little change is observed within this ± 10° window.
A small change in the thickness of one layer may have a huge impact on the performance of the designed coating. Therefore, it is important to be able to precisely control the thickness of the deposited layer in the optical thin film coating process. A good coating design should also have a good tolerance to fabrication errors. A Monte Carlo tolerance analysis was carried out for this dielectric mirror design on a silicon substrate. In this analysis, random errors of up to ± 10% thickness was introduced to each layer and the corresponding reflectance of the dielectric mirror was calculated across the test wavelength range. This process was repeated for 100,000 times. It has shown that the minimum reflectance across the test wavelength remained >98% in all 100,000 reflectance curves.
2.3 Dielectric mirror characterisation
The designed dielectric mirror was coated onto the LCOS silicon backplane by the thermal evaporation method. The same coating was applied to an aluminium substrate using the exact same setup. This sample was later used for the analysis of the electrical properties of the dielectric mirror structure.
In order to evaluate the quality of the coating process, an ellipsometry measurement was carried out on the coated LCOS backplane. The ellipsometry measurement was chosen due to its non-destructive nature. The ellipsometry measurement operates on the principle that the polarisation state of the reflected beam will be affected by the thickness and optical properties of each layer in the dielectric mirror. This relationship is also wavelength-dependent. The dotted data points in the Fig. 8 show the measured results as the wavelength of the test beam moved from 400 nm, ∼3 eV, to 1700nm, ∼0.75 eV. Is and Ic in Fig. 8 can be described by Eq. (1) and Eq. (2), respectively:
where Ψ and Δ represent the relative amplitude and phase between the s-pol and the p-pol of the reflected beam, respectively.The measured relationships between wavelength and the values of Is and Ic can be used to fit the thickness of each in the coated dielectric mirror structure. The fitted curves are plotted as the solid lines in Fig. 8, which match the measured data points reasonably well. The corresponding thickness values are listed in the fourth column in Table 1. When compared with the design values, it can be seen that the deposited SiO2 layer thickness tended to be thicker than the design, while the deposited the ZrO2 layer thickness tended to be thinner. For the ZrO2 layers, the deviation in thickness from the design values was slightly more than 10%. This may cause the reflectance of the fabricated dielectric mirror to be lower than the design value of >98%. However, it should be noted that the measurement and the curve fitting process could also introduce errors.
The reflectance for the LCOS backplanes was subsequently measured across the test wavelength range using unpolarised light at an 80° incident angle. The results for the backplane with and without the dielectric mirror coating are shown in Fig. 9. The measured reflectance of the uncoated backplane was ∼78% across the wavelength range, which was significantly lower than the reflectivity of the aluminium pixels. The reason for this was explained in Section 2.1. The reflectance of the coated LCOS backplane was measured to be ∼97% across the test wavelength range. This was slightly lower than the designed value. However, this could be due to fabrication errors as identified previously. Overall, these results indicate that the dielectric coating suppressed the effect of the pixelated structure, and therefore significantly improved the reflectance of the LCOS backplane.
In the final step, the resistivity of the fabricated dielectric mirror was measured. Due to the potential sensitivity of the LCOS backplane, this measurement was carried out on an aluminium substrate that was coated with the designed dielectric mirror structure. The measured voltage-current (VI) curve for the dielectric mirror is plotted in Fig. 10(a), from which its resistivity under different voltage levels can be derived as plotted in Fig. 10(b). It can be seen that the maximum resistivity of the coated structure is ∼3.1×109 Ω*m. This compares favourably with the resistivity of the LC material, which is usually 1.0×1010 Ω*m. Furthermore, the dielectric mirror structure has a thickness of 3.16 µm while the LC layer for the C-band wavelength application needs to be at least 5 µm in thickness. Therefore, the majority of the voltage drop will occur within the liquid crystal layer.
Fig. 10. (a) the measured VI curve and (b) the derived resistivity of the dielectric mirror structure.
3. Characterisation and optimisation of the LCOS device
An LCOS device was assembled based on a backplane coated with the designed dielectric mirror structure. The nematic LC material was homogeneously aligned in this device, and therefore, it operated in a phase-only mode. The front-surface coverplate glass was properly anti-reflective coated to minimise the higher diffraction orders. The following sub-sections characterise various performance parameters of the assembled LCOS device.
3.1 Reflectance
The reflectance of the assembled LCOS device was measured across the test wavelength range at an incident angle of 80°. The results are shown in Fig. 11. The difference was negligible compared to the reflectance results of the backplanes in Fig. 9. This means that the dielectric mirror coating did not introduce any unintended reflectance effects, and therefore it performed as designed. Additionally, the other layers (e.g. the LC layer, alignment layer and coverplate, etc.) absorbed little light.
Fig. 11. A comparison between the reflectance of LCOS devices based on an uncoated backplane and a coated backplane.
3.2 Phase response
In order for the assembled LCOS device to operate efficiently, the device must realise 2π phase modulation for the wavelength in use. In a standard LCOS device, the thickness of the LC layer is determined by the electrically-controlled birefringence property of the LC material, and the voltage range that is supported by the silicon backplane. For the 1550 nm wavelength, the LC layer normally needs to have a thickness of >5 µm so that 2π phase modulation can be achieved. Such a thickness is already close to the pixel size of the LCOS backplane. Further increasing the LC thickness will increase the distance between the pixel electrode on the backplane and the common electrode on the coverplate. This will create a stronger effective fringing field, which negatively affects the diffractive performance of the LCOS.
When the dielectric mirror structure is coated on the silicon backplane, the distance between the pixel electrode and the common electrode becomes the thickness of the dielectric mirror plus the LC layer. This enhances the fringing field effect, which is undesirable. Moreover, the dielectric mirror will share some of the voltage drop between the two electrodes. If there is insufficient voltage drop on the LC layer, it cannot achieve the necessary 2π phase modulation. As a result, the LC layer thickness needs to be increased, which further affects the diffractive performance. Therefore, it is important to verify that the LCOS device can still achieve 2π phase modulation in the presence of the coated dielectric mirror.
The digital LCOS device used in this study was controlled by an HDMI cable, which loaded the bitmaps from the control PC. The LCOS driving circuits converted the grey levels in the bitmaps to unique sequences of pulse patterns, each of which has a different root mean square (RMS) value. As the grey level increases, its corresponding RMS voltage value also increases. In this way, the digital LCOS backplane generates various effective driving voltage levels and therefore realises various phase levels. In this work, three sets of driving waveforms were evaluated. The pulse patterns for the grey levels were kept the same between these sets of waveforms. However, the voltage levels for the on-pulse and off-pulse were different, as detailed in Table 2. In other words, the assembled the LCOS operated at different driving voltage ranges, i.e. the phase ranges, in this experiment. This enabled evaluation of the performance of the LCOS device under these operating conditions.
Table 2. The voltage levels for the on pulse and off pulse in the test waveform sets.
The phase response of the LCOS device was measured by displaying binary gratings with a fixed period but varied peak-valley phase depths. The power of the 1st diffraction order was measured as the grey level for the peak phase region increased where the valley phase region remained at zero. The measured values were referenced to the maximum and minimum power values for all the grey levels. The results were plotted against the RMS voltage levels for each waveform as set in Fig. 12. It should be noted that an immediate change in the power of the 1st diffraction order in all three curves was observed as soon as the grey level increased from zero. This means that the RMS voltage levels were above the threshold voltage of the LC material. The phase response of the LCOS device, i.e. the relative phase change compared to the first grey level, can be calculated from Fig. 12 based on Eq. (3):
where PR stands for the phase response and P1 for the normalised power of the 1st diffraction order. The results are shown in Fig. 13.Fig. 12. The relationship between the RMS voltage levels and the normalised power of the 1st diffraction order.
Fig. 13. The relationship between the RMS voltage levels and the phase depths as well as the phase flicker.
It can be seen from both figures that the assembled LCOS device with the coated silicon backplane was able to achieve 2π phase modulation with an RMS voltage level just under 4.0 V. This also confirms that the majority of the voltage drop occurs on the LC layer instead of the dielectric mirror structure. The low voltage level required in this device may indicate that the thickness of the LC layer could be further reduced, considering that the maximum RMS voltage supported by the LCOS backplane is beyond 5 V.
3.3 Beam steering performance
The intrinsic inability of an LCOS device to display a large phase discontinuity between neighbouring pixels is a fundamental problem that restricts its beam steering performance. As shown in Fig. 14, the fringing field and the fluid elasticity of the LC material prevent abrupt phase changes in the area between the electrodes. As a result, the LC molecules tilt at intermediate angles within this area. This blurs the designed phase patterns, limits the spatial resolution of the LCOS device, and gives rise to unintended diffraction orders. This problem becomes especially pronounced if the hologram displayed by the LCOS device contains multiple large phase discontinuities. Smaller periods of the beam-steering blazed gratings specifically lead to larger areas with phase discontinuities. Therefore, the diffraction efficiency decreases as the grating period reduces. State-of-art LCOS devices operating at 1550 nm without holographic optimisation are able to achieve a diffraction efficiency of 80% when displaying a blazed grating with a period of 8 pixels.
It should be noted that the diffraction efficiency is referenced to the 0th order reflectance when the LCOS device is not displaying any holograms in this paper. Therefore, the total optical efficiency of an LCOS device, i.e. the percentage of input optical power that goes to the 1st diffraction order of a beam-steering hologram, is the product of both the diffraction efficiency and the LCOS reflectance.
In this work, blazed gratings with various periods were theoretically designed for each set of driving waveform, based on the phase response curves shown in Fig. 13. These grating phase patterns were subsequently displayed on the assembled LCOS device and their corresponding diffraction efficiencies for the 1st diffraction order were measured at 1550 nm. The results for LCOS devices operating under different driving waveform sets are plotted in Fig. 15. When the LCOS device operated under the first waveform set, its diffraction efficiency decreased from 94% for the blazed grating with a period of 40 pixels, to 70% for the 8-pixel-period blazed grating. The decrease became sharper as the period was reduced below 16 pixels. The diffraction efficiency consistently improved as the assembled LCOS switched to the second set of driving waveforms. The improvement became particularly obvious when the grating period was smaller than 16 pixels. The diffraction efficiency was increased to 76% for the blazed grating with a period of 8 pixels. On one hand, this improvement could be attributed to the change in the fringing field, i.e. the elevated voltage range altered the electrical field distribution across the LCOS layer. On the other hand, the elevated voltage range in the second set of waveforms introduced relatively larger tilting to the LC molecules, which made them less viscous. This could facilitate the abrupt phase changes required in the blazed gratings. As a result, the LCOS device could display the designed blazed grating more accurately and achieve higher diffraction efficiency. However, a small decrease in the diffraction efficiency was observed for the third set of waveforms with an even higher voltage range which further increased the LC tilting. This could be attributed to the effect of polarisation modulation. When an elevated driving voltage tilts the LC molecules at sharp angles within a homogeneously aligned LC cell, the LC molecules in the central area of the LC cell along the z-axis tend to twist along the z-axis as well [26,27]. As a result, the LC layer introduces both phase and polarisation modulation to the incoming light. Polarisation modulation will negatively affect the diffraction efficiency and offset the gain in the diffraction efficiency created by the second set of driving waveforms.
It can be seen from these results that the driving voltage range could be used as a variable to optimise the diffraction efficiency of an LCOS device. This method is compatible with the existing hologram optimisation algorithms [28–31]. Therefore, they could be used together to further increase the diffraction efficiency of the LCOS device.
Figure 16 compares the total optical efficiencies between the LCOS devices for different grating periods, with and without the dielectric mirror coating on the silicon backplane. It can be seen that improvement was consistently achieved by the LCOS device with the coated backplane. The improvement was particularly large when the blazed grating period was large, e.g. ∼18% improvement was observed for the period of 40 pixels. Even when the grating period was reduced to 8 pixels, ∼12% improvement was achieved in the total optical efficiency.
Fig. 16. The total optical efficiencies of LCOS devices with and without the dielectric mirror coated backplane.
4. Conclusion
The optical loss due to the structure of the LCOS backplane was theoretically analysed. The pixelated structure of the backplane introduces both amplitude and phase modulation to the incoming beam, which can reduce the reflectance beyond the combination of the pixel reflectivity and the fill factor.
In order to address this problem, a simple and effective dielectric mirror structure was proposed and designed. The designed structure shows >98% reflectance over the test wavelength range between 1530 nm and 1565 nm, within an incident angle window of ± 10°. It also shows a good tolerance to fabrication errors. The design was successfully implemented on a digital LCOS backplane. It was able to improve the reflectance of the backplane from <80% to ∼97%. Its electrical properties were also characterised in this work. The results showed that the dielectric mirror structure shares no more than 30% of the voltage drop between the pixel electrode on the LCOS backplane and the common electrode on the glass coverplate.
An LCOS device was assembled based on a backplane with the dielectric mirror coating. The reflectance of this LCOS device was measured as >96%, which is considerably higher than the <80% reflectance measured in the device without the coating. Additionally, the assembled LCOS device was able to achieve the necessary 2π phase modulation with an RMS voltage level just under 4.0 V. This further confirmed that the electrical properties of the dielectric mirror were properly optimised, and the majority of the voltage drop took place across the LC layer.
It was experimentally demonstrated that the LCOS device with a coated backplane was able to achieve high diffraction efficiencies, if its operating voltage range was properly optimised. When the driving voltage range was low, the fringing field effect and the fluid elasticity of the LC material blurred the phase patterns displayed on the LCOS device and caused a reduction in the diffraction efficiency. The diffraction efficiency could be increased by slightly raising the driving voltage range. However, an excessively high voltage range caused twisting of the LC molecules, which led to polarisation modulation of the incoming beam and thus offset the gain in the diffraction efficiency.
Therefore, the relationship between the driving voltage range, fringing field effect and the LC material properties needs to be carefully considered when optimising the LCOS device for maximum diffraction efficiency. For example, it is possible to further reduce the thickness of the LC layer in our LCOS device with the silicon backplane, in order to suppress the fringing field effect. However, in this situation the LC molecules would need to operate at higher tilting angles. This could introduce the polarisation modulation effect and reduce the diffraction efficiency.
Overall, it was demonstrated that the total optical efficiency in the LCOS device with a dielectric mirror coating was 12%–18% higher than the standard LCOS device, depending on the diffraction angle. The total optical efficiency could be further increased by using advanced hologram generation algorithms.
Funding
Fundamental Research Funds for the Central Universities (2242019k1G001).
References
1. D. Vettese, “Microdisplays: liquid crystal on silicon,” Nat. Photonics 4(11), 752–754 (2010). [CrossRef]
2. Z. Zhang, Z. You, and D. P. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(10), e213 (2014). [CrossRef]
3. N. Collings, W. A. Crossland, P. J. Ayliffe, D. G. Vass, and I. Underwood, “Evolutionary development of advanced liquid crystal spatial light modulators,” Appl. Opt. 28(22), 4740–4747 (1989). [CrossRef]
4. https://uk.jvc.com/projectors/4k/DLA-Z1/
5. https://www.sony.com/electronics/projector/vpl-vw995es
6. https://www.microsoft.com/en-us/hololens
7. Y. Huang, Z. He, and S. T. Wu, “Fast-response liquid crystal phase modulators for augmented reality displays,” Opt. Express 25(26), 32757–32766 (2017). [CrossRef]
8. N. Matsuda, A. Fix, and D. Lanman, “Focal surface displays,” ACM Trans. Graph. 36(4), 1–14 (2017). [CrossRef]
9. G. Hass, “Microdisplays for Augmented and Virtual Reality,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 49(1), 506–509 (2018). [CrossRef]
10. S. Frisken, H. Zhou, D. Abakoumov, G. Baxter, S. Poole, H. Ereifej, and P. Hallemeier, “High performance ‘drop and continue’ functionality in a wavelength selective switch,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2006), paper PDP14.
11. T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1150–1157 (2010). [CrossRef]
12. S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23(21), 3911–3915 (1984). [CrossRef]
13. Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High Quality Assembly of Phase-Only Liquid Crystal on Silicon (LCOS) Devices,” J. Disp. Technol. 7(3), 120–126 (2011). [CrossRef]
14. J. L. Fergason, “Display devices utilizing liquid crystal light modulation,” US Patent US3731986; (1973).
15. S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices(John Wiley & Sons, 2006).
16. E. Hällstig, T. Martin, L. Sjöqvist, and M. Lindgren, “Polarization properties of a nematic liquid-crystal spatial light modulator for phase modulation,” J. Opt. Soc. Am. A 22(1), 177–184 (2005). [CrossRef]
17. L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4(1), 7441 (2015). [CrossRef]
18. F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic Reconstructions Using Phase-Only Spatial Light Modulators,” 2008 3DTV Conference: The True Vision - Capture, Transmission and Display of 3D Video, Istanbul, pp. PD-1-PD-4, (2008).
19. J. L. M. Fuentes and I. Moreno, “Random technique to encode complex valued holograms with on axis reconstruction onto phase-only displays,” Opt. Express 26(5), 5875–5893 (2018). [CrossRef]
20. G. Lazarev, F. Kerbstadt, and J. Luberek, “High-resolution high-reflective LCOS spatial light modulator for beam manipulation beyond visible spectrum,” Proc. SPIE 10090, 100900T (2017). [CrossRef]
21. E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004). [CrossRef]
22. U. Efron, B. Apter, and E. Bahat-Treidel, “Fringing-field effect in liquid-crystal beam-steering devices: an approximate analytical model,” J. Opt. Soc. Am. A 21(10), 1996–2008 (2004). [CrossRef]
23. A. Marquez, J. Campos, M. J. Yzuel, I. S. Moreno, J. A. Davis, C. C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39(12), 3301 (2000). [CrossRef]
24. https://www.jasperdisplay.com/products/wafer/jd2552-sp55/
25. J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W.H. Freeman, 2017).
26. Z. He, T. Nose, and S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35(Part 1), 3529–3530 (1996). [CrossRef]
27. S. R. Harris, “Polarization effects in nematic liquid crystal optical phased arrays,” Proc. SPIE 5213, 26–39 (2003). [CrossRef]
28. R. W. Gerchber and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
29. M. A. Cibula and D. H. McIntyre, “General algorithm to optimize the diffraction efficiency of a phase-type spatial light modulator,” Opt. Lett. 38(15), 2767–2769 (2013). [CrossRef]
30. P. W. M. Tsang, Y. T. Chow, and T.-C. Poon, “Generation of patterned-phase-only holograms (PPOHs),” Opt. Express 25(8), 9088–9093 (2017). [CrossRef]
31. M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. Vaquero Caballero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(4), 22 (2017). [CrossRef]
