1. Introduction

Static analog holography based on photosensitive medium consisted of grains less than a few ten nanometers such as silver halide [1], photopolymer film [2] and photorefractive materials [3] are showing realistic reconstructed images. However, dynamic and real time holography requires digital holography [4–7], which requires pixelated digital devices of advanced digital image sensors such as charged couple devices (CCDs) for hologram capture and digital spatial light modulators (SLMs) for hologram reconstruction such as liquid crystal spatial light modulators [8–13].

Among these digital components, particularly digital SLMs for reconstruction of real-time three-dimensional digital hologram limit the realization of realistic digital holography due to their pitches far larger than the wavelength of illuminating light. This causes a low diffraction efficiency, small diffraction angle and small reconstructible image size. The maximal spatial frequency of the pitch acts as a cutoff frequency for high frequency regime and the lateral size of a SLM act as a cutoff frequency for low frequency regime in a band pass filter. Typical spatial frequency of local hologram fringe pattern is much higher than the high cutoff frequency while the global spatial frequency is much lower than the low cutoff frequency. Thus the limited bandwidth of SLMs causes the poor distorted reconstructed image quality. In general, digital SLMs for practical holography require small pitch for the higher spatial cutoff frequency (bandwidth) and large physical dimension (space) for smoother image and laterally or distantly moving viewers [6, 7]. For example, one of finest SLMs (LETO Phase Only Spatial Light Modulator, Resolution: 1920 × 1080, HOLOEYE) has 6.4 μm × 6.4 μm in pitch and 12.3 mm x 7 mm in physical dimension. The maximum possible viewing angle, ${\sin }^{-1}\left(\lambda /P\right)$, is about 4.7°. The space-bandwidth products of available digital SLMs are more or less comparable to that shown in the example. This is related to many technological issues of SLM technology to be resolved such as optical switching behavior of the optical component at small pitch scale, integration of the electronic switching components with the optical components as mentioned in [14].

Additionally unnecessary terms such as dc term and conjugate image terms are bothering viewers and causing lowering of power efficiency. There have been theoretical studies regarding on elimination of the dc term and the conjugate images [15–18] in digital holography. The dc term can be blocked by a spatial filter or removed by taking computational difference holograms recorded with optically phase shifted reference waves. The simplest one to achieve this goal is taking 0 and π phase shifted two holograms while the elimination of the conjugate terms requires more phase sifted holograms. These methods all require time consuming multiple step optical recordings and computations. Thus this may not be suitable for real-time dynamic hologram recording for moving or deforming objects with time.

In the previous publication [14], a method of overlaying a passive binary amplitude diffractive component on a SLM, called a SLM-μM heterostructure, was developed. This method improves the demultiplexing capability of SLMs even with their intrinsic poor diffraction properties due to their large pitches. In SLM-μM heterostructures, the even undiffracted beam from the SLM is diffracted out through the binary amplitude micromesh (AM) and this largely improves the reconstructed image quality and brightness at particularly high diffraction orders due to the enhanced demultiplexing capability by μMs. Thus, this method does not require the technically formidable SLMs with smaller than or comparable to the wavelength of illuminating light for realizing realistic dynamical digital holography. However we realized that this method is not the best yet; the brightest 0th order beam and the blocking of the diffracted light from the SLM by AMs causing low power efficiency. In SLM-AM heterostructures, the first diffraction order of the AM is the second brightest diffraction order of the SLM-AM heterostructures and never becomes the brightest as the zeroth order does.

In this study, without requiring any further time consuming process, to increase the power efficiency, to eliminate the dc term and to increase the effective space-bandwidth product simultaneously, we propose a method of overlaying a passive binary phase diffractive element on a SLM, called a SLM-phase micromesh (PM) heterostructure. Even though this approach is similar to the previously employed method [14], in which binary AMs are employed instead of binary PMs, the SLM-PM heterostructures are able to increase the power efficiency and to eliminate the dc term with simultaneously enhanced effective space-bandwidth product. Thus SLM-PM heterostructures can make a selected diffraction order of the SLM to be the brightest. The simple SLM-PM heterostructures are enable to provide arbitrary multiple viewers to see bright three-dimensional information at an appropriate angle without requiring any sophisticated arrangements or structures [9-13].

2. Scalable micromesh spatial light modulators

The proposed heterostructures consist of a SLM with a micromesh (μM) overlaid as shown in Fig. 1. In general, the SLM and the μM are pixelated two-dimensional structures with the pitch of $P_{SLM}$ and its opening width of $W_{SLM}$, and with the pitch of $P_{\mu M}$and its opening width of W_μM in both horizontal and vertical direction, respectively. In this study, we chose one-dimensional μM structures to reduce the computational burden in simulation while the main theme of the proposed work is well illustrated.

 

Fig. 1 Schematics showing diffraction by a SLM-AM and (b) a SLM-PM heterostructure. In (b), the 0th order principal maximum of the SLM is suppressed down to zero due to the binary PM with modulation depth of π. As a result, the 1st order becomes the brightest and largely intensified.

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The transmission coefficient (transfer function) of a one-dimensional μM per pitch can be expressed as

where P_μM and W_μM are the pitch and the opening (furrow) width of the μM, respectively and $rect\left(x\right)$is rectangular function. R and α are reflectance and absorption coefficient of the μM materials, respectively. λ is wavelength of the illuminating light and k is the corresponding wave number. In the equation, $\exp \left(i{n}_{\mu M}kd\right)$and $\exp \left(i{n}_{0}kd\right)$ indicate the phase modulation through the μM material and the air with thickness of d where n_μM and n₀ are refractive index of the μM material and air, respectively. There are two extreme cases. One case is where α or R is extremely large and the corresponding μMs are binary amplitude micromeshes (AMs). The other case is where α and R are negligible and the corresponding μMs are phase modulated micromeshes (PMs).

To efficiently illustrate the primary features of the proposed SLM-μM heterostructures, Fraunhofer diffraction approximation is adapted with the assumption of the zero gap distance between the SLM and the μM. The diffraction profile of the μM for a single pitch at the screen $\left(X,Y\right)$is expressed by using the Fourier transform as Eq. (2).

where $\mathbb{F}$ indicates Fourier transformation. The coordinates are x and y for the μM plane, and X and Y for observation plane (screen).

The Fraunhofer diffraction through the SLM and the μM can be viewed as the Fourier transform of the transfer functions of the SLM and the μM as shown below.

The coordinates are x and y for the SLM plane. $U_i\left(x,y\right)$is the electromagnetic wave profile at the SLM plane with image addressed (or unaddressed), $U_{screen}\left(X,Y\right)$ is the electromagnetic wave profile at the observation plane, and $T_{\mu M}\left(x,y\right)$ is the transfer function of the μM structure shown in Eq. (1).

When α or R is extremely large, the μM acts as one-dimensional binary amplitude micromesh (AM) [Fig. 1 (a)]. The normalized diffracted intensity can be expressed as below.

N is the total number of the SLM pitch along the X-direction, and typically is larger than 480. N* is the effective number of the AM pitch $\left(P_{\mu M}\right)$ within a single aperture of the SLM $\left(W_{SLM}\right)$ in the X-direction. Inside this equation, the term $X/Z$ can be approximated as sinθ in Fraunhofer diffraction regime where θ is the diffraction angle with respect to the surface normal of the SLM. The first parenthesized term of the Eq. (4) is the squared sinc function, which is weighted with a prefactor, ${\left(W_{AM}/P_{\mu M}\right)}^2$, which is related to the aperture ratio as shown in Fig. 2(b) (red curve). The first minima of the envelop function occurs at $\theta ~\lambda /W_{AM}$. Thus the envelop of the sinc function can be broaden by the smaller opening width of the AM than that of the SLM $\left(W_{AM}<W_{SLM}\right)$ while the transmittance can be reduced by ${\left(W_{\mu M}/P_{\mu M}\right)}^2$. Thus the SLM-AM heterostructures can largely increase the demultiplexing capability while their transmittances are lower than those of SLMs alone.

 

Fig. 2 (a) The zeroth to the third order principal maxima intensity profiles of PM8 are shown as a function of the thickness of the transparent materials when $W_{PM}/W_{PM}$ = 1/2, α = 0.1/μm and R = 0.04705. (b) Diffraction profiles of μSLM-AM8 based on Eq. (4) is showing the highest zeroth order beam intensity. (c) and (d) are Diffraction profile of μSLM-AM8 based on Eq. (5) with the optimum ratio of W_PM/P_PM (c) and (d) W_PM/P_PM = 1/2, respectively when α = 0.1/μm and R = 0.04705.

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The second and third parenthesized terms are the Dirichlet functions driven by the periodic structure of the SLM (N) and by the number of N*. Due to a significant large value of the number N, the Dirichlet function of the second term can be approximated as a sum of Dirac delta functions located at $X_{SLM}=mZ\lambda /P_{SLM}\left(m=0,1,\mathrm{2...}\right)$ where m is the corresponding diffraction order. While the third term can be considered as a broaden delta function located at $X_{\mu M}=nZ\lambda /P_{\mu M}\left(n=0,1,\mathrm{2...}\right)$ due to the relatively small value of N*. The peak positions of two Dirichlet functions are occurred at the same position when the ratio of $P_{SLM}/P_{\mu M}$ is an integer. The multiplication of the envelop function and the Dirichlet function of the AM (green curve) is shown in Fig. 2(b). Thus this enhances the intensities of higher diffraction orders as described below.

The diffraction of the heterostructures [blue bar in Fig. 2(b)] can be considered as the multiplication of Dirichlet functions generated by the SLM and AM with the envelop function generated by the AM. Due to wider envelop function (higher demultiplexing), their intensities at high diffraction angles are largely enhanced when the peak of the Dirichlet functions occurs at the same position as shown in the previous publication [14]. This suggests that by controlling the pitch ratio of $P_{SLM}/P_{\mu M}$, a selected higher diffraction order can be significantly brighten even though the intensity of the diffraction order by the SLM alone is due to its poor diffraction properties. For example, for a SLM-AM heterostructure with the SLM with 32 μm pitch and the AM with 8 μm pitch as shown in Fig. 2(b), the ratio of $P_{SLM}/P_{\mu M}$ is 4 and thus the 4th diffraction order of the SLM becomes 13 times brighter than the 4th order by the SLM alone and 3 times brighter than the 1st order by the SLM alone. The selected diffraction order peak by the SLM-AM heterostructure is much higher than that by the SLM alone. This approach is applicable to any SLMs with any pitch size and any physical dimension and becomes significant with higher ratio of $P_{SLM}/P_{\mu M}$. That is why the SLM-μM herterostructures are affordable for a scalable SLM-μM heterostructure for wave optics [14].

However, as mentioned in introduction, binary AMs have an intrinsic problem, which is blocking the light beam propagating from the SLM. As a result, the transmittance of the heterostructure is largely reduced by ${\left(W_{AM}/P_{AM}\right)}^2$ for one-dimensional AMs and ${\left(W_{AM}/P_{AM}\right)}^4$ for two-dimensional AMs as indicated by Eq. (4). Thus the significance of the SLM-μM heterostructures is not fully appreciated yet.

When α and R are negligible, the μM acts as one-dimensional binary phase micromesh (PM) [Fig. 1 (b)]. SLM-PM heterostructures schematically shown in Fig. 1(b) resolve the issues related to SLM-AM heterostructures because there is no blocking of the beam from the SLM. Thus SLM-PM heterostructures efficiently enhance the diffraction efficiency and selectively brighten a certain higher diffraction orders of the SLM, and further diminish the bothering and power consuming zeroth order.

The binary PMs can be fabricated using a mediocre lithography facility because this may not require the sub-micrometer patterns to achieve the high transmittance by maximizing the opening width ratio $\left(W_{\mu M}/P_{\mu M}\right)$. The PMs can be achieved by the modulation of the vertical thickness (d) as shown in Fig. 2(a) rather than the lateral pattern. The control of the vertical thickness (d) of low absorption materials is much more feasible with current thin film technology, which is able to control the thickness down to sub-angstrom with a mediocre facility. To adjust the phase of optical beam propagating in the PM materials, the thickness (d) of PMs is controlled. As a result of the variation of the thickness, the intensity of each diffraction order is periodically varied as shown in Fig. 2(a). Ideally the intensity of the zeroth diffraction order (red curve) can be completely eliminated but that of the first diffraction order (green curve) is maximized when the phase contrast is $\left(2m-1\right)\pi$ and m is a non-zero integer.

In general, α or R may not be negligible. As a result, when the mesa width to the furrow width ratio of PMs is 1, the zeroth order may not be completely diminished even though the phase contrast is satisfied with $\left(2m-1\right)\pi$ as shown in Fig. 2(a). With increasing of the thickness, the diminishing is getting worse. However, the mesa width, $\left(P_{PM}-W_{PM}\right)$, can be optimized to completely diminish the zeroth order beam while the first diffraction order can be strongly intensified. This allows to selectively highlighting a certain diffraction order of a SLM while its zeroth order beam is completely diminished in SLM-PM heterostructures.

The Fraunhofer diffraction profile of SLM-PM heterostructures can be expressed as Eq. (5) when the in-plane pattern structure of the PM is the same as that of the AM.

In this diffraction profile, the Dirichlet terms are the same as those of the Eq. (4). However, there are two sinc functions, which are originated from the furrow and mesa of the PM, respectively. The first sinc function corresponding to the furrow of PMs is the same as the sinc function of AMs. Their phase contrast of PMs depends on refractive index (n), thickness (d) and wavelength (λ) of the illuminating light. In general, α or R is not negligible. Thus the transmittance depends on the reflection (R) and absorption $e^{-\alpha d}$by the transparent materials with thickness of d.

When both α and R are negligible and the width of the phase mesa $\left(P_{PM}-W_{PM}\right)$ is an half of the pitch $\left(P_{PM}/2\right)$, the condition for completely diminishing the zeroth order is $d=\left(2m-1\right)\lambda /2\left(n_{\mu M}-n_0\right)$, where $m=1,2,\mathrm{3...}$. As a result, total transmittance by SLM-PM heterostructures is the same as that by the SLM alone and increases by 4 times compared to that of the corresponding SLM-AM heterostructures. The positions of principal maxima at the screen SLM-PM heterostructures are identical to those of SLM-AM heterostructures due to the identical pitch of micromeshes. Thus the 0_th order is diminished but the ${\left(P_{SLM}/P_{\mu M}\right)}^{th}$diffraction order becomes the brightest one rather than the 0th order beam unlike that in the SLM-AM heterostructures.

In general, there is absorption and reflection by transparent materials. In this case, the thickness of the materials should be as thin as possible. To completely diminish the zeroth order beam, this requires the mesa width $\left(P_{PM}-W_{PM}\right)$ of the phase material region,$P_{PM}-W_{PM}=P_{PM}/\left[1+\sqrt{\left(1-R\right)n_0/n_{\mu M}}\exp \left(-\alpha d/2\right)\right]$, is wider than $\left(P_{PM}/2\right)$. At the complete diminishing condition of the zeroth order beam, the relative beam intensity of the first order can be approximated by ~${\left[\sin c\left(\pi /2\right)\right]}^2{\left[W_{PM}+\sqrt{\left(1-R\right)n_0/n_{\mu M}}\exp \left(-\alpha d/2\right)\left(P_{PM}-W_{PM}\right)\right]}^2$.

As an example, when a PM is made with photoresistive materials having absorption property (α ~0.1/ μm at λ = 532 nm) and reflectance of 0.04705, the expected intensity of the ${\left(P_{SLM}/P_{\mu M}\right)}^{th}$ order beam by a SLM-PM heterostructure with the complete diminishing condition is 3 times higher than that by a SLM-AM as shown in Fig. 2(c).

When the width of the phase mesa is an half of the pitch $\left(W_{PM}=P_{PM}/2\right)$, the power balance is reduced and the zeroth order beam intensity ${\left\{W_{PM}\left[1-\sqrt{\left(1-R\right)n_0/n_{\mu M}}\exp \left(-\alpha d/2\right)\right]\right\}}^2$is not completely diminished. However, with the incomplete diminishing condition of the zeroth order beam, the intensity ratio becomes higher as shown in Fig. 2(d).

As expected, the intensity of the zeroth diffraction order is largely diminished but the ${\left(P_{SLM}/P_{\mu M}\right)}^{th}$ order intensity is relatively high even though the phase control material is not ideal (photoresistive materials with α ~0.1/μm and R = 0.04705).

This suggests that the SLM-PM heterostructures are highly power efficient and superior to the SLM-AM heterostructures. Using SLM-PM heterostructures, brighter holographic images using any size SLMs at wider viewing angles can be achieved while unnecessary zeroth and the other diffraction order terms are eliminated.

3. Experiment and simulation

3.1. Micromeshes

Binary amplitude micromesh AM6 [Fig. 3(a) and 3(d)] is one-dimensional chrome bar array with opening width of 2.8 μm and pitch of 6 μm, and AM8 [Fig. 3(a) and 3(e)] with opening width of 3.75 μm and pitch of 8 μm on soda lime glass as shown in Fig. 3. Additionally, using these binary amplitude micromeshes as a mask, we fabricated binary phase micromesh PM6 [Fig. 3(b) and 3(f)] and PM8 [Fig. 3(c) and 3(g)] by photolithography using photoresist (AZ-1502 positive photoresist (PR)) on quartz glass plates. Based on the measured transmittances of the PR films on glass, the extracted refractive index $\left(n_{PR}\right)$ and absorption coefficient α are ~1.54 and ~0.1/μm, respectively.

 

Fig. 3 (a) Chrome-gilt four micromeshes patterned on a single glass plate as AMs. (b) and (c) PMs fabricated on a glass by utilizing the binary amplitude micromeshes as a mask shown in (a). (d) and (e) The magnified images of AM6 (opening width of 2.8μm and pitch of 6μm) and AM8 (opening width of 3.75μm and pitch of 8μm), respectively. (f) and (g) Microscopic images of PM6 (mesa width of 3.07μm and pitch of 6μm) and PM8 (mesa width 4.09μm and pitch of 8μm), respectively.(h) and (i) the two and three dimensional topographical images of PM6 taken by an AFM.

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We also obtained the topographical profile of the PM6 using an atomic force microscope (AFM) (XE-100 Park Systems Atomic Force Microscope, Korea Institute of Science and Technology) as shown in Fig. 3(i) and 3(h). From this, the thickness of the PR mesa structure is obtained as about 1.47 μm. However, the mesa width is wider than the estimated one by an optical microscope (3.07 μm) as shown in Fig. 3(f). This is attributed to the convolution of the tip shape in measuring the highly steep mesa structures.

3.2. Computationally generated hologram

A computationally generated holographic image to be addressed on the SLM is obtained from the graphically drawn alphabet characters, “CGH” [Fig. 4(a)] by using MATLAB. The generated fringe pattern (interference image) of “CGH” [Fig. 4(b)] is obtained by the interference of the Fresnel diffracted beam from the “CGH” to the distance R_rec with a digital plane wave as shown in Eq. (6).

 

Fig. 4 (a) Optical image of graphically generated letters. (b) Computationally generated hologram (CGH) of the letter “CGH” by Fresnel diffraction method. (c) Optical reconstruction setup. The CGH is addressed into the SLM, and light propagates through the SLM and μM and arrives on the screen.

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The recording distance R_rec (860 mm) is complied with the employed recording distance for optically generated hologram in the previous publication [14]. The inclination angle of propagating plane wave of$(\theta ,\varphi )=(-1.23°,1.23°)$with respect to the surface normal is selected to comply with the optical reconstruction. The resultant phase image of computationally generated hologram is shown in Fig. 4(b).

3.3. Optical image reconstruction and simulation

The detailed information of the reconstruction setup shown in Fig. 4(c) can be found in elsewhere [14]. The setup consists of a light source (λ = 532nm), lens system to modulate the curvature of wavefront, a SLM, and binary amplitude/phase micromeshes located behind the SLM [Fig. 4 (c)]. The beam focuses at 925 mm from the lens system. Among various scale SLMs obtainable from commercial flat panel displays, in this study, a SLM extracted from a projector (ASSA XGA-2000X Projector 640 × 480 pixels), which is a twisted nematic liquid crystal cell with 32 μm horizontal pixel pitch, 27.2 μm opening width, is employed due to the limited optical components in the laboratory. This SLM is called micro SLM (μSLM) as before [14]. The micromeshes are overlaid on SLMs [Fig. 4 (c)]. There is a negligible small gap between the μSLM and AM8 (PM8) except the thickness of the glass housing of the μSLM (~1 mm). However the gap between the μSLM and AM6 (PM6) is of 58.2 mm, which is an optimum distance. At the optimum gap distance, the first diffraction order beam of the μM is overlapped with the near diffraction order beam of the SLM. The detailed optimization processes can be found in [14].

The observation screen is located at 925 mm beyond the SLM-μM heterostructure, and is scaled in angle from zero degree to 10 degree for reference. The diffraction profile at the screen and real images corresponding to each principal maximum are taken by a CCD camera. The experiment results are confirmed by computer simulation using Fresnel diffraction approximation by harnessing MATLAB as elsewhere [14].

4. Results and discussions

Figure 5 shows the experimental diffraction profiles and the reconstructed real images obtained from the μSLM alone, μSLM-AM8, μSLM-PM8, μSLM-AM6, and μSLM-PM6 heterostructures. Since the pitches of PMs are the same as those of the corresponding AMs, the angular positions of diffraction principal maxima of the heterostructures occur at the same diffraction angles. However, there are distinct differences in brightness of the principal maxima and this behavior depends on the type of the micromesh as shown in Fig. 5.

 

Fig. 5 The experimental diffraction profiles of the μSLM alone, μSLM-AM8, μSLM-PM8, μSLM-AM6, and μSLM-PM6 heterostructures (a) without and (b) with addressing the hologram image on the μSLM (μSLM-I). Optically reconstructed real images corresponding to the 0th through the 9th order principal maxima by (c) the μSLM alone, (d) μSLM-AM8, (e) μSLM-PM8, (f) μSLM-AM6, and (g) μSLM-PM6.

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First, we investigated diffraction profiles of the μSLM, AMs, and PMs individually. Intensity of diffraction profile of the SLM alone is centered on the zeroth order due to the sixty times larger pitch (32 μm) compared to the illuminating wavelength (532 nm). The intensity of first order principal maximum is just only about 3% of the zeroth order. The intensity of the other higher orders are dramatically reduced. The diffraction profiles of AMs are similar to those of the SLM alone but the second brightest principal maximum (the first diffraction order of AMs) is stronger due to the wider envelop function and located at wider angle, which is proportional to the ratio of $P_{SLM}/P_{\mu M}$. The first order principal maxima of AM6 and PM6 are at 5.087° while the first order principal maximum of the μSLM is located at 0.95°.

The principal maxima of PM6 and PM8 are located at the same angular locations of AM6 and AM8, respectively. However, there is significant difference in the intensity of the corresponding diffraction orders. The measured intensities of the first order principal maximum of the PM6 and PM8 are 20 and 8 times higher than those of the zeroth order principal maximum of the PM6 and PM8, respectively. This suggests that the fabricated binary PMs do not meet the completely diminishing condition of the zeroth order beam. This is attributed to the mesa widths of the fabricated PMs, which do not meet the complete diminishing condition as explained above as indicated by optical and AFM images shown in Fig. 3.

Then SLM-μMs heterostructures are formed by overlaying the μMs on the SLM and the distance between the SLM and μMs are optimized [14]. The μSLM itself and the μSLM-AM (AM8 and AM6) heterostructures show the brightest spot at the 0th order. This does not depend on the size of the pitch. But the intensity of the 0th order beam intensity at a given input power depends on the envelop function governed by the opening width ($W_{SLM}$ for SLM alone and W_ΑM for SLM-ΑM heterostructures) as shown in Eq. (4). Thus the 0th order diffraction beam intensity of the SLM can be reduced by using the SLM-AM heterostructures with smaller opening width (or pitch) compared to that of the SLM. The intensity of principal maximum, real and conjugate image are intensified for AM8 and AM6 at the fourth and fifth order principal maxima of the SLM, respectively. Thus we were able to increase the diffraction angle as well as the reconstructed image quality due to the enhanced diffraction properties originated from the micromesh-dominant envelop function (depends on $W_{AM}$) and Dirichlet function (depends on P_AM, Eq. (4)). Even though the fifth order intensity for μSLM-AM6 is not as high as the zeroth order intensity, the brightness ratio of the fourth order diffraction peak to the zeroth order peak by the μSLM-AM6 heterostructure is highly intensified from 0.03 of the SLM alone to 0.4 (~13 times) as expected from the simulation. However, this intensification of the diffraction order is largely limited by 4 times lowered transmittance by the one-dimensional AMs with respect to the SLM alone due to the blocking of the light from the SLM by the opaque part of the AM. To increase the power efficiency, the large opening width is advisable while the reduction of the pitch is simultaneously achieved. But this is not trivial with conventional lithography technologies. Thus the blocking of the light by the AMs is intrinsically problematic in power efficiency.

These disadvantages of the SLM-AM heterostructures are resolved by replacing the AMs with PMs. The ideal heterostructures of the μSLM-PMs are able to completely diminish the 0th order beam intensity while the first order of the micromesh (${\left(P_{SLM}/P_{\mu M}\right)}^{th}$ diffraction order of the SLM) is strongly intensified and becomes the brightest one as explained in Fig. 2. However, the experimental results shown in Fig. 5 show the zeroth order beam intensity is largely diminished but is not completely zero yet. This is attributed to the incomplete light power balance through the PM mesa and furrow, and incomplete cancellation as explained in Fig. 2(d).

Changing binary amplitude micromesh to phase micromesh (PM6, PM8) reduces the zeroth order of principal maximum and further intensifies the fourth or fifth order of the SLM by PM8 and PM6, respectively compared to those of corresponding SLM-AMs as shown in Fig. 5. With an optimum phase mask, the first diffraction order is maximized while the other orders become suppressed to zero. By this way, we can selectively turn on and off the selected diffraction order and corresponding real images by controlling the pitch and phase contrast of PMs.

With image addressed into the SLM, real images corresponding to principal maximum are taken as shown in Fig. 5(c) to 5(g). The real images by the SLM alone and SLM-AM heterostructures are the brightest at zeroth order as expected. In the SLM-AM heterostructures, the fourth and fifth order images located at high diffraction angles for AM8 and AM6 are the second brightest, respectively while the second brightest image by the SLM alone is the first order image.

However, this trend is largely changed when the SLM-PM heterostructures are employed. Whereas the intensity of real images corresponding to the zeroth diffraction order is dramatically reduced, the fourth and fifth order real images are highly intensified and become the brightest one.

These experimental results for diffraction and reconstruction are confirmed by simulation using the Fresnel diffraction approximation and MATLAB as done in the previous work [14].

As an example, the simulation results are shown in Fig. 6(a) for the μSLM-AM6 and Fig. 6(b) for the μSLM-PM6. Their corresponding reconstructed real images are shown in Fig. 6(c) and 6(d), respectively. Particularly the phase information obtained from the AFM topographical height image [Fig. 3(h) and 3(i)] of the PM6 is utilized for simulation. The diffraction profiles by SLM-PM6 heterostructures are calculated with the addressed hologram image of the letter “CGH”, but the size is reduced by the factor of 1/16 due to the limited computing power in the laboratory (2 Intel Xeon E5-2609 v2 2.50GHz processors, 192GB RAM). For the efficient calculation using the laboratory computer, the 48 sampling points per pitch (6 μm) is used rather than the original 72 sampling points per one pitch from the AFM height image.

 

Fig. 6 (a) and (b) Fresnel diffraction based simulated diffraction profiles of μSLM-AM6 (P_AM = 2W_AM = 6 μm) and μSLM-PM6 using the computationally generated hologram of the letter “CGH” while the topographical profile of the PM6 obtained from the AFM topography [Fig. 3(h)] is used when n_PR~1.54, α ~0.1/μm, R ~0.04705 and d ~1.47μm. (c) and (d) Real images of (a) and (b), respectively. The distance between the SLM and the meshes was optimized [14].

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The calculated relative zeroth order beam intensity is higher than the experimental one. This clearly indicates that the micromesh profile obtained by AFM is distorted due to the serious tip convolution in imaging of high aspect ratio step pattern. Thus the AFM overestimates the mesa width of the PM6. Even though the AFM image overestimates the mesa width, by switching from the SLM-AM6 to SLM-PM6 heterostructures, the zeroth order real image is largely reduced and the fifth order image becomes the brightest.

Instead of using the AFM profile, the simulation for SLM-μMs (μMs = AM8, PM8, AM6 and PM6) is conducted with $P_{\mu M}=2W_{\mu M}$ as shown in Fig. 7. This does not satisfy the complete diminishing condition of the zeroth order due to the finite α and R of the employed PR materials. The general trend in diffraction profiles and real images is similar to experimentally observed as shown in Fig. 5 but the simulation results show the higher zeroth order intensities than experimental ones. This indicates that the employed mesa width to the pitch ratio in the simulation is different from that in the experiment.

 

Fig. 7 The computational diffraction profiles using Fresnel diffraction approximation [11] (a) for μSLM alone, μSLM-AM8 (W_PM = 4μm), μSLM-PM8 (n_PR~1.54, α ~0.1/μm, R ~0.04705, d ~1.47μm, W_PM = 4μm), μSLM-AM6 (W_PM = 3μm), and μSLM-PM6 (n_PR~1.54, α ~0.1/μm, R ~0.04705, d ~1.47μm, W_PM = 3μm) heterostructures, and (b) for the μSLM with the letter “CGH” hologram image addressed (μSLM-I). Computationally reconstructed real images corresponding to the 0th through 9th order principal maxima from (c) the μSLM alone, (d) μSLM-AM8, (e) μSLM-PM8, (f) μSLM-AM6 and (g) μSLM-PM6.

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To illustrate efficiently the behaviors dependent on the SLM-μM heterostructures, the intensities are numerically compared by using the reference intensity, which is the zeroth order intensity of the SLM alone at a given input power. Thus the normalized intensities of the 0th, 1st, 4th and 5th diffraction orders by the SLM alone are 1, 0.03, 0.008 and 0.002, respectively. The normalized intensities of the 0th and 4th diffraction orders by SLM-AM8 heterostructures are 0.25 and 0.1, respectively. The normalized intensities of the 0th and 5th diffraction orders by SLM-AM6 heterostructures are 0.26 and 0.11, respectively. This indicates that the zeorth order intensity of the SLM-AM heterostructures is reduced by 4 times as expected by ${\left(W_{AM}/P_{AM}\right)}^2=1/4$. Further, the 4th or 5th diffraction order intensities of the SLM-AM heterostructures increases by more than 10 times and 50 times, respectively. The intensities of the 4th and 5th diffraction orders by SLM-AM heterostructures are even 3 times higher than the 1st order intensity of the SLM alone.

Further, when the SLM-PM heterostructures are employed, the variation becomes more significant. The normalized intensities of the 0th and 4th diffraction orders by SLM-PM8 heterostructures are 0.02 and 0.29, respectively. The normalized intensities of the 0th and 5th diffraction orders by SLM-PM6 heterostructures are 0.02 and 0.33, respectively. Even though the SLM-PM heterostructures are not optimized, the normalized intensities of the 0th orders are 50 times lower than that of the SLM alone. Their 4th and 5th intensities are 25 times and 150 times higher than those of the SLM alone. The 4th and 5th intensities are 10 times higher than that of the 1st diffraction order of the SLM alone. This clearly indicates that the selected diffraction order intensities become firstly higher by AMs and then another giant jump happened by the PMs while the zeroth order beam intensity is diminishing.

This clearly indicates that the SLM-PM heterostructures are an efficient way to reduce the 0th order intensity, to increase the diffraction angle, and to intensify the selected diffraction order.

5. Conclusions

We proposed and demonstrated how the higher power efficiency, the zeroth order elimination and the selectively brightening a certain diffraction order can be achievable using the SLM-PM heterostructures rather than SLM-AM heterostructures.

Compared with SLM-AMs, SLM-PMs have many great advantages. First, the total transmittance of SLM-PM heterostructures is almost equal to that of the SLM alone and is much better than that of SLM-AM heterostructures. Binary AMs are blocking light from the SLMs. Thus the transmittance of the SLM-AM heterostructures is at least 4 times (16 times) lower than that of the SLM when one (two)-dimensional binary AMs are employed with the opening width, an half of the pitch. However, SLM-PM heterostructures shows almost the same transmittance of the SLM because PMs utilize their whole area for transmission and only absorption and reflectance by the thin phase film affect the transmittance, which can be minimized by choosing a low absorptive transparent material. Thus the transmittance of the SLM-PM heterostructures is almost equal to that of the SLM. Second, the power transfer efficiency of SLM-PM heterostructures to the higher orders becomes better due to the power consumed for the zeroth order is not required any more but transferred to the higher diffraction orders.

With conjunction of the previously identified strength of the scalable SLM-μM heterostructures, SLM-PM heterostructures allow for holographic information to be located at a wide angle corresponding to a specific diffraction order of the SLM with the brightest light intensity, high power efficiency and some unnecessary terms removed. These scalable power efficient SLMs are powerful tools to efficiently manipulate light and can be utilized in various areas including in realization of practical digital holography for multiviewers and wave optics to name a few.