1. Introduction

Pixelated digital spatial light modulators (SLMs) consisting of independently addressable patterned structures spatially control the optical amplitude and phase properties of transmitted (reflected) coherent or incoherent light through (from) each individual pixel in real time. Digital SLMs [1,2] play an essential role as platforms for modern optical signal and image information processing such as parallel signal and image processing [3], three-dimensional displays [4–7], digital holography [5–9], optical communications [10], biomedical applications [11], wave front sensors [12], microscopes [13], defense [14], atomic manipulation [15,16], and quantum information technology [16,17] including consumer information displays [18–23]. These prevalent utilizations and potential optical information processing applications of the SLMs have become the driving force for perusing advanced SLMs as large as 100 inches in diagonal for TVs (large-scale SLMs) [18–21], several ten inches for PC monitors (medium-scale SLMs, Fig. 1(a)) [18–22], several inches for smart phones (small-scale SLMs, Fig. 1(b)) [22] and as small as one half inch for projection displays (mini-scale SLMs, Fig. 1(c)) [8,9,23] with as many as several millions pixels [8,9,18–23]. The typical roles of these SLMs for consumer optoelectronic devices are the real time modulation of the intensity, propagation and polarization of incoherent light [1,2,18–23].

 

Fig. 1 (a) A medium-scale SLM (19 inch diagonal, 300 μm x 300 μm pixel pitch) demounted from a PC monitor, (b) a small-scale SLM (3.5 inch diagonal, 77.4 μm x 77.4 μm pixel pitch) from an iPod and (c) a mini-scale SLM (1.3 inch diagonal, 32 μm x 32 μm pixel pitch) from a projection display with a micromesh (μM). The inset of each figure shows the microscopic view of pixels. (d) A schematic shows the light propagation through SLMs with weak diffraction due to the coarse pitches and opening widths (weakly diffractive projection mode). (e) A schematic showing the mode transfer from the projection mode to the diffraction mode by inserting a micromesh structure between the SLMs and the screen. P_SLM (P_μM) and W_SLM (W_μM) are the pixel pitch and the opening width of the SLM (μM), respectively.

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With the development of efficient and compact solid state coherent or partially coherent light sources with narrow spectral bandwidth such as laser diodes and light emitting diodes [24–29], the demand for wave optical information processing using SLMs is rapidly increasing [9]. This is attributed to the wave optical properties of light that are highly beneficial for information processing beyond the capacity achievable by ray optics.

To comply with these opportunities, SLMs should be able to efficiently demultiplex each pixel information of the SLMs and effectively multiplex the individual demultiplexed optical signals from all pixels of the SLMs at a target plane. The demultiplexing capability is directly related to the diffraction angle ($\theta$), which is proportional to $\lambda /P_{SLM}$where λ is the wavelength of the illuminating light and P_SLM is the pitch of the SLM. Thus for wave optical applications, SLMs require small pitches equivalent to large diffraction angle and high spatial bandwidth (inversely proportional to the pitch size) with high aperture ratio for high power efficiency.

Another requirement for wave optical applications is the large-scale physical dimension of SLMs. As the distance between the SLM and an observation point increase, the viewable area by the observer increases. However, the physical size (space) and the maximal spatial bandwidth of the SLM are fixed. Thus the supportable space bandwidth product (SBP) by the SLM decreases as the observation distance increases. The maximum supportable SBP of SLMs is fixed by their physical dimension and pitch. SBP is considered as a metric for the estimation of wave optical SLMs [5, 6]. High quality imaging requires higher SBP. The demand for SBP increases with observation distance as well as lateral and rotational motion of the observers. If the SBP of SLMs does not meet the required SBP, the image qualities become poor and distorted. Thus, the applications of SLMs in motion at a large distance require large-scale SLMs with fine pitches [6]. This requires SLMs with smaller pixel pitch, higher spatial frequency band width, larger pixel numbers and larger physical dimensions with wider phase modulation depth capability and higher speed operation.

Information display technology is continuously marching towards large-scale displays in their physical dimension by increasing the number of pixels with high operation speed while there is no substantial change in the pixel pitch. In these large-scale information displays, each pixel is addressed by active matrix methods, requiring space-demanding opaque transistors and capacitors for each pixel, which are essential for large-scale high resolution displays due to various reasons including high speed operation and minimal crosstalk among pixels. Thus the reduction of the pixel size down to the wavelength of the illuminating light is not trivial with the intricately integrated structure of transistors, capacitors, wiring electrodes and optical components [18–22]. These advanced information displays may satisfy all the requirements for wave optical applications except the desirable pitch size requirement comparable to the wavelength of the illuminating light, which is essential for efficient demultiplexing of wave optical information by diffraction.

Among various types of SLMs [1,2], liquid crystal (LC) based transmissive and reflective mode SLMs are promising for optical information processing due to their excellence in optical properties, operation speed and large-scale integration [1–23, 30–33]. Commercially available specialized SLMs have pitches ranging from several micrometers to a few ten micrometers and show better diffractive behaviors [2, 8, 9, 30–32]. In particular, liquid crystal on silicon (LCOS) SLMs are available with a pitch of a few micrometers [2, 8, 9, 32]. However, LCOS SLMs are only operational in reflective mode [2, 8, 9, 32]. Even with the most specialized SLMs having 3 μm pitch, the diffraction angle is just ~10°. Typical physical sizes of these specialized or demounted SLMs from projection displays are less than one inch in diagonal. Thus the physical size of the mini-scale SLMs limits their applications such as stationary and small distance observation [6].

When light goes through large-scale SLMs with large pixel and opening width, the light propagates in straight with weak diffraction. SLMs available from small, medium and large-scale information displays act like a weakly diffractive projector as schematically shown in Fig. 1(d). In this study, we show how the weakly diffractive projection mode SLMs can be converted into strong diffraction mode SLMs, and the effective spatial bandwidth and the physical dimension simultaneously increase with the proposed heterostructures as schematically shown in Fig. 1(e) and how the intensities of the high diffraction orders increase.

This study clearly demonstrates that the proposed heterostructures dramatically improve the demultiplexing and multiplexing efficiency of optical information given to each pixel of SLMs by enhancing the diffraction efficiency. As a result, the reconstructed image formation properties by SLMs are largely enhanced even though the initial diffraction properties of the SLMs is extremely poor due to their large pixel size, which is many orders of magnitude larger than the wavelength of the illuminating light. The SLM-μM heterostructures are applicable to not only the wave optical signal processing including multiplexing/demultiplexing of the ubiquitous pixel information given to the each large pixel of the SLM for further necessary optical information process but also to optical image processing including real time holography.

2. Experimental methods

The medium-scale SLM (mSLM) [Fig. 1(a)] demounted from a PC monitor (18.5 inch diagonal, Green ITC, GL-ST1850LED PC Monitor (1366 x 768 pixels)), the small-scale SLM (sSLM) [Fig. 1(b)] from a smart phone (3.5 inch diagonal, iPod Touch 4th Generation (960 × 640 pixels)) and the mini-scale SLM (μSLM) [Fig. 1(c)] from a projector (1.3 inch diagonal ASSA XGA-2000X Projector (640 × 480 pixels)) are investigated with optical beam of diameter less than 2 inch due to the size limit of the available experimental setup in the investigators’ laboratory. The μSLM, the sSLM and the mSLM are twisted nematic (TN) mode, in plane switching mode and TN mode liquid crystal SLMs with 32 μm x 32 μm, 77.4 μm x 77.4 μm and 300 μm x 300 μm pixel pitches while the opening width for the μSLM, the sSLM and the mSLM are 27.2 μm x 21.1 μm, 56.12 μm x 21.27 μm x 3 (for red, green, and blue)), and 82.2 μm x 258.9 μm x 3, respectively. The phase modulation depth of the SLMs for green light was tunable with applied bias voltage, and the maximum phase modulation depth of the SLMs for green light is ~π.

Using the schematically shown experimental set-up in Fig. 2(a) and Korean coins with a diameter of 2.4 cm [Fig. 2(b)] as an object, real-time far-field holograms [Fig. 2(c)] were recorded with a charge coupled device (CCD) camera (Hitachi HV-D30, 1/3 inch in diagonal (4.88 mm × 3.66 mm) with 7.6 μm horizontal pixel pitch, 640 × 480 pixels). The recording setup resembles that of a Michelson interferometer as shown in Fig. 2(a). Green light sources are 532 nm Nd:YAG DPSS (Diode-Pumped Solid State) lasers with the maximum power of ~125 mW. The recording angle ${\theta }_{record}$between the object beam axis and the reference beam axis is ~1°. The object distance between the object and the CCD, $R_{obj}$, is 86 cm.

 

Fig. 2 Schematic diagram of the experimental setup for (a) recording and (d) reconstruction of the hologram (c) of the object (b). f₁ and f₂ are the focal lengths of the employed convex and concave lenses. $\left(\xi ,\eta \right)$, $\left(x,y\right)$ and $\left(X,Y\right)$ are the coordinate systems for the SLM, the micromesh and the observation plane, respectively.

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The set-up for the study of diffraction and image reconstruction is schematically shown in Fig. 2(d). A paper screen with angular scale is placed at the focal length of the image from the SLMs. The image distance $R_{img}$is estimated using the reconstruction equation, $1/R_{img}=\left(1/R_{obj}{}^{*}-1/R_{ref}\right)+1/R_{recon}$ [34] where $R_{obj}{}^{*}$is the effective objective distance. $R_{recon}$ and $R_{ref}$are the laser beam focal length for reconstruction and the reference beam focal length for recording, respectively. The effective objective distance ($R_{obj}{}^{*}$) is estimated by the following relation, $R_{obj}{}^{*}=a^2{R}_{obj}$, when the ratio of the CCD pixel pitch (P_CCD) to the spatial light modulator pixel pitch (P_SLM) is $a$.

The SLMs were addressed with the optically generated digital hologram recorded with 480 × 480 pixels. The angle (${\theta }_{recon}$) between the p^th order principal maximum and the corresponding reconstructed real image is reduced by the ratio of $a$(${\theta }_{recon}=2{\sin }^{-1}\left(\sin \left({\theta }_{record}/2\right)/a\right)$) due to the increased pitch from the CCD to the SLMs. For example, the angle is reduced to ~0.24° (~0.1°) when the μSLM (sSLM) is used for the image reconstruction. The reconstructed real images corresponding to each order diffraction principal maxima were taken by a CCD camera within the diffraction angle of 10°.

3. Computational simulations

In the simulation of the experimental results, we assume that a converging spherical wave source with the focal length of $R_{recon}$ from the SLM and the wave number k propagates through the heterostructure of a SLM and a micromesh (μM) structure and arrives at the screen (observation plane) as schematically shown in Figs. 1(d), 1(e) and 2(d). The distances between the SLM and the micromesh, and the micromesh and the observation plane are z and Z, respectively. Thus, the light reaches the screen after the two-step diffractions through the SLM and the micromesh when $R_{img}=z+Z$. The employed SLMs are assumed to be N_x × N_y arrays of square pixels with a pitch of P_SLM and an opening width of W_SLM.

For efficient simulation, the two-step Fresnel diffraction integral through the SLM-μM heterostructure is considered as the convolutions of the SLM binary amplitude transfer function ($T_{SLM}\left(\xi ,\eta \right)$), weighted with the addressed image on the SLM ($U_i\left(\xi ,\eta \right)$), the micromesh binary amplitude transfer function ($T_{\mu M}\left(x,y\right)$), and the Fresnel transfer function ($\exp \left[-i\pi \lambda z\left(f_{\xi }^2+f_{\eta }^2\right)/m\right]$) where f_u are the spatial frequencies along the u (u = $\xi$, $\eta$, $x$, and $y$) direction [35, 36]. Further, to reduce the computational burden while complying with the sampling requirement in the discrete Fourier transform, a scaling factor, the ratio of the computational grids at the input plane and at the output plane is introduced [36].

With this, the diffraction profile from the SLM to the micromesh is simulated with a scaling factor, m, the ratio of the computational grids at the micromesh $\left(x,y\right)$ and the SLM $\left(\xi ,\eta \right)$planes as shown in the Eq. (1) [36].

Based on Eqs. (1)–(2), the diffraction behaviors of the SLM-μM heterostructures are simulated with the scaling factors, $m=1$and $l=1$ and $R_{img}=z+Z$ (for μSLM, $R_{obj}$ = 92.5 cm) using a commercial code, Matlab.

4. Diffraction and holographic image formation by SLMs

The far field diffraction profile of the μSLM [Fig. 1(c)] with the pitch of 32 μm x 32 μm pitch is shown in Fig. 3(a). The diffraction angle ($\theta$) is just ~0.95 degree and light intensity is largely focused at the zeroth diffraction order and distributed over several higher diffraction orders with decreasing light intensity.

 

Fig. 3 (a), (b) and (c) Diffraction profiles of the μSLM [Fig. 1(c0], the sSLM [Fig. 1(b)], and the mSLM [Fig. 1(a)]. (d), (e) and (f) Diffraction profiles of the μSLM, the sSLM and the mSLM with the hologram [Fig. 2(c)] addressed. g), h) and i) Captured real images corresponding to each principal maximum from the 0th (0th, 0th) order to the 9th (21st, 11th) diffraction order of the μSLM (sSLM, mSLM). Note: The data shown in Fig. 3 are repeatedly reproduced in the following figures for efficient data explanation by comparison.

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The far field diffraction profile of the sSLM with the pitch of 77.4 μm x 77.4 μm [Fig. 1(b)] [31,33] is shown in Fig. 3(b). The first order principal maximum diffraction angle (${\theta }_D$) of the sSLM is only ~0.39 degree due to the large pitch. Most light intensity is focused at the zeroth and first diffraction orders due to the large opening width (56.12 μm). The intensity of the higher order diffraction maxima decreases dramatically with the diffraction order.

The far field diffraction profile of the mSLM with the pitch of 300 μm x 300 μm [Fig. 1(a)] is shown in Fig. 3(c). The first order principal maximum diffraction angle (${\theta }_D$) of the mSLM is only ~0.10 degree due to the large pitch. The diffracted light intensity is mostly distributed over within the diffraction angle of 0.5° over the several diffraction orders. This is attributed to the large opening width.

When these SLMs are addressed with the optically recorded digital hologram from the Korean coin object, the far field diffraction profiles by the μSLM, the sSLM, and the mSLM are shown in Figs. 3(d)–3(f) respectively. When the μSLM of Fig. 1(c) is used, several reconstructed images are visible at the corresponding zeroth, first, second and third diffraction orders as shown in Fig. 3(g) and their brightness is lowered with the diffraction order. But the other images corresponding to the higher order principal maxima are not discernible at the employed optical power because of the dramatically decreasing optical power distribution as shown in Figs. 3(d) and 3(g).

When the sSLM of Fig. 1(b) is used, the only reconstructed images corresponding to the zeorth and first order diffraction principal maxima are barely visible with large image distortion as shown in Fig. 3(h). Further, when the mSLM of Fig. 1(a) is used, there were no discernible images at all as shown in Fig. 3(i). The greatest portion of the optical power is allocated at the 0th order beam while the diffracted beam intensity is very low. These are attributed to the poor diffraction properties and the large cutoff of high spatial frequency component as the pixel pitch increases. As a result, the reconstructed images are low in brightness, distorted, aliased, and invisible as shown in Fig. 4.

 

Fig. 4 (a) A photographic image of a micromesh mask used in the experiment. The 1 inch x 1 inch chrome metal micromesh pattern with variation in the pitch is formed on the 5 inch x 5 inch soda lime glass using photolithography process. (b) A freestanding nickel metal micromesh sheet (μM16). Microscopic images of (c) μM4, (d) μM6, (e) μM8-1 and (f) μM8-2. Diffractions profiles of (g) μM4, (h) μM6, (i) μM8-1, (j) μM8-2 and k) μSLM The angular scale shown on the top of the figure is the diffraction angle where the 0th order principal maximum is located at the origin (0 degree) of the scale.

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5. SLM-μM heterostructures

To overcome the issues mentioned above, we propose and present here simple novel SLM-μM heterostructures which consist of SLMs of any size and μMs as shown in Figs. 1 and 2.

5.1. Micromeshes (μMs)

The employed SLM-μM Heterostructure approach does not deal with the structurally intricate SLMs themselves but with a micromesh (μM) sheet (or film), of which the pixel size is smaller than that of the SLM and can be comparable to the wavelength of the employed visible light. Unlike the SLMs with intricate device structures requiring a sophisticated patterning and fabrication process, the implementation of micromeshes is simple, scalable and cost-effectively achievable by various fabrication methods [37–41]. The micromeshes can be fabricated on transparent substrates such as glass as shown in Fig. 4(a) or a freestanding sheet or film as shown in Fig. 4(b). Thus, the SLM-μM heterostructures can be formed with SLMs of any size.

The employed micromeshes are the patterned chrome metal layers on 3 mm thick soda lime glasses (Transmittance ~82%) shown in Fig. 4(a) and a freestanding nickel metal sheet with 16 μm × 16 μm pitch with 10 μm × 10 μm opening width (μM16) shown in Fig. 4(b). Four different types of micromeshes patterned on glass, 4 μm × 4 μm pitch with 2.1 μm × 2.1 μm opening width (27.6% aperture ratio) (μM4) [Fig. 4(c)], 6 μm × 6 μm pitch with 3.15 μm × 3.15 μm opening width (27.6% aperture ratio) (μM6) [Fig. 4(d)], 8 μm × 8 μm pitch with 3.65 μm × 3.65 μm opening width (20.8% aperture ratio) (μM8-1) [Fig. 4(e)], and 8 μm × 8 μm pitch with 5.1 μm × 5.1 μm opening width (40.6% aperture ratio) (μM8-2) [Fig. 4(f)] in average). In this study, the micromeshes are identified by their abbreviations related to their pitch sizes as shown in the parentheses. For example, micromesh 4 μm × 4 μm pitch with 2.1 μm × 2.1 μm opening width called μM4.

The experimental diffraction profiles of the individual micromesh structures [Figs. 4(c)–4(f)] by illuminating green laser (λ = 532 nm) are shown in Figs. 4(g)–4(j) and confirmed by the simulation based on Eqs. (1)–(2). The far field diffraction profiles for μM8-2, μM8-1, μM6 and μM4, with the pitch of 8, 8, 6 and 4 μm, respectively, show that the angular separation between the diffracted principal maxima of the individual micromesh is ~3.8, 3.8, 5.1, and 7.6°, which are 4, 4, 5.33 and 8 times wider than that (0.95°) of the μSLM [Fig. 4(k)], respectively. The first order diffraction angles (3.8 and 7.6°) of the μM8 and μM4 correspond to the angle of the fourth (4th) and the eighth (8th) diffraction order of the μSLM, respectively. The first order diffraction angle of the μM6 is 5.1°, which is less than the sixth (6th) order diffraction angle (5.7°) of the μSLM but higher than the fifth (5th) order diffraction angle (4.75°) of the μSLM.

Additionally, Figs. 4(g)–4(j) say that the relative light intensity of the diffracted principal maxima compared to the zeroth order diffraction principal maximum becomes higher as the opening width becomes smaller due to the broader far field diffraction envelop function proportional to the inverse of the opening width. The envelop function of the μMs is broader by ~13, 8.6, 7.5, and 5.3 times compared to that of the μSLM because of the smaller opening width of the μMs (2.1, 3.15, 3.65, and 5.1 μm) compared to that of the μSLM (27.2 μm).

5.2. Mini-scale SLM-μM heterostructures

The experimental diffraction profiles of the μSLM-μM heterostructures are shown in Fig. 5 when the μSLM and the μM are in physical contact but the gap distance between them ~1mm due to the thickness of the glass housing of the μSLM. This also is confirmed by the simulation based on Eqs. (1)–(2). The heterostructures increase the relative light intensity of the higher diffraction orders as shown in Fig. 5(a). The heterostructures cause a large reduction of the zeroth diffraction order light intensity compared to that of the μSLM alone due to the promoted diffraction efficiency with the wider diffraction angles caused by the narrower opening width of the μMs (better demultiplexing).

 

Fig. 5 The experimental diffraction profiles (a) for the μSLM alone and the μSLM-μM8-2, μSLM-μM8-1, μSLM-μM6, and μSLM-μM4 heterostructures, and (b) for the μSLM with the coin hologram image addressed (μSLM-I), the μSLM-μM heterostructures with the hologram image addressed (μSLM-I-μM8-2, μSLM-I-μM8-1, μSLM-I-μM6 and μSLM-I-μM4). Reconstructed real images corresponding to each principal maximum along the horizontal axis within 10° diffraction angle by (c) the μSLM alone, (d) the μSLM-μM8-2, (e) μSLM-μM8-2, (f) μSLM-μM4 and (g) μSLM-μM6 heterostructures. The center of the reconstructed images is located at ~0.2° higher diffraction angle from the corresponding principal maxima. Notice that the angular scale for the μSLM-μM6 is different from that of others.

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The diffraction peaks corresponding to the first diffraction order principal maxima of the μMs located at large angles (~3.8, 3.8, 5.1, and 7.6°) become largely brighter compared to the others. When the ratio (R_P) of the SLM pitch (P_SLM) to the μM pitch (P_μM) is an integer, the first order diffraction angle of the μMs occurs at the R_P^th order diffraction angle of the SLM as shown in Fig. 5(a). Otherwise, the first order diffraction angle of the μMs is located between the floor(R_P)^th and the floor(R_P + 1)^th diffraction order angle of the SLM, where floor(R_p) is the largest integer, which is smaller than or equal to R_p. Additionally, as shown in the diffraction profile of the μSLM-μM6 heterostructure, there are relatively weak satellite diffraction peaks other than the principal maxima of the μSLM and the μM6. The satellite peaks are originated from the effective global pitch determined by the least common multiple (LCM) of the μSLM pitch and the μM6 pitch. In the case of the μSLM-μM6, the LCM is 96 μm, which is three times the pitch of the μSLM. Thus the diffraction angle by the LCM effective pitch is smaller by three times the diffraction angle of the μSLM alone as shown in Fig. 5(a).

When the μSLM is addressed with the optically generated hologram of the coins [Fig. 2(c)], the experimental diffraction profiles for the μSLM and the μSLM-μM heterostructures are shown in Fig. 5(b). There is no significant change in the overall diffraction profile, but there are new features on the left and the right hand side of the diffraction principal maxima corresponding to the real and the conjugate reconstructed images, respectively.

The detailed reconstructed real images corresponding to the each principal diffraction maximum of the μSLM from the 0th to 9th order with and without the micromesh structures are shown in Figs. 5(c)–5(g) and are also confirmed by the simulation. The more reconstructed images with the heterostructures than with the μSLM alone [Fig. 6(a)] are shown at the larger diffraction angles.

 

Fig. 6 (a) Experimental and (c) simulated physical gap distance (z = 0 (simulation only), 1, 10, 30 and 58.2 mm) dependent diffraction profiles of the μSLM-μM6 heterostructures without (top left column)/with (top right column) the hologram addressed on the μSLM. The detailed reconstructed images by (b) experiment and (d) simulation.

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When the heterostructure of the μSLM with μM8-2 is used, the reconstructed real coin images are visible at the diffraction angles corresponding to the 0th, 1st, 2nd, 3rd, 4th, 5th, 6th, and 8th diffraction orders as shown in Fig. 5(d). The intensity of the reconstructed images is periodically modulated by every 4 diffraction orders of the μSLM. As the period becomes higher, the overall intensity is reduced. The periodicity corresponds to the pitch ratio, R_P. Each pitch of the μSLM along on the horizontal axis is shared with every 4 pitches of the μM8-2. Thus, the uniform optical information in a single pixel of the μSLM is demultiplexed into the R_P² pixels of the μMs, and the diffraction angle increases to R_p times of the diffraction angle by the SLM alone. Further, the real image corresponding to the 4th (1st) order principal maximum by the μSLM (μM8-2) is the second brightest image after that corresponding to the 0th order due to the reinforced diffraction (demultiplexing) and interference (multiplexing) by the μSLM-μMs.

When the opening width is reduced while the pitch is maintained, the brightness of the reconstructed image is reduced due to the lower transmittance (from ~40% to ~20%) as shown in Fig. 5(e). As a result, the reconstructed images by the heterostructure of the μSLM-μM8-1 (the same pitch as that of the μM8-2 but with ~50% lower aperture ratio) are visible at the 0th, 1st, 2nd, 4th, 5th, 6th and 8th orders with less brightness compared to those by the μSLM-μM8-2 heterostructure. Every four diffraction order periodicity is maintained in the intensity modulation. This strongly suggests that the opening width of the micromesh should be as wide as possible while the pitch is as narrow as possible for better diffraction efficiency even though this sounds against each other.

In addition to reducing the opening width only, the effect of the micromesh pitch reduction can be found in Fig. 5(f) and Fig. 5(g) while the opening ratio is maintained at approximately 27.6%. The reconstructed images by the μSLM-μM4 heterostructure are visible at the 0th, 1st, 2nd, 3rd, 8th and 9th orders with the periodicity of the 8 diffraction orders of the SLM as shown in Fig. 5(f). The periodicity (R_P = 8) is due to the sharing of one single pitch of the μSLM with 8 pitches of the μM4. The real images corresponding to the 8th, 1st and 9th order principal maximum of the μSLM are the brightest second, third and fourth to the 0th order.

The reconstructed images by the μSLM-μM6 heterostructure are shown in Fig. 5(g) and correspond to the 0th, 1st, 2nd, 3rd, 5th, 6th, and 7th orders of the μSLM. The 5th (1st) order real image reconstructed by the μSLM-μM6 (μM6) is the brightest second to the 0th order. Among the reconstructed images, the reconstructed images located closely at the diffraction angles corresponding to the principal maxima of the μSLM are only visible. The images corresponding to the other diffraction orders at angular positions within the diffraction angle of 10° were not visible even though there are triply dense principal maxima by this global pitch of the μSLM-μM6 heterostructure (96 μm) along the x-axis. The angular location and separation of the principal maxima are driven by this global pitch of the μSLM-μM6 heterostructure (96 μm). But the diffraction intensity is proportional to the number of the originating unit cells and their intensity arrived at the observation point. The number of unit cells with the global pitch is reduced by square of the ratio of the global pitch to the μSLM pitch compared to that with the μSLM pitch. This explains why the only images closely located at the angular position of the principal maxima by the μSLM alone are visible and shown in Fig. 5(g).

Unlike the reconstructed images by the other heterostructures, the relatively bright satellite peaks caused by the larger global pitch of the μSLM-μM6 heterostructure (96 μm) compared to the μSLM (32 μm) are overlapped with the reconstructed real images by the μSLM-μM6 as shown in Fig. 5(g). Thus we develop the way to remove these features causing the image distortion from the reconstructed images by controlling the gap distance between the μSLM and the μM as shown below.

5.3. Optimization for eliminating satellite peaks

As a function of the gap distance (0, 1, 10, 30, 58.2 mm) between the μSLM and the μM6, the diffraction profiles and the reconstruction images of the μSLM-μM6 heterostructure are investigated as shown in Figs. 6(a) and 6(b) (by experiment) and Figs. 6(c) and 6(d) (by simulation). The simulated diffraction profiles and the reconstructed images at the physical gap of 1 mm closely resemble those at the zero physical gap distance. This suggests that the diffraction behavior of the heterostructure is not significantly affected by the small gap distance.

In the diffraction profiles shown in Fig. 6, there are two types of principal maxima. The first type is caused by the pitch of the SLM and its angular position is not changed with the gap distance. The second type depends on the gap distance and is related to the effective pitch of the SLM-μM6 heterostructure varying with the gap distance. If one adjusts the distance between the micromesh and the SLM while the distance between the SLM and the screen is maintained (the Z + z remains as the constant $R_{img}$), one finds that the satellite peaks are merged into the principal maxima of the SLM at a certain distance as shown in Fig. 6. With increasing gap distance, the separation of the principal maxima caused by the SLM-μM6 heterostructure from the principal maxima of the SLM becomes smaller and finally overlaps each other when the gap distance is ~58 mm as shown in Figs. 6(a) and 6(c).

This suggests that the effective pitch ratio (R^e_P) of the μSLM pitch (P_SLM) to the effective micromesh pitch (P^e_μM) at the zero gap distance varies with the gap distance, and becomes an integer at an optimum gap distance. The larger effective pitch reduces the diffraction angle by P^e_μM / P_μM. Thus the non-integer ratio of the SLM pitch to the micromesh pitch at the zero gap distance becomes an integer effective pitch ratio as the gap distance is optimized. This makes the peaks caused by the μSLM-μM6 heterostructure overlapped with the diffraction peaks of the μSLM. As a result, the peaks appearing in the reconstructed image fields are shifted away and the reconstructed images are free from distortions. Additionally, the gap distance becomes closer to the optimum distance, and the reconstructed images become brighter. This suggests that the more efficient power transfer to the reconstructed images occurs though the optimization process. The effective pitch of the μM6 in the μSLM-μM6 with the gap distance of 58.2 mm is 6.4 μm larger than the physical pitch, 6 μm of the μM6. This is the optimized process for eliminating satellite peaks.

At the optimum distance as shown in the schematic of Fig. 7(a), the principal diffraction maxima by the SLM and the micromesh are overlapped at the screen and this can be expressed by Eq. (3).

 

Fig. 7 (a) Schematic showing the overlapping of the principal maxima by the SLM and the μM of a SLM-μM heterostructure at the optimized distance z. θ is the angle between the 0th order and the ($n_{op}\cdot j$)^th order principal maxima of the SLM, and ф is the angle between the 0th order and j^th order principal maxima of the μM. The distance between the SLM and the screen, $R_{img}=z+Z$, remains intact, and X is the distance from the 0th order to the ($n_{op}\cdot j$)^th order principal maxima at the screen where the ($n_{op}\cdot j$)^th diffraction order beam of the SLM and the j^th diffraction order beam of the micromesh meet the screen. (b) The graphical method to find the optimum gap distances, at which the plots for the left hand side (red, orange, light green, green, blue, indigo, and violet solid lines) and the right hand side (red, orange, light green, green, blue, indigo, and violet dotted lines) of Eq. (3) are intersected. The parentheses (($n_{op}\cdot j$), j) above the plotted lines denote (the principal maximum diffraction order of the μSLM, the principal maximum diffraction order of the μM6). The dotted line is the connection of the cross point. The intersections occur at z = 58.2 mm for j = 1, z = 59.5 mm for j = 2 and z = 61. 8 mm for j = 3.

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For example, one can find the optimized z value for the μSLM-μM6 heterostructure by plotting the left and the right hand side of Eq. (3) as a function of the gap distance, z, as shown in Fig. 7(b) where the pitches of the μSLM and the μM6 are 32 μm and 6 μm, respectively, $n_{op}$ is 5, and the distance $R_{img}$ is 925 mm.

However, as shown in Fig. 7(b), the crossing z position increases with the higher diffraction orders due to the parabolic phase term in the Fresnel diffraction. Figure 7(c) shows the zoomed view for j = 1, 2, and 3. The intersections occur at z = 58.2 mm for j = 1, z = 59.5 mm for j = 2 and z = 61.8 mm for j = 3. This suggests that parabolic curved micromeshes are desirable for their wide diffraction angle applications.

5.4. Small-scale SLM-μM heterostructures

Figure 8 show the diffraction profiles and reconstructed images by the small-scale SLM (sSLM)-μM heterostructures. To remove the unnecessary satellite features appearing in the reconstructed images due to the non-integer pitch ratio (R_P), the distance between the sSLM and the μMs has been optimized as explained above.

 

Fig. 8 Diffraction profiles of the small-scale SLM alone (sSLM) and the sSLM-μM heterostructures, sSLM-μM8-2, sSLM-μM8-1, sSLM-μM6, sSLM-μM4 and sSLM-μM16 (a) without and (b) with the hologram image addressed on the SLM (sSLM-I-μM8-2, sSLM-I-μM8-1, sSLM-I-μM6, sSLM-I-μM4 and sSLM-I-μM16). The scale shown on the top of the figure is the diffraction angle. The distance between the sSLM and the micromeshes is optimized to z = 6.48 cm for μM8-2 and μM8-1, z = 6.5 cm for μM6, z = 1.7 cm for μM4 and z = 13 cm for μM16. Reconstructed real images corresponding to their principal maxima by (c) the sSLM (d) sSLM-μM8-2, (e) sSLM-μM8-1, (f) sSLM-μM6, (g) sSLM-μM4 and (h) sSLM-μM16. The right 22 boxes (90° clockwise rotated) denote the layer-out of the reconstructed images corresponding to the diffraction order principal maxima.

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Due to the large pitch (77.4 μm) of the sSLM, the diffraction angle is only 0.39°. Thus, the diffraction peaks are arranged close to each other as shown in Fig. 8(a). The diffraction profiles of the sSLM-μM heterostructures show that the first order principal diffraction maxima of the gapped micromeshes shift to 3.6 (R^e_p = 9), 3.6 (R^e_p = 9), 4.7 (R^e_p = 12), 7.4° (V = 19), and 1.6° (R^e_p = 4) for sSLM-μM8-1, sSLM-μM8-2, sSLM-μM6, sSLM-μM4, and sSLM-μM16, respectively. The effective pitches of the μM8-1, μM8-2, μM6, μM4 and μM16 are 8.6, 8.6, 6.45, 4.1 and 19.4 μm, respectively.

After addressing the optical hologram on the sSLM, the resultant diffraction profiles of the sSLM-μM heterostructures are shown in Fig. 8(b). The detailed reconstructed images captured by a CCD camera are shown in Figs. 8(c)–8(h). Only 0th and 1st order images by the sSLM alone are barely visible with very poor image quality due to the poor diffraction and demultiplexing caused by large pixel and opening width as schematically shown in Fig. 1(d).

However, the sSLM-μM heterostructures with optimized gap distances show dramatic enhancements in the image quality of the reconstructed images as well as in the number of visible reconstructed images within the monitored diffraction angles of 10° as shown in Figs. 8(c)–8(h). Literally the reconstructed images are visible all over the diffraction orders with improved image quality and brightness. The image brightness is modulated with the periodicity of the effective pitch ratio (R^e_P). The initially weakly diffracted beam by the sSLM alone becomes highly diffracted and demultiplexed to wide angle by cooperation of the μMs, the wave optical promoters. Thus higher diffraction efficiency, larger diffraction angle and stronger multiplexing of the widely demultiplexed beams by diffraction over all observation points are achieved by the heterostructures as schematically explained in Fig. 1(e). The brightness modulation periodicity is related to the effective number of the μM pitch corresponding to the single pitch of the SLM along one axis (9, 9, 12, 19 and 4 for sSLM-μM8, sSLM-μM8, sSLM-μM6, sSLM-μM4, and sSLM-μM16, respectively).

This should be mentioned that the reconstructed image quality by the sSLM-μMs [Fig. 8] is little lower compared to that by the μSLM-μMs [Fig. 5]. This is attributed to the smaller physical size of the employed micromeshes (1 inch x 1 inch) than the size of the sSLM (3.5 inch in diagonal). This causes that the only ~40% of the addressed pixels on the sSLM is utilized for the image reconstruction in the sSLM-μMs. This leads to the relatively poor image quality. One can expect the better pixel number utilization rate and the better image quality by employing the sSLM-μM16 with the larger physical size of the micromesh (~2 inch x 2 inch). However, the reconstructed image quality shown in Fig. 8 does not show any significant improvement. This is attributed to a technical issue: how the free-standing thin nickel micromesh sheet is evenly located without any wrinkle and strain. As shown in Fig. 4(b), there were wrinkles.

5-5. Medium-scale SLM-μM heterostructures

Figure 9 shows the diffraction profiles without [Fig. 9(a)] and with [Fig. 9(b)] the addressed hologram on the medium-scale SLM (mSLM)-μM heterostructures. As mentioned previously, the diffracted light by the mSLM is only observed at around the zero diffraction angle due to the large pitch and opening width of the mSLM.

 

Fig. 9 Diffraction profiles of the medium-scale SLM alone (mSLM) and the mSLM-μM heterostructures, mSLM-μM8-2, mSLM-μM8-1, mSLM-μM6, mSLM-μM4 and mSLM-μM16 (a) without and (b) with the hologram image addressed on the mSLM (mSLM-I-μM8-2, mSLM-I-μM8-1, mSLM-I-μM6, mSLM-I-μM4 and mSLM-I-μM16). The distance between the mSLM and the micromeshes is optimized to z = 1.0 cm for μM8-2 and μM8-1, z = 0 cm for μM6, z = 0 cm for μM4 and z = 3.0 cm for μM16. The scale shown on the top of the figure is the diffraction angle where the 0th order principal maximum is located at the origin (0 degree) of the scale. (c) The aperture diameter dependent reconstructed images by using the μSLM and a controllable circular aperture located at the front of the μSLM for d = 22 (c1), 20 (c2), 18 (c3), 16 (c4), 14 (c5), 12 (c6), 10 (c7), 8 (c8), 6 (c9), 4 (c10), 2 (c11) and 1 mm (c12). (d) The μSLM pixel number utilization rate percentage as a function of the aperture diameter when the hologram image is addressed on the μSLM using 480 x 480 pixels.

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In the mSLM-μM heterostructures, to remove the unnecessary satellite features appearing in the reconstructed images due to the non-integer pitch ratio (R_P), the distance between the mSLM and the μMs has been optimized. Unlike the mSLM, the mSLM-μM (mSLM-μM8-2, mSLM-μM8-1, mSLM-μM6, mSLM-μM4, and mSLM-μM16) heterostructures efficiently distribute the light power over the larger diffraction angles (3.6, 3.6, 4.8, 7.4 and 1.6°, respectively) as shown in Figs. 9(a) and 9(b).

However, the clear reconstructed images by the mSLM-μMs were not observed. This is attributed to two technical factors. The first factor is the size of the illumination light beam, which is less than 2 inch in diameter. When the hologram image is addressed over 480 x 480 pixels of the mSLM, the addressed physical image size is 144 mm x 144 mm. As a result, the maximum possible illumination area of the mSLM by using the 2 inch diameter light beam is less than 9.8% of the addressed pixels. The image shown in Fig. 3(i) is obtained with the 2 inch diameter light beam but the coin image is not recognizable due to the poor diffraction and demultiplexing rather than the low pixel information utilization rate as explained in Figs. 9(c) and 9(d).

Further, the second factor is related to the physical size of the μMs. The μMs patterned on glass have the physical size of 1 inch x 1 inch. As explained previously, the light beam passing through the weakly diffractive mSLM is further blocked by the μMs due to the smaller physical aperture size of μMs than the light beam diameter and the mSLM. As a result, the effective utilization rate of the addressed pixel information is largely reduced by the micromesh. In the present set-up of the mSLM-μMs, the effective utilization rate of the addressed pixel information becomes less than 3.1% and this corresponds to invisible reconstructed image formation.

This can be ascertain by the effective pixel utilization rate dependent reconstructed image qualities formed by using the μSLM with a controllable circular aperture at the front of the μSLM as shown in Fig. 9(c). As the aperture diameter decreases, the pixel utilization rate becomes lower. Surprisingly, when the utilization rate is higher than 30%, there is no significant image distortion clearly showing the merit of the holography. However, when the utilization rate is between 10% and 30%, the image quality degradation is recognizable as shown in Figs. 9(c) and 9(d). When the utilization rate is about 6%, the outline of the image is barely configurable. However, when the rate is less than 6%, the image is not recognizable any more. This clearly says that the beam diameter and the physical aperture size of the micromesh is not necessary equal to the size of the SLMs as long as they are able to cover up the one-third of the addressed SLM.

6. Conclusions

In this study, we show how to harness various scale SLMs obtainable from the consumer information displays for real time large-scale wave optical applications by employing simple scalable heterostructures of a SLM-a micromesh (μM) sheet, where the SLMs act as scalable digital real time spatial light modulators and the micromeshes act as promoters of the wave optical properties such as diffraction and interference. Even though large-scale SLMs with coarse pitch and large opening width show poor diffraction properties, their high pixel numbers and large physical size are beneficial and can play an important role as powerful real time large-scale spatial light modulators for wave optical applications by forming SLM-μM heterostructures. SLM-μM heterostructures make for weakly diffractive SLMs to be highly diffractive wave optical components while the angular separation between the principal maxima originated from the SLM is preserved. These heterostructures dramatically improve the demultiplexity and multiplexity of the information given to the SLMs by enhancing the diffraction efficiency, the diffraction angle, the power efficiency, the image quality of reconstructed images and the number of observable reconstructed images. These large-scale SLM-μM heterostructures are operable even with low power density light sources for many viewers.

We also show that SLM-μM heterostructures can be formed with zero or a small gap distance for distortion free reconstruction when the ratio of the SLM pitch to the μM pitch is an integer. However, when the pitch ratio is not an integer, bright satellite diffraction peaks appeared in the image field at zero or a small gap. This study shows that the satellite peaks can be cleared from the image field by tuning the physical gap distance between the SLM and the μMs. This tunability for the optimum optical signal and image processing by controlling the gap distance largely reduce the burden for the micromesh fabrication and the assembly of the SLM and μMs. It should be noticed that the fine mesh pattern can be directly deposited on SLMs (when the pitch ratio is an integer) or prepared on transparent substrates or freestanding sheets or rolled films which can be prepared by using a simple facile scalable cost-effective conventional photolithography process or a roll-to-roll process, etc.

Finally large-scale SLM-μM heterostructures simultaneously satisfy both requirements of large physical dimension and high spatial bandwidth for large-scale real time wave optical applications by employing any large-scale SLMs from consumer information displays as real time spatial light modulators and micromeshes as wave optical promoters. This can’t be achieved with presently available SLMs alone as explained above.