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Quantum Dots in Photonic Structures (Nanophotonics with Quantum Dots) Jan Suffczyński Wednesdays, 17.00, SDT Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki Plan for today 1. Overview of the course 2. EM radiation 3. Optical cavities Overview of the course I Physics of the lightmatter interaction Overview of the course: I. Physics of the light- matter interaction E 1 1/e 0 t Overview of the course I Physics of the lightmatter coupling II Semiconductor Quantum Dot as a source of the light Overview of the course: II. Semiconductor Quantum Dot as a source of the light CdTe/ZnTe Quantum Dot emission -PL Intensity [arb. units] InAs/AlAs Quantum Dot T=2K CX XX Correlated counts 2210 Transmission Electron Microscope cross-sectional image, Offermans et al., Phys. Rev. B 2005 X 2215 2220 2225 Photon Energy [m eV] Overview of the course I Physics of the lightmatter interaction III Quantum Dot in Optical microcavity II Semiconductor Quantum Dot as a source of the light Overview of the course: III. Quantum Dot in Optical microcavity Overview of the course IV Implementations, challenges, … III Quantum Dot in Optical microcavity I Physics of the lightmatter interaction II Semiconductor Quantum Dot as a source of the light Overview of the course: IV. Practical implementations and outlook © Evident Technologies X. Gao et al., Nature Biotechnology’ 2004 + QDs and plasmonics © Wolfram Alpha Exercises 1988: Wolfram Mathematica - symbolic language for algorithmic computation 2009: - web computational engine accepting free form input © Wolfram Alpha Exercises • Downloadable .nb files at www.fuw.edu.pl/~jass/wyklad.html on the evening before the lecture • Calculations and interactive data plotting during the lecture 1988: Wolfram Mathematica - symbolic language for algorithmic computation 2009: - web computational engine accepting free form input 1500 "Quantum Dot" or QD 1000 500 0 1970 1980 1990 2000 Publication Year 2010 Published Items in Each Year Published Items in Each Year A trendy subject of the course 3000 2500 photonic 2000 1500 1000 500 0 1970 1980 1990 2000 Publication Year 2010 source: ISI Web of Knowledge 1250 "Quantum Dot" or QD "Quantum Well" or QW 1000 750 500 250 0 1970 1980 1990 2000 Publication Year 2010 Published Items in Each Year Published Items in Each Year A trendy subject of the course 3000 2500 photonic 2000 1500 1000 500 0 1970 1980 1990 2000 Publication Year 2010 source: ISI Web of Knowledge • Development of the technology of the sample production • Nanoscale control of the structure parameters Photonics • The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com) • The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation Photonics • The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com) • The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation Photonics • The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. (after: photonics.com) • The science of light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation • Photonics = electronics using a photons instead of electrons A brief history of the photon • Ancient Greek φῶς (phōs) = “light” • Particle vs wave models of the light • 1850 – Young experiment A brief history of the photon • Ancient Greek φῶς (phōs) = “light” • Particle vs wave models of the light • 1850 – Young’s experiment Interference Pattern Develops • Stages of two-slit interference pattern. • The pattern of individually exposed grains progresses from (a) 28 photons to (b) 1000 photons to (c) 10,000 photons. • As more photons hit the screen, a pattern of interference fringes appears. Interference Pattern for three slits? A brief history of the photon • • • • • • • • • Ancient Greek φῶς (phōs) = “light” Particle vs wave models of the light 1805 – Young’s experiment – wave! 1865 – James Clerk Maxwell's prediction that light was an electromagnetic wave 1888 – Heinrich Hertz's experimental confirmation by detection of radio waves 1905 – Albert Einstein, “light quantum” (das Lichtquant) and photoelectric effect 1923 – Compton, particle-like character of the light Nature (1926) 1926 - “un-creatable and indestructible” photons by Gilbert N. Lewis 1977 - unambiguous confirmation – single photon correlation experiment, Kimble et al. The light Classical picture The light Classical picture Quantum picture Maxwell’s Equations • Electromagnetism - one of the four fundamental forces (others: gravity and strong & weak nuclear forces) • Fundamental quantities: Electric field E, magnetic field H, and D(E), B(H). • In free space: D=0E, B=0H. • Electric and Magnetic fields produce forces on charges Maxwell’s Equation’s (in Differential Form) Gauss’s Law D James Clerk Maxwell B 0 Gauss’s Law for Magnetism B E Faraday’s Law t D Ampere’s Law (in full extent) H J t Changing E-field results in changing H-field resulting in changing E-field…. Electromagnetic wave 2B 2B 0 0 2 2 x t Speed: v 1 o o . E Emax coskx t B Bmax coskx t Properties of EM Waves • The solutions to Maxwell’s equations in free space are wavelike • Electromagnetic waves travel through free space at the speed of light. • The electric and magnetic fields of a plane wave are perpendicular to each other and the direction of propagation (they are transverse). • The ratio of the magnitudes of the electric and magnetic fields is c. • EM waves obey the superposition principle. Some Important Quantities E Emax coskx t B Bmax coskx t 1 c 0 0 c f Wavelength 2f k k k Speed of Light 2 c Angular Frequency Wavenumber Dispersion relation Electromagnetic spectrum λ ≈ 700 - 420 nm λ ≈ 10-4 - 10-6 m λ≈ λ ≈ 10-1 - 103 m 10-2 - 10-3 m λ ≈ 10-9 - 10-11 m λ ≈ 10-12 - 10-14 m Cavity quantum electrodynamics (CQED) • Developed from the 50s of XX cent. • CQED deals with modications of the electromagnetic field properties that are induced by the presence of boundaries for the field (mirrors, interfaces...) Cavity quantum electrodynamics (CQED) What happens to a photon confined in a box? 5 (10*10-9 m)3 10 10 10 Energy density emitted by the Sun Optical cavity mode (lat. modus) mirror mirror d Condition for resonance in a cavity: 2d = N N = 1, 2, 3, ... (round trip distance 2d equal to an integral number of wavelengths) Surprising cavity effects at the nanoscale: the Casimir effect Hendrik Casimir (1909-2000) • A net pressure from the excluded wavelengths H. B. G. Casimir, On the attraction between two perfectly conducting plates, Proceedings of the Royal Netherlands Academy of Arts and Sciences, Vol. 51, pp. 793–795 (1948). The Casimir effect – how to measure it and how strong is it? Example: two mirrors with an area of 1 cm2 separated by a distance of 1 μm have an attractive Casimir force of about 10–7 N When the sphere is brought near to the plate, an attractive Casimir force causes the cantilever to bend. Bouncing a laser off the top of the cantilever and photodiodes to monitors the effect. The Casimir effect: a „particle” view Electron-positron production Quantum fluctuations of the vacuum create virtual particles (real for an instant) that produce mechanical force Optical resonator Two basic types: Linear resonators: the light bounces back and forth between two end mirrors. There are counter propagating waves, which interfere with each other to form a standingwave pattern. Ring resonators: the light circulates in two different directions. A ring resonator has no end mirrors Cavities: important parameters Intrinsic ones: • Cavity mode (= elecromagnetic field distribution) • Quality factor (= temporal time) • Mode volume (= spatial confinement) • Free spectral range (= spectral mode separation) Some others: • Ease of fabrication • Connectivity to waveguides • Integration in larger circuits Quality factor of the optical cavity • Ideal cavity: the photon preserved infinitely long • In real: the photon escapes from the cavity within the finite time Quality factor Q: • Describes ability of the cavity to preserve a photon • Compares the frequency at which a system oscillates to the rate at which it dissipates its energy A resonant cavity analogue: resonant LC curquit Quality factor Q Consider leak-out of the photon from a cavity: E = Electric field at a E certain position 1 t 1 u = Energy density 2 E t cos 0 t e 1/e 0 t 2/ = photon decay time Optical period T = 1/f0 = 2/0 1. Definition of Q via energy storage: u t 1 t e 2 2 e t Energy density decay: dut e t dt 0 StoredEnergy u t 2 Q 2 2 dut EnergyLostPerOptCycle T T dt Summary • General properties of EM radiation • Basics of optical microcavities Next lecture: • Spontaneous emission and its control (Prucell effect, strong light matter-coupling)