OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26620–26630
« Show journal navigation

Arbitrary birefringent metamaterials for holographic optics at λ = 1.55 μm

Yu-Ju Tsai, Stéphane Larouche, Talmage Tyler, Antonio Llopis, Matthew Royal, Nan M. Jokerst, and David R. Smith  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26620-26630 (2013)
http://dx.doi.org/10.1364/OE.21.026620


View Full Text Article

Acrobat PDF (2600 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

This paper presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, we present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of λ = 1.55 μm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices.

© 2013 Optical Society of America

1. Introduction

Artificially structured metamaterials allow for unprecedented control of light propagation [1

1. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

3

3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

]. Entirely new design concepts—such as transformation optics (TO) [4

4. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef] [PubMed]

,5

5. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

]—have been fueled by the realization that the material properties required for these new media may indeed be within reach. TO devices—such as invisibility cloaks [6

6. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2012). [CrossRef] [PubMed]

8

8. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009). [CrossRef]

], light harvesters [9

9. J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation Optics and Subwavelength Control of Light,” Science 337(6094), 549–552 (2012). [CrossRef] [PubMed]

], and optical “black holes” [10

10. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

]—require exquisite control over the anisotropy and spatial distribution of their magnetic and electric material properties; both these requisite properties and their precise control are difficult to achieve in conventional materials. Access to extreme material parameters can breathe new life into traditional optical devices, bringing advanced capabilities and providing a bridge between conventional and emerging methods such as TO. Herein, we demonstrate the impact of controlled anisotropy by engineering arbitrary birefringence in three-dimensional polarization-multiplexed diffractive optical elements (PMDOEs). The results indicate that anisotropic metamaterials can be leveraged for unique, manufacturable, high-quality optics and represent a viable foundation for future TO designs.

Optical materials that provide distinct functionality for different polarizations of incident light require controlled birefringence. The birefringence associated with crystals can be used to form polarization-dependent optical devices [11

11. F. Xu, J. E. Ford, and Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34(2), 256–266 (1995). [CrossRef] [PubMed]

,12

12. R. K. Kostuk, M. Kato, and Y.-T. Huang, “Polarization Properties Of Substrate-Mode Holographic Interconnects,” Appl. Opt. 29(26), 3848–3854 (1990). [CrossRef] [PubMed]

]; however, the magnitude and form of this birefringence is limited in naturally occurring crystals. Form-birefringence, produced by micro- or nano-structuring materials, can provide an alternative path towards enhanced and controlled birefringence [13

13. A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt. 49(23), 4355–4361 (2010). [CrossRef] [PubMed]

15

15. U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30(16), 2089–2091 (2005). [CrossRef] [PubMed]

]. PMDOEs, for example, have been previously demonstrated based on the form-birefringence associated with subwavelength gratings, which can be fabricated in a single layer diffractive optical element (DOE), either through electron beam lithography [16

16. M. S. Mirotznik, D. M. Pustai, D. W. Prather, and J. N. Mait, “Design of Two-Dimensional Polarization-Selective Diffractive Optical Elements with Form-Birefringent Microstructures,” Appl. Opt. 43(32), 5947–5954 (2004). [CrossRef] [PubMed]

,17

17. W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-Multiplexed Diffractive Optical Elements Fabricated by Subwavelength Structures,” Appl. Opt. 41(1), 96–100 (2002). [CrossRef] [PubMed]

] or femtosecond laser direct writing [18

18. W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14(9), 3785–3791 (2006). [CrossRef] [PubMed]

]. An interesting approach to PMDOEs was presented by Schonbrun et al., who used elliptical nanowires to demonstrate a wide range of birefringence values [19

19. E. Schonbrun, K. Seo, and K. B. Crozier, “Reconfigurable Imaging Systems Using Elliptical Nanowires,” Nano Lett. 11(10), 4299–4303 (2011). [CrossRef] [PubMed]

].

The use of form-birefringence represents an important step towards general artificial birefringent media, but is inherently a two-dimensional (2D) planar approach that does not lend itself to the more advanced volumetric design paradigms such as TO. Accessing extreme anisotropy through form-birefringent approaches requires high aspect ratio features, leading to challenging lithographic fabrication processes and limiting the practical number of phase levels. In fact, at the time of this study, only binary phase levels have been experimentally demonstrated for the elliptical nanowire medium described above [19

19. E. Schonbrun, K. Seo, and K. B. Crozier, “Reconfigurable Imaging Systems Using Elliptical Nanowires,” Nano Lett. 11(10), 4299–4303 (2011). [CrossRef] [PubMed]

], leading to a diffraction efficiency (DE) of 40.5% [20

20. B. Kress, Applied digital optics: from micro-optics to nanophotonics (Wiley, Chichester, U.K., 2009).

]. PMDOEs based on birefringent metamaterials can significantly enhance existing optical devices and systems where DOEs are used, such as imaging, spectroscopy, and beam shaping devices. Indeed, as photonic devices undergo continued miniaturization, the footprints of constituent optical components must decrease while retaining or advancing their functionality [21

21. B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and Spectral Light Shaping with Metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012). [CrossRef] [PubMed]

]. PMDOEs can translate to greater device densities for photonic systems; easier device alignment; improved energy efficiency; reduced fabrication costs; and reduced overall device size. Looking towards the future, a hint of the potential associated with controlled birefringent devices can be seen in a polarization-multiplexed TO device recently proposed by Danner et al. [22

22. A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5(6), 357–359 (2011). [CrossRef]

] and experimentally realized by Smolyaninova et al. The device consists of a planar waveguide that acts as a Luneburg lens for guided TM polarized waves and as a cloak for guided TE polarized waves [23

23. V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87(7), 075406 (2013). [CrossRef]

]. While using a constrained geometry, this device nevertheless reveals that new functionality can be found through the engineering of artificial materials.

The use of metamaterials enables a precise control of material properties at the micro- and nano-scale. Recent examples include a mid-infrared metamaterial hologram [24

24. S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11(5), 450–454 (2012). [CrossRef] [PubMed]

], in which the relatively small size of metallic, metamaterial elements enables efficient and precise control over the aperture, resulting in an increased pixel density and hence larger field-of-view. The strong scattering associated with metallic elements also enables the realization of meta-surfaces—single-layer structures that can be described by surface properties. For example, V-antenna arrays have been shown to offer great control over polarization conversion and have been used to fabricate cross-polarized DOEs in the mid- and near-infrared wavelengths [25

25. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012). [CrossRef] [PubMed]

,26

26. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]

]. Plasmonic nanorods have also been used to produce an achromatic quarter-wave plate at visible wavelengths [27

27. Y. Zhao and A. Alù, “Tailoring the Dispersion of Plasmonic Nanorods To Realize Broadband Optical Meta-Waveplates,” Nano Lett. 13(3), 1086–1091 (2013). [CrossRef] [PubMed]

]. Moreover, since birefringence and other properties of interest are determined by the geometry of the metallic inclusions—and not the material parameters of the underlying substrate or host material—there is much more freedom in material selection, which in turn allows given designs to be tailored to particular wavelength bands. An additional advantage of the metamaterial inclusions is that the number of phase levels that can be encoded into a device is significantly increased [28

28. Y. J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express 19(24), 24411–24423 (2011). [CrossRef] [PubMed]

], limited only by the fabrication precision. Indeed, this approach provides a distinct advantage over form-birefringent and sub-wavelength grating methods, which rely on the patterning of dielectric-only materials; the weaker dielectric contrast of these structures requires high-aspect ratios, posing a fabrication challenge, and does not allow variation in all three dimensions simultaneously.

In this paper, we demonstrate an approach that provides controlled birefringence throughout a volume for incorporation into advanced metamaterial optical devices. Our metamaterial design allows a precise and independent control of refractive indices for the two orthogonal linear polarizations. To illustrate our approach, we present metamaterial (MM) optical components that combine diffractive optics with polarization selectivity, or metamaterial polarization-multiplexed diffractive optical elements (MM-PMDOEs). Specifically, we present a polarization-multiplexed hologram and a polarization-multiplexed diffraction grating, both operating at a wavelength of 1.55 μm. We demonstrate that these devices provide much greater polarization contrast ratios (x-925:1 and y-910:1) and a significantly larger number of phase levels (20) than previously reported optical devices. The larger number of phase levels can lead to a DE approaching 100%. Furthermore, we demonstrate that the approach presented herein lends itself to the fabrication of multilayer 3D devices.

2. Design

The design of the PMDOEs is based on non-resonant, metallic, cross-shaped metamaterial elements embedded in a volume of background dielectric material and fabricated using a multilayer lithographic process. The cross metamaterial element, when considered as an infinite medium, has effective material parameters that exhibit relatively low losses and can easily be used to introduce anisotropy, producing arbitrary birefringence that can be simply determined through two-dimensional (2D) interpolations. By varying the length of the cross arms in the x-direction (Lx) and in the y-direction (Ly), birefringence can be engineered locally at the position of each individual element. As shown in Fig. 1(a)
Fig. 1 Engineered birefringence using metamaterial cross elements. (a) Schematics of the metamaterial unit cell design. The unit cell size is 250 nm × 250 nm × 100 nm. The geometry of metamaterial cross element is defined by arm lengths (Lx and Ly), line-width of 30 nm and thickness of 30 nm. The electric field is oriented in the x-y plane and the electromagnetic wave propagates along the z direction. (b) By controlling the arm lengths of Lx and Ly in each individual crosses, we can obtain a wide range of birefringence. . Each line is separated by equally spaced values ΔLx or ΔLy of 18.33 nm. In this work, we chose moderate values of refractive indices bounded inside the red box. (c) Imaginary parts of refractive indices—κx (left) and κy (right).
, each cell consists of a 30 nm thick Au (εAu=-132+12.65i [29

29. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]

]) cross-shaped inclusion and a 100 nm thick benzocyclobutene (BCB) polymer dielectric host (εBCB=2.356). Both the line width and thickness of the cross-shaped inclusion are 30 nm. The effective complex refractive indices (n + iκ) of the metamaterial cross elements were obtained using a standard scattering (S-) parameter retrieval method based on full-wave numerical simulations performed using a commercial finite element software—COMSOL Multiphysics [30

30. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]

]. This procedure treats the inhomogeneous metamaterial layer as an effective homogenous medium described by constitutive parameters such as the electric permittivity and magnetic permeability. For such a simple case, analytical expressions can be utilized to describe the optical properties of the medium. The effective constitutive parameters can then be obtained by comparing the S-parameters obtained from the simulated structures with those calculated for a planar slab of material.

An important feature of the metamaterial design is the possibility to control for the two orthogonal linear polarizations of light, by controlling the in-plane refractive indices, with a high degree of independence. Figure 1(b) shows a 2D birefringence map, in which each blue vertical or horizontal line corresponds to a fixed Ly or a fixed Lx, respectively, with values from 40 nm to 205 nm. Each line is separated by equally spaced values ΔLx or ΔLy of 18.33 nm. Any combination of nx and ny refractive indices between lines can be obtained using linear interpolation to select the proper values of Lx and Ly. The increments of refractive indices are not linear with the arm lengths; that is, the change in refractive indices between each line becomes larger when Lx or Ly increases. Therefore, the fabrication tolerance is tighter for larger index contrasts. In light of the practical fabrication tolerance as well as the absorption concerns, we designed the hologram and the grating using a moderate index contrast of Δn = 1.94, as shown within the red box in Fig. 1(b). Figure 1(c) shows the imaginary parts of refractive indices and indicates a very high degree of independence of the imaginary parts of the refractive indices, with κx and κy depending mostly on nx and ny, respectively.

PMDOEs can therefore be realized with 1D or 2D phase panels in which each pixel represents a specific birefringence. Metamaterial elements with a specific birefringence can locally alter the incident light and control the phase delay of the transmitted light based on the polarization state. However, a single metamaterial layer is not sufficient to provide enough phase contrast; in our design, a single layer can provide a maximum phase contrast of 0.79 radians, according toΔϕ=Δnkd. To optimize the diffraction efficiency, an 8 layer metamaterial design is thus required to provide the optimal 2π phase contrast [31

31. B. Goebel, L. L. Wang, and T. Tschudi, “Multilayer technology for diffractive optical elements,” Appl. Opt. 35(22), 4490–4493 (1996). [CrossRef] [PubMed]

]. To illustrate the level of control possible in a 2D phase panel using the artificially birefringent metamaterial, we design a computer-generated, polarization-multiplexed hologram. A polarization-multiplexed hologram can generate two independent diffraction patterns (images) for the two orthogonal linear polarizations of light; our design methodology is illustrated in Fig. 2
Fig. 2 Design flowchart of metamaterial based polarization multiplexed hologram. (a) Desired patterns for x-and y-polarization. (b) The phase holograms that are generated independently from the two desired patterns. (c) A Scanning electron micrograph showing a multilayer metamaterials construction combining the two phase holograms into a single optical component. (d) The simulated reconstructions of the 8 layer metamaterial holograms for the two orthogonal linear polarizations. *The Blue Devil is a registered trademark of Duke University
. The process started from two individual images down-sampled to 300 × 300 pixels. To calculate the corresponding phase holograms, we independently implemented the Gerchberg-Saxton iterative algorithm for each image [32

32. R. W. Gerchber and W. O. Saxton, “Pratical Algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

]. The two phase holograms can then be combined into a single multilayer metamaterial device, with each pixel consisting of 10 × 10 cross-shaped metamaterial elements designed to produce the proper birefringence. Since the phase delay depends not only on the refractive index, but also on the thickness of the hologram, the polarization multiplexed hologram required 8 metamaterial layers to achieve the optimum 2π phase radians for the chosen index range. As a final step in the design, we included the loss and impedance mismatch in the calculated reconstructions of our designed hologram based on scalar diffraction theory. In this design, the real part of the refractive index for the two orthogonal linear polarizations is independently controlled. The imaginary part of the refractive index, however, cannot be independently controlled for the two polarizations; therefore, the amplitude modulation for one polarization is slightly correlated to the phase modulation for the other polarization. The correlation in amplitude modulation may cause some degree of crosstalk between the two polarizations; however, as seen in Fig. 2(d), the crosstalk is found to be extremely small in the reconstructed images. The hologram design approach can readily be applied to other polarization-multiplexed optical elements, such as Fresnel zone plates, which can be constructed to form lenses with tunable focal lengths [33

33. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett. 35(3), 336–338 (2010). [CrossRef] [PubMed]

] and may have particular relevance in holographic microscopy [34

34. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008). [CrossRef]

].

To better assess the performance of the fabricated MM-PMDOEs, a polarization multiplexed blazed diffraction grating was designed as a means to quantify the refractive index contrast and the polarization contrast ratio. A polarization-multiplexed grating can split signals based on the polarization state of incident light, a capability having widespread potential applications in optical switching [35

35. T. Ikeda and O. Tsutsumi, “Optical Switching and Image Storage by Means of Azobenzene Liquid-Crystal Films,” Science 268(5219), 1873–1875 (1995). [CrossRef] [PubMed]

], 3D displays [36

36. H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the Art in Stereoscopic and Autostereoscopic Displays,” Proc. IEEE 99(4), 540–555 (2011). [CrossRef]

], and polarization spectroscopy [37

37. T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization Spectroscopy of Single Fluorescent Molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999). [CrossRef]

]. As can be seen in Fig. 3(a)
Fig. 3 Scanning electron micrograph of the fabricated eight layer samples. (a,b) Polarization-multiplexed blazed diffraction grating. The refractive index profiles for x-polarization (top) and for y-polarization (bottom) are plotted in (a) to emphasize the two distinct diffraction periods—Λx = 8 μm and Λy = 6 μm. (c) Polarization-multiplexed computer-generated hologram. The images were taken after the lift-off process.
, the blazed grating is designed such that it has two diffraction periods—Λx=8μm;Λy=6μm—for the two orthogonal linear polarization states. This polarization multiplexed grating has its + 1st diffraction peak located at 11.2 degrees for an x-polarized beam and at 15 degrees for a y-polarized beam. Therefore, the polarization multiplexed grating splits the incoming beam by polarization, steering the two orthogonal polarizations to different locations. The total width of the grating is 744 μm, which is a common multiple of both diffraction periods. With this polarization multiplexed grating, the polarization contrast ratio is
Polarizationcontrastratio{P+1(Λx)P+1(Λy),forx-polarizedbeamP+1(Λy)P+1(Λx),fory-polarizedbeam
(1)
where P+1(Λx)is the peak intensity of the + 1 diffracted order spot that is located at 11.2 degrees created by the grating with Λx=8μmand P+1(Λy)is the peak intensity of the + 1 diffracted order spot that is located at 15 degrees created by the grating with Λy=6μm. In the absence of crosstalk, there should be no diffracted spot at 15 degrees when illuminating the grating with an x-polarized beam, or a peak at 11.2 degrees when illuminating the grating with a y-polarized beam.

3. Fabrication

Fabrication of the sample began with a 2-inch diameter double-side polished silicon wafer, of <111> orientation, with a resistivity of 30 Ω-cm and a nominal thickness of 500 μm. Alignment marks were first patterned using electron-beam lithography (EBL, Elionix ELS-7500 EX) of ZEP 520A resist, followed by electron-beam evaporation of Cr (3 nm) / Au (100 nm). Patterning was completed using the lift-off technique, with N-Methyl-2-pyrrolidone used to dissolve the electron-beam resist. A 50nm thick layer of benzocyclobutene (BCB, Dow Chemical) was then spin-coated and cured at 210°C under vacuum, forming the first dielectric half-layer (while the vertical period of the multilayer metamaterial is 100 nm, the first and last spacer layers were designed to be 50 nm to maintain symmetry). BCB was chosen as the dielectric spacer layer, because this material is self-planarized and nearly transparent to the wavelength of interest. The first metal layer of both the grating and hologram were then patterned using EBL. In order to pattern the large areas of the grating (744 μm × 750 μm) and hologram (750 μm × 750 μm), it was necessary to stitch together multiple fields of view in the EBL. The smallest field of view available (75 μm × 75 μm) was used to achieve maximum resolution, thus a 10 × 10 array of fields were stitched to form each device. Metal evaporation and lift-off were again used to form the metamaterial pattern, with a metal stack of Cr (3 nm) / Au (30 nm) used. A BCB film was then spin-coated to a thickness of 100 nm and cured, forming the first full dielectric spacer layer. Subsequent EBL patterning and BCB depositions were repeated to form the 8 layer grating and hologram. Both the grating and hologram were measured throughout the fabrication process at 2, 4, 6, and 8 layers. Additionally, each layer of the grating and hologram was inspected using scanning electron microscopy (SEM) to verify that the dimensions of the patterned metamaterial elements matched the design. As a final step after the eight layer fabrication process, we covered the sample with a gold aperture to block the light hitting outside of the patterned areas. Figure 3 shows scanning electron micrographs (SEM) of the fabricated 8 layer grating and hologram. The standard deviation of the fabricated arm lengths of the crosses is about 3.3 nm; the effective number of phase levels, limited by fabrication error can therefore be estimated to be around 20. Also, based on the SEM images taken from every two layers, we estimate the misalignments between layers to be less than 500 nm. Such misalignments reduce the + 1st order diffraction efficiency from 90% to 85% for the x-polarization refractive index profile and from 88% to 82% for the y-polarization refractive index profile, according to a simulation that considers the loss and the impedance mismatch. The + 1st order diffraction efficiency is defined by the power measured at the + 1st diffracted order normalized to the total transmitted power.

4. Experimental characterization

To characterize the polarization multiplexed hologram, we illuminated the hologram with a near-infrared laser (λ = 1.55 μm) using a 2-f imaging system (f = 40 mm). A collimator (Thorlabs F810FC-1550) was placed at the output port of the laser, followed by a linear polarizer (Thorlabs LPNIR100) and a half-wave plate. The half-wave plate is mounted on a motorized rotation stage to precisely rotate the linear polarizations of the beam that illuminates the hologram. An infrared camera (Goodrich SU320MS-1.7RT InGaAs Snapshot MiniCamera) was placed at the back focal plane of the lens. A background image was taken in the absence of laser illumination and subtracted from every hologram image. The experimental setup for the grating characterization is similar except that the camera was placed 8 cm behind the sample with no lens in between. Figure 4
Fig. 4 Characterization results of the 8 layer polarization multiplexed hologram. Measured images of the + 1st diffracted order of the hologram for linear polarizations at the specified orientation angles. All images were normalized by their maximum values. The three images at the bottom (30, 45, 60 degrees) are enhanced with a Gamma-filter (γ = 0.75) to highlight the crosstalk. *The Blue Devil is a registered trademark of Duke University
shows images generated by the hologram in the + 1st diffracted order collected with an IR camera for a series of polarization angles. The result shows very little crosstalk between the two images for the two orthogonal linear polarizations (0 and 90 degrees).

Figure 5(a)
Fig. 5 Characterization results of an 8 layer metamaterial polarization multiplexed grating. (a) Images captured at the + 1st diffracted order for polarization angles at 0, 45, and 90 degrees (from top to bottom), respectively. (b) Surface plots of the line profiles across the peaks of the spots for polarization angles from 0 to 90 degrees. (c) The relative intensity for two linear polarizations as a function of polarization angles. (d) The experimentally obtained polarization contrast ratio for x-polarization (red circle) and y-polarization (blue circle).
shows images generated by the diffraction grating captured at the + 1st diffracted order for polarization angles at 0, 45, and 90 degrees (from top to bottom), respectively. Figure 5(b) is a surface plot that combines all the line profiles across the peaks of the spots from the + 1st diffracted order for polarization angles varying from 0 to 90 degrees. Figure 5(c) shows the relative intensities measured at the + 1st diffracted order for the x-polarization index profile (red) and for the y-polarization index profile (blue). The relative intensities were calculated by integrating the intensity of the main lobe and the first side lobes and normalizing them to their maximum values while the polarization was varied from 0 to 360 degrees, every 1 degree. The slightly different peak intensities between the two orthogonal polarizations may be the result of layer-to-layer misalignments and unequal index contrasts caused by the unequal offsets in arm lengths of the fabricated metamaterial crosses. Because of the correlation between the imaginary parts of the two spatial refractive index components, we expect to observe some degrees of crosstalk between the two polarization gratings. To quantitatively investigate the crosstalk, we adjusted the laser power to have a dynamic range large enough to capture the two + 1st order diffraction spots for two linear polarizations and obtained the polarization contrast ratio according to Eq. (1). The measured polarization contrast ratio shown in Fig. 5(d) was measured to be 925:1 for x-polarized light and 910:1 for y-polarized light. The actual polarization contrast ratios may be slightly higher than these numbers since the measurements were affected by the side lobes from the neighboring diffracted orders. The measured + 1st order efficiency normalized to the transmitted power is 29% for x-polarization and 27% for y-polarization. The measured + 1st order efficiency is significantly smaller than anticipated, implying that the index contrast of the fabricated structure is different from the expected value. Using the ratio of the + 1st order efficiency to the −1st order efficiency and comparing with the ratio obtained from simulations, we can extract the index contrast of the fabricated structure. This extraction procedure is valid because the ratio of the + 1st order efficiency to the −1st order efficiency is a monotonically increasing function of the index contrast. The experimentally extracted index contrast of the fabricated 8 layer metamaterial grating is Δnx = 0.86~0.91 and Δny = 0.96~1.05. The uncertainties of the index contrast were estimated based on the uncertainties in the layer-to-layer misalignments considered in numerical simulations. In the simulations, we assumed a worst case scenario in which the misalignments were accumulated to ± 500 nm. The extracted index contrast is significantly smaller than that theoretical predicted Δn = 1.94. This difference can be attributed to the offsets in the arm lengths and the rounded corners in the fabricated structures. According to simulations, the rounded corner (radius of curvature = 14 nm) in the cross-shaped element causes the index contrast drop from 1.94 to 1.40. Therefore, to further increase the index contrast, a fabrication method with higher accuracy and the ability to obtain sharp edges is essential.

5. Concluding remarks

In conclusion, we have designed, fabricated and experimentally characterized a polarization multiplexed computer generated hologram and a polarization multiplexed blazed diffraction grating for λ = 1.55 μm. This MM-PMDOE is compact and exhibits polarization multiplexing with very high polarization contrast ratios (x-925:1 and y-910:1). Although the index contrast of this MM-PMDOE is not significantly superior to the traditional approaches such as subwavelength gratings, this new approach can be further optimized in the design and the fabrication to further increase the index contrast. Also, the fabrication time can be significantly reduced with the 193nm immersion lithography, which is capable of producing feature sizes similar to what we utilize. In addition, multilayer MM-PMDOEs enable variation of MM inclusions in three dimensions, and are scalable to larger areas using standard commercial nanopatterning equipment, opening up the possibility to mass produce functionalized micro-scale optical devices.

Acknowledgments

References and links

1.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

2.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration Of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

3.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

4.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef] [PubMed]

5.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

6.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2012). [CrossRef] [PubMed]

7.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009). [CrossRef] [PubMed]

8.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009). [CrossRef]

9.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation Optics and Subwavelength Control of Light,” Science 337(6094), 549–552 (2012). [CrossRef] [PubMed]

10.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

11.

F. Xu, J. E. Ford, and Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34(2), 256–266 (1995). [CrossRef] [PubMed]

12.

R. K. Kostuk, M. Kato, and Y.-T. Huang, “Polarization Properties Of Substrate-Mode Holographic Interconnects,” Appl. Opt. 29(26), 3848–3854 (1990). [CrossRef] [PubMed]

13.

A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt. 49(23), 4355–4361 (2010). [CrossRef] [PubMed]

14.

F. Xu, R. C. Tyan, P. C. Sun, Y. Fainman, C. C. Cheng, and A. Scherer, “Form-birefringent computer-generated holograms,” Opt. Lett. 21(18), 1513–1515 (1996). [CrossRef] [PubMed]

15.

U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30(16), 2089–2091 (2005). [CrossRef] [PubMed]

16.

M. S. Mirotznik, D. M. Pustai, D. W. Prather, and J. N. Mait, “Design of Two-Dimensional Polarization-Selective Diffractive Optical Elements with Form-Birefringent Microstructures,” Appl. Opt. 43(32), 5947–5954 (2004). [CrossRef] [PubMed]

17.

W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-Multiplexed Diffractive Optical Elements Fabricated by Subwavelength Structures,” Appl. Opt. 41(1), 96–100 (2002). [CrossRef] [PubMed]

18.

W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14(9), 3785–3791 (2006). [CrossRef] [PubMed]

19.

E. Schonbrun, K. Seo, and K. B. Crozier, “Reconfigurable Imaging Systems Using Elliptical Nanowires,” Nano Lett. 11(10), 4299–4303 (2011). [CrossRef] [PubMed]

20.

B. Kress, Applied digital optics: from micro-optics to nanophotonics (Wiley, Chichester, U.K., 2009).

21.

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and Spectral Light Shaping with Metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012). [CrossRef] [PubMed]

22.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5(6), 357–359 (2011). [CrossRef]

23.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87(7), 075406 (2013). [CrossRef]

24.

S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11(5), 450–454 (2012). [CrossRef] [PubMed]

25.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012). [CrossRef] [PubMed]

26.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]

27.

Y. Zhao and A. Alù, “Tailoring the Dispersion of Plasmonic Nanorods To Realize Broadband Optical Meta-Waveplates,” Nano Lett. 13(3), 1086–1091 (2013). [CrossRef] [PubMed]

28.

Y. J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express 19(24), 24411–24423 (2011). [CrossRef] [PubMed]

29.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]

30.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]

31.

B. Goebel, L. L. Wang, and T. Tschudi, “Multilayer technology for diffractive optical elements,” Appl. Opt. 35(22), 4490–4493 (1996). [CrossRef] [PubMed]

32.

R. W. Gerchber and W. O. Saxton, “Pratical Algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

33.

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett. 35(3), 336–338 (2010). [CrossRef] [PubMed]

34.

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008). [CrossRef]

35.

T. Ikeda and O. Tsutsumi, “Optical Switching and Image Storage by Means of Azobenzene Liquid-Crystal Films,” Science 268(5219), 1873–1875 (1995). [CrossRef] [PubMed]

36.

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the Art in Stereoscopic and Autostereoscopic Displays,” Proc. IEEE 99(4), 540–555 (2011). [CrossRef]

37.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization Spectroscopy of Single Fluorescent Molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999). [CrossRef]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(230.5440) Optical devices : Polarization-selective devices
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: September 13, 2013
Revised Manuscript: October 10, 2013
Manuscript Accepted: October 13, 2013
Published: October 28, 2013

Citation
Yu-Ju Tsai, Stéphane Larouche, Talmage Tyler, Antonio Llopis, Matthew Royal, Nan M. Jokerst, and David R. Smith, "Arbitrary birefringent metamaterials for holographic optics at λ = 1.55 μm," Opt. Express 21, 26620-26630 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26620


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature470(7334), 369–373 (2011). [CrossRef] [PubMed]
  2. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration Of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005). [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  4. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010). [CrossRef] [PubMed]
  5. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  6. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater.12(1), 25–28 (2012). [CrossRef] [PubMed]
  7. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009). [CrossRef] [PubMed]
  8. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009). [CrossRef]
  9. J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation Optics and Subwavelength Control of Light,” Science337(6094), 549–552 (2012). [CrossRef] [PubMed]
  10. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009). [CrossRef]
  11. F. Xu, J. E. Ford, and Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt.34(2), 256–266 (1995). [CrossRef] [PubMed]
  12. R. K. Kostuk, M. Kato, and Y.-T. Huang, “Polarization Properties Of Substrate-Mode Holographic Interconnects,” Appl. Opt.29(26), 3848–3854 (1990). [CrossRef] [PubMed]
  13. A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt.49(23), 4355–4361 (2010). [CrossRef] [PubMed]
  14. F. Xu, R. C. Tyan, P. C. Sun, Y. Fainman, C. C. Cheng, and A. Scherer, “Form-birefringent computer-generated holograms,” Opt. Lett.21(18), 1513–1515 (1996). [CrossRef] [PubMed]
  15. U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett.30(16), 2089–2091 (2005). [CrossRef] [PubMed]
  16. M. S. Mirotznik, D. M. Pustai, D. W. Prather, and J. N. Mait, “Design of Two-Dimensional Polarization-Selective Diffractive Optical Elements with Form-Birefringent Microstructures,” Appl. Opt.43(32), 5947–5954 (2004). [CrossRef] [PubMed]
  17. W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-Multiplexed Diffractive Optical Elements Fabricated by Subwavelength Structures,” Appl. Opt.41(1), 96–100 (2002). [CrossRef] [PubMed]
  18. W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express14(9), 3785–3791 (2006). [CrossRef] [PubMed]
  19. E. Schonbrun, K. Seo, and K. B. Crozier, “Reconfigurable Imaging Systems Using Elliptical Nanowires,” Nano Lett.11(10), 4299–4303 (2011). [CrossRef] [PubMed]
  20. B. Kress, Applied digital optics: from micro-optics to nanophotonics (Wiley, Chichester, U.K., 2009).
  21. B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and Spectral Light Shaping with Metamaterials,” Adv. Mater.24(47), 6300–6304 (2012). [CrossRef] [PubMed]
  22. A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011). [CrossRef]
  23. V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B87(7), 075406 (2013). [CrossRef]
  24. S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater.11(5), 450–454 (2012). [CrossRef] [PubMed]
  25. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science335(6067), 427 (2012). [CrossRef] [PubMed]
  26. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science334(6054), 333–337 (2011). [CrossRef] [PubMed]
  27. Y. Zhao and A. Alù, “Tailoring the Dispersion of Plasmonic Nanorods To Realize Broadband Optical Meta-Waveplates,” Nano Lett.13(3), 1086–1091 (2013). [CrossRef] [PubMed]
  28. Y. J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express19(24), 24411–24423 (2011). [CrossRef] [PubMed]
  29. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt.22(7), 1099–20 (1983). [CrossRef] [PubMed]
  30. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002). [CrossRef]
  31. B. Goebel, L. L. Wang, and T. Tschudi, “Multilayer technology for diffractive optical elements,” Appl. Opt.35(22), 4490–4493 (1996). [CrossRef] [PubMed]
  32. R. W. Gerchber and W. O. Saxton, “Pratical Algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
  33. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett.35(3), 336–338 (2010). [CrossRef] [PubMed]
  34. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics2(3), 190–195 (2008). [CrossRef]
  35. T. Ikeda and O. Tsutsumi, “Optical Switching and Image Storage by Means of Azobenzene Liquid-Crystal Films,” Science268(5219), 1873–1875 (1995). [CrossRef] [PubMed]
  36. H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the Art in Stereoscopic and Autostereoscopic Displays,” Proc. IEEE99(4), 540–555 (2011). [CrossRef]
  37. T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization Spectroscopy of Single Fluorescent Molecules,” J. Phys. Chem. B103(33), 6839–6850 (1999). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited