DOCSLIB.ORG

Superconducting Metamaterials for Waveguide Quantum Electrodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Superconducting Metamaterials for Waveguide Quantum Electrodynamics ARTICLE DOI: 10.1038/s41467-018-06142-z OPEN Superconducting metamaterials for waveguide quantum electrodynamics Mohammad Mirhosseini1,2,3, Eunjong Kim1,2,3, Vinicius S. Ferreira1,2,3, Mahmoud Kalaee1,2,3, Alp Sipahigil 1,2,3, Andrew J. Keller1,2,3 & Oskar Painter1,2,3 Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in 1234567890():,; the transmission band, outside the gap, allows for studying waveguide quantum electro- dynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter–emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of −28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states. 1 Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125, USA. 2 Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA. 3 Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA. Correspondence and requests for materials should be addressed to O.P. (email: [email protected]) NATURE COMMUNICATIONS | (2018) 9:3706 | DOI: 10.1038/s41467-018-06142-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-06142-z avity quantum electrodynamics (QED) studies the inter- In this paper, we utilize an array of coupled lumped-element action of an atom with a single electromagnetic mode of a microwave resonators to form a compact bandgap waveguide C fi 1,2 λ high- nesse cavity with a discrete spectrum . In this with a deep sub-wavelength lattice constant ( /60) based on the canonical setting, a large photon–atom coupling is achieved by metamaterial concept. In addition to a compact footprint, these repeated interaction of the atom with a single photon bouncing sort of structures can exhibit highly nonlinear band dispersion many times between the cavity mirrors. Recently, there has been surrounding the bandgap, leading to exceptionally strong con- much interest in achieving strong light–matter interaction in a finement of localized intra-gap photon states. We present the cavity-free system such as a waveguide3,4. Waveguide QED refers design and fabrication of such a metamaterial waveguide, and to a system where a chain of atoms are coupled to a common characterize the resulting waveguide dispersion and bandgap optical channel with a continuum of electromagnetic modes over properties via interaction with a tunable superconducting trans- a large bandwidth. Slow-light photonic crystal waveguides are of mon qubit. We measure the Lamb shift and lifetime of the qubit particular interest in waveguide QED because the reduced group in the bandgap and its vicinity, demonstrating the anomalous velocity near a bandgap preferentially amplifies the desired Lamb shift of the fundamental qubit transition as well as selective radiation of the atoms into the waveguide modes5–7. Moreover, in inhibition and enhancement of spontaneous emission for the first this configuration an interesting paradigm can be achieved by two excited states of the transmon qubit. placing the resonance frequency of the atom inside the bandgap – of the waveguide8 11. In this case, the atom cannot radiate into Results the waveguide but the evanescent field surrounding it gives rise to Band-structure analysis and spectroscopy. We begin by con- a photonic bound state9. The interaction of such localized bound sidering the circuit model of a CPW that is periodically loaded states has been proposed for realizing tunable spin–exchange with microwave resonators as shown in the inset to Fig. 1a. The interaction between atoms in a chain12,13, and also for realizing Lagrangian for this system can be constructed as a function of the effective non-local interactions between photons14,15. fl Φb Φa37 node uxes of the resonator and waveguide sections n and n . While achieving efficient waveguide coupling in the optical Assuming periodic boundary conditions and applying the rotat- regime requires the challenging task of interfacing atoms or ing wave approximation, we derive the Hamiltonian for this 16–20 ω atomic-like systems with nanoscale dielectric structures , system and solve for the energies h ± ;k along with the corre- ji¼; α^ ji superconducting circuits provide an entirely different platform sponding eigenstates ± k ± ;k 0 as (see Supplementary for studying the physics of light–matter interaction in the Note 1) microwave regime4,21. Development of the field of circuit QED qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi has enabled fabrication of tunable qubits with long coherence 1 2 2 ω ; ¼ ðÞΩ þ ω ± ðÞΩ À ω þ4g ; ð1Þ times and fast qubit gate times22,23. Moreover, strong coupling is ± k 2 k 0 k 0 k readily achieved in coplanar platforms due to the deep sub- wavelength transverse confinement of photons attainable in ω À ω microwave waveguides and the large electric dipole of super- ± ;k 0 24 α^ ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigk ^ : conducting qubits . Microwave waveguides with strong disper- ± ;k ak bk ð Þ 2 2 2 sion, even “bandgaps” in frequency, can also be simply realized by 2 2 ω ; À ω þg ω ; À ω þg periodically modulating the geometry of a coplanar transmission ± k 0 k ± k 0 k line25. Such an approach was recently demonstrated in a pio- neering experiment by Liu and Houck26, whereby a qubit was ^ ^ coupled to the localized photonic state within the bandgap of a Here, ak and bk describe the momentum-space annihilation modulated coplanar waveguide (CPW). Satisfying the Bragg operators for the bare waveguide and bare resonator sections, the Ω ω condition in a periodically modulated waveguide requires a lattice index k denotes the wavevector, and the parameters k, 0, and gk constant on the order of the wavelength, however, which trans- quantify the frequency of traveling modes of the bare waveguide, lates to a device size of approximately a few centimeters for the resonance frequency of the microwave resonators, and complete confinement of the evanescent fields in the frequency coupling rate between resonator and waveguide modes, respec- α^ range suitable for microwave qubits. Such a restriction sig- tively. The operators ± ;k represent quasi-particle solutions of the nificantly limits the scaling in this approach, both in qubit composite waveguide, where far from the bandgap the quasi- number and qubit connectivity. particle is primarily composed of the bare waveguide mode, while ω fi An alternative approach for tailoring dispersion in the in the vicinity of 0 most of its energy is con ned in the microwave domain is to take advantage of the metamaterial microwave resonators. ω concept. Metamaterials are composite structures with sub- Figure 1a depicts the numerically calculated energy bands ±,k wavelength components, which are designed to provide an as a function of the wavevector k. It is evident that the dispersion effective electromagnetic response27,28. Since the early micro- has the form of an avoided crossing between the energy bands of wave work, the electromagnetic metamaterial concept has been the bare waveguide and the uncoupled resonators. For small gap expanded and extensively studied across a broad range of sizes, the midgap frequency is close to the resonance frequency of 29–31 ω classical optical sciences ; however, their role in quantum uncoupled resonators 0, and unlike the case of a periodically optics has remained relatively unexplored, at least in part due to modulated waveguide, there is no fundamental relation tying the the lossy nature of many sub-wavelength components. midgap frequency to the lattice constant in this case. The form of ω Improvements in design and fabrication of low-loss super- the band structure near the higher cut-off frequency c+ can be ω − ω ∝ 2 conducting circuit components in circuit QED offer a new approximated as a quadratic function ( c+) k , whereas the ω prospect for utilizing microwave metamaterials in quantum band structure near the lower band-edge c− is inversely 32 ω − ω ∝ 2 applications . Indeed, high quality-factor superconducting proportional to the square of the wavenumber ( c−) 1/k . components such as resonators can be readily fabricated on a The analysis above has been presented for resonators which are chip33, and such elements have been used as a tool for achieving capacitively coupled to a waveguide in a parallel geometry; a phase-matching in near quantum-limited traveling wave similar band structure can also be achieved using series inductive amplifiers34,35 and for tailoring qubit interactions in a multi- coupling of resonators (see Supplementary Note 1 and Supple- mode cavity QED architecture36. mentary Fig. 1). 2 NATURE COMMUNICATIONS | (2018) 9:3706 | DOI: 10.1038/s41467-018-06142-z | www.nature.com/naturecommunications NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-06142-z ARTICLE abthe resonators be of high impedance. Use of high impedance 10 x resonators allows for a larger photonic bandgap and greater +, k waveguide–qubit coupling. For the waveguide QED application of 9 interest this enables denser qubit circuits, both spatially and Bare waveguide 1/2 Ck 8 dispersion spectrally. The impedance of the resonators scales roughly as the inverse 7 square-root of the pitch of the wires in the spiral coils. 0/2 6 Bandgap region Complicating matters is that smaller wire widths have been (imaginary k-vector) Symmetry axis found to introduce larger resonator frequency disorder due to 5 L 39 r kinetic inductance effects .
Load more

Recommended publications
  • Computational Characterization of the Wave Propagation Behaviour of Multi-Stable Periodic Cellular Materials∗
    Computational Characterization of the Wave Propagation Behaviour of Multi-Stable Periodic Cellular Materials∗ Camilo Valencia1, David Restrepo2,4, Nilesh D. Mankame3, Pablo D. Zavattieri 2y , and Juan Gomez 1z 1Civil Engineering Department, Universidad EAFIT, Medell´ın,050022, Colombia 2Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA 3Vehicle Systems Research Laboratory, General Motors Global Research & Development, Warren, MI 48092, USA. 4Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, TX 78249, USA Abstract In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these ma- terials is interesting because they combine the ability of periodic cellular materials to exhibit stop and pass bands with the ability to dissipate energy through cell-level elastic instabilities. Here, we use Bloch periodic boundary conditions to compute the dispersion curves and in- troduce a new approach for computing wide band directionality plots. Also, we deconstruct the wave propagation behavior of this material to identify the contributions from its various structural elements by progressively building the unit cell, structural element by element, from a simple, homogeneous, isotropic primitive. Direct integration time domain analyses of a representative volume element at a few salient frequencies in the stop and pass bands are used to confirm the existence of partial band gaps in the response of the cellular material. Insights gained from the above analyses are then used to explore modifications of the unit cell that allow the user to tune the band gaps in the response of the material.
    [Show full text]
  • Calibrating Evanescent-Wave Penetration Depths for Biological TIRF Microscopy
    Oheim et al. (2019) TIRF calibration Calibrating evanescent-wave penetration depths for biological TIRF microscopy Short title: TIRF image quantification Martin Oheim, *,†,‡,1 *, Adi Salomon, ¶,2 Adam Weissman, ¶ Maia Brunstein, *,†,‡,§ and Ute Becherer£ * SPPIN – Saints Pères Paris Institute for the Neurosciences, F-75006 Paris, France; † CNRS, UMR 8118, Brain Physiology Laboratory, 45 rue des Saints Pères, Paris, F-75006 France; ‡ Fédération de Recherche en Neurosciences FR3636, Faculté de Sciences Fondamentales et Biomédicales, Université Paris Descartes, PRES Sorbonne Paris Cité, F-75006 Paris, France; ¶Department of Chemistry, Institute of Nanotechnology and Advanced Materials (BINA), Bar-Ilan University, Ramat-Gan, 5290002, Israel; §Chaire d’Excellence Junior, Université Sorbonne Paris Cité, Paris, F-75006 France; £Saarland University, Department of Physiology, CIPMM, Building 48, D-66421 Homburg/Saar, Germany; * Address all correspondence to Dr Martin Oheim SPPIN – Saints Pères Paris Institute for the Neurosciences 45 rue des Saints Pères F-75006 Paris Phone: +33 1 4286 4221 (Lab), -4222 (Office) Fax: +33 1 4286 3830 E-mails: [email protected] 1) MO is a Joseph Meyerhof invited professor with the Department of Biomolecular Sciences, The Weizmann Institute for Science, Rehovot, Israel. 2) AS was an invited professor with the Faculty of Fundamental and Biomedical Sciences, Paris Descartes University, Paris, France during the academic year 2017-18. arXiv - presubmission 1 Oheim et al. (2019) TIRF calibration ABSTRACT. Roughly half of a cell’s proteins are located at or near the plasma membrane. In this restricted space, the cell senses its environment, signals to its neighbors and ex- changes cargo through exo- and endocytotic mechanisms.
    [Show full text]
  • Vector Wave Propagation Method Ein Beitrag Zum Elektromagnetischen Optikrechnen
    Vector Wave Propagation Method Ein Beitrag zum elektromagnetischen Optikrechnen Inauguraldissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften der Universitat¨ Mannheim vorgelegt von Dipl.-Inf. Matthias Wilhelm Fertig aus Mannheim Mannheim, 2011 Dekan: Prof. Dr.-Ing. Wolfgang Effelsberg Universitat¨ Mannheim Referent: Prof. Dr. rer. nat. Karl-Heinz Brenner Universitat¨ Heidelberg Korreferent: Prof. Dr.-Ing. Elmar Griese Universitat¨ Siegen Tag der mundlichen¨ Prufung:¨ 18. Marz¨ 2011 Abstract Based on the Rayleigh-Sommerfeld diffraction integral and the scalar Wave Propagation Method (WPM), the Vector Wave Propagation Method (VWPM) is introduced in the thesis. It provides a full vectorial and three-dimensional treatment of electromagnetic fields over the full range of spatial frequen- cies. A model for evanescent modes from [1] is utilized and eligible config- urations of the complex propagation vector are identified to calculate total internal reflection, evanescent coupling and to maintain the conservation law. The unidirectional VWPM is extended to bidirectional propagation of vectorial three-dimensional electromagnetic fields. Totally internal re- flected waves and evanescent waves are derived from complex Fresnel coefficients and the complex propagation vector. Due to the superposition of locally deformed plane waves, the runtime of the WPM is higher than the runtime of the BPM and therefore an efficient parallel algorithm is de- sirable. A parallel algorithm with a time-complexity that scales linear with the number of threads is presented. The parallel algorithm contains a mini- mum sequence of non-parallel code which possesses a time complexity of the one- or two-dimensional Fast Fourier Transformation. The VWPM and the multithreaded VWPM utilize the vectorial version of the Plane Wave Decomposition (PWD) in homogeneous medium without loss of accuracy to further increase the simulation speed.
    [Show full text]
  • Evanescent Wave Imaging in Optical Lithography
    Evanescent wave imaging in optical lithography Bruce W. Smith, Yongfa Fan, Jianming Zhou, Neal Lafferty, Andrew Estroff Rochester Institute of Technology, 82 Lomb Memorial Drive, Rochester, New York, 14623 ABSTRACT New applications of evanescent imaging for microlithography are introduced. The use of evanescent wave lithography (EWL) has been employed for 26nm resolution at 1.85NA using a 193nm ArF excimer laser wavelength to record images in a photoresist with a refractive index of 1.71. Additionally, a photomask enhancement effect is described using evanescent wave assist features (EWAF) to take advantage of the coupling of the evanescent energy bound at the substrate-absorber surface, enhancing the transmission of a mask opening through coupled interference. Keywords: Evanescent wave lithography, solid immersion lithography, 193nm immersion lithography 1. INTRODUCTION The pursuit of optical lithography at sub-wavelength dimensions leads to limitations imposed by classical rules of diffraction. Previously, we reported on the use of near-field propagation in the evanescent field through a solid immersion lens gap for lithography at numerical apertures approaching the refractive index of 193nm ArF photoresist.1 Other groups have also described achievements with various configurations of a solid immersion lens for photolithography within the refractive index limitations imposed by the image recording media, a general requirement for the frustration of the evanescent field for propagation and detection. 2-4 We have extended the resolution of projection lithography beyond the refractive index constraints of the recording media by direct imaging of the evanescent field into a photoresist layer with a refractive index substantially lower than the numerical aperture of the imaging system.
    [Show full text]
  • Electromagnetism As Quantum Physics
    Electromagnetism as Quantum Physics Charles T. Sebens California Institute of Technology May 29, 2019 arXiv v.3 The published version of this paper appears in Foundations of Physics, 49(4) (2019), 365-389. https://doi.org/10.1007/s10701-019-00253-3 Abstract One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. Contents 1 Introduction2 arXiv:1902.01930v3 [quant-ph] 29 May 2019 2 The Weber Vector5 3 The Electromagnetic Field of a Single Photon7 4 The Photon Wave Function 11 5 Lorentz Transformations 14 6 Conclusion 22 1 1 Introduction Electromagnetism was a theory ahead of its time. It held within it the seeds of special relativity. Einstein discovered the special theory of relativity by studying the laws of electromagnetism, laws which were already relativistic.1 There are hints that electromagnetism may also have held within it the seeds of quantum mechanics, though quantum mechanics was not discovered by cultivating those seeds.
    [Show full text]
  • Matter Wave Speckle Observed in an Out-Of-Equilibrium Quantum Fluid
    Matter wave speckle observed in an out-of-equilibrium quantum fluid Pedro E. S. Tavaresa, Amilson R. Fritscha, Gustavo D. Tellesa, Mahir S. Husseinb, Franc¸ois Impensc, Robin Kaiserd, and Vanderlei S. Bagnatoa,1 aInstituto de F´ısica de Sao˜ Carlos, Universidade de Sao˜ Paulo, 13560-970 Sao˜ Carlos, SP, Brazil; bDepartamento de F´ısica, Instituto Tecnologico´ de Aeronautica,´ 12.228-900 Sao˜ Jose´ dos Campos, SP, Brazil; cInstituto de F´ısica, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, RJ, Brazil; and dUniversite´ Nice Sophia Antipolis, Institut Non-Lineaire´ de Nice, CNRS UMR 7335, F-06560 Valbonne, France Contributed by Vanderlei Bagnato, October 16, 2017 (sent for review August 14, 2017; reviewed by Alexander Fetter, Nikolaos P. Proukakis, and Marlan O. Scully) We report the results of the direct comparison of a freely expanding turbulent Bose–Einstein condensate and a propagating optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. The cal- culated second-order correlation together with the typical correlation length of each system is used to compare and substantiate our observations. We believe that the close analogy existing between an expanding turbulent quantum gas and a traveling optical speckle might burgeon into an exciting research field investigating disordered quantum matter. matter–wave j speckle j quantum gas j turbulence oherent matter–wave systems such as a Bose–Einstein condensate (BEC) or atom lasers and atom optics are reality and relevant Cresearch fields. The spatial propagation of coherent matter waves has been an interesting topic for many theoretical (1–3) and experimental studies (4–7).
    [Show full text]
  • A Photomechanics Study of Wave Propagation John Barclay Ligon Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1971 A photomechanics study of wave propagation John Barclay Ligon Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Applied Mechanics Commons Recommended Citation Ligon, John Barclay, "A photomechanics study of wave propagation " (1971). Retrospective Theses and Dissertations. 4556. https://lib.dr.iastate.edu/rtd/4556 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 72-12,567 LIGON, John Barclay, 1940- A PHOTOMECHANICS STUDY OF WAVE PROPAGATION. Iowa State University, Ph.D., 1971 Engineering Mechanics University Microfilms. A XEROX Company, Ann Arbor. Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED A photomechanics study of wave propagation John Barclay Ligon A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject; Engineering Mechanics Approved Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1971 PLEASE NOTE; Some pages have indistinct print.
    [Show full text]
  • 1 the Principle of Wave–Particle Duality: an Overview
    3 1 The Principle of Wave–Particle Duality: An Overview 1.1 Introduction In the year 1900, physics entered a period of deep crisis as a number of peculiar phenomena, for which no classical explanation was possible, began to appear one after the other, starting with the famous problem of blackbody radiation. By 1923, when the “dust had settled,” it became apparent that these peculiarities had a common explanation. They revealed a novel fundamental principle of nature that wascompletelyatoddswiththeframeworkofclassicalphysics:thecelebrated principle of wave–particle duality, which can be phrased as follows. The principle of wave–particle duality: All physical entities have a dual character; they are waves and particles at the same time. Everything we used to regard as being exclusively a wave has, at the same time, a corpuscular character, while everything we thought of as strictly a particle behaves also as a wave. The relations between these two classically irreconcilable points of view—particle versus wave—are , h, E = hf p = (1.1) or, equivalently, E h f = ,= . (1.2) h p In expressions (1.1) we start off with what we traditionally considered to be solely a wave—an electromagnetic (EM) wave, for example—and we associate its wave characteristics f and (frequency and wavelength) with the corpuscular charac- teristics E and p (energy and momentum) of the corresponding particle. Conversely, in expressions (1.2), we begin with what we once regarded as purely a particle—say, an electron—and we associate its corpuscular characteristics E and p with the wave characteristics f and of the corresponding wave.
    [Show full text]
  • 7 Plasmonics
    7 Plasmonics Highlights of this chapter: In this chapter we introduce the concept of surface plasmon polaritons (SPP). We discuss various types of SPP and explain excitation methods. Finally, di®erent recent research topics and applications related to SPP are introduced. 7.1 Introduction Long before scientists have started to investigate the optical properties of metal nanostructures, they have been used by artists to generate brilliant colors in glass artefacts and artwork, where the inclusion of gold nanoparticles of di®erent size into the glass creates a multitude of colors. Famous examples are the Lycurgus cup (Roman empire, 4th century AD), which has a green color when observing in reflecting light, while it shines in red in transmitting light conditions, and church window glasses. Figure 172: Left: Lycurgus cup, right: color windows made by Marc Chagall, St. Stephans Church in Mainz Today, the electromagnetic properties of metal{dielectric interfaces undergo a steadily increasing interest in science, dating back in the works of Gustav Mie (1908) and Rufus Ritchie (1957) on small metal particles and flat surfaces. This is further moti- vated by the development of improved nano-fabrication techniques, such as electron beam lithographie or ion beam milling, and by modern characterization techniques, such as near ¯eld microscopy. Todays applications of surface plasmonics include the utilization of metal nanostructures used as nano-antennas for optical probes in biology and chemistry, the implementation of sub-wavelength waveguides, or the development of e±cient solar cells. 208 7.2 Electro-magnetics in metals and on metal surfaces 7.2.1 Basics The interaction of metals with electro-magnetic ¯elds can be completely described within the frame of classical Maxwell equations: r ¢ D = ½ (316) r ¢ B = 0 (317) r £ E = ¡@B=@t (318) r £ H = J + @D=@t; (319) which connects the macroscopic ¯elds (dielectric displacement D, electric ¯eld E, magnetic ¯eld H and magnetic induction B) with an external charge density ½ and current density J.
    [Show full text]
  • Quantization of the Free Electromagnetic Field: Photons and Operators G
    Quantization of the Free Electromagnetic Field: Photons and Operators G. M. Wysin [email protected], http://www.phys.ksu.edu/personal/wysin Department of Physics, Kansas State University, Manhattan, KS 66506-2601 August, 2011, Vi¸cosa, Brazil Summary The main ideas and equations for quantized free electromagnetic fields are developed and summarized here, based on the quantization procedure for coordinates (components of the vector potential A) and their canonically conjugate momenta (components of the electric field E). Expressions for A, E and magnetic field B are given in terms of the creation and annihilation operators for the fields. Some ideas are proposed for the inter- pretation of photons at different polarizations: linear and circular. Absorption, emission and stimulated emission are also discussed. 1 Electromagnetic Fields and Quantum Mechanics Here electromagnetic fields are considered to be quantum objects. It’s an interesting subject, and the basis for consideration of interactions of particles with EM fields (light). Quantum theory for light is especially important at low light levels, where the number of light quanta (or photons) is small, and the fields cannot be considered to be continuous (opposite of the classical limit, of course!). Here I follow the traditinal approach of quantization, which is to identify the coordinates and their conjugate momenta. Once that is done, the task is straightforward. Starting from the classical mechanics for Maxwell’s equations, the fundamental coordinates and their momenta in the QM sys- tem must have a commutator defined analogous to [x, px] = i¯h as in any simple QM system. This gives the correct scale to the quantum fluctuations in the fields and any other dervied quantities.
    [Show full text]
  • Analytical and Numerical Analysis of Low Optical Overlap Mode Evanescent Wave
    Analytical and Numerical Analysis of Low Optical Overlap Mode Evanescent Wave Chemical Sensors A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Anupama Solam August 2009 © 2009 Anupama Solam. All Rights Reserved. 2 This thesis titled Analytical and Numerical Analysis of Low Optical Overlap Mode Evanescent Wave Chemical Sensors by ANUPAMA SOLAM has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology by Ralph D. Whaley, Jr. Assistant Professor of Electrical Engineering and Computer Science Dennis Irwin Dean, Russ College of Engineering and Technology 3 ABSTRACT SOLAM, ANUPAMA, M.S., August 2009, Electrical Engineering Analytical and Numerical Analysis of Low Optical Overlap Mode Evanescent wave Chemical Sensors (106 pp.) Director ofThesis: Ralph D. Whaley, Jr Demands for integrated optical (IO) sensors have tremendously increased over the years due to issues concerning environmental pollution and other biohazards. Thus, an integrated optical sensor with good detection scheme, sensitivity and low cost is needed. This thesis proposes a novel evanescent wave chemical sensing (EWCS) technique for ammonia (gaseous) and nitrite (aqueous) detection utilizing a low optical overlap mode (LOOM) waveguide structure. This design has the advantage of low modal fill factor and more field interaction with the sensing region compared to fiber sensors; hence eliminating the difficulty faced by traditional EWCS designs. Effective refractive index is a crucial parameter for analyzing the sensitivity, which is compared using the analytical and numerical methods such as finite element method (FEM) and semi-vectorial beam propagation method (BPM).
    [Show full text]
  • Types of Waves Periodic Motion
    Lecture 19 Waves Types of waves Transverse waves Longitudinal waves Periodic Motion Superposition Standing waves Beats Waves Waves: •Transmit energy and information •Originate from: source oscillating Mechanical waves Require a medium for their transmission Involve mechanical displacement •Sound waves •Water waves (tsunami) •Earthquakes •Wave on a stretched string Non-mechanical waves Can propagate in a vacuum Electromagnetic waves Involve electric & magnetic fields •Light, • X-rays •Gamma waves, • radio waves •microwaves, etc Waves Mechanical waves •Need a source of disturbance •Medium •Mechanism with which adjacent sections of medium can influence each other Consider a stone dropped into water. Produces water waves which move away from the point of impact An object on the surface of the water nearby moves up and down and back and forth about its original position Object does not undergo any net displacement “Water wave” will move but the water itself will not be carried along. Mexican wave Waves Transverse and Longitudinal waves Transverse Waves Particles of the disturbed medium through which the wave passes move in a direction perpendicular to the direction of wave propagation Wave on a stretched string Electromagnetic waves •Light, • X-rays etc Longitudinal Waves Particles of the disturbed medium move back and forth in a direction along the direction of wave propagation. Mechanical waves •Sound waves Waves Transverse waves Pulse (wave) moves left to right Particles of rope move in a direction perpendicular to the direction of the wave Rope never moves in the direction of the wave Energy and not matter is transported by the wave Waves Transverse and Longitudinal waves Transverse Waves Motion of disturbed medium is in a direction perpendicular to the direction of wave propagation Longitudinal Waves Particles of the disturbed medium move in a direction along the direction of wave propagation.
    [Show full text]