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Holographic Fabrication and Optical Property of Graded Photonic Super-Crystals with a Rectangular Unit Super-Cell Safaa Hassan 1 , Oliver Sale 1 , David Lowell 1 , Noah Hurley 1 and Yuankun Lin 1,2, * 1 2

*

Department of Physics, University of North Texas, Denton, TX 76203, USA; [email protected] (S.H.); [email protected] (O.S.); [email protected] (D.L.); [email protected] (N.H.) Department of Electrical Engineering, University of North Texas, Denton, TX 76203, USA Correspondence: [email protected]; Tel.: +1-940-565-4548

Received: 25 September 2018; Accepted: 9 October 2018; Published: 11 October 2018

Abstract: Recently developed graded photonic super-crystals show an enhanced light absorption and light extraction efficiency if they are integrated with a solar cell and an organic light emitting device, respectively. In this paper, we present the holographic fabrication of a graded photonic super-crystal with a rectangular unit super-cell. The spatial light modulator-based pixel-by-pixel phase engineering of the incident laser beam provides a high resolution phase pattern for interference lithography. This also provides a flexible design for the graded photonic super-crystals with a different ratio of length over the width of the rectangular unit super-cell. The light extraction efficiency is simulated for the organic light emitting device, where the cathode is patterned with the graded photonic super-crystal. The high extraction efficiency is maintained for different exposure thresholds during the interference lithography. The desired polarization effects are observed for certain exposure thresholds. The extraction efficiency reaches as high as 75% in the glass substrate. Keywords: photonic crystals; graded photonic super-crystals; holographic lithography; extraction efficiency; organic light emitting device; spatial light modulator

1. Introduction The photonic crystals have been extensively studied for the integration of functional optical devices, photonic band gap engineering, and enhanced light–matter interactions [1–3]. Traditional two-dimensional (2D) photonic crystals [4] have uniform lattices, as shown inside the solid green rectangle in Figure 1. The second generation 2D photonic crystals [5,6] have dual lattices with one set of lattices, one set indicated by the blue dots and the other by the red dots in Figure 1. The second-generation photonic crystals have shown enhanced light–matter interactions [5,6]. Very recently, we have studied a new type of photonic crystals titled graded photonic super-crystals (GPSC) [7–11]. Although the lattices are grouped by the blue and red dots, the size of the basis is different in GPSC. The basis size is the gradient, becoming smaller along the arrows for both blue and red lattice sets in Figure 1, and then becoming larger after a quarter of period. The unit cell becomes a unit super-cell in the GPSC, as opposed to the dual lattice in the second-generation photonic crystals. “Period 1” is the period for the traditional photonic crystal, while “Period 2” is the second period in the x-direction for the GPSC, as shown in Figure 1. The lattice described by “Period 1” have a square symmetry, while the lattice described by “Period 2” can have square, hexagonal, or five-fold symmetry [7–11]. Thus, the GPSC can have dual-periods and dual-symmetries. The lattice with “Period 1” can have other symmetries, with a cost of reduced resolution in a phase pattern if a spatial light modulator (SLM) is used in the fabrication [7–11]. The filling fraction of the dielectric material in

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(SLM) is used in the fabrication [7–11]. The filling fraction of the dielectric material in the GPSC is alsoGPSC the gradient for the regions the dashed green rectangular region has a high filling the is also the gradient forwhere the regions where the dashed green rectangular region hasfraction a high and the solid green rectangular region has a low filling fraction. filling fraction and the solid green rectangular region has a low filling fraction.

Figure 1. 1. Image Figure Image of of aa graded graded photonic photonic super-crystals: super-crystals: the the lattices lattices can can be be grouped grouped by by blue blue and and red red dots. dots. The size of the basis becomes smaller along the blue and red arrows, and then becomes larger The size of the basis becomes smaller along the blue and red arrows, and then becomes largerafter aftera green aquarter quarterofof“Period “Period2”. 2”.The Thefilling fillingfraction fractionof ofthe thedielectric dielectricmaterial material is is higher higher inside inside the the dashed dashed green rectangle than than the the solid solid green green rectangle. rectangle. The The graded graded photonic photonic super-crystals super-crystals have have aa unit unit super-cell super-cell as as rectangle indicated by by Period Period 22 in in x-direction. x-direction. indicated

photonic Multiple-beam-based interference lithography lithography has been used for the fabrication of a photonic crystal template [12–19]. The The use use of of a phase mask or single reflection optical element has greatly reduced the complexity and has improved the mechanical stability of the optical optical setup setup [13–19]. Recently, SLM been used as anaselectrically adjustable phase mask for the interference lithography Recently, SLMhas has been used an electrically adjustable phase mask for the interference [20–27]. The[20–27]. computer-generated hologram method can be used fabrication of the desired lithography The computer-generated hologram method canfor be the used for the fabrication of the structure using SLM. the pixel-by-pixel phase engineering in in SLM desired structure using However, SLM. However, the pixel-by-pixel phase engineering SLMcan canreach reach aa high resolution in the the holographic holographic fabrication fabrication [7,10,11,26,27]. [7,10,11,26,27]. Another Another advantage advantage of of using using pixel-by-pixel pixel-by-pixel be predicted, predicted, and and the the aforementioned aforementioned reflective optical phase engineering is that a Fourier filter can be large area area holographic holographic fabrication fabrication [10]. [10]. Using the pixel-by-pixel phase element can be integrated for large five-fold engineering method, graded photonic super-crystals with square [7], hexagonal [7], and five-fold fabricated. These four-, five-,five-, and six-fold structures were symmetric [11] [11] unit unitsuper-cells super-cellshave havebeen been fabricated. These four-, and six-fold structures formed by four beamsbeams with large interfering angles, plus four, five, or sixorinner beams with were formed by outer four outer with large interfering angles, plus four, five, six inner beams smallsmall interfering angles, respectively [7,11].[7,11]. The interfering anglesangles of these common outer beams with interfering angles, respectively The interfering offour these four common outer can be can increased using ausing singlea reflective opticaloptical element for the for formation of graded photonic superbeams be increased single reflective element the formation of graded photonic crystals with awith smalla Period 1 [10].1The structures are less than the four-, five-, super-crystals small Period [10].rectangular The rectangular structures aresymmetric less symmetric than the four-, and six-fold structures. It is It interesting to know whether there is isa apolarization five-, and six-fold structures. is interesting to know whether there polarizationeffect effect and and whether the light extraction can be improved or reduced if the cathode of the organic light emitting device is patterned with with less less symmetric symmetric graded graded photonic photonic super-crystals. super-crystals. patterned thispaper, paper,we wehave have studied holographic fabrication of graded photonic super-crystals In this studied thethe holographic fabrication of graded photonic super-crystals with a rectangular super-cell. A rectangular unit super-cell a phasepattern patternisisdesigned designedto to have awith rectangular unit unit super-cell. A rectangular unit super-cell in in a phase length over width. We We have have also also studied studied the the extraction extraction efficiency efficiency and and polarization polarization a desired ratio of length effect of light from the organic light emitting device, where the cathode is patterned with the graded photonic super-crystal. super-crystal. An extraction extraction efficiency efficiency of of up up to to 75% 75% can can be be reached reachedin inthe thesimulation. simulation. photonic

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Graded Photonic Photonic Super-crystal Super-crystal 2. Description of Experimental Methods and Formation of Graded 532nm nmlaser laserbeam beam (Cobolt Samba 50 mW) expanded and collimated lens and a A 532 (Cobolt Samba 50 mW) waswas expanded and collimated using using lens and a spatial spatialThe filter. The phase ofbeam the laser beam was using modulated using thephase engineered phase pattern filter. phase of the laser was modulated the engineered pattern displayed in a 2 2 with 1920 displayed in a phase-only SLM (Holoeye PLUTO). It has an active area of 15.36 × 8.64 mm phase-only SLM (Holoeye PLUTO). It has an active area of 15.36 × 8.64 mm with 1920 × 1080 pixels. × 1080 pixels. pixel size the8 SLM is 8 ×is8 the μm2side (“P”length is the of side lengthsquare of a pixel square = 8 μm, The pixel size The of the SLM is of 8× µm2 (“P” a pixel = 8 µm, which has whichused has in been in this paper). laser is linearly polarized longer of the active been thisused paper). The laser isThe linearly polarized along the along longerthe side of theside active area and area and is onto incident SLM an incident four degrees, to the normal the is incident the onto SLMthe with an with incident angle ofangle four of degrees, relativerelative to the normal of the of SLM. SLM. As shown in Figure the diffracted from the phase are displayed As shown in Figure 2a, the2a, diffracted beamsbeams from the phase patternpattern (Figure(Figure 2b) are2b) displayed in the in theand SLM are collected through lensselected 1 and selected by a Fourier at the Fourier SLM areand collected through lens 1 and by a Fourier filter atfilter the Fourier plane. plane.

Figure 2. (a) Schematic of the optical setup for the holographic fabrication. The spatial light modulator Figureis2.used (a) Schematic optical setup The for the holographic Theare spatial light modulator (SLM) to displayof thethe phase patterns. diffracted beamsfabrication. from the SLM filtered at the Fourier (SLM) is used to display the phase patterns. The diffracted beams from the SLM are filtered at the plane and form interference patterns through a 4f imaging system of lens 1 and lens 2. α1 , α2 , and α3 1, α2, Fourier plane and diffraction form interference through a 4f imaging lens 1 and lensof2.aαpixel are the first order angles patterns due to the periodic array of 2Psystem (“P” isof the side length are the first order angles due topixels the periodic of 2P (“P” the side of a and α3 = square 8 µm, which has diffraction been used in this paper) in x andarray y directions, 24Pispixels in ylength direction, pixel square = 8 μm, which has been used in this paper) pixels in x and y directions, 24P pixels in and 18P pixels in x-direction in the phase pattern in (b), respectively. θ 1 and θ 2 (zenith angle) are they θ2 (zenith direction, and 18Pofpixels in x-direction in thebeams phasein pattern in (b), respectively. θ1 andview interfering angles the outer beam and inner (c), respectively. (b) An enlarged of the angle) arephase the interfering of the outer beam and inner beams (c), respectively. (b) An designed patterns. Aangles unit super-cell is indicated by the dashed redin square. Inside the unit-cell, enlarged view12 of× the phase patterns. A unit super-cell is indicated by the dashed redlevels square. there are two 12designed square pixel patterns and two 12 × 6 square pixel patterns. The gray of Inside the254) unit-cell, there to arethe two 12 × 12 square and two × 6 254) square pixel patterns. (190 and correspond dashed green andpixel blue patterns regions, while (12812and correspond to the The gray levels of (190 andthe 254) correspond theThe dashed and blue regions, (128 and 254) remaining regions inside unit super-cell.to(c) lasergreen diffraction pattern fromwhile the phase pattern correspond the remaining regions filter insideisthe unit (c) The laser diffraction pattern from in (b) at the to Fourier plane. A Fourier used to super-cell. allow the diffraction spots inside the red circles the phase pattern(d) in Schematic (b) at the Fourier Fourier filter to is the used to allow the diffraction spots passing through. of eight plane. beams A corresponding outer and inner beams in (c) for inside the red circles passing through. (d) Schematic offor eight beams corresponding to the outer and inner the interference lithography. β is an azimuthal angle one of inner beams in (c). beams in (c) for the interference lithography. β is an azimuthal angle for one of inner beams in (c).

A unit super-cell of the phase pattern is indicated by a dashed red square in Figure 2b. The unit super-cell dividedofinto 12 pattern × 12 checkerboard and two 12 × 6 checkerboard regions. A unitwas super-cell thetwo phase is indicated regions by a dashed red square in Figure 2b. The unit The gray levels of (190 and are×used for the regions inside thetwo dashed and blue squares, super-cell was divided into 254) two 12 12 checkerboard regions and 12 × green 6 checkerboard regions. while (128levels and 254) are used for the of theinside dashedthe green and green blue squares in squares, the unit The gray of (190 and 254) areregions used foroutside the regions dashed and blue super-cell. The 254) gray are levels were based on the a small-period pattern while (128 and used for selected the regions outside ofdiffraction the dashedefficiency green andofblue squares in the unit verses a large-period pattern, theirselected ratio, and the formation of a graded photonic super-cell. The gray levels were based on the diffraction efficiency of asuper-crystals small-periodthrough pattern simulation [7,11]. A simulation of an ratio, interference pattern of multi-beams with measured diffraction verses a large-period pattern, their and the formation of a graded photonic super-crystals through simulation [7,11]. A simulation of an interference pattern of multi-beams with measured diffraction efficiencies and a certain exposure threshold was used to determine the gray level

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efficiencies and a certain exposure threshold was used to determine the gray level selection [11]. A gamma curve modulated a 0π and 2π phase into the laser beam when it as reflected by a gray level of 0 and 255, respectively, and related the phase and gray level almost linearly between 0 and 255. A gray level of 190 corresponds to a phase of (190 × 2π/255). A gray level of 254 was typically used instead of 255, because 255 corresponds to 2π or 0π in the cosine function in the simulation. When the 532 nm laser is the incident onto the phase pattern in the SLM, it is diffracted using the following equation: D × sin αi = nλ, i = 1, 2, 3 (1) where D is the structural period; α the first order diffraction angle, as defined in Figure 2a and described below; and n is the diffraction order. α1 is the first order diffraction angle due to the periodic array of the gray levels of (128 and 254) or (190 and 254), and can be obtained by setting D = 2P in Equation (1). For a large period in x- and y-directions, D in Equation (1) equals 18P and 24P, and αi equals α3 and α2 , respectively. The distance Lsp , Lx , and Ly between the +1 and −1 order diffractions due to small period (SP) 2P arrays, 18P arrays in x-direction, and 24P arrays in the y-direction, and can be measured in Figure 2, respectively. The diffraction condition in Equation (1) was tested by verifying Lsp = 2 × f1 tan(α1 ), Lx = 2 × f1 tan(α3 ), and Ly = 2 × f1 tan(α2 ), as shown in Figure 2a,c. Theoretically, Lsp /Lx = 9 and Lsp /Ly = 12. As measured in Figure 2c, Lsp /Lx = 9.20 and Lsp /Ly = 12.23. The agreement between the measured and theoretical values is high, indicating the correct assignment for D. In the experimental setup, the lenses with focal lengths of f1 = 400 mm and f2 = 200 mm for lens 1 and lens 2, respectively, were used. The 4f setup, as shown in Figure 2a, was used. The graded photonic super-crystal was fabricated by exposing the dipentaerythritol penta/hexaacrylate (DPHPA) mixture to the inference pattern with similar spin-coating, exposure, and development conditions, as in reference [7,10,11]. 3. Results 3.1. Holographic Fabrication Results The red circles in Figure 2c are the Fourier filter, which is used to allow these eight beams to pass through. These eight beams are represented by the following equations: E1 (r, t) = E1 cos[+(k sin θ1 cos 45) x + (k sin θ1 sin 45)y + (k cos θ1 )z − ωt + φ1 ]

(2)

E2 (r, t) = E2 cos[−(k sin θ1 cos 45) x + (k sin θ1 sin 45)y + (k cos θ1 )z − ωt + φ2 ]

(3)

E3 (r, t) = E3 cos[−(k sin θ1 cos 45) x − (k sin θ1 sin 45)y + (k cos θ1 )z − ωt + φ3 ]

(4)

E4 (r, t) = E4 cos[+(k sin θ1 cos 45) x − (k sin θ1 sin 45)y + (k cos θ1 )z − ωt + φ4 ]

(5)

E5 (r, t) = E5 cos[+(k sin θ2 cos β) x + (k sin θ2 sin β)y + (k cos θ2 )z − ωt + φ5 ]

(6)

E6 (r, t) = E6 cos[−(k sin θ2 cos β) x + (k sin θ2 sin β)y + (k cos θ2 )z − ωt + φ6 ]

(7)

E7 (r, t) = E7 cos[−(k sin θ2 cos β) x − (k sin θ2 sin β)y + (k cos θ2 )z − ωt + φ7 ]

(8)

E8 (r, t) = E8 cos[+(k sin θ2 cos β) x − (k sin θ2 sin β)y + (k cos θ2 )z − ωt + φ8 ]

(9)

where E is the electric field; k is the wave vector; θ 1 and θ 2 (zenith angle) are the interfering angles of the outer beam and inner beams in Figure 2, respectively; 45◦ and β are the azimuthal angles for outer and inner beams in Figure 2, respectively; and φ is the initial phase of the beam. When the eight beams are overlapped, the intensity distribution in the interference pattern is determined by the following: 8

I (r ) = h

∑

i=1

8 Ei2 (r, t)i + ∑ Ei ·E j cos k j − k i ·r + φj − φi . i< j

(10)


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The The nine nine (Equations (Equations (2)–(10)) (2)–(10)) were were programed programed inin MATLAB, MATLAB, which which produced produced interference interference patterns patternswith withone one example example in in Figure Figure 3a. 3a. The Theeight-beam eight-beaminterference interferencecan canalso alsobe beapproximately approximately understood thethe interference of beams 1–4 and beams 5–8. The of beams 1–4 forms understoodbybyadding adding interference of beams 1–4 and beams 5–8.inference The inference of beams 1–4 aforms structure with a small Λs = 2π/(k 1) cos(45)), θ1 is where determined by tan(θ1) = by f1 a structure with√period a smallofperiod of Λsin(θ sin(θ 1where ) cos(45)), θ 1 is determined s = 2π/(k tan (α11))×= √2/f 2 . (α Thus, Λ s 2/f = (f 2./fThus, 1) 2P. The period Λ x inThe x-direction in the interference among beams 5tan(θ f1 tan ) × Λ = (f /f ) 2P. period Λ in x-direction in the interference s x 2 2 1 1 8among is different from period Λy in thefrom y-direction, and arethe calculated as follows: Λx calculated = 2π/(k sin(θ cos(β)) beams 5–8 is different period Λ y-direction, and are as2) follows: y in and y = 2π/(k sin(θ 2) sin(β)), sin(θ2sin(θ ) cos(β) ≃ (Di/fwhere 2)(0.5 sin(θ Lx/Di) sin(θ 2) sin(β) ≃ L(Di/f 2)(0.5 Λx =Λ2π/(k sin(θ and where Λy = 2π/(k cos(β) ' (Di/f and x /Di) 2 ) cos(β)) 2 ) sin(β)), 2 ) and 2 )(0.5 Lsin(θ y/Di),)as shown in Figure 2c,d. Thus, Λ x = (f 2 /f 1 ) 18P and Λ y = (f 2 /f 1 ) 24P. 2 sin(β) ' (Di/f2 )(0.5 Ly /Di), as shown in Figure 2c,d. Thus, Λx = (f2 /f1 ) 18P and Λy = (f2 /f1 ) 24P.

Figure 3. (a) Simulated eight-beam interference pattern; (b) the charge-coupled device (CCD, attached Figure 3. (a) Simulated eight-beam interference pattern; (b) the charge-coupled device (CCD, attached to an optical microscope) image of the fabricated graded photonic super-crystal in dipentaerythritol to an optical microscope) image of the fabricated graded photonic super-crystal in dipentaerythritol penta/hexaacrylate (DPHPA); (c) diffraction pattern of a fabricated sample from 532 nm laser. penta/hexaacrylate (DPHPA); (c) diffraction pattern of a fabricated sample from 532 nm laser.

A simulated eight-beam interference pattern, as shown in Figure 3a, assumes the same initial A simulated eight-beam interference pattern, as shown in Figure 3a, assumes the same initial phase for all eight beams in Equation (10). The periodicity in the x- and y-directions (Λx , Λy ) is labeled phase for all eight beams in Equation (10). The periodicity in the x- and y-directions (Λx, Λy) is labeled for the size of the unit super-cell in the holographic structure in Figure 3a. Although both the square for the size of the unit super-cell in the holographic structure in Figure 3a. Although both the square (12 × 12) and rectangular (6 × 12) sub-unit cells are used in Figure 2b, the sub-unit cell, as indicated (12 × 12) and rectangular (6 × 12) sub-unit cells are used in Figure 2b, the sub-unit cell, as indicated by the dashed red line, is in a rectangular shape in Figure 3a. The unit super-cell in Figure 3a has a by the dashed red line, is in a rectangular shape in Figure 3a. The unit super-cell in Figure 3a has a ratio of length over width of Λy /Λx = 24/18, which is obtained from (12 + 12)/(12 + 6), in Figure 2b. ratio of length over width of Λy/Λx = 24/18, which is obtained from (12 + 12)/(12 + 6), in Figure 2b. The The design of the phase pattern is flexible for obtaining a rectangular unit super-cell in a holographic design of the phase pattern is flexible for obtaining a rectangular unit super-cell in a holographic structure. For example, the unit super-cell in the phase pattern can have a sub-unit of k × k and k × m structure. For example, the unit super-cell in the phase pattern can have a sub-unit of k × k and k × m pixels. The obtained holographic structure can have a rectangular unit super-cell with a ratio of side pixels. The obtained holographic structure can have a rectangular unit super-cell with a ratio of side lengths defined by 2k/(k + m). lengths defined by 2k/(k + m). Figure 3b shows a CCD (attached to the optical microscope) image of the fabricated graded Figure 3b shows a CCD (attached to the optical microscope) image of the fabricated graded photonic super-crystals in DPHPA. The graded pattern and dual periodicity (one in 4 µm and the others photonic super-crystals in DPHPA. The graded pattern and dual periodicity (one in 4 μm and the in 18 × 4 µm and 24 × 4 µm) are clearly demonstrated in Figure 3b. The fabricated pattern has a unit others in 18 × 4 μm and 24 × 4 μm) are clearly demonstrated in Figure 3b. The fabricated pattern has super-cell indicated by a dashed red rectangle with a size of (18 × 4 µm) × (24 × 4 µm). The super-cell a unit super-cell indicated by a dashed red rectangle with a size of (18 × 4 μm) × (24 × 4 μm). The can be divided into four sub-units, dictated by the blue square in Figure 3b, which correspond to super-cell can be divided into four sub-units, dictated by the blue square in Figure 3b, which the sub-unit dictated by the dashed red rectangle in simulation in Figure 3a. The lattice has a small correspond to the sub-unit dictated by the dashed red rectangle in simulation in Figure 3a. The lattice period of 4 µm for both the x and y-directions. The graded lattice clusters have a rectangular symmetry. has a small period of 4 μm for both the x and y-directions. The graded lattice clusters have a Thus, we have a graded photonic super-crystal with square lattices and rectangular lattice clusters. rectangular symmetry. Thus, we have a graded photonic super-crystal with square lattices and The diffraction pattern of the fabricated sample is shown in Figure 3c, using a 532 nm laser. rectangular lattice clusters. Near the 0th order diffraction spot, there are several high order diffractions. In the four corners, The diffraction pattern of the fabricated sample is shown in Figure 3c, using a 532 nm laser. Near there are more than nine diffraction spots in each, due to the small periodic lattice and graded feature. the 0th order diffraction spot, there are several high order diffractions. In the four corners, there are The multiple-order diffraction indicates not only the quality of the fabricated sample, but also the more than nine diffraction spots in each, due to the small periodic lattice and graded feature. The strong light-matter interaction, which can be used for light extraction, as described in next section. multiple-order diffraction indicates not only the quality of the fabricated sample, but also the strong light-matter interaction, which can be used for light extraction, as described in next section.

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3.2. Simulation of Light Extraction Efficiency 3.2. Simulation of Light In this section, weExtraction simulatedEfficiency the light extraction efficiency in the organic light emitting device (OLED), where the cathode is patterned with the graded photonic withemitting the rectangular In this section, we simulated the light extraction efficiency insuper-crystal the organic light device unit super-cell, using the MIT Electromagnetic Equation Propagation (MEEP) simulation tool [28]. (OLED), where the cathode is patterned with the graded photonic super-crystal with the rectangular The small periodusing of 4 μm, in Figure 3, can be reduced to a Propagation desirable value usingsimulation the single reflective unit super-cell, the MIT Electromagnetic Equation (MEEP) tool [28]. optical element method [10]. In this simulation, a lattice period (small period) of μm isreflective used, as The small period of 4 µm, in Figure 3, can be reduced to a desirable value using the1single shown in Figuremethod 4a. The[10]. 100 nm organic-layer includes lightperiod) emitting optical element In this simulation,(ORG) a lattice periodthe (small of layer, 1 µm electron is used, transport layer, and the hole transport layer. We assigned refractive indices n for the glass (n = as shown in Figure 4a. The 100 nm organic-layer (ORG) includes the light emitting layer, electron 1.45), organic (n = 1.8), and indium tin oxide (ITO) (n = 1.8) layers [8,29]. Ten different incoherent transport layer, and the hole transport layer. We assigned refractive indices n for the glass (n = 1.45), electric (n point-dipole sourcestin were placed a vertical in the of the ORG layer and organic = 1.8), and indium oxide (ITO)along (n = 1.8) layers line [8,29]. Tencenter different incoherent electric dipoles with different polarization directions are assigned [29]. The interference pattern in Figure3a point-dipole sources were placed along a vertical line in the center of the ORG layer and dipoles with can be divided into four sections. top two sections have a low-intensity lattice3a setcan starting from different polarization directions areThe assigned [29]. The interference pattern in Figure be divided the top-left corner The of each indicated the yellow lines. The two sections have acorner highinto four sections. top section, two sections haveby a low-intensity lattice setbottom starting from the top-left intensity lattice set starting from the corner, as indicated by the blue lines. The simulation results of each section, indicated by the yellow lines. The bottom two sections have a high-intensity lattice should be the same we select a quarter by of unit super-cell or the whole one, basedshould on ourbe experience set starting from theifcorner, as indicated the blue lines. The simulation results the same [8,9,11]. One case for the simulation of different sections, described in Figure 4, is from the literature if we select a quarter of unit super-cell or the whole one, based on our experience [8,9,11]. One case [9]. the To save the computation a quarter of theinunit super-cell (bottom left section Figure 3a) for simulation of differenttime, sections, described Figure 4, is from the literature [9].inTo save the was used in the simulation. shows a permittivity output from 3a) the was MEEP toolinwith computation time, a quarterFigure of the4b unit super-cell (bottomstructure left section in Figure used the a sub-unit cell size of 9a × 12a (a = 1000 nm). Due to the large unit super-cell (12 × 9 times larger than simulation. Figure 4b shows a permittivity structure output from the MEEP tool with a sub-unit cell the one photonic crystal), weunit performed parallel the one Simpetus size of 9ain×the 12atraditional (a = 1000 nm). Due to the large super-cell (12 × 9simulations times largerusing than the in the Electromagnetic Simulation Platform in Amazon Web Services (AWS). The E-field intensity was traditional photonic crystal), we performed parallel simulations using the Simpetus Electromagnetic monitored, as shown in Figure 4c for example, in the glass substrate in OLED. The fraction of the Simulation Platform in Amazon Web Services (AWS). The E-field intensity was monitored, as shown total power function in of the the glass wavelength can obtained the light in total the glass substrate, light in Figure 4c as foraexample, substrate inbe OLED. The for fraction of the power as a function absorbed by Al cathode (in plasmonic mode), and trapped as a waveguide mode, as shown in Figure of the wavelength can be obtained for the light in the glass substrate, light absorbed by Al cathode 4d. plasmonic mode), and trapped as a waveguide mode, as shown in Figure 4d. (in

Figure 4. (a) Schematic of the organic light emitting device (OLED) where the cathode (Al) is patterned Figure 4. (a) Schematic of the organic light emitting device (OLED) where the cathode (Al) is patterned with the graded photonic super-crystal that has a rectangular unit super-cell; (b) output of the with the graded photonic super-crystal that has a rectangular unit super-cell; (b) output of the structure design from the simulation software MIT Electromagnetic Equation Propagation (MEEP); structure design from the simulation software MIT Electromagnetic Equation Propagation (MEEP); (c) electric-field intensity in the glass substrate in OLED at the location 740 nm away from indium (c) electric-field intensity in the glass substrate in OLED at the location 740 nm away from indium tin tin oxide (ITO) layer; (d) the fraction of the total emitted power in glass substrate, both in the surface oxide (ITO) layer; (d) the fraction of the total emitted power in glass substrate, both in the surface plasmonic mode and in the waveguide. plasmonic mode and in the waveguide.

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The light intensity in air in fraction is 6.6% less than that in the glass substrate, as simulated for The light intensity in air in fraction is 6.6% less than that in the glass substrate, simulated for other structures [11]. However, the simulation of the extraction efficiency into theasglass substrate other structures [11]. However, the simulation of the extraction efficiency into the glass substrate takes takes much less time. To save the computation time and focus on the fabrication effect, we simulated much less time.efficiency To save the time and onwhere the fabrication effect, simulatedwith the the extraction intocomputation the glass substrate for focus OLED, the cathode (Al)we is patterned extraction efficiency into the glass substrate for OLED, where the cathode (Al) is patterned with the the graded photonic super-crystal holographically formed under different exposure thresholds. graded photonic super-crystal holographically formed under different exposure thresholds. Figure 5 Figure 5 shows the percentage of light in the glass substrate over the total power as a function of the shows the percentage light in thesub-unit, glass substrate overin theFigure total power as alaser function of thethresholds wavelengths wavelengths for the of rectangular as shown 4b. The exposure of for the rectangular sub-unit, as shown in Figure 4b. The laser exposure thresholds of 25%, 30%,dipole 35%, 25%, 30%, 35%, and 40% of the maximum intensity Imax were used. The results for the and 40% of the Imax z-directions were used. The results for the dipole of Overall, E in the polarization of maximum E in the y-,intensity x-, xy-, and are shown in Figure 5a–d,polarization respectively. y-, x-, xy-, and z-directions are shown in Figure 5a–d, respectively. Overall, the extraction efficiency is the extraction efficiency is between 70% and 80% for the dipole polarization in the xy plane, except between 70% and 80% for the dipole polarization in the xy plane, except for the exposure threshold for the exposure threshold of 30% Imax for the Ey dipole polarization. The extraction efficiency is 86.8% of for thefor Eythe dipole extraction 86.8% for the at Ey524 dipoles for30% the IEmax y dipoles 30%polarization. Imax threshold,The while they areefficiency 76.6% foristhe Ex dipoles nm. Itfor is the 30% I threshold, while they are 76.6% for the E dipoles at 524 nm. It is reasonable, because max x reasonable, because the graded intensity is modulated in a higher number of steps along a length of the intensity is modulated in a higher number of steps a length of the rectangle the graded rectangle in the y-direction, rather than the x-direction. If along a polarization effect is neededininthe an y-direction, rather than the x-direction. If a polarization effect is needed in an OLED [30], a grade OLED [30], a grade photonic super-crystal with a rectangular unit super-cell can help to reach the photonic with athreshold rectangular unit30% super-cell help to reach the goal. For the laser goal. For super-crystal the laser exposure of the Imax, thecan maximum extraction efficiency is at the exposure threshold of the 30% Imax , the maximum extraction efficiency is will at the infrared range beyond infrared range beyond 800 nm. Further study in the discussion section shift the wavelength for 800 nm. Further study in the discussion section will shift the wavelength for the maximum efficiency the maximum efficiency toward the visible range. The extraction efficiency for the Ez dipoles in Figure toward visible range. The extraction for the Ez dipoles in Figure 5d is significantly 5d is notthe significantly dependent on the efficiency exposure threshold, as the groove depth ofnot 40 nm in Figure dependent on the the simulation. exposure threshold, the groove depth of 40 nm 4a is fixed in the 4a is fixed in An overallaslight extraction efficiency, ρ, in canFigure be calculated using the simulation. An overall light extraction efficiency, ρ, can be calculated using the average efficiency of average efficiency of the dipoles polarized in x − y (parallel dipole) and z (perpendicular dipole) [8,29], the dipoles polarized in x − y (parallel dipole) and z (perpendicular dipole) [8,29], as follows: as follows:

𝜌 ρ==

22 11 𝜌ρ x−y + + ρ𝜌z 3 3 3 3

(11) (11)

for ten ten dipoles. dipoles. The The extraction extraction It should should be be noted notedthat thatρρxx−y It and ρρzz are are also also the the average average efficiency efficiency for −y and efficiency is calculated to be 71.5% at 563 nm and 73.6% at 633 nm. Under all of the exposure threshold efficiency is calculated to be 71.5% at 563 nm and 73.6% at 633 nm. Under all of the exposure threshold conditions, the lowest overall extraction efficiency is 64.9% at 434 nm in the visible range. conditions, the lowest overall extraction efficiency is 64.9% at 434 nm in the visible range.

Figure 5. (a) Fraction of total emitted power (light in glass substrate over total emitted power) as Figure 5. (a) Fraction of total emitted power (light in glass substrate over total emitted power) as a a function of the wavelengths for different exposure thresholds of 25% Imax , 30% Imax , 35% Imax , function of the wavelengths for different exposure thresholds of 25% Imax, 30% Imax, 35% Imax, and 40% and 40% Imax for the Ey dipoles (a), Ex dipoles (b), Exy dipoles (c), and Ez dipoles (d). Imax for the Ey dipoles (a), Ex dipoles (b), Exy dipoles (c), and Ez dipoles (d).


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4.4.Discussion Discussion The parameters used usedininFigure Figures 4 and 5 the are same the same the graded photonic The simulation simulation parameters 4 and 5 are as theasgraded photonic supersuper-crystal a square super-unit [8], where the maximum efficiency forEzthe Ez dipoles occurred crystal with awith square super-unit [8], where the maximum efficiency for the dipoles occurred at 400 at 760The nm.maximum The maximum efficiency ofz dipoles the Ez dipoles in Figure 5 was in the infrared range or400 760or nm. efficiency of the E in Figure 5 was in the infrared range beyond beyond nm. If we scale down the latticefrom period 1000 750wavelength nm, the wavelength for the 800 nm.800 If we scale down the lattice period 1000from nm to 750nm nm,tothe for the maximum maximum efficiency to from be shifted to 800 =×600 750/1000 = 6006 nm. Figure 6 shows efficiency is expectedistoexpected be shifted 800 tofrom 800 ×800 750/1000 nm. Figure shows the simulated the simulated extraction for OLED, whereisthe cathodewith is patterned a graded photonic extraction efficiency for efficiency OLED, where the cathode patterned a gradedwith photonic super-crystal super-crystal with a sub-unit size(aof 9a ×nm) 12a with (a = 750 nm) with a similar depth of 40 with a sub-unit cell size of 9acell × 12a = 750 a similar groove depthgroove of 40 nm. There arenm. no There are no large differences in the extraction efficiencies for the E , E , and E dipoles in Figure 6a. large differences in the extraction efficiencies for the Ex, Ey, and Exyx dipoles in xy Figure 6a. As shown in y As shown Figure 6b, the wavelength for the maximum efficiency 633 nm, close to the Figure 6b,inthe wavelength for the maximum extraction extraction efficiency is 633 nm,isclose to the expected expected wavelength. In the range between 608 nm, and the 690extraction nm, the extraction above 75%. wavelength. In the range between 608 and 690 efficiencyefficiency is above is 75%.

Figure 6. Fraction of total emitted power as a function of wavelengths with an exposure threshold of Figure 6. Fraction of total emitted power as a function of wavelengths with an exposure threshold of 35% Imax for the Ex , Ey , and Exy dipoles (a), and the Ez dipoles (b) for the OLED patterned with the 35% Imax for the Ex, Ey, and Exy dipoles (a), and the Ez dipoles (b) for the OLED patterned with the graded photonic super-crystal with a sub-unit cell size of 9a × 12a (a = 750 nm). graded photonic super-crystal with a sub-unit cell size of 9a × 12a (a = 750 nm).

The high-light extraction efficiency can be understood through the effective light coupling The provided high-lightbyextraction efficiency be understood through the effective light coupling condition the graded photoniccan super-crystals in Equation (12) [31], as follows: condition provided by the graded photonic super-crystals in Equation (12) [31], as follows: 2π 2π 2π ne f f − 2π sin(θ ) = R (12) (12) λ𝑛 − λ sin 𝜃 = 𝑅

𝜆

𝜆

where is the the effective effectiverefractive refractiveindex indexof ofthe thegraded gradedphotonic photonicsuper-crystal, super-crystal,λλisisthe thewavelength wavelengthin in wherenneffeff is free freespace, space,and andRRisisthe thereciprocal reciprocallattice latticevector. vector.The Theeffective effectiverefractive refractiveindex indexisisrelated relatedto tothe thefilling filling fraction fractionf f by byEquation Equation(13), (13),as asfollows: follows:

= 𝑛 ne f f =

q

2 2 (1 − f ) n 𝑛metal f 𝑓++norg 𝑛 1−𝑓

(13) (13)

where and norg are the refractive index of the metal and organic material in the graded photonic wherennmetal metal and norg are the refractive index of the metal and organic material in the graded photonic super-crystal, super-crystal, respectively. respectively. Due Due to to the the graded graded filling filling fraction fraction in in the thegraded gradedphotonic photonic super-crystal, super-crystal, the coupling condition can be met by many wavelengths simultaneously. the coupling condition can be met by many wavelengths simultaneously. The Thewavelength-dependent wavelength-dependent plasmonic plasmonic loss loss is is related related to to the the size sizeof ofthe thebasis basisat atthe thelattice latticeof ofthe the graded gradedphotonic photonicsuper-crystal super-crystal [32]. [32]. When When the the sizes sizes of of the the basis basis at atneighboring neighboring lattices lattices are are different, different, as Figure 4a (d1 plasmonic resonance conditioncondition is destroyed, thus less plasmonic asshown shownin in Figure 4a and (d1 d2), andthe d2), the plasmonic resonance is destroyed, thus less loss can be seen in the simulation. plasmonic loss can be seen in the simulation. 5. Conclusions 5. Conclusions A graded photonic super-crystal with a rectangular unit super-cell has been holographically A graded photonic super-crystal with a rectangular unit super-cell has been holographically fabricated through the pixel-by-pixel phase engineering of a laser beam in SLM. The design of the fabricated through the pixel-by-pixel phase engineering of a laser beam in SLM. The design of the phase pattern in the SLM has shown a capability to fabricate the graded photonic super-cell with phase pattern in the SLM has shown a capability to fabricate the graded photonic super-cell with a a desired ratio of length over width in the rectangular unit super-cell. A light extraction efficiency of desired ratio of length over width in the rectangular unit super-cell. A light extraction efficiency of up to 75% has been predicted in simulations from the OLED, where the cathode is patterned with the up to 75% has been predicted in simulations from the OLED, where the cathode is patterned with the


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graded photonic super-cell. A good extraction efficiency tolerance to the holographic fabrication has been predicted for the OLED devices. Author Contributions: S.H., N.H., and D.L. performed the simulations; O.S., D.L., and N.H. performed the holographic fabrication; S.H. and D.L. contributed the parallel computation tools; Y.L. analyzed the data; Y.L., S.H., and O.S. wrote the paper. All of the authors read and commented on the manuscript. Funding: This research was funded by U.S. National Science Foundation, grant number 1661842. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; and in the decision to publish the results.

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