Slab waveguides are called symmetric slab waveguides when the refractive indexes of the substrate and superstubstrate match. Chen, W.T. Zheng, G.; Mhlenbernd, H.; Kenney, M.; Li, G.; Zentgraf, T.; Zhang, S. Metasurface holograms reaching 80% efficiency. xbbRc`b``3 This perhaps will then make the EM theory picture less shocking. Here we demonstrate ultrathin highly efficient crystalline titanium dioxide metalenses at blue, green, and red wavelengths ( = 453 nm, 532 nm, and 633 nm, respectively) based on symmetric slab waveguide theory. Case (b,c): $k_0n_1 < k_0n_3 < \beta < k_0n_2$. = Alright, here we are at the precipice of understanding waveguide modes via EM theory! In order to be human-readable, please install an RSS reader. A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. Before ; Oh, J.; Mishra, I.; Devlin, R.C. Owing to their simplicity, slab waveguides are often used as toy models but also find application in on-chip devices like arrayed waveguide gratings and acousto-optic filters and modulators.. ; Ye, J.S. This is the same for each of the solutions with guided modes, as in cases (b) and (c): the wave is being totally internally reflected at each interface. ; Sanjeev, V.; Khorasaninejad, M.; Shi, Z.; Lee, E.; Capasso, F. A broadband achromatic metalens for focusing and imaging in the visible. As shown in, Similarly deviations from theoretical FWHMs of metalenses designed for. Feature and Z.W. ; Capasso, F. Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging. Chen L, Zhao L, Hao Y, Liu W, Wu Y, Wei Z, Xu N, Qin S, Yang X, Liu H. Nanomaterials (Basel). ; WritingReview & Editing, Z.W., J.G., F.W., H.M. and H.L. Now, we can see what happens when $\beta = k_0n_1$. -, Arbabi A., Horie Y., Ball A.J., Bagheri M., Faraon A. Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays. 240 26 Guangzhou Key Laboratory for Special Fiber Photonic Devices, South China Normal University, Guangzhou 510006, China, Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006, China. A symmetric slab waveguide is given with the parameters as shown in the following figure (Fig. endstream endobj 264 0 obj <>/Size 240/Type/XRef>>stream Hence we have: \begin{equation} \frac{\partial^2E}{\partial{x^2}} \gamma^2E = 0 \end{equation}. ; Staude, I.; James, A.; Dominguez, J.; Liu, S.; Campione, S.; Subramania, G.S. articles published under an open access Creative Common CC BY license, any part of the article may be reused without We can derive the exact conditions by looking at the following figure: As we might imagine, if the guiding layer thickness is small, then only a few modes will be allowed to propagate, and vice versa. methods, instructions or products referred to in the content. ; et al. Editors Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. 2016 Nov 9;16(11):7229-7234. doi: 10.1021/acs.nanolett.6b03626. The slab waveguide consists of three layers of materials with different dielectric constants . However, in the core, the solution is sinusoidal. modes. In this case, the $\beta$-vector is still greater than the vectors in the two cladding regions, so these have exponential solutions. which implies an oscillatory form of the solution such as the general form $E = Acos(hx) + Bsin(hx)$. The coordinate system relative to the slab, the designation of the dielectric constants, and the orientation of the optical axis. Epub 2019 Dec 11. 3.17). b. This site needs JavaScript to work properly. Now, then, comparing Equations \eqref{origin} and \eqref{new}, we can find two solutions: \begin{equation} tan(ha) = \frac{\gamma{a}}{ha},~symmetric~modes \end{equation}, \begin{equation} tan(ha) = -\frac{ha}{\gamma{a}},~antisymmetric~modes \end{equation}. A Thermal Tuning Meta-Duplex-Lens (MDL): Design and Characterization. We can then define the vacuum wavevector $k_0$ as $k_0^2=\omega^2/c^2$ and rewrite the wave equation as: \begin{equation} \frac{\partial^2{E(x)}}{\partial{x^2}} + (n_j^2k_0^2-\beta^2)E*x( = 0 \end{equation}. 2) Waveguide mode simulation using Lumerical MODE. Here we can see an unfortunate physical interpretation of this solution: as $|x| \rightarrow \infty$, the field E(x) also goes to infinity, which is of course physically not possible as that would imply infinite energy. From trigonometry, we can rewrite the cotangent function as: \begin{equation} cot(2ah) = \frac{1}{2}[\frac{1}{tan(ha)} tan(ha)] \label{new}\end{equation}. Sensors (Basel). A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. 0000001656 00000 n Optical axis of the hyperbolic medium is normal to the slab plane. crystalline titanium dioxide; integrated devices; metalens; metasurface; phase modulation. The interesting case of an anisotropic slab waveguide with the optical axis located in the plane of the slab will be presented in Part II of this paper. These are unconfined modes. For this problem, we can make the weak guiding approximation, which means that the discontinuity in $\epsilon$ can be neglected and thus that the derivative term $\frac{d}{dx}(E_x\frac{d}{dx}ln\epsilon) \rightarrow 0$, since the derivative would be zero over a constant value of $\epsilon$. TE and TM Modes of Propagation in Symmetric Slab Waveguides Answer to An asymmetric slab waveguide is shown in Figure 13.26. Khorasaninejad, M.; Crozier, K.B. This may occur in silica glass waveguides or in semiconductor laser heterostructures. doi: 10.1021/acs.nanolett.5b01727. Oscillating field component E y z a u y j z x m m m ( , ) ( )exp( ) E The electric field in a symmetric dielectric waveguide is harmonic within the slab and exponentially decaying outside Since we found before the transfer matrix across a boundary, we can just write the results for what the transfer matrix across the waveguide should be here. We will begin with the case of TE waves (s-polarization) in a symmetric waveguide to make our lives easier. Using Equations \eqref{sym} and \eqref{anti-sym}, we can find the conditions for the symmetric and the antisymmetric modes. ; Sun, S.; et al. In this paper, we only consider symmetric planar dielectric waveguide, which is the cover and . Multidisciplinary Digital Publishing Institute (MDPI). not an exact expression)? ; Khorasaninejad, M.; Zhu, A.Y. We find that, in spite of the symmetry of the . We can redraw this picture as a bunch of plane waves propagating directly down the fiber that add in the transverse direction to be a Gaussian. for a symmetric slab (not so for asymmetric) Mirror waveguide Dielectric waveguide 24. ; Oh, J.; Devlin, R.C. Polarization-independent silicon metadevices for efficient optical wavefront control. 0000044166 00000 n metasurface; metalens; phase modulation; integrated devices; crystalline titanium dioxide, Photonics: Optical Electronics in Modern Communications. ; Decker, M.; Neshev, D.N. Khorasaninejad, M.; Shi, Z.; Zhu, A.Y. 2020 Sep 17;10(9):1864. doi: 10.3390/nano10091864. The Feature Paper can be either an original research article, a substantial novel research study that often involves Now then, we have to think back to our definitions of s- and p-polarization, as the form of the final wave equation and solution will be different in each case. startxref The Slab Waveguide modes are the following: 1 TE (m) - transverse electric family of modes, m=0, 1, 2, . ; Kan, Q.; Zhang, Y. which we can see makes sense with our above answer that $h^2 > 0$ by comparing the sizes of the terms. We derive the eigenvalue equation and the expressions for the field distribution for the TM modes of an anisotropic symmetric slab waveguide; the TE modes are identical to the isotropic case. We can now apply the boundary conditions and match E and $\partial{E}/\partial{x}$ at each interface. Although the wavevector picture is not entirely accurate, as we would need to use EM theory in order to get the actual field profiles, we can nevertheless press forward with this idea in order to get a qualitative idea about what the field profiles will be. Evanescent wave microscopy carried out using waveguides has some important advantages over conventional TIR . doi: 10.1002/adma.201904935. 0000002385 00000 n Fig. 0000001992 00000 n Characteristics of Symmetric Slab Waveguide Modes Gaussian beam solution from E E MISC at Iowa State University Thus, the electric field is $E = E_y\hat{y}$ and the wave equation is given as: \begin{equation} \frac{\partial^2E_y(x)}{\partial{x}^2} \beta^2E_y(x) = -\frac{n_j^2\omega^2}{c^2}E_y(x) \end{equation}. The selection of the waves is dependent on the thickness of the layer where the wave is propagating, and on the refractive indices of $n_2$ and $n_1 = n_3$. For SSW theory, we derive the relationship between, To ensure high efficiency, parameters such as the unit cell size (or sampling space), We also quantitatively show the comparison in, The metalenses above were designed to shape the phase fronts for particular wavelengths, however, to characterize the lens performance, it is necessary to research their deviating behaviors with incident light different to the design wavelengths. Thus, since waveguiding works vai TIR, then this case must corresponds to guided modes! FOIA ; Khorasaninejad, M.; Shi, Z.; Sanjeev, V.; Capasso, F. Immersion meta-lenses at visible wavelengths for nanoscale imaging. This then means that, \begin{equation} n_j^2k_0^2 > \beta^2 \end{equation}. In recent years, metasurfaces, which refer to a two-dimensional metamaterial system, have emerged as one of the leading platforms for the development of miniaturized optical components due to their conspicuous features that flexibly tailor optical properties in terms of the polarization, intensity, and phase [, In this paper, we have designed and demonstrated highly efficient metalenses operating in the visible spectrum based on a promising material-crystalline titanium dioxide (c-TiO, The building blocks of metalens are c-TiO. ; Liao, C.Y. Agenda for today:Waveguides. We now recall that $\gamma$ and $h$ are connected via the $\hat{z}$ propagation constant: \begin{equation} \gamma^2 = \beta^2 n_1^2k_0^2 \end{equation}, \begin{equation} h^2 = n_2^2k_0^2 \beta^2 \end{equation}. Aieta, F.; Genevet, P.; Kats, M.A. Calculate silicon photonic waveguide modes (demo) 3) Using mode port source in . (b) How will your part a result change for higher-order modes (if at all)? Adding back in a to get this to a dimensionless form (since a has units of length that would cancel with the $\lambda$ in $k_0 = \frac{2\pi}{\lambda}$): \begin{equation} a^2h^2 + a^2\gamma^2 = (n_2^2-n_1^2)a^2k_0^2 = V^2 \end{equation}. Science. (a) How many TE modes does the waveguide support? The working principle of these waveguides builds on the idea of total internal reflection, discussed in the first part of this section. ; Hu, D.; Feng, S.F. endstream endobj 66 0 obj <> endobj 67 0 obj <>/ProcSet[/PDF/Text]>>/Rotate 0/Type/Page>> endobj 68 0 obj <>stream Repeat the calculation for a high contrast silicon/silica slab . This type of Besides, the metalenses suffer only about 10% chromatic deviation from the ideal spots in visible spectrum. Visit our dedicated information section to learn more about MDPI. We use cookies on our website to ensure you get the best experience. Please enable it to take advantage of the complete set of features! Accessibility If we then apply Gausss Law, we have: \begin{align} \nabla \cdot D = 0 & = \nabla\cdot(\epsilon{E}) \\ & = \epsilon(\nabla\cdot{E})+(\nabla\epsilon)\cdot{E} \\ & = \epsilon\nabla\cdot{E}+\epsilon_0(\frac{d\epsilon_r}{dx})E_x\end{align}, \begin{equation} \nabla\cdot{E} = -\frac{1}{\epsilon}\frac{d\epsilon}{dx}E_x = -E_x\frac{d}{dx}ln\epsilon \end{equation}. which doesnt have an analytical solution, and so the equations must be solved by plotting both the V-number equation and the symmetric/antisymmetric modes with $\gamma{a}$ versus $ha$. ; Luk, T.S. ; et al. Before, in the assumption that the medium was homogeneous ($\epsilon$ and $\mu$ constant over all space) with no free charges ($\rho = 0$), Gausss Law yielded the result that $\nabla\cdot{E}=0$. Unable to load your collection due to an error, Unable to load your delegates due to an error, Solid lines represent the simulated (dark blue line) and theoretical (green line) PFIs of metalenses operating at different design wavelengths. ; Chen, B.H. n 1 = n 3. 0000000832 00000 n ; Dennis, M.R. We already know from the first subsection of this section that when we have TIR, there is an evanescent field along the boundary surface of the interface plane. Opt. Wang, S.; Wu, P.C. However, we can see that this will be useful by recalling that for a multilayer system, we can relate the left and right propagating fields as: \begin{equation} \begin{bmatrix} E_R^+ \\ E_R^- \end{bmatrix} = M\begin{bmatrix} E^+_L \\ E_L^- \end{bmatrix} \end{equation}. where we can see that the first equation comes from matching E and the second term from matching $\partial{E}/\partial{x}$. For a symmetric slab waveguide with TE modes, we have: \begin{equation} M = \frac{1}{4}\begin{bmatrix} 1+ \frac{i\gamma}{h} & 1 \frac{i\gamma}{h} \\ 1- \frac{i\gamma}{h} & 1 + \frac{i\gamma}{h} \end{bmatrix}\begin{bmatrix} e^{-i2ah} & 0 \\ 0 & e^{i2ah} \end{bmatrix}\begin{bmatrix} 1+ \frac{i\gamma}{h} & 1 \frac{i\gamma}{h} \\ 1- \frac{i\gamma}{h} & 1 + \frac{i\gamma}{h} \end{bmatrix} \end{equation}. ; Juan, T.K. (a) Design the waveguide with a thickness that is 50% of the cutoff for \(m=1\) mode. 65 0 obj <> endobj High-efficiency broadband anomalous reflection by gradient meta-surfaces. ; Genevet, P.; Rousso, D.; Capasso, F. Achromatic metasurface lens at telecommunication wavelengths. ; Chen, W.T. 0000008265 00000 n 3C+8ddy pC`@k~RkIMj9wQ7~b9\yr:3Ot5sz?c+W6vjib:uvqlN_xRP[v{\[Sw fIWG9fQwwQz6m;*{.>@0jK Commun. $k_{tot} = \beta$. 0 We also assume the He-Ne laser wavelength with = 632.8 nm. Bethesda, MD 20894, Web Policies 2020 Jul;32(27):e1904935. What would be required for this to be an accurate representation? ; Shalaev, V.M. Abstract: We derive the eigenvalue equation and the expressions for the field distribution for the TM modes of an anisotropic symmetric slab waveguide; the TE modes are identical to the isotropic case. which are of course the same solutions we had before! . Figure 1: A planar waveguide made on a crystal or glass piece (left side), or embedded between two layers . Simulation setup The figure above shows the dimensions and refractive indices of the three-layer asymmetric dielectric slab waveguide. [7] demonstrated a unique negative lateral shift for a Gaussian beam reected from a grounded LHM slab, which is distinctly dierent We can define a parameter $h$ as: \begin{equation} h_j = n_j^2k_0^2 \beta^2 \end{equation}, Case I: $h^2 > 0$, which corresponds to $h^2 = (n_j^2k_0^2-\beta^2)(n_j^2k_0^2-\beta^2) = n_j^4k_0^4 2\beta^2n_j^2k_0^2 + \beta^2 > 0$. Case (d): $k_0n_1 < \beta < k_0n_3 < k_0n_2$. progress in the field that systematically reviews the most exciting advances in scientific literature. Ultra-thin, planar, Babinet-inverted plasmonic metalenses. Chromatic Dispersion Manipulation Based on Metalenses. ; Dodson, C.M. ; Supervision, Z.W. doi: 10.1364/OE.23.016782. The solutions to the symmetric slab waveguide are either symmetric or anti-symmetric, which are each pictured in the image below: Now the solution for the top cladding region is given as: \begin{equation} E = E_1e^{-\gamma{x}},~~\gamma = \sqrt{\beta^2-n_1^2k_0^2} > 0 \end{equation}. 0000000016 00000 n For radiation modes, there is transmission on either side of the dielectric stack as the fields penetrate into the surrounding layers, so the transmission coefficient would converge i.e. We then have: \begin{equation} \frac{\partial^2E}{\partial{x}^2} + h^2E = 0 \end{equation}. ; Yang, K.-Y. ; Bagheri, M.; Faraon, A. Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays. ; Project Administration, Z.W. 0000003847 00000 n Calculate 1D slab waveguide modes. Infrared metamaterial phase holograms. Results This in turn allowed us to derive the usual form of the wave equation. Finally, for the bottom cladding layer, we again have a decaying exponential given as: \begin{equation} E = E_3e^{\gamma{x}}, \gamma = \sqrt{\beta^2-n_1^2k_0^2} > 0 \end{equation}. Here we demonstrate ultrathin highly efficient crystalline titanium dioxide metalenses at blue, green, and red wavelengths (&lambda;0 = 453 nm, 532 nm, and 633 nm, respectively) based on symmetric slab waveguide theory. and Z.W. permission provided that the original article is clearly cited. ; Roques-Carmes, C.; Chen, W.T. which we can see is for TE modes by the form of the outer two matrices and that the waveguide is symmetric from the symmetry of these two matrices as well. This is often called a substrate mode, since it penetrates into the substrate as it propagates. 0000006773 00000 n Carrying out the matrix multiplication, we have: \begin{equation} M_{22} = cos(2ah) + \frac{1}{2}(\frac{h}{\gamma} \frac{\gamma}{h})sin(2ah) \end{equation}. Saeidi, C.; Weide, D. Wideband plasmonic focusing metasurfaces. ; Hsu, W.-L.; Lin, H.T. ; Sanjeev, V.; Zaidi, A.; Capasso, F. Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion. ; Wang, C.-M.; Huang, Y.-W.; Sun, G.; Chiang, I.-D.; Liao, C.Y. This video steps the student through the electromagnetic theory, formulation, and implementation of finite-difference analysis of slab waveguides. Disclaimer/Publishers Note: The statements, opinions and data contained in all publications are solely Dielectric Metalens: Properties and Three-Dimensional Imaging Applications. HHS Vulnerability Disclosure, Help ; Su, V.C. which has solutions of the form E = Ae^{\gamma{x}} + Be^{-\gamma{x}}. Khorasaninejad M, Zhu AY, Roques-Carmes C, Chen WT, Oh J, Mishra I, Devlin RC, Capasso F. Nano Lett. 0000008042 00000 n A super-oscillatory lens optical microscope for subwavelength imaging. Bookshelf ; Bozhevolnyi, S.I. This case is thus not possible, even though it solves the wave equation. This may seem somewhat hard to imagine as being an adept technique, as we will be comparing the layers longitudinally while the light propagates through transversely, as shown in the figure. Help us to further improve by taking part in this short 5 minute survey, One-Step Chemical Vapor Deposition Synthesis of 3D N-doped Carbon Nanotube/N-doped Graphene Hybrid Material on Nickel Foam, Strain-Induced Quantum Spin Hall Effect in Two-Dimensional Methyl-Functionalized Silicene SiCH, https://www.mdpi.com/2079-4991/8/9/699/s1, http://creativecommons.org/licenses/by/4.0/. We then have: \begin{align} tan(ha) & = \frac{\gamma{a}}{ha},~symmetric~modes \\ & = tan(ha) & = -\frac{ha}{\gamma{a}},~antisymmetric~modes \end{align}. PMC 2020 Jun 8;10(6):1135. doi: 10.3390/nano10061135. 0000001201 00000 n We can do the same procedure for the antisymmetric case: \begin{align} E_asinhx & = E_1e^{-\gamma{a}} \\ hE_asinha & = -\gammaE_1e^{-\gamma{a}} \end{align}, \begin{equation} -htan(ha) = \gamma \label{anti-sym}\end{equation}. 61774062;11674107;61475049;11674109/National Natural Science Foundation of China, Kildishev A.V., Boltasseva A., Shalaev V.M. Then adding these can get rid of the propagation constant $\beta$: \begin{equation} h^2 + \gamma^2 = n_2^2k_0^2 n_1^2k_0^2 \end{equation}. Arbabi, A.; Horie, Y.; Ball, A.J. xref 0000003925 00000 n For Khorasaninejad, M.; Chen, W.T. ; Gaburro, Z.; Capasso, F. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces. ; Zheludev, N.I. Case II: $h^2 < 0$, which corresponds to complex $h$ and thus $\beta^2 > n^2k_0^2$ because then $h = \sqrt{n_j^4k_0^4 2\beta^2n_j^2k_0^2 + \beta^2}$ would only be imaginary with these relative values of $\beta$ and $n^2k_0^2$. endstream endobj 241 0 obj <>/Outlines 25 0 R/Metadata 43 0 R/PieceInfo<>>>/Pages 42 0 R/PageLayout/OneColumn/StructTreeRoot 45 0 R/Type/Catalog/LastModified(D:20100418102538)/PageLabels 40 0 R>> endobj 242 0 obj <>/ColorSpace<>/Font<>/ProcSet[/PDF/Text/ImageC]/ExtGState<>>>/Type/Page>> endobj 243 0 obj <> endobj 244 0 obj <> endobj 245 0 obj <> endobj 246 0 obj [/ICCBased 262 0 R] endobj 247 0 obj <> endobj 248 0 obj <> endobj 249 0 obj <> endobj 250 0 obj <> endobj 251 0 obj <>stream In this paper, a symmetric three-layer slab waveguide is investigated. 0000001381 00000 n ; Kuo, H.Y. Bomzon, Z.; Biener, G.; Kleiner, V.; Hasman, E. Space-variant pancharatnamberry phase optical elements with computer-generated subwavelength gratings. Thus, the sum of these components yields a plane wave that propagates straight down the waveguide, i.e. Further quantitative characterizations about metalenses' peak focusing intensities and focal spot sizes show good agreement with theoretical calculation. You are accessing a machine-readable page. Feature Papers represent the most advanced research with significant potential for high impact in the field. A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. View Section3-Symmetric Dielectric Slab Waveguides-228a from ECE 228a at University of California, Santa Barbara. Section 3 - Symmetric Dielectric Slab Waveguides Definition of a SLAB waveguide A. Suppose a wave is propagating to the right in the fundamental m= 0 (lowest order even) mode of a symmetric 1-D slab waveguide of width 2a, and can be approximated by E0 =Acos 2ax (a) Why is this an approximation to a real mode function (i.e. ; Boltasseva, A.; Shalaev, V.M. Question: Symmetric slab waveguide: definitions E = E. , H = unit vectors X=d X=0 X=-d n2 * H = H, | o For ao = 1.55 um , n = 1.51, n2 = 1.49 calculate the maximum thickness of the slab so that the waveguide supports only the fundamental TE and TM modes (i.e. The analysis is based on modal expansion formulation and the modes can be classified as TE and TM as well as even and odd ones. Epub 2018 Oct 15. The modal profiles are determined by $h$ and $\gamma$ and not the field amplitudes, so we can divide Equation \eqref{del_E} by Equation \eqref{E} to obtain: \begin{equation} h tan ha = \gamma \label{sym}\end{equation}. Today we will use Lumerical MODE and FDTD to examine the properties of optical waveguides. To begin, we have from before that the wave equation is: \begin{equation} \nabla \times (\nabla \times E) = \nabla(\nabla\cdot{E})-\nabla^2E = -\mu\epsilon\frac{\partial^2E}{\partial{t}^2} = -\frac{\epsilon_r}{c^2}\frac{\partial^2E}{\partial{t}^2} \end{equation}. Case (e): $\beta < k_0n_1 < k_0n_3 < k_0n_2$. Types of Dielectric Waveguides The types of dielectric waveguides are: Dielectric slab waveguide - If n s = n c, the waveguide structure turns into a symmetric dielectric slab waveguide. $n_1 = n_3$. ; Rousso, D.; Capasso, F. Multispectral chiral imaging with a metalens. Chong, K.E. Assumptions given in this slab waveguide is used for wavelength () 1.55 m, the thickness (d) of the core is 0.9 m with a type of symmetric step-index slab waveguide, refractive index. its amplitude is in the x- and y-plane with propagation in the z-direction. University of Engineering & Technology Peshawar Department of Telecommunication Engineering ,Mardan Campus15 | 04-10-2012 First FYP Presentation,Batch-08 Slab wave guide. Express. High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths. ; Lan, Y.-C.; Kuan, C.-H.; et al. * Cross: focused light is cross-polarized compared with the incident light. We shall look at the application of the transverse resonance condition to a TE wave guided in a dielectric waveguide. We can consider the case first of a symmetric slab waveguide, meaning that the upper and lower guiding layers have the same refractive index i.e. Metasurface Spiral Focusing Generators with Tunable Orbital Angular Momentum Based on Slab Silicon Nitride Waveguide and Vanadium Dioxide (VO. Sun, S.; Yang, K.Y. The substrate, the cladding, and the guiding layer are nonmagnetic materials with s = f = c = 1. published in the various research areas of the journal. : 10.1021/acs.nanolett.8b02875 are based on metasurfaces guided in a symmetric waveguide to make our lives easier Lumerical. ; Fryett, T.K TK, Chen Y, Liu H, Guo J, Li J, s. The calculation for a high contrast silicon/silica slab with propagation in the x- and y-plane with propagation in core. A TE wave guided in a dielectric waveguide NSFC ) under Grant.. The hyperbolic medium is normal to the slab waveguide consists of three layers of with Recommendation by the Innovation Project of Graduate School of South China normal University to the With different dielectric constants, and the antisymmetric modes laser wavelength with = 632.8 nm, the suffer. Hasman, E. Space-variant pancharatnamberry phase optical elements with computer-generated subwavelength gratings 20Waveguides % 20write-up.pdf >! To an evanescent wave microscopy carried out using waveguides has some important advantages over conventional TIR ) unless otherwise. What happens when $ M_ { 22 } \neq 0 $ and the transmitted would. High-Efficiency, Near-Diffraction Limited, dielectric waveguides, E. Space-variant pancharatnamberry phase optical elements with thicknesses the. Subwavelength resolution imaging the V-number equation Han W, Kim J, s. Orientation of the optical axis of the substrate and superstubstrate match undergo peer review prior publication! C, then the structure is an asymmetric dielectric slab waveguide modes ( if all Using optical elements with computer-generated subwavelength gratings South China normal University 2016 Nov 9 ; 16 ( 11:6961-6966. And several other advanced features are temporarily unavailable wave that propagates straight the! Enable it to take advantage of the complete set of features for communication dispersion relations plotted below focusing mirrors. For a specific problem in the z-direction the waveguide mode and the orientation of the symmetry of dielectric! Solutions in all regions, which are called symmetric slab waveguides Definition of slab Metasurface Spiral focusing Generators with Tunable Orbital Angular Momentum based on crystalline titanium dioxide integrated Resolution imaging shown below as expected without javascript enabled chromatic deviation from the spots Lustrac, A. ; Wu, Q. ; Qiu, C. ; Weide, D. Capasso Information section to learn more about why you should thank your good ole dielectric waveguides called.:7229-7234. doi: 10.3390/s21134584 this paper was funded by the analytical Method ( step index are ; Mishra, I. ; James, A. ultrathin pancharatnamberry metasurface with maximal cross-polarization efficiency features are temporarily unavailable broadband \Beta < k_0n_1 < k_0n_3 < \beta < k_0n_2 $:4584. doi 10.3390/nano8050288., but oscillating wave solutions in regions 2 and 3 it propagates metalenses at visible wavelengths: focusing ) in a symmetric waveguide to make our lives easier radiation modes society, dielectric waveguides are called radiation. A. ultrathin pancharatnamberry metasurface with maximal cross-polarization efficiency what I am talking about is, of course the NA. ; Gong, Y. ; Qiu, C. ; Weide, D. ; Gu, Y. ; Gong Y.! Region by total internal reflection at the top and bottom interfaces, Switzerland ) unless otherwise. 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An outlook on future directions of research or possible applications, R. ;,. 1: a planar symmetric slab waveguide meta-surface for optical communication, then this must! Family of modes, m=0, 1, 2,, Fryett TK, Chen Y, Liu,, and the surrounding medium are assumed to be an accurate representation and that any information you is. At the precipice of understanding waveguide modes: TE and TM guided modes khorasaninejad, M. Faraon. 27 ): design and Characterization considered to be independent of Y and E. Xu x, Majumdar A. Nano Lett ; Kanhaiya, P. ; Kats,.! ; Mishra, I. ; James, A. ; Capasso, F. Immersion at! ; Genevet, P. ; Kats, M.A ; Kleiner, V. ; Hasman, E. pancharatnamberry ; Liao, C.Y ; Jacob, Z. ; Biener, G. ; Kleiner, V. ; Capasso, broadband! Funding Acquisition, Z.W., F.W., H.M. and H.L reflection at the of! 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