Multicolor waveguide holography remains a challenge due to its inherent design complexity, compounded by the limited low-loss materials available in the optical range as well as challenges in nanofabrication. In this study, we first propose and experimentally demonstrate a multicolor, computer-generated hologram (CGH) in an all-dielectric waveguide metasurface system. Light beams from three different color laser sources (red, green, and blue) are coupled into the waveguide via a single-period grating without any beam splitters or prisms. A multicolor holographic image can be decoupled in the far field through a binary metasurface CGH without any lenses. This technology enables lens-free, ultraminiature augmented and virtual reality displays.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
A hologram encodes a three-dimensional (3D) image into a two-dimensional (2D) surface [1,2], having numerous applications in modern technologies such as optical computing, communication, information storage, and security [3,4]. Traditional holograms are generated by recording interference patterns formed by a reference wave and an object wave on some photosensitive medium—usually requiring specialized equipment and time-consuming positioning and alignment of the object . The alternative to traditional holograms is the computer-generated hologram (CGH), in which an interference pattern is synthesized digitally using readily available algorithms. Another benefit of the CGH is that it can be rapidly produced utilizing a variety of nanofabrication techniques, allowing the production of arbitrary images with high accuracy and at low cost [6–8].
While there have been numerous approaches to the fabrication of CGHs, subwavelength-diffractive elements and metamaterials (MMs) potentially provide the flexibility needed for precise control of the wavefront, leading to the capability of arbitrary image formation. MMs are artificially engineered materials with electromagnetic properties that relate to their subwavelength geometry as well as their inherent material properties [9–13]. Combined with advanced nanofabrication techniques, MMs can significantly expand the accessibility of material properties over the optical spectrum, enabling precise control of the phase, amplitude, polarization, and the nonlinear properties of electromagnetic waves [14–18]. CGHs implemented with metasurfaces (2D MMs) have been used to generate vivid holographic images, including single-color [19–22], multicolor, and full-color 2D or 3D images [23–27], and reprogrammable or reconfigurable images [28,29]; these examples vividly illustrate the possibilities of metasurface holography. Distinct from conventional optical components, metasurfaces rely on carefully designed nanoscale metal or dielectric elements to control the phase and amplitude of the optical wavefront [30–32].
To date, multicolor metasurface holograms have relied on excitation by free-space beams in either reflection or transmission modes [23–27,30–32]. This form of illumination is convenient for demonstrations and for certain applications, but not the best match for integrated photonics, where light can be generated, confined, and propagated in a compact, planar device. Such configurations favor the use of a waveguide mode as the reference wave, with a hologram integrated into the waveguide structure for off-plane projection. The basic concept of a waveguide hologram (WGH) was initially proposed by Suhara in 1976 . Rather than in the free space the incident beam acting as the reference wave, the light is first coupled into the waveguide structure, with the corresponding waveguide mode serving as the reference wave for a hologram designed for a given color. Therefore, compared with conventional holography and reflection or transmission metasurface holography, a WGH is more compact, tolerant to alignment error, and compatible with integrated photonics technology . In Suhara’s study, holograms were exposed to an interference pattern, with two primary images generated on both sides of the waveguide . Building on the early developments in CGHs, a series of studies on edge-illuminated, in-plane computer-generated waveguide holograms (IP-CGWH) followed in the 1990s [35–37], in which additional techniques were introduced. These techniques include interleaving of multiple holograms using gratings with different spatial frequencies  or orthogonal grooves , integrated-optics waveguide fabrication , coupled beam focus within a waveguide , and waveguide holographic read-only memories realization . Nevertheless, progress in IP-CGWHs has been hampered by limitations in fabrication capabilities, which leads to hologram feature sizes that are relatively large, resulting in poor image resolution with only simple monochromatic patterns [43,44]. Furthermore, the working wavelengths for the reported holograms are not in the optical range, but at longer wavelengths [45–47]. Importantly, most of the reported experimental demonstrations make use of in-plane, end-fire coupling, meaning the incident light sources come from either edge fibers  or built-in surface-emitting lasers , all of which require complicated design and demanding fabrication. One proposed solution to alleviate some of the challenges is to couple light external to the waveguide—from a free-space beam, for example—using a grating coupler that can be implemented by a variety of methods. Initial explorations have included a simple silicon (Si) grating waveguide coupler in silicon-on-insulator (SOI) at telecommunication wavelengths  and an efficient metal grating coupler working at 800 nm .
It must be pointed out that in most of the early studies on WGHs, the generated holographic images are just simple monochromatic patterns, such as dot arrays [35,39], rather than the complex colorful images that would be desired in most conceivable applications. While multicolor waveguide holography has attracted tremendous interest, the field remains in its infancy. For instance, in an eyewear display developed by Sony Corporation, a holographic waveguide was used to transfer a full-color image generated external to the waveguide, and project it to a user’s eye . Similarly, in a guided-wave illumination technique introduced by Hewlett-Packard Corporation (HP), based on external images, three groups of gratings were combined to render a 3D display . In a surface plasmon holography study, a 3D color image was generated, while the hologram was not computer generated but rather formed in the traditional way .
In this paper, we first theoretically propose and experimentally demonstrate a multicolor, CGH using out-of-plane excitation of an all-dielectric waveguide system. To realize multicolor waveguide holography, we propose a new design concept in which the three colors are mapped to the Fourier domain with distinct spatial frequencies; therefore, the coupling angle into the waveguide for each color varies and so does the decoupling angle. For the system structure design, we multiplex several wavelengths through a single grating into a waveguide and demultiplex them via a CGH. The coupling grating serves to combine wavelengths, obviating the need for external beam splitters or prisms. In free-space illumination schemes, path length variation across the hologram surface is limited to that achievable by free-space propagation, making it often difficult to separate the desired diffracted beam from the main beam or other diffracted orders. By contrast, the waves inside the guiding structure propagate orthogonal to the hologram surface, so that the phase variation of the reference wave is quite large. The structures for all three wavelengths are fabricated in a single lithography step, ensuring excellent registration and reproduction of features.
To form the multicolor WGH, the design objective is a pair of coupled diffraction elements, the first of which couples multiple out-of-plane optical light beams of various wavelengths into a waveguide slab and the second one decouples the waves off-plane by a CGH, generating a multicolor holographic image in free space. A schematic diagram of a multicolor computer-generated optical waveguide holographic system is shown in Fig. 1(a), and a 3D conceptual illustration is given in Fig. 1(b). A thin metasurface layer () that works as the core guiding medium is made of an electron beam resist ZEP (ZEP520A, ZEON Corporation, Japan), which exhibits low extinction at optical wavelengths. The air interface on top and a relatively thick layer () of silicon dioxide () are the cladding layers, while the bottom silicon (Si) substrate is a supporting buffer layer. For multicolor holography, red, green, and blue semiconductor laser sources enter the waveguide through a grating coupler incident at specific angles. The guided modes propagate through the slab waveguide and then are scattered by a CGH and decoupled out of the plane to generate a multicolor holographic image in the intended range of angles (the gray region), which can be observed by human eyes without any further image formation optics.
We divide the multicolor waveguide holography design into three interrelated parts: the waveguide and associated propagation modes; the grating coupler; and the CGH decoupler.
For the waveguide design, we apply a quasi-analytical model that serves as a first-pass analysis of the waveguide modes. To simplify this analysis, we replace the Si substrate with air to obtain guided modes for the core and cladding layers. Since the cladding layer is many wavelengths thick, the magnitude of the fields is negligible in the buffer layer. All the dielectric materials used in the multilayer system are assumed to be lossless to further facilitate the analytical model. To calculate the propagation modes in the waveguide, the optical transfer matrix method for a multilayer system is used . As shown in Fig. 2(a), when the waves are guided by the dielectric layers, no input fields exist as the mode is mainly confined to the metasurface slab, which means . On the other hand, the fields on the right side of a layer are related to those on the left side through a transfer matrix with coefficients of ; thus, . Since , the propagation constants for guided modes correspond to the coefficient case, and all possible modes can be obtained.
For a sufficiently thin guiding layer, only the fundamental mode for each color is considered, since it has the largest propagation constant and most of the energy is confined within the waveguide. The fundamental modes for the red (635 nm), green (532 nm), and blue (450 nm) (RGB) light sources in one of the designed systems are shown in Fig. 2(b), with all the fundamental propagation constants () listed.
The second design part is related to the grating coupler. Once the propagation constants of the fundamental modes for each color are obtained, the grating coupler period and the required incident angles can be determined. The grating period must satisfy the phase-matching equation with an integer. Here, is the wave vector related to the grating period through . is the component of the incident beam wave vector in free space, and the corresponding incident angle is determined by the equation , with being the free-space wave vector of the incident beam.
The -space diagram of the input grating coupler is shown in Fig. 2(c), indicating the directions of the reflected and transmitted beams. The radii of the concentric semicircles represent the amplitudes of the wave vectors in the air and waveguide regions, respectively . In the multicolor holographic case, in addition to coupling the beams into the metasurface waveguide, the single-period grating acts to combine the beams as well. For an input grating with a period of 280 nm, the incident angles for the three different colors are then determined to be (red), (green), and (blue) (indicated by the angle ). Here the negative sign of the incident angles means the light sources come from the right side of the gratings, which are specially designed such that the decoupled holographic images would be directed to the left side to avoid interference during optical characterization. As shown, there are two diffraction orders of waves in the transmission region for each light source, but only the st-order waves propagate to the hologram decoupler. It should be noted that no attempt was made here to optimize the efficiency of the grating couplers, so that the overall efficiency of the hologram is low (1% light output). The efficiency is mainly determined by the etch depth of the grating [56,57]. Matching the efficiencies of the three wavelengths is not possible with a single etch depth except at the limit of small etch depth and low efficiency. If larger efficiency is desired, the efficiency may be optimized for the wavelength for which the least power is available, and the power balanced between the laser sources to compensate for efficiency differences. Figure 2(d) shows a scanning electron microscope (SEM) image of a fabricated grating coupler.
The third part of the design is to synthesize the CGH for an arbitrary input object (or object wave), assuming the excitation by the propagating waves (guided reference waves). For the hologram decoupler design, the output angles from the hologram for different colors are mapped to disjoint regions of the colors’ spatial frequencies in a single Fourier space; when excited by the different color components, the hologram is designed to reassemble the components into a common field-of-view, creating a multicolor image. In principle, full-color images are possible based on mixing the RGB components; however, for this demonstration, we chose to demonstrate a simpler three-color image to avoid more intricate alignment. For the holograms in this study, the angles of the decoupled waves vary from to in the direction and from to in the direction, all measured from the surface normal [indicated by the angle in Fig. 1(a)]. The coupling between the vector of the guided waves (given by the propagation constants) and the free-space -space vector (given by the scattering angles) is considered. (See Supplement 1.)
We take a multicolor letter combination of the word as an example to illustrate the developed CGH algorithm. As shown in Fig. 3(a), the object has three colors spatially separated with red , green , and blue . In the Fourier space plot of Fig. 3(b) (rotated by 90°), the amplitudes of the spatial frequencies for the three-color letters are disjoint as designed, meaning the decoupling angles are separated in free space. Then the iterative Fourier transform algorithm (IFTA), also known as the Gerchberg–Saxton (GS) algorithm , is used to generate a binary hologram on this single space, shown in Fig. 3(c). The entire size of the designed CGH is with the smallest feature size of 100 nm. To validate the generated hologram, the original designed image has been successfully reproduced using a reconstruction algorithm, as shown in Fig. 3(d).
As for sample fabrication, a thick layer is deposited on a Si substrate through a plasma-enhanced chemical vapor deposition (PECVD) system, followed with a spin-coating process of ZEP e-beam resist. Then the grating coupler and hologram patterns are transfered to the ZEP metasurface by electron beam lithography (EBL). During the characterization process, a multicolor holographic image is reconstructed in the far field while illuminating the hologram with the guide waves. The generated holographic images could be observed without any visual tools (Fig. 4). The distance between the grating and the CGH is set to be around 1 mm for the demonstration. The binary state of each pixel of the CGH corresponds to the etch depth of the metasurface layer, which in turn determines whether or not each point in the CGH region of the metasurface is exposed in the EBL process. (See Supplement 1 for more details.)
A theoretical and experimental comparison of a group of holographic images can be found in Fig. 5, and an excellent agreement has been reached. The left column images are analytically reconstructed holographic images based on CGHs for multicolor images, while the right column figures are experimental holographic images generated from a designed metasurface sample and collected by a digital camera. (Details on the system design can be found in Supplement 1.)
Note that there is a slight image distortion, possibly caused by the collector lens in the imaging system. Compared to free-space transmission and reflection metasurface holography, which require large numbers of elements to realize better control over the amplitude and phase, the image resolution obtained in this study is relatively low. This is mainly due to the limitation of a binary hologram, as shown in the theoretical predictions in Fig. 5, where it can be seen that some pixels are missed. Though the current image quality is not ideal, the simplicity of design and fabrication of the method is still considered as a strength; i.e., a multicolor hologram can be achieved with a single patterning process, and enlarging the hologram size (e.g., ) definitely can improve the resolution, since more information could be stored in a CGH, while the compactness might be influenced. Besides, the material used in the study was not ideal considering the optical absorption for the red source is relatively high, as shown in Supplement 1. If another low-loss material can be found, it may significantly improve the efficiency. Furthermore, the mode shapes and beam sizes of the diode lasers used for illumination are those available from commercial sources and not necessarily optimized for our application. Even though the beam shape of green source is Gaussian, the beam profile for the red laser is annular and that for the blue source is elliptical. If better or more uniform sources can be used or if appropriate optics can be introduced to modify the incident beams, better performance should be achievable. On the other hand, it is noted that high efficiency is not necessary for all applications of holography, and many holograms are quite vivid even with relatively low efficiency [57,59,60]. To realize a 3D holographic display, better phase and amplitude control would provide better performance [24–27]. In this respect, nanoparticles can be used as dispersive MM elements to replace the current nondispersive dielectric binary holograms to achieve increased wavelength selectivity, which will be pursued in future work.
In this study, we have designed and experimentally verified out-of-plane excited multicolor optical waveguide holography using CGHs in an all-dielectric multilayer nanosystem. The reconstructed holographic images are diffracted into the intended range of angles and closely match the theoretical predictions. The authors believe that this is the first time that out-of-plane excited computer-generated waveguide holography has been realized in experiment. Moreover, complex multicolor holographic images have been obtained at working wavelengths in the optical range. Furthermore, all the materials used in the system are dielectric, which are compatible with current integrated photonics technologies. Different from transmission or reflection metasurface holography, the proposed multicolor CGH is one binary hologram, which greatly simplifies the fabrication processes, and the one-step patterning can be readily scaled to large-scale manufacturing at low costs. This type of designed metasurface system can find numerous applications, such as eyewear in augmented reality or for smart phone holographic display. Though we have demonstrated only static images generated by fixed holograms, this technique can be extended to dynamic control on the images by using active components such as spatial light modulators (SLM) or liquid crystals.
Air Force Office of Scientific Research (AFOSR) (FA9550-12-1-0491, FA9550-18-1-0187).
The authors thank Duke SMIF staff Jay Dalton and Dr. Talmage Tyler for helpful fabrication discussion. The authors also would like to express their gratitude to Jeff Wendorff for the bird (painted bunting) image usage.
See Supplement 1 for supporting content.
1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948). [CrossRef]
2. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963). [CrossRef]
3. B. J. Thompson, “Applications of holography,” Rep. Prog. Phys. 41, 633–674 (1978). [CrossRef]
4. T. H. Jeong, “Basic principles and applications of holography,” in Fundamentals of Photonics (Lake Forest College, 2010), pp. 381–417.
5. M. J. Richardson and J. D. Wiltshire, The Hologram Principles and Techniques (Wiley, 2018).
6. B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969). [CrossRef]
7. W. J. Dallas, “Computer-generated holograms,” Comput. Opt. Res. 41, 291–366 (1980). [CrossRef]
8. D. Abookasis and J. Rosen, “Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints,” J. Opt. Soc. Am. A 20, 1537–1545 (2003). [CrossRef]
9. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef]
10. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004). [CrossRef]
11. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef]
12. J. B. Pendry, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef]
13. J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013). [CrossRef]
14. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009). [CrossRef]
15. L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014). [CrossRef]
16. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016). [CrossRef]
17. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015). [CrossRef]
18. A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015). [CrossRef]
19. S. Larouche, Y.-J. Tsai, T. Tyler, N. Jokerst, and D. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11, 450–454 (2012). [CrossRef]
20. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013). [CrossRef]
21. W. T. Chen, K. Y. Yang, C. M. Wang, Y. W. Huang, G. Sun, I. D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014). [CrossRef]
22. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015). [CrossRef]
23. B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016). [CrossRef]
24. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). [CrossRef]
25. X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015). [CrossRef]
26. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2, e1601102 (2016). [CrossRef]
27. W. Wan, J. Gao, and X. Yang, “Full-color plasmonic metasurface holograms,” ACS Nano 10, 10671–10680 (2016). [CrossRef]
28. L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C.-W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017). [CrossRef]
29. S. C. Malek, H. S. Ee, and R. Agarwal, “Strain multiplexed metasurface holograms on a stretchable substrate,” Nano Lett. 17, 3641–3645 (2017). [CrossRef]
30. Y. Yifat, M. Eitan, Z. Iluz, Y. Hanein, A. Boag, and J. Scheuer, “Highly efficient and broadband wide-angle holography using patch-dipole nanoantenna reflectarrays,” Nano Lett. 14, 2485–2490 (2014). [CrossRef]
31. K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photon. 3, 514–519 (2016). [CrossRef]
32. L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3, 1504–1505 (2016). [CrossRef]
33. T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976). [CrossRef]
34. M. D. Drake, M. L. Lidd, and M. A. Fiddy, “Waveguide hologram fingerprint entry device,” Opt. Eng. 35, 2499–2505 (1996). [CrossRef]
35. M. Li, M. Hagberg, J. Bengtsson, N. Eriksson, and A. Larsson, “Optical waveguide fan-out elements using dislocated gratings for both outcoupling and phase shifting,” IEEE Photon. Technol. Lett. 8, 1199–1201 (1996). [CrossRef]
36. M. Li, A. Larsson, N. Eriksson, M. Hagberg, and J. Bengtsson, “Continuous-level phase-only computer-generated hologram realized by dislocated binary gratings,” Opt. Lett. 21, 1516–1518 (1996). [CrossRef]
37. M. Li, J. Bengtsson, M. Hagberg, A. Larsson, and T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996). [CrossRef]
38. M. Li, S. Kristjánsson, N. Eriksson, and A. Larsson, “Multiplexed computer-generated waveguide hologram using gratings with different spatial frequencies,” IEEE Photon. Technol. Lett. 8, 1653–1655 (1996). [CrossRef]
39. M. Li and S. Kristj, “Independent image replay in a multiplexed computer-generated waveguide hologram using interlaced gratings with orthogonal grooves,” IEEE Photon. Technol. Lett. 10, 385–387 (1998). [CrossRef]
40. D. A. P. Bulla, B.-H. V. Borges, M. A. Romero, N. Morimoto, and L. G. Neto, “Design and fabrication of SiO2/Si3N4 integrated-optics waveguides on silicon substrates,” IEEE Trans. Microwave Theory Tech. 50, 9–12 (2002). [CrossRef]
41. J. Backlund and C.-F. Carlstro, “Incoupling waveguide holograms for simultaneous focusing into multiple arbitrary positions,” Appl. Opt. 38, 5738–5746 (1999). [CrossRef]
42. T. Imai, T. Kurihara, S. Yagi, Y. Kurokawa, M. Endo, and T. Tanabe, “Orthogonal aperture multiplexing for multilayered waveguide holographic read-only memories,” Appl. Opt. 42, 7085–7092 (2003). [CrossRef]
43. S. Takushima, M. Uemukai, and T. Suhara, “GaInP red distributed-Bragg-reflector laser integrated with phase-shifted grating coupler for multispot focusing,” Jpn. J. Appl. Phys. 48, 030206 (2009). [CrossRef]
44. K. Uenishi, M. Uemukai, and T. Suhara, “Rotation-symmetric multispot focusing phase-shifted grating coupler for integrated semiconductor laser,” Jpn. J. Appl. Phys. 51, 058001 (2012). [CrossRef]
45. M. Li, P. Modh, S. Kristj, and A. Larsson, “Demonstration of computer-generated waveguide hologram on InGaAsP-InP waveguide for 1550-nm optical wavelength,” IEEE Photon. Technol. Lett. 9, 958–960 (1997). [CrossRef]
46. J. Bengtsson, J. Backlund, N. Eriksson, P. Modh, J. Vukusic, and A. Larsson, “Diffractive optics at the surface of light-emitting/receiving semiconductor components,” J. Mod. Opt. 47, 2455–2466 (2000). [CrossRef]
47. V. O. Smolsk, O. V. Smolski, E. C. Browy, E. G. Johnson, and Z. A. Shellenbarger, “Design and experimental study of the controlled two-dimensional-intensity profile of the output beam from a broad-area laser diode using grating outcouplers,” Opt. Eng. 51, 074204 (2012). [CrossRef]
48. P. Modh, J. Backlund, J. Bengtsson, A. Larsson, N. Shimada, and T. Suhara, “Multifunctional gratings for surface-emitting lasers: design and implementation,” Appl. Opt. 42, 4847–4854 (2003). [CrossRef]
49. M. T. W. Ang, G. T. Reed, A. P. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Blazed-grating couplers in unibond SOI,” Proc. SPIE 3896, 360–368 (1999). [CrossRef]
50. A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11, 4207–4212 (2011). [CrossRef]
51. T. Oku, K. Akutsu, M. Kuwahara, T. Yoshida, E. Kato, K. Aiki, I. Matsumura, S. Nakano, A. Machida, and H. Mukawa, “High-luminance see-through eyewear display with novel volume hologram waveguide technology,” SID Int. Symp. Dig. Tech. Pap. 46, 192–195 (2015). [CrossRef]
52. D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free 3D display,” Nature 495, 348–351 (2013). [CrossRef]
53. S. K. M. Ozaki and J.-I. Kato, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011). [CrossRef]
54. Z. Knittl, Optics of Thin Films (An Optical Multilayer Theory) (Wiley, 1976).
55. K. R. Harper, “Theory, design, and fabrication of diffractive grating coupler for slab waveguide,” Ph.D. thesis (Brigham Young University, 2003), p. 193.
56. S. Peng, H. Bertoni, and T. Tamir, “Analysis of periodic thin-film structures with rectangular profiles,” Opt. Commun. 10, 91–94 (1974). [CrossRef]
57. K. A. Winick, “Effective-index method and coupled-mode theory for almost-periodic waveguide gratings: a comparison,” Appl. Opt. 31, 757–764 (1992). [CrossRef]
58. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
59. M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
60. S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997). [CrossRef]