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Abstract
We have developed a magneto-optical spatial light modulator (MO-SLM) with a 10 k × 5 k pixel layout and with a pixel pitch horizontally of 1 µm and vertically of 4 µm. An MO-SLM device pixel has a magnetic nanowire made of Gd-Fe magneto-optical material whose magnetization was reversed by current-induced magnetic domain wall motion. We successfully demonstrated the reconstruction of holographic images, showing large viewing zone angles as wide as 30 degrees and visualizing different depths of the objects. These characteristics are unique to holographic images, providing physiological depth cues which may play a vital role in three-dimensional (3D) perception.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Holography [1] has been considered an ultimate method for three-dimensional (3D) video, and it has been actively developed by many research groups [2–13], since the reconstructed image is very natural and lifelike because it satisfies physiological depth cues, which are critical for the perception of 3D in humans [14]. Spatial light modulators (SLMs) have played an essential role in reconstructing 3D images; however, high performance SLMs as a holographic display is required for realizing satisfactory 3D images. For example, one micron pixel pitch is required for viewing zone angle of 30 degrees. Therefore, when the size of the SLM is 100 mm2, number of the pixels becomes 100 k × 100 k. As you can easily imagine, realizing a large image with large viewing zone requires tremendous number of pixels, which is known for the space-bandwidth-product (SBP) issue of the holographic display [15]. The large SBP of the SLM is essential for the high-quality holographic images but small pixel pitch is also important for simplifying optical systems. Various SLMs have been used to create holographic displays with acousto-optical modulator (AOM) devices [3,4], liquid crystal on silicon (LCoS) SLM devices [6–8], and magneto-optical SLM (MO-SLM) devices [9]. LCoS-SLMs have demonstrated the successful reconstruction of holographic images [12,13]. Sasaki et al. [12] have shown a large image size of 85 mm, but the viewing zone angle was small (5.6 degrees). Hwang [13] has shown a large viewing zone angle of 30 degrees with a pixel pitch of 1 µm and an image size of 30 mm using an LCoS-SLM device; however, the viewing zone angle for the vertical axis was very limited due to its pixel pitch of 9 µm. An LCoS-SLM with the pixel pitch of 2.6 µm and 8 K format has been developed using CMOS technologies [16]. Further pixel size reduction may not be easy since the liquid crystal (LC) light modulator (LM) is controlled by pixel-selection (backplane) transistors, which require a certain area for sufficient performance. There are mainly two ways to drive LC, one is analog driving which uses a transistor and a capacitor (DRAM-type), and the other is digital driving which uses six transistors (SRAM-type) [17]. It is difficult to reduce the size of a capacitor, as it requires a certain area for voltage retention or to fit a complex six-transistor circuit into the pixel, especially a pixel size near the one µm range. Reducing the pixel pitch for LC is also challenging due to the crosstalk of adjacent LC pixels. Although there are some proposals to reduce pixel crosstalk, a small-scale pixel array with passive driving has been demonstrated [18,19]. Therefore, it is essential to simplify the backplane transistor and reduce the size of the LM.
An MO-SLM device has been developed that is driven by current-induced magnetization switching for a small pixel pitch [20–22]. We recently developed a different type of MO-LM device driven by current-induced domain wall motion [23,24], which can be driven by smaller currents. Since an MO-LM device itself is a nonvolatile memory, it does not require memory in the backplane transistor, unlike LC-LMs, which require a voltage supply from the backplane transistor (and capacitor) circuitry to maintain the alignment of the LC. Therefore, the backplane pixel selection transistor can be very simple and small, which is good for reducing the size of the pixels in the MO-LM device. Furthermore, unlike continuous LC devices, the MO-LM is a physically separated and crosstalk-free device, which may have further potential for pixel pitches smaller than one µm. Simple passive-device demonstrations and diffraction performance of magnetic grating driven by external magnetic field have been demonstrated [24–26]; however, large-scale MO-SLM devices controlled by active-matrix driving have not been realized.
In this article, we show first large-scale demonstration of an active MO-SLM, whose magnetization was switched by current-induced domain wall motion with its pixel layout of 10 k × 5 k and pixel pitch horizontally of 1 µm and vertically of 4 µm and successful reconstruction of holographic images.
2. MO-SLM device structure and its operating principle
A schematic illustration of the MO-SLM device is shown in Fig. 1. A pixel comprises an MO-LM and an n-type metal-on-silicon (nMOS) pixel selection transistor. MO-LMs were arranged in a 10 k × 5 k layout (10 mm × 20 mm) with a horizontal pixel pitch of 1 µm and vertical 4 µm. The MO-LM consists of two hard magnets (HMs); one is longer (long HM or LHM) than the other (short HM or SHM). It also has a magnetic nanowire for light modulation. HM and nanowire are made of [Co(0.3 nm)/Pt(0.6 nm)] × 25 multilayers and the Gd-Fe alloy, respectively, having perpendicular magnetic anisotropy. The length of the LHM and SHM is 500 and 0.8 µm, respectively, which differentiates coercivity (Hc). The Hc of the LHM is smaller than that of the SHM. Therefore, an external magnetic field realizes the antiparallel magnetization configuration (AP configuration), which is essential to drive the MO-LM [24,26]. The schematic illustration in Fig. 2 shows how the MO-LM is operated using current-induced domain-wall motion. An initial magnetic domain is induced by a fringe magnetic field from the SHM, as shown in Fig. 2(a). The domain is expanded by current injection along with the electron flow direction until just before the complete reversal of the magnetization due to the fringe field from the LHM (Fig. 2(b)), and the expansion stops. The opposite current direction induces the magnetization to change in the opposite direction. Polarization plane of incident polarized light (parallel to x-direction) reflected in the Gd-Fe nanowire rotated (Kerr effect) clockwise or counterclockwise which depends on the direction of the magnetization of the nanowire as shown in Fig. 2(a) and (b). The component of y-direction of the reflected light in the up-magnetization has 180 degrees (π radian) phase shift compared to the reflected light in the down-magnetization. Basically, the MO-SLM is a re-writable binary phase grating. We installed a linear polarized filter which is orthogonal to the polarization plane of the incident light to cut the x-direction component of the reflected light which does not contribute to the interference. Amplitude of the Kerr rotation of the Gd-Fe was about 0.1 degrees and was almost flat for the wavelength range of visible light. The MO-SLM is reflective type modulator since the light modulator material is metal (Gd-Fe) and the back plane transistor is silicon. You could make a transparent MO-SLM if you use the transparent magnetic materials such as garnet for the light modulators and oxide TFT for the backplane transistors.
Fig. 2. Schematic illustration of a pixel of the MO-SLM showing how the light is modulated, and the magnetization is driven by current-induced domain motion.
Note that because MO-LM devices are made of magnetic material, they are selected and driven by a simple nMOS transistor without any memory, which the LCoS devices require. These memory characteristics contribute to reducing the pixel size of the MO-SLM device.
The MO-SLM device has digital drivers (row and column) for serial-to-parallel data transfer, as shown in Fig. 1, an active-matrix method for pixel selection. The column drivers are connected to the gate terminals of the pixel selection transistors in each column and turn on the pixel transistors. The row digital driver turns on the row selection transistors, which are connected to the source terminals of the pixel selection transistors. As the high- and low-voltage supply rails (VSP and VSM) are connected to the high-voltage source and the ground, respectively, current can pass through the nanowire and switch the magnetization direction of a selected pixel(s).
3. MO-SLM device
3.1 Fabricated MO-SLM device
Figure 3(a) shows a photograph of the backplane with a rectangular pixel area of 10 mm × 20 mm and an inset photo indicates a secondary electron micrograph of the fabricated MO-SLM. The dimension of the LM pixel is 2.9 µm long and 0.45 µm wide as illustrated in Fig. 3(b). Since the MO-LM has initial domains which size was about 0.8 µm for both sides, the fill factor of current MO-LM was about 14.6%. Theoretically the maximum fill factor can be 32.6% when the initial domain size is closer to zero using an artificial ferrimagnetic technique [27] which is used for memory application.
Fig. 3. (a) A photograph of an MO-SLM; An inset photo is magnified SEM image of pixels (b) A schematic illustration of MO-LMs.
3.2 Current-induced domain expansion
After we completed the AP state of SHM magnetization direction up, LHM magnetization down, and the LM magnetization up, as shown in Fig. 2(a) using an external magnetic field, we applied 0 V and 3 V to the VSM- and the VSP-terminal, respectively. Figure 4(a) shows an image of an MO microscope after current injection for an area of 90 × 15 pixels (yellow square), with a pulse width of 1 ms. The white dots outside the yellow area indicate the initial domains. Not all pixels have initial domains; however, we confirm that the current injection induced initial domain nucleation and promoted domain expansion (not shown). Eighty percent of the pixels completed the domain expansion; however, we see error pixels with no initial domain or initial domains without expansion, as shown in Fig. 4(b). The initial domain expanded along with the direction of the electron flow, as shown in Fig. 4(c), is consistent with the current-induced motion of the domain wall [24]. We think the incomplete AP configuration is the main origin of the error pixels as well as the nMOS failure. The AP configuration is realized by different switching field (coercivity) of the LHM and the SHM. Distribution of the coercivities may be large which may cause the P configuration. We controlled the coercivity of the LHM and the SHM by changing the length of the HMs [26]. We may reduce the error by designing the further long LHM and shorter SHM which may provide larger coercivity difference between the LHM and SHM.
Fig. 4. Magneto-optical micrograph of the MO-SLM device after writing data for 90 × 15 pixels. (b) Magnified magneto-optical image; (c) Schematic illustration of domain expansion for an MO-LM.
3.3 Probability of domain expansion versus various drive pulse widths
We investigated the probability of domain expansion for the MO-SLM device with various driving pulse durations. Figure 5 shows the probability versus voltage pulse width for the same area of 90 × 15 pixels. The probability was approximately 15% for a pulse width of 1 µs and increased significantly with the pulse width to 90% at 10 ms. The domain expansion velocity was confirmed at approximately 1.4 m/s by an injection current of 1 mA using a passive LM device with the same material and dimension (not shown). This indicated that a few µs should be enough for the full expansion length of the MO-SLM device (about 1.9 µm). The pulse width required for the complete expansion is much longer than the estimated width.
Figure 6(a) shows transmission electron micrographs (TEM) of an MO-LM device. Steps of the LM were observed at the electrode edge (shown in circles). A magnified TEM image (Fig. 6(b)) shows the clear step of the LM right above the electrode edge. We attributed the longer pulse width for complete expansion to the structural steps in the LM, which can be a type of potential barrier.
4 Optical properties of the MO-SLM device
4.1 Diffraction properties of the MO-SLM device
The diffraction properties of the MO-SLM device were evaluated with one-dimensional stripe patterns on the SLM. The gaps of the stripe patterns were 4 and 6 µm as shown in Fig. 7. Gray and white indicate magnetization up and down, respectively, written by the same current injections explained in Chapter 2. The laser beam (λ=532 nm) was incident perpendicular to the stripe. Spot-shaped diffracted light was observed at approximately 5 and 7.5 degrees, corresponding to the diffraction angles of the first diffracted light with stripe pitches of 6 and 4 µm, respectively. The diffraction efficiency of the 4 µm stripe was 0.58 × 10−6, almost half the efficiency observed with a similar passive magnetic stripe [25]. This lower efficiency is attributed to the shorter effective domain motion length due to the large initial domains [28]. This type of MO-SLM device shows a low diffraction efficiency compared to commercial SLM devices, which is mainly due to a small Kerr rotation angle of 0.1 degrees [20,24]. This would be a drawback of this MO-SLM device; however, there are magneto-optical material compounds with a Kerr effect of an order of magnitude larger, such as MnBi or PtMnSb, for which we expect an efficiency of two orders of magnitude larger [29].
4.2 Various angle observations of holographic images
Figure 8 shows the optical setup for the reconstruction of the hologram image. Linear polarized laser light with a wavelength of 532 nm was used for illumination, which was expanded and incident on the SLM with an incident angle of in-plane 15° and vertical 3°. A camera with a linear polarizer captured the reconstructed image from an in-plane angle of 0 to +30° with a vertical offset angle of 3°, which reduces the 0th-order diffracted light. We wrote a computer-generated hologram (CGH) pattern for the MO-SLM device, corresponding to an image in which the sampling pitch was horizontally 1 µm and vertically 4 µm pitch for the rectangular 1 × 4 µm pixel of the MO-SLM device. The CGH was generated by calculating the propagated light from slices of the 3D model using the angular spectrum method and superimposing all the light from the slices of the 3D model [25,30]. To prevent overlapping the reconstructed image with the conjugate image, the propagation of the object light was restricted to half the vertical angle using the half-zone plate processing [25,31]. Owing to the method, the reconstructed image was observed without overlapping the conjugate image within the horizontal viewing zone angle of 0 to 30 degrees and vertical viewing zone angle of 0 to 3.8 degrees. To simplify the optical system, 4f optical system nor a stop aperture was not used. Therefore, outside the vertical viewing zone, only the conjugate image was observed. The calculated grayscale CGH data was binarized with a threshold of the middle of the amplitude for the binary MO-SLM.
Figure 9 shows photographs of a reconstructed holographic image of an open book with letters on the book cover at a depth position of z = -20 mm observed from 0 ° to 30 °, as shown in Fig. 8. A clear reconstructed image was obtained for a wide viewing zone angle as large as 30 ° with smooth motion parallax throughout the viewing zone angle [See Visualization 1]. The images at the edge of the viewing zone angle (0° and 30°) were partially truncated. This is because the display area is not yet sufficient for the motion parallax of the open book with depth position (z = -20 mm).
4.3 Various depth observations
We wrote a hologram pattern of two objects (a cartoon character and some text) with different depth positions of 20 and 40 mm from the SLM plane, as shown in Fig. 10, and evaluated the reconstructed holographic image with an angle of +18 degrees. Figure 11 shows photographs of the image with different focus positions of the camera. A clear cartoon image with blurred text was observed when the camera was focused on the cartoon [Fig. 11(a)], whereas a clear text image with a blurred cartoon was observed when the text was focused on [Fig. 11(b)]. These results indicated that an eye accommodation response could be expected for the reconstructed images, which gives a strong depth perception.
Fig. 11. (a) Reconstructed holographic image with focus position of 20 mm, (b)focus position of 40 mm.
4.4 Image writing process
We wrote a hologram pattern on the SLM which frame rate was about 0.2 Hz for a viewable image [see Visualization 2] with a pulse width of 50 µs, however, if there is no step in the magnetic light modulator (Fig. 6), the domain expansion can be completed in a few µs as we discussed in the chapter 2.2. and the frame rate can be ten times faster. Furthermore, domain expansion can be 1000 times faster if we use a better spin injection method, such as domain wall motion by spin-orbit torque [32], indicating that a frame rate of 200 Hz is achievable.
5. Conclusions
We have designed and fabricated a magneto-optical spatial light modulator (MO-SLM) with a 10 k × 5 k pixel layout and with a pixel pitch horizontally of 1 µm and vertically of 4 µm. A light modulator pixel has a magnetic nanowire, the MO effect being responsible for the light modulation. The magnetization direction of the nanowire was changed by current-induced domain wall motion (expansion), where the current was driven by a simple nMOS transistor. This simple pixel selection device is one of the important factors for the small pixel pitch of the MO-SLM. The MO-SLM successfully reconstructed holographic images, which displayed objects with viewing zone angles as wide as 30 degrees and at different depths. These physiological depth cues play an essential role in three-dimensional perception. Our current MO-SLM device must improve the domain expansion velocity and provide a larger Kerr rotation for a higher frame rate and diffraction efficiency to fully realize holographic videos. However, our reported MO-SLM device developments solve the long-standing narrow-viewing-zone issue of holography, which has been difficult for conventional SLMs to overcome.
Acknowledgment
Some parts of this work were presented at the Society for Information Display (SID) International Symposium in 2023, “A Magneto-optical Spatial Light Modulator with Narrow Pixel Pitch for Holography Application”.
Disclosures
The authors declare that they have no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon reasonable request.
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