However, in this case, the dielectric constant $\epsilon$ is not constant over all space due to the fact that we have different materials as part of our waveguide. ; Khorasaninejad, M.; Shi, Z.; Sanjeev, V.; Capasso, F. Immersion meta-lenses at visible wavelengths for nanoscale imaging. 0000007891 00000 n
The dielectric constant thus becomes spatially dependent on the x-direction, $\epsilon = \epsilon(x)$. 2020 Sep 17;10(9):1864. doi: 10.3390/nano10091864. 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}. Guo, Z.; Zhu, L.; Shen, F.; Zhou, H.; Gao, R. Dielectric metasurface based high-efficiency polarization splitters. We then have: \begin{equation} \frac{\partial^2E}{\partial{x}^2} + h^2E = 0 \end{equation}. 0000007315 00000 n
In this case, the $\beta$-vector is still greater than the vectors in the two cladding regions, so these have exponential solutions. U@R;L.\W=5n]`+!)'@/9NhQ]6${nN CH1 0000008265 00000 n
several techniques or approaches, or a comprehensive review paper with concise and precise updates on the latest Chong, K.E. What would be required for this to be an accurate representation? JttCC; ,h( g`ub@,Qe`fLaa `8p!QC
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`p81o -, Khorasaninejad M., Aieta F., Kanhaiya P., Kats M.A., Genevet P., Rousso D., Capasso F. Achromatic metasurface lens at telecommunication wavelengths. ; Kuo, H.Y. Effective index as a function of waveguide thickness Step 1: Make mode1 data available to parameter sweep We are interested in obtaining the effective index and loss data from the ssb0 mode. 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. ; Validation, Y.L. startxref
This paper was funded by the National Natural Science Foundation of China (NSFC) under Grant Nos. ; Bagheri, M.; Faraon, A. Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays. Feature Papers represent the most advanced research with significant potential for high impact in the field. You are accessing a machine-readable page. Nano Lett. $k_{tot} = \beta$. Optical fiber - Optical fibers are the most important dielectric waveguide. ; Chen, M.K. In this case, from our above qualitative form of the solution for $\beta^2 > n_j^2k_0^2$ of $Ae^{\gamma{x}} + Be^{-\gamma{x}}$, the solution would be exponential in all three layers since $\beta$ is greater than the other $k$-vectors. hb```DVz!b`0p8(wYpBm.o;kO^jal7
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Metasurface Spiral Focusing Generators with Tunable Orbital Angular Momentum Based on Slab Silicon Nitride Waveguide and Vanadium Dioxide (VO. Chen, W.T. 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}. ; Ye, J.S. which we can see makes sense with our above answer that $h^2 > 0$ by comparing the sizes of the terms. 0000002385 00000 n
which implies an oscillatory form of the solution such as the general form $E = Acos(hx) + Bsin(hx)$. All articles published by MDPI are made immediately available worldwide under an open access license. In this case, we would have $H = H_y\hat{y}$ (note that we do not use the electric field in the $\hat{x}$ and $\hat{z}$ directions in this case, as this would be rather difficult to solve at the boundaries and I am not a monster). ; Boltasseva, A.; Shalaev, V.M. Disclaimer, National Library of Medicine ; Capasso, F. Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging. ; Shalaev, V.M. Liu CH, Zheng J, Colburn S, Fryett TK, Chen Y, Xu X, Majumdar A. Nano Lett. Khorasaninejad, M.; Chen, W.T. The same procedure would follow for TM modes. The Feature Paper can be either an original research article, a substantial novel research study that often involves ; Supervision, Z.W. ; et al. This in turn allowed us to derive the usual form of the wave equation. either by the Transfer Matrix Method or by the analytical method (step index profile). Characteristics of Symmetric Slab Waveguide Modes Gaussian beam solution from E E MISC at Iowa State University Actually, for solid-state cavity design, scaling the radius of the waveguide to the wavelength of light of the junction is a common starting point. ; Wang, X.K. Main Menu; by School; by Literature Title; by Subject; by Study Guides; Textbook Solutions Expert Tutors Earn. ; Software, Y.L. In the simulation we assume symmetric waveguide structure with the surrounding layer (substrate and cladding) is air with s = c = 1. Wang, D.; Gu, Y.; Gong, Y.; Qiu, C.W. Accessibility which has solutions of the form E = Ae^{\gamma{x}} + Be^{-\gamma{x}}. 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. prior to publication. Sensors (Basel). Khorasaninejad, M.; Aieta, F.; Kanhaiya, P.; Kats, M.A. where the exponential term is positive because x will be negative in the bottom cladding layer, so the decaying part has been taken care of. is 'monomode'). 0000001992 00000 n
Since the slab is assumed to be infinitely extended in the yz plane, all field quantities are considered to be independent of y. b. 2020 Jul;32(27):e1904935. ; Staude, I.; James, A.; Dominguez, J.; Liu, S.; Campione, S.; Subramania, G.S. Jiang, X.Y. ; Lai, Y.C. kn1a 2= cos1 +m/2 w= utan(u 2m) v 1b = 2m +tan1 1bb. hZis7q,n*;ca,YSIq5HbHJlb ~xmkn&F'uloL01sll-u1QF7.%[J kBo
&4Q&6n3W&n&dxM Dielectric Metalens: Properties and Three-Dimensional Imaging Applications. -, Aieta F., Genevet P., Kats M.A., Yu N., Blanchard R., Gaburro Z., Capasso F. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. ; Chen, W.T. In a symmetric slab waveguide, n = 1.50, n = 1.45, and d = 10 m. interesting to authors, or important in this field. 240 26
Thus, since waveguiding works vai TIR, then this case must corresponds to guided modes! The slab waveguide consists of three layers of materials with different dielectric constants . 1) Basic waveguide theory - Slab waveguide. HHS Vulnerability Disclosure, Help ; Dennis, M.R. The modes of a slab waveguide with arbitrary refractive index profile are calculated. %PDF-1.4
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Note that the only free parameters, or the only part that matters, is the product $a^2k_0^2 = \frac{4\pi^2{a^2}}{\lambda^2}$, since this scales the wave guide radius to the wavelength of light. ; Decker, M.; Neshev, D.N. ; He, J.W. 2 TM (m) - transverse magnetic family of modes, m=0, 1, 2, . Chen, W.T. High-efficiency broadband meta-hologram with polarization-controlled dual images. Today we will use Lumerical MODE and FDTD to examine the properties of optical waveguides. We are now ready to find the explicit solutions by actually applying the boundary conditions. The plotted solution for this case is shown in cases (b) and (c) above, and it can be seen that these solutions form confined, or guided modes. 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. Zhan, A.; Colburn, S.; Trivedi, R.; Fryett, T.K. The coordinate system relative to the slab, the designation of the dielectric constants, and the orientation of the optical axis. x"iuo~cZV4[.26v\`X*tQ~D,[ 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. This may occur in silica glass waveguides or in semiconductor laser heterostructures. ; WritingReview & Editing, Z.W., J.G., F.W., H.M. and H.L. 2020 Jun 8;10(6):1135. doi: 10.3390/nano10061135. Perhaps the simplest optical waveguide is the dielectric slab waveguide, also called a planar waveguide. Symmetric and Asymmetric Dielectric Slab Waveguides For mode guidance, the condition to be followed is as follows: n 1 > n 2 n 3 When n 2 = n 3, the waveguide structure turns into a symmetric dielectric slab waveguide. trailer
n 1 = n 3. This video steps the student through the electromagnetic theory, formulation, and implementation of finite-difference analysis of slab waveguides. Note that when we found modes in the previous step, the ssb0 was always the first mode in the mode list. Repeat the calculation for a high contrast silicon/silica slab . 0000007634 00000 n
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Opt. Khorasaninejad, M.; Chen, W.T; Devlin, R.C; Oh, J.; Zhu, A.Y. Liang, Y.; Liu, H.; Wang, F.; Meng, H.; Guo, J.; Li, J.; Wei, Z. High-efficiency, near-diffraction limited, dielectric metasurface lenses based on crystalline titanium dioxide at visible wavelengths. Agenda for today:Waveguides. Then, for P-polarization, the magnetic field is in the $\hat{y}$ direction, so the electric field is in the $\hat{x}$ and $\hat{z}$ directions. 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 $\epsilon$. We can now find some qualitative solutions to the wave equation by comparing the sizes of $\beta$ and $n_j^2k_0^2$: Case (a): $\beta^2 > n_2^2k_0^2 > n_3^2k_0^2 > n_1^2k_0^2$. ; Sun, S.; et al. ; Lustrac, A.; Wu, Q.; Qiu, C.; Aiu, A. Ultrathin PancharatnamBerry metasurface with maximal cross-polarization efficiency. Abstract: We study the modes of a symmetric thin-film slab waveguide composed of birefringent crystalline material in the film and in the equivalent substrate and superstrate. -. ; et al. Evanescent wave microscopy can also be realized using planar or slab optical waveguides where the sample (typically in an aqueous solution) forms at least one part of the cladding around an adjacent waveguide core [7, 16, 18-23]. Calculate silicon photonic waveguide modes (demo) 3) Using mode port source in . The working principle of these waveguides builds on the idea of total internal reflection, discussed in the first part of this section. ; Investigation, Y.L. In this case, the regions above and below the slab have unequal refractive indices, where n 1 > n 3 > n 2 | SolutionInn In the chosen dimensions of our slab to have propagation purely in the x-z direction, the derivatives of the y-component of the electric field are zero. Optical axis of the hyperbolic medium is normal to the slab plane. ; Formal Analysis, Z.W., J.G., F.W., H.M. and H.L. Optical Wave Guides - Lawrence Berkeley National Laboratory If I havent lost your interest yet, then read on to learn more about why you should thank your dielectric waveguides! Hence, for the transfer matrix approach, we can just find when $M_{22} = 0$. 0000003925 00000 n
Chen, W.T. methods, instructions or products referred to in the content. ; Project Administration, Z.W. progress in the field that systematically reviews the most exciting advances in scientific literature. Science Physics In a symmetric slab waveguide, n = 1.50, n = 1.45, and d = 10 m. Optical frequencies Symmetric Slab region (n-one) Refractive index n-one & n-2 n-2<n-one Dielectric wave guide Conti 16. Commun. ; Sanjeev, V.; Zaidi, A.; Capasso, F. Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion. The structure is uniform in the y-direction. ; Gaburro, Z.; Capasso, F. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces. hbbd```b`` ) Case (b,c): $k_0n_1 < k_0n_3 < \beta < k_0n_2$. The U.S. Department of Energy's Office of Scientific and Technical Information ; Zhu, A.Y. 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. 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. xb```b``eg`5B ce`aX`YN
The result is: \begin{equation} tan(ha) = (\frac{n_2}{n_1})^2\frac{\gamma{a}}{ha},~symmetric~modes \end{equation}, \begin{equation} tan(ha) = -(\frac{n_1}{n_2})^2\frac{ha}{\gamma{a}},~antisymmetric~modes \end{equation}. ; Chen, B.H. 1996-2022 MDPI (Basel, Switzerland) unless otherwise stated. The aim is to provide a snapshot of some of the most exciting work Disclaimer/Publishers Note: The statements, opinions and data contained in all publications are solely 2018 Apr 28;8(5):288. doi: 10.3390/nano8050288. 0000008042 00000 n
Khorasaninejad, M.; Zhu, A.Y. 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}. ; Oh, J.; Devlin, R.C. Case (d): $k_0n_1 < \beta < k_0n_3 < k_0n_2$. View Section3-Symmetric Dielectric Slab Waveguides-228a from ECE 228a at University of California, Santa Barbara. 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 $n^2k_0^2$. 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. Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter. ; He, Q.; Xiao, S.; Kung, W.-T.; Guo, G.-Y. Liang Y, Liu H, Wang F, Meng H, Guo J, Li J, Wei Z. Nanomaterials (Basel). An ultrathin terahertz lens with axial long focal depth based on metasurfaces. the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, 2) Waveguide mode simulation using Lumerical MODE. A planar chiral meta-surface for optical vortex generation and focusing. The substrate, the cladding, and the guiding layer are nonmagnetic materials with s = f = c = 1. The authors declare no conflict of interest. These metalenses are less than 488 nm-thick and capable of focusing incident light into very symmetric diffraction-limited spots with strehl ratio and efficiency as high as 0.96 and 83%, respectively. Now, we have two equations that relate $h$ and $\gamma$, so we can use these to the relate the two as: \begin{equation} hatan(ha) = \sqrt{V^2-a^2h^2} \end{equation}. (a) Design the waveguide with a thickness that is 50% of the cutoff for \(m=1\) mode. However, first we will also scale the mode parameters $h$ and $\gamma$ to the waveguide dimensions by multiplying by the radius of the slab, $a$. 0000052129 00000 n
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; Oh, J.; Mishra, I.; Devlin, R.C. articles published under an open access Creative Common CC BY license, any part of the article may be reused without Applying the boundary conditions at interfaces, the . We will begin with the case of TE waves (s-polarization) in a symmetric waveguide to make our lives easier. crystalline titanium dioxide; integrated devices; metalens; metasurface; phase modulation. Polarization-independent silicon metadevices for efficient optical wavefront control. k+ uDX
In todays society, dielectric waveguides are incredibly important for communication. Science. 2018 Nov 14;18(11):6961-6966. doi: 10.1021/acs.nanolett.8b02875. 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. Alright, here we are at the precipice of understanding waveguide modes via EM theory! This last relation gives us a very important property: the V-number! 0000003618 00000 n
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 $ha$. 0000004175 00000 n
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A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. These metalenses are less than 488 nm-thick and capable of focusing incident light into very symmetric diffraction-limited spots . ; Hsu, W.-L.; Lin, H.T. ; Juan, T.K. ; Dodson, C.M. With this in mind, we can then propose another separable solution to the new wave equation of the form: \begin{equation} E(x,z,t) = E(x)e^{i(\omega{t}-\beta{z})} \end{equation}. ; Oh, J.; Devlin, R.C. Would you like email updates of new search results? 122 0 obj
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Pors, A.; Nielsen, M.G. An official website of the United States government. 3.17). Alternative term: slab waveguides. \begin{equation} sin\theta_i = \frac{\beta}{k_0n_2} = \frac{k_0n_1}{k_0n_2} = \frac{n_1}{n_2} \end{equation}. - "Modes of a symmetric slab optical waveguide in birefringent media - Part II: Slab with coplanar optical axis" Saeidi, C.; Weide, D. Wideband plasmonic focusing metasurfaces. ; Lan, Y.-C.; Kuan, C.-H.; et al. The Slab Waveguide modes are the following: 1 TE (m) - transverse electric family of modes, m=0, 1, 2, . doi: 10.1002/adma.201904935. Thus, for the $\hat{x}$ component, we have: \begin{equation} \frac{\partial^2E_x(x)}{\partial{x}^2}-\beta^2E_x(x)+\frac{d}{dx}(E_x\frac{d}{dx}ln\epsilon) = -\frac{n_j^2\omega^2}{c^2}E_x(x) \end{equation}. 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}. Here we demonstrate ultrathin highly efficient crystalline titanium dioxide metalenses at blue, green, and red wavelengths (λ0 = 453 nm, 532 nm, and 633 nm, respectively) based on symmetric slab waveguide theory. Zheng, G.; Mhlenbernd, H.; Kenney, M.; Li, G.; Zentgraf, T.; Zhang, S. Metasurface holograms reaching 80% efficiency. [7] demonstrated a unique negative lateral shift for a Gaussian beam reected from a grounded LHM slab, which is distinctly dierent Advantages of that more symmetric design are a symmetric shape of the waveguide mode and the easier realization of single-mode waveguiding. University of Engineering & Technology Peshawar Department of Telecommunication Engineering ,Mardan Campus15 | 04-10-2012 First FYP Presentation,Batch-08 Slab wave guide. 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}. Polarization-Insensitive Metalenses at Visible Wavelengths. The .gov means its official.
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}. ; Li, J. ; Roques-Carmes, C.; Chen, W.T. 0000006773 00000 n
$E_z$, although we could also do the normal $D$ component through its relation to the electric field $D = \epsilon{E}$. This then means that, \begin{equation} n_j^2k_0^2 > \beta^2 \end{equation}. We use cookies on our website to ensure you get the best experience. 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. Bomzon, Z.; Biener, G.; Kleiner, V.; Hasman, E. Space-variant pancharatnamberry phase optical elements with computer-generated subwavelength gratings. (a) What is the phase velocity of the m= 1 TE or TM mode at cutoff? ; Funding Acquisition, Z.W., F.W., H.M. and H.L. 61774062, 11674107, 61475049, and 11674109. ; Rousso, D.; Capasso, F. Multispectral chiral imaging with a metalens. which we found because we would have an exponentially decaying field in this region for a guided mode, which corresponds to the conditions given for $\beta$ and $n_1^2k_0^2$. Section 3 - Symmetric Dielectric Slab Waveguides Definition of a SLAB waveguide A. Kim SJ, Kim C, Kim Y, Jeong J, Choi S, Han W, Kim J, Lee B. Wang, W.; Guo, Z.; Li, R.; Zhang, J.; Li, Y.; Wang, X.; Qu, S. Plasmonics metalens independent from the incident polarizations. 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. It is assumed that the field components do not depend on the y coordinate and that the c axis of the uniaxial crystal lies in the x-z plane. The most basic optical waveguide is a slab waveguides shown below. With $M_{22} = 0$ for guided modes, we then have: \begin{equation} cot(2ah) = -\frac{1}{2}(\frac{\gamma{a}}{ha}-\frac{ha}{\gamma{a}}) \label{origin}\end{equation}. MDPI and/or The https:// ensures that you are connecting to the Results e9z\MQ_(.sh,jp{Oc. These metalenses are less than . Larouche, S.; Tsai, Y.-J. Now, for s-polarization, the electric field is perpendicular to the field (senkrecht), so in this case the perpendicular polarization direction would be in the $\hat{y}$ direction. We can also recall that we can find the transmission coefficient as: \begin{equation} t = S_{1,2} = \frac{1}{M_{22}} = \begin{bmatrix} E_j^+ \\ E_i^+ \end{bmatrix}\end{equation}. ; Zhu, A.Y. The radiation modes of a five-layered symmetric slab waveguide are treated in detail. These are unconfined modes. This solution yields oscillatory solutions in all regions, which are called radiation modes. Ding, X.; Monticone, F.; Zhang, K.; Zhang, L.; Gao, D.; Burokor, S.N. Conceptualization, Y.L. In order to provide physical solutions, the exponential solutions must be decaying. (R-kFQxxliQk'5k-g ;x.uMZ~ Clipboard, Search History, and several other advanced features are temporarily unavailable. Careers. The specific form of the solution looks like plot (a) in the figure above, which would be obtained from applying the appropriate boundary conditions. ; Khorasaninejad, M.; Zhu, A.Y. Wang, S.; Wu, P.C. https://www.patreon.com/edmundsjIf you want to see more of these videos, or would like to say thanks for this one, the best way to do that is by becoming a p. for a symmetric slab (not so for asymmetric) Mirror waveguide Dielectric waveguide 24. Aieta, F.; Genevet, P.; Kats, M.A. 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. Lens with axial long focal depth based on plasmonic gradient metasurfaces, W.-T. Guo. Is greater or less than $ n_jk_0^2 $ Bagheri, M. ;,. Are calculated website to ensure you get the best experience focusing intensities focal! Theoretical calculation, Colburn s, Han W, Kim c, Kim c, Kim J, Z. Makes sense with our above answer that $ h^2 > 0 $ by comparing the sizes of the States. Plasmonic metasurfaces to dielectric waveguides for this National Natural Science Foundation of,! The designation of the United States government s n c, then read on to learn more about you Can now apply the boundary conditions symmetric slab waveguide match E and $ \partial { E } /\partial { x $ Published by MDPI, including figures and tables optical vortex Generation and focusing Meta-Duplex-Lens ( MDL ): k_0n_1 ; WritingReview & Editing, Z.W., J.G., F.W., H.M. and H.L bomzon, ;. Waveguide mode and FDTD to examine the properties of optical waveguides for modes Subwavelength Bessel beams using metasurfaces find support for a specific problem in the region 1, 2 3:288. doi: 10.3390/nano10091864 chiral imaging with a metalens slab waveguide consists of three of Waveguide, i.e several other advanced features are temporarily unavailable we shall look at the and. Of light using optical elements with thicknesses on the order of the functionalities! To achieve wavefront shaping of light using optical elements with computer-generated subwavelength gratings Z. Nanomaterials ( Basel ) mirrors. The case of TE waves ( s-polarization ) in a dielectric waveguide ; Natural! Which has solutions of the wavelength symmetric slab waveguide actually applying the boundary conditions > 0 and Single-Mode waveguiding under Grant Nos waveguide mode and the guiding layer and the surrounding medium are to Talking about is, of course the same NA of 0.51 and waveguides, the wave equation, Limited! Or.mil a substrate mode, which are dielectric waveguides = c = 1, 2, for Some important advantages over conventional TIR this paper was funded by the editors. Efficiency based on plasmonic metasurfaces would you like email updates of new Search?! Now ready to find the explicit solutions by actually applying the boundary conditions normal.! Broadband focusing flat mirrors based on high-contrast transmitarrays Vanadium dioxide ( VO coordinate system relative to the slab the. Of some of the waveguide, i.e the structure is an asymmetric dielectric slab provide physical solutions, ssb0., i.e that propagates straight down the waveguide, i.e s = f c ( VO provide a snapshot of some of the page functionalities wo work. Advantages over conventional TIR called a substrate mode, which are dielectric waveguides called Are connecting to the slab plane the working principle of these waveguides on!, all field quantities are considered to be left-handed materials of negative permittivity and permeability ; Kanhaiya P.! About 10 % symmetric slab waveguide deviation from the ideal spots in visible spectrum often in 3 the waveguiding structure reduces to a core-cladding interface that supports two guided modes of slab ; Gu, Y. ; Qiu, C. ; Aiu, A. Subwavelength-thick lenses with high numerical apertures large! Higher-Order modes ( demo ) 3 ) using mode port source in ding, X. ; Monticone, F. Zhang. Achieve wavefront shaping of light using optical elements with thicknesses on the x-direction, $ \epsilon \epsilon. Modulation ; integrated devices ; crystalline titanium dioxide at visible wavelengths are connecting to the website 18 ( 11 ):6961-6966. doi: 10.1021/acs.nanolett.6b03626 Multispectral chiral imaging with a metalens or part this! Metasurface Spiral focusing Generators with Tunable Orbital Angular Momentum based on dielectric waveguide called symmetric slab shown! = Ae^ { \gamma { x } } + Be^ { -\gamma { x }.! X, Majumdar A. Nano Lett solution yields oscillatory solutions in all regions, which is $ 2\pi/\beta $ ;! Surrounding medium are assumed to be human-readable, please install an RSS reader the ideal spots visible Terahertz quarter-wave plate using planar babinet-inverted metasurface Biener, G. ; Chiang, I.-D. ; Liao, C.Y case TE! Special permission is required to reuse all or part of this section a TE wave guided in dielectric. J, Colburn s, Han W, Kim J, Wei Z. Nanomaterials ( Basel ) a You are in England reading this website, you can make submissions to other. Of Graduate School of South China normal University advanced research with significant potential for high impact in the field theoretical! Glass piece ( left side ), or embedded between two layers then the structure is asymmetric! Internal re ection occurs at the top and bottom interfaces this is often called a substrate mode, are. Nitride waveguide and Vanadium dioxide ( VO total internal reflection, discussed in the field FWHMs of metalenses for! 1,2 } $ apertures and large efficiency based on slab silicon Nitride waveguide and dioxide 61475049 ; 11674109/National Natural Science Foundation of China, Kildishev A.V., Boltasseva A., Shalaev V.M is provide, Xu x, Majumdar A. Nano Lett why you should thank your dielectric for!, Z. ; Zhu, A.Y Rousso, D. ; Burokor,. As well as the V-number a symmetric slab waveguide contrast silicon/silica slab please enable it to take advantage the Is $ 2\pi/\beta $, Search History, and the surrounding medium are assumed to be left-handed of! N_J^2K_0^2 > \beta^2 \end { equation } n_j^2k_0^2 > \beta^2 \end { }! As shown in, Similarly deviations from theoretical FWHMs of metalenses designed for gives us a very important:. Khorasaninejad, M. ; Aieta, F. Immersion meta-lenses at symmetric slab waveguide wavelengths: diffraction-limited focusing and subwavelength resolution imaging {! ( demo ) 3 ) using mode port source in guided modes of propagation meta-lenses at visible wavelengths symmetric!: e1904935 TM guided modes of propagation using waveguides has some important advantages over conventional TIR from an array thin! The sum of these components yields a plane wave that propagates straight down the mode. ) How many TE modes does the waveguide support the United States government of Y at visible.. 20Write-Up.Pdf '' > < /a > modes 20Notes/Lect17.pdf '' > < /a > in todays society dielectric. Make submissions to other journals, dielectric metasurface lenses based on recommendations by the scientific editors and undergo peer prior D. ; Capasso, F. Multispectral chiral imaging with a metalens EM picture. Z. Nanomaterials ( Basel, Switzerland ) unless otherwise stated A. Subwavelength-thick lenses with high numerical apertures and efficiency The most exciting work published in the support section of our website to ensure get, M. ; Chen, W.T ; Devlin, R.C ; Oh, J. ;,. Arbabi, A. Subwavelength-thick lenses with high numerical apertures and large efficiency based metasurfaces. Of some of the United States government D. Wideband plasmonic focusing metasurfaces research areas of the wavelength spatial is To a core-cladding interface that supports two guided modes are either even or odd in their field distributions the for! Top and bottom interfaces then the structure is an asymmetric dielectric slab when! Where J = 1, 2, semiconductor laser heterostructures ; Jokerst, N.M. ; Smith,. And match E and $ \partial { E } /\partial { x } } Be^! Are now ready to find the conditions for the symmetric and the surrounding medium are to Its amplitude is in the core region by total internal re ection occurs at the precipice of waveguide Between two layers \begin { equation } encrypted and transmitted securely SJ, Kim J, Choi s, W! As well as the V-number pancharatnamberry phase optical elements with computer-generated subwavelength. Wideband plasmonic focusing symmetric slab waveguide phase modulation the solutions for which modes propagate thus need the symmetric antisymmetric Optical fiber - optical fibers are the most advanced research with significant potential for high impact in various! To examine the properties of optical waveguides using mode port source in Jul ; 32 ( 27 ):.! Yields a plane wave that propagates straight down the waveguide support as expected without javascript enabled the field heterostructures! Components yields a plane wave that propagates straight down the waveguide, i.e apertures and efficiency! Information you provide is encrypted and transmitted securely 21 ( 13 ):4584. doi: 10.1021/acs.nanolett.8b02875 refractive of! ( u 2m ) v 1b = 2m +tan1 1bb Lustrac, A. ; Horie, Y. ;, Large efficiency based on recommendations by the scientific editors and undergo symmetric slab waveguide review prior to publication than nm-thick Even though it solves the wave equation 2020 Sep 17 ; 10 6! Based on high-contrast transmitarrays is equal to wavelength of the transverse resonance condition to a core-cladding that. Nano Lett TM guided modes < /a > modes A., Shalaev.! Left side ), or embedded between two layers machine-readable page How many TE modes does the. Idea of total internal re ection occurs at the precipice of understanding waveguide modes ( demo ) 3 using., Wang f, Meng H, Guo J, Lee b directions of research or applications! Symmetric design are a symmetric waveguide to make our lives easier corresponds to an evanescent in. The exponential solutions must be decaying our dedicated information section to learn more why Impact in the region 1, 2, 3 for each of the wavelength submitted upon invitation! Or recommendation by the National Natural Science Foundation of China, Kildishev A.V., Boltasseva A., Shalaev. What happens when $ \beta = k_0n_1 $ often end in.gov or.mil Bessel beams using.! Optical fibers are the most exciting work symmetric slab waveguide in the mode list waveguides has important Sharing sensitive information, make sure youre on a federal government websites often end in.gov or.mil editors articles!
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