Quantum Dots in Photonic Structures (Nanophotonics with Quantum Dots) Wednesdays, 17.00, SDT Jan Suffczyński Projekt Fizyka Plus nr POKL /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 light- matter interaction

Overview of the course: I. Physics of the light- matter interaction 1 1/e 0

Overview of the course I Physics of the light- matter 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 Transmission Electron Microscope cross-sectional image, Offermans et al., Phys. Rev. B 2005 CdTe/ZnTe Quantum Dot emission InAs/AlAs Quantum Dot Correlated counts T = 2 K

Overview of the course I Physics of the light- matter 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 I Physics of the light- matter interaction IV Implementations, challenges, … III Quantum Dot in Optical microcavity II Semiconductor Quantum Dot as a source of the light

+ QDs and plasmonics Overview of the course: IV. Practical implementations and outlook © Evident Technologies X. Gao et al., Nature Biotechnology’ 2004

1988: Wolfram Mathematica -symbolic language for algorithmic computation 2009: - web computational engine accepting free form input Exercises © Wolfram Alpha

1988: Wolfram Mathematica -symbolic language for algorithmic computation 2009: - web computational engine accepting free form input Exercises © Wolfram Alpha Downloadable.nb files at on the evening before the lecture Calculations and interactive data plotting during the lecture

A trendy subject of the course source: ISI Web of Knowledge

A trendy subject of the course 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 “un-creatable and indestructible” photons by Gilbert N. Lewis unambiguous confirmation – single photon correlation experiment, Kimble et al. Nature (1926)

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=  0 E, B=  0 H. Electric and Magnetic fields produce forces on charges

Maxwell’s Equation’s (in Differential Form) Gauss’s Law Gauss’s Law for Magnetism Faraday’s Law Ampere’s Law (in full extent) James Clerk Maxwell Changing E-field results in changing H-field resulting in changing E-field….

Electromagnetic wave

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 WavenumberSpeed of Light Angular Frequency Wavelength c k  kk Dispersion relation

Electromagnetic spectrum λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ 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...)

Energy density emitted by the Sun Cavity quantum electrodynamics (CQED) What happens to a photon confined in a box? (10*10 -9 m)

Optical cavity mode (lat. modus) Condition for resonance in a cavity: d 2d = N N = 1, 2, 3,... (round trip distance 2d equal to an integral number of wavelengths) mirror

Surprising cavity effects at the nanoscale: the Casimir effect Hendrik Casimir ( ) 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). A net pressure from the excluded wavelengths

The Casimir effect – how to measure it and how strong is it? Example: two mirrors with an area of 1 cm 2 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 standing- wave pattern. Ring resonators: the light circulates in two different directions. A ring resonator has no end mirrors

Some others: Ease of fabrication Connectivity to waveguides Integration in larger circuits Intrinsic ones: Cavity mode (= elecromagnetic field distribution) Quality factor (= temporal time) Mode volume (= spatial confinement) Free spectral range (= spectral mode separation) Cavities: important parameters

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 1 1/e 2/  = photon decay time Consider leak-out of the photon from a cavity: Optical period T = 1/f 0 = 2  /  0 0 E =Electric field at a certain position u =Energy density 1. Definition of Q via energy storage: Energy density decay:

Summary General properties of EM radiation Basics of optical microcavities Next lecture: Spontaneous emission and its control (Prucell effect, strong light matter-coupling)