Nanophysics: Main trends - uio.no

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Nanomechanics Nano-opto-electronics Nanophysics: Main trends 1. Why light is of particular interest for nanophysics?

Transcript of Nanophysics: Main trends - uio.no

Page 1: Nanophysics: Main trends - uio.no

Nan

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Nano-opto-electronics

Nanophysics:Main trends

1. Why light is of particular interest for nanophysics?

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Nanophotonics• Main issues• Light interaction with small structures

• Molecules• Nanoparticles (semiconductor and metallic)• Microparticles

• Photonic crystals• Nanoplasmonics• Quantum cascade laser

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Nanophotonics 3

The photon (Greek: φῶς, phōs, light) is an elementary particle. It is the quantum ofthe electromagnetic field including electromagnetic radiation such as light andradio waves, and the force carrier for the electromagnetic force. Photons aremassless, so they always move at the speed of light in vacuum, 299792458 m/s.The photon belongs to the class of bosons. Photon has no electrical charge andspin equal to 1. In contrast, phonons, also bosons, which are quantum particles ofmechanical vibrations, have spin 0.

https://en.wikipedia.org/wiki/Photon

The photon

Fermions

Bosons

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4Nanophotonics

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The Abbe diffraction limit

The observation of sub-wavelength structures with microscopes is difficult

because of the Abbe diffraction limit. found in 1873 that light with

wavelength λ, traveling in a medium with refractive index n and converging to a

spot with angle will make a spot with radius d = / 2n sin.

The denominator n sin is called the (NA) and can reach

about 1.4–1.6 in modern optics, hence the Abbe limit is d = λ/2.8. Considering green

light around 500 nm and a NA of 1, the Abbe limit is roughly d = λ/2 = 250 nm

(0.25 μm), which is small compared to most biological cells (1 μm to 100 μm), but

large compared to viruses (100 nm), proteins (10 nm) and less complex molecules

(1 nm). To increase the resolution, shorter wavelengths can be used such as UV and

X-ray microscopes. These techniques offer better resolution but are expensive,

suffer from lack of contrast in biological samples and may damage the sample.

https://en.wikipedia.org/wiki/Diffraction-limited_system

4. What limitation in resolution sets Abbe diffraction limit? What are the numerical aperture and optical resolution in comparison with

wavelength of light? Is it possible to overcome diffraction limit in imaging?

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Press Release

8 October 2014 has decided to award the Nobel Prize in Chemistry for 2014 to

Eric BetzigJanelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA,

Stefan W. HellMax Planck Institute for Biophysical Chemistry, Göttingen, and German Cancer Research Center, Heidelberg, Germany and

William E. MoernerStanford University, Stanford, CA, USA

“for the development of

super-resolved fluorescence microscopy"

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/press.html

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Nanophotonics 7

Eric Betzig - Nobel Lecture slides - Nobelprize.org

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Surpassing the limitations of the light microscope

For a long time optical microscopy was held back by a presumed limitation: that it would never obtain a better resolution than half the wavelength of light. Helped by fluorescent molecules the Nobel Laureates in Chemistry 2014 ingeniously circumvented this limitation. Their ground-breaking work has brought optical microscopy into the nanodimension.

In what has become known as nanoscopy, scientists visualize the pathways of individual molecules inside living cells. They can see how molecules create synapses between nerve cells in the brain; they can track proteins involved in Parkinson's, Alzheimer's and Huntington's diseases as they aggregate; they follow individual proteins in fertilized eggs as these divide into embryos.

It was all but obvious that scientists should ever be able to study living cells in the tiniest molecular detail. In 1873, the microscopist Ernst Abbe stipulated a physical limit for the maximum resolution of traditional optical microscopy: it could never become better than 0.2 micrometres. Eric Betzig, Stefan W. Helland William E. Moerner are awarded the Nobel Prize in Chemistry 2014 for having bypassed this limit. Due to their achievements the optical microscope can now peer into the nanoworld.

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/press.html

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Two separate principles are rewarded. One enables the method stimulated emission depletion (STED) microscopy, developed by Stefan Hell in 2000. Two laser beams are utilized; one stimulates fluorescent molecules to glow, another cancels out all fluorescence except for that in a nanometre-sized volume. Scanning over the sample, nanometre for nanometre, yields an image with a resolution better than Abbe's stipulated limit.

Eric Betzig and William Moerner, working separately, laid the foundation for the second method, single-molecule microscopy. The method relies upon the possibility to turn the fluorescence of individual molecules on and off. Scientists image the same area multiple times, letting just a few interspersed molecules glow each time. Superimposing these images yields a dense super-image resolved at the nanolevel. In 2006 Eric Betzig utilized this method for the first time.

Today, nanoscopy is used world-wide and new knowledge of greatest benefit to mankind is produced on a daily basis.

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/press.html

5. Explain principle of super-resolved fluorescence microscopy (Nobel Prize in Chemistry 2014) that ‘brought optical microscopy

into the nanodimension’.

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http://www.nobelprize.org/nobel_prizes/physics/laureates/2014/

New light to

illuminate the world

This year's Nobel Laureates are

rewarded for having invented a new

energy-efficient and environment-

friendly light source – the blue

light-emitting diode (LED). In the

spirit of Alfred Nobel the Prize

rewards an invention of greatest

benefit to mankind; using blue

LEDs, white light can be created in

a new way. With the advent of LED

lamps we now have more long-

lasting and more efficient

alternatives to older light sources.

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‘When Isamu Akasaki, Hiroshi Amano and Shuji Nakamura produced bright blue light beamsfrom their semiconductors in the early 1990s, they triggered a fundamental transformation oflighting technology. Red and green diodes had been around for a long time but without blue light,white lamps could not be created. Despite considerable efforts, both in the scientific communityand in industry, the blue LED had remained a challenge for three decades.

They succeeded where everyone else had failed. Akasaki worked together with Amano at theUniversity of Nagoya, while Nakamura was employed at Nichia Chemicals, a small company inTokushima. Their inventions were revolutionary. Incandescent light bulbs lit the 20th century; the21st century will be lit by LED lamps.

White LED lamps emit a bright white light, are long-lasting and energy-efficient. They areconstantly improved, getting more efficient with higher luminous flux (measured in lumen) perunit electrical input power (measured in watt). The most recent record is just over 300 lm/W,which can be compared to 16 for regular light bulbs and close to 70 for fluorescent lamps. Asabout one fourth of world electricity consumption is used for lighting purposes, the LEDscontribute to saving the Earth's resources. Materials consumption is also diminished as LEDs lastup to 100,000 hours, compared to 1,000 for incandescent bulbs and 10,000 hours for fluorescentlights.

The LED lamp holds great promise for increasing the quality of life for over 1.5 billion peoplearound the world who lack access to electricity grids: due to low power requirements it can bepowered by cheap local solar power.

The invention of the efficient blue LED is just twenty years old, but it has already contributed tocreate white light in an entirely new manner to the benefit of us all.’

http://www.nobelprize.org/nobel_prizes/physics/laureates/2014/press.html

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2018

https://www.nobelprize.org/prizes/physics/2018/summary/

The Nobel Prize in Physics 2018 was awarded "for groundbreaking inventions in the

field of laser physics" with one half to Arthur Ashkin "for the optical tweezers and their

application to biological systems", the other half jointly to Gérard Mourou and Donna

Strickland "for their method of generating high-intensity, ultra-short optical pulses."

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2018

https://www.nobelprize.org/prizes/physics/2018/summary/

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2018

https://www.nobelprize.org/prizes/physics/2018/summary/

Ultra-short optical pulses

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2018

https://www.nobelprize.org/prizes/physics/2018/summary/

Ultra-short optical pulses

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Introduction 16

2018 highlights

• Engineers produce smallest 3-D transistor yet: 2.5 nm

• Light triggers gold in unexpected way

• Borophene advances as 2-D materials platform

• Insights into magnetic bacteria may guide research into medical nanorobots

• Nanoscale tweezers can perform single-molecule 'biopsies' on individual cells

• Holey graphene as Holy Grail alternative to silicon chips

Nanotweezers extracting a mitochondrion from a cell. Credit: Imperial College London

Next-generation optical components. Credit: Link Research Group/Rice University

Transistors that measure only 3 nm wide. Credit: Massachusetts Institute of Technology

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Introduction 17

2018 highlights

• Boron can form a purely honeycomb, graphene-like 2-D structure

• Exploring new spintronics device functionalities in graphene – topological insulator heterostructures

• Covalently modified two-dimensional arsenic is explored

• Cost-effective method produces semiconducting films from materials that outperform silicon

• Flexy, flat and functional magnets are produced

• Researchers discover directional and long-lived nano-light in a 2-D material

Directional nanolight propagation: Credit: Shaojuan Li

Graphene – topological insulator: Credit: Dmitrii Khokhriakov, Chalmers University of Technology

High resolution STM images of borophenemonolayer. Credit: ©Science China Press

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2019 highlights

• Next-generation optics in just two minutes of cooking time.

• Laser physicists have taken snapshots of how C60 carbon molecules react to extremely short pulses of intense infrared light.

• Researchers develop direct-write quantum calligraphy in monolayer semiconductors allowing single-photon emission.

• A polariton filter turns ordinary laser light into

quantum light.

Credit: Macquarie University

The laserinduced diffraction of the ejected electron is used to image the transformation of C60. Credit: Alexander Gelin

The new method employs a natural process already used in fluid mechanics: dewetting. Credit: © Vytautas Navikas / 2019 EPFL

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Electro-optical device provides solution to faster computing memories and processors

https://phys.org/news/2019-11-electro-optical-device-solution-faster-memories.html

"Plasmonic nanogap enhanced phase-change devices with dual electrical-optical functionality" Science Advances (2019). advances.sciencemag.org/content/5/11/eaaw2687

2019 highlight

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Electro-optical device provides solution to faster computing memories and processors

"Plasmonic nanogap enhanced phase-change devices with dual electrical-optical functionality" Science Advances (2019). advances.sciencemag.org/content/5/11/eaaw2687

2019 highlight

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January 10, 2020

Laser physics: At the pulse of a light wavehttps://phys.org/news/2020-01-laser-physics-pulse.html

M. Kubullek et al, Single-shot carrier–

envelope-phase measurement in ambient

air, Optica (2020).

DOI: 10.1364/OPTICA.7.000035

2020 highlight

Physicists in the Laboratory for

Attosecond Physics at Ludwig-

Maximilians-Universitaet (LMU) in Munich

and at the Max Planck Institute for

Quantum Optics (MPQ) have developed

a novel type of detector that enables the

oscillation profile of light waves to be

precisely determined.

In the case of visible light, the physical

distance between successive peaks of

the light wave is less than 1 micrometer,

and peaks are separated in time by less

than 3 millionths of a billionth of a second

(< 3 femtoseconds).

The interaction between the pulse and

molecules in the air results in a short

burst of electric current, whose direction

depends on the position of the peak of

the light wave.

by Ludwig Maximilian University of Munich

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https://phys.org/news/2020-01-physicists-nanoresonators.html

2020 highlight

Conversion (doubling) of light frequency using a nanoresonator Credit: (left)

Anastasia Shalaeva; (right) Koshelev et al. Science

by ITMO University

JANUARY 22, 2020

Physicists trap light in nanoresonators for record time

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https://phys.org/news/2020-01-physicists-nanoresonators.html

2020 highlightby ITMO University

JANUARY 22, 2020

Physicists trap light in nanoresonators for record time

• "We used gallium arsenide to create cylinders around 700nanometers in height and with varying diameters close to 900nanometers. They're almost invisible to the naked eye. As ourexperiments have shown, the reference particle had capturedlight for a time exceeding 200 times the period of one waveoscillation. Usually, for particles of that size the ratio is five to tenperiods of wave oscillations. And we obtained 200! " says KirillKoshelev, the the first co-author of the paper.

• It has potential applications in various sensing devices and evenspecial glass coatings that would make it possible to producecolorful night-vision.

Kirill Koshelev et al, Subwavelength dielectric resonators for nonlinear

nanophotonics, Science (2020). DOI: 10.1126/science.aaz3985

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https://phys.org/news/2021-02-nanolight.html

2021 highlight

by Carla Cantor, Columbia University

Nature sets a limit on how tightly light can be focused. Even in microscopes, two differentobjects that are closer than this limit would appear to be one. But within a special classof layered crystalline materials—known as van der Waals crystals—these rules can,sometimes, be broken. In these special cases, light can be confined without any limit inthese materials, making it possible to see even the smallest objects clearly.

A. J. Sternbach et al, Programmable hyperbolic polaritons in van der Waals semiconductors, Science (2021). DOI:10.1126/science.abe9163

Switching nanolight on and off

FEBRUARY 4, 2021

An optically excited gas ofelectronic carriers confinedto the planes of thelayered van-der Waalssemiconductor tungstendiselenide is shown. Theconsequent hyperbolicresponse permits passageof nanolight. Credit: EllaMaru Studio

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Quantum dots 25

http://www.idtechex.com/research/reports/quantum-dots-2016-2026-applications-markets-manufacturers-000452.asp

QDs promise to make LCD screens more colourful and more energy efficient. Sony wasthe first to commercialize a quantum dot LCD TV in 2013 and there are now severalcompanies (including Samsung) offering TVs with quantum dots.

3. Give examples of nano application in generation and transmission of light.

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Distribution of Pd-loaded bacteria on a glass substrate

(a magnified view, polarized image)

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Distribution of Pd-loaded bacteria on a glass substrate

(a magnified view, polarized image)

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Distribution of Pd-loaded bacteria on a glass substrate (a

magnified view, polarization cancelled on the right image)

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Josephson generation in living organisms

Typical voltages in a human body vary between 20 and 200 mV with the average membrane potential

of about 70 mV. These voltages correspond to 4.8, 48.4 and 16.9 THz if generated by normal

conductor and to 9.6, 96.8 and 33.8 THz if generated by Josephson junctions. The corresponding

wavelengths are in the range from 3.1 to 31 m in superconducting and 6.2 to 62 m in normal case.

The Josephson membrane-potential voltage could produce radiation with wavelength 8.8 m, which

is in the transparency window for surrounding atmosphere. There is possibility of

electromechanical resonance in cell microtubules.

Atmospheric absorption across the electromagnetic

spectrum. Image Credit: NASA (public domain).

Mikheenko, Pavlo (2020). Nano superconductivity and quantum processing of information in living organisms, In 2020

IEEE 10th International Conference on “Nanomaterials: Applications & Properties” (NAP – 2020). IEEE. ISBN 978-1-

7281-8506-4. Article. s 02SNS02-1 - 02SNS02-4

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Is it possible to engineer new materials with useful optical properties?

Scientists have gone from big lenses to optical fibers, photonic crystals , …

What are the smallest possible devices with optical functionality ? Does the diffraction set a fundamental limit ?

Possible solution: metal optics/plasmonics

Main issues

Basic problem to solve:

Understand behaviors of systems with non-uniform distributions of dielectric response

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Light interaction with small structures

Main features

Molecules:Light scattering due to harmonically driven dipole oscillator.

Nanoparticles:• Insulators: Rayleigh Scattering (blue sky)• Semiconductors: Resonant absorption at ħω ≥ EGAP (size dependent

fluorescence…)• Metals: Resonant absorption at surface plasmon frequency.

Microparticles (Particles with dimensions on the order of λ or bigger ):• Enhanced forward scattering,• Intuitive ray-picture useful,• Rainbows due to dispersion H20,• Applications: resonators, lasers, etc…

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2. What are main features of the interaction of light with nano and micro particles? Could you describe scattering of light by

molecular dipoles, insulating, semiconducting and metal nanoparticles? What are specific features of light scattering on particles with

dimensions on the order of its wavelength or bigger?

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Scattered light

Molecules: Scattering by a harmonic oscillator

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Radiation field

6. Describe resonance scattering of light by a harmonic oscillator. To what power of frequency is proportional the intensity of

scattered light? Does scattering occur in backward direction only?

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The blue sky

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ω0 ≈ 1015 Hz

7. What are specific features of non-resonant scattering on O2 and N2 molecules or insulating nanoparticles? Why sky is blue and

clouds are white?

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Semiconductor nanopartilces

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Movie 2

8. Explain bandgap value and photoluminescence frequency dependence on the size of semiconducting nanoparticles. How can one

vary size of semiconducting nanoparticles?

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Important application: Tagging biomaterials with semiconductor nanocrystals

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9. Give examples of the use of metallic and semiconducting nanoparticles in art of visual effects and biomaterials tagging.

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Metallic nanoparticles

Lycurgus cup, 4th century AD (now at the British Museum, London).

The colors originate from metal nanoparticles embedded in the glass. At places, where light is transmitted through the glass it appears red, at places where light is scattered near the surface, the scattered light appears greenish.

Schematic view of the excitation of a particleplasmon oscillation in a metal nanoparticle by an external light field.

Applications: • stained glass, • gold nanoparticles or colloids are used to label organic substances or biological

material (gold has a very high contrast compared to organic substances due to its high electron density, and is therefore easily distinguished in electron microscopy);

• enhance nonlinear optical effects;• confinement of electromagnetic energy in a very small region in space on plasmon excitation has been suggested to guide light in future photonic devices

36Nanophotonics

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Nanophotonics 37

Drude model of the dielectric function of a bulk metal (1)

Newton’s law for an electron:

Fourier:

Current:

10. Describe Drude model of the dielectric function in a metal. Why are metals shiny? What is cut-off frequency for total reflection?

Polarization:0

1 0

00 0

1

https://en.wikipedia.org/wiki/Maxwell%27s_equations

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Nanophotonics 38

Drude model of the dielectric function of a bulk metal (2)

http://halas.rice.edu/conversions

Somewhat below plasma frequency

0

0

0

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Nanophotonics 39

11. Give example of cut-off frequency use in energy saving window nano-coatings.

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Nanophotonics 40

12. Describe the plasmon resonance. What technique is usually used for observation of bulk and surface plasmons? How the energies of

bulk and surface plasmon modes are related to each other??

𝜔𝑝2 ≡

𝑛𝑒2

𝜀0𝑚∗

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Nanophotonics 41

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Nanophotonics 42

Drude model of the dielectric function of a bulk metal (2)

http://halas.rice.edu/conversions

Somewhat below plasma frequency

0

0

0

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Simple model for nanoparticles – the quasi-static Rayleigh theory

Relative to the medium dielectric function,

leads to polarizability

The scattering and absorption cross-sections are then

Resonance condition:For free particles in vacuum, resonance energies of 3.48 eV for silver (near UV) and 2.6 eV for gold (blue) are calculated. When embedded in polarizable media, the resonance shifts towards lower energies, i.e. towards the red side of the visible spectrum.

43Nanophotonics

http://farside.ph.utexas.edu/teaching/jk1/lectures/node45.html

13. Introduce relative to the medium dielectric function and describe quasi-static Rayleigh theory in application to nanoparticles. What are

condition of resonance and the calculated resonance energies for silver and gold nanoparticles in vacuum and a polarizable media?

What are the limits and problems of this electrodynamic description?

https://en.wikipedia.org/wiki/Clausius%E2%80%93Mossotti_relation

cross-section

CGS:

SI:

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Dielectric function is usually calculated using the so-called Mie theory.

Results for a 60 nm gold sphere embedded in a medium with refractive index n = 1.5.

Limits of the electrodynamic theory:

• bulk values for the material properties entering the calculations can be invalid for particles with nanometer dimensions;

• Possible effects could be quantum mechanical confinement, surface melting, surface adsorbates, etc;

• it is unclear whether the assumptions in the theoretical models, for example sharp boundaries, no many-body effects, etc., are reasonable.

44Nanophotonics

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45Nanophotonics

14. Describe peculiarities of the light scattering by nanoparticles with size d , d and d 2. In what case there is very strong

forward scattering and peaks corresponding to different colours? What happens with light-matter interaction when size of particles (in

particular spheres) goes above the nanometer scale?

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Microspheres:

•The picture is well described by geometric optics;• Microsphere can act as a resonator

46Nanophotonics

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Nanophotonics 47

Photonic crystals – “Optical semiconductors”

Photonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons.

SEM micrographs of a photonic -crystal fiber produced at US Naval Research Laboratory.

The diameter of the solid core at the center of the fiber is 5 µm, while (right) the diameter of the holes is 4 µm

To create a biosensor, a Photonic Crystal may be optimized to provide an extremely narrow resonant mode whose wavelength is particularly sensitive to modulations induced by the deposition of biochemical material on its surface.

15. Introduce photonic crystals. What are they used for and what is the similarity in their behaviour with the behaviour of electron in a

crystal? Can they be used as biosensors? If yes - how? Give examples of artificial and natural photonic crystals.

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Natural photonic crystals

Cyanophrys remus

Macroporous Si

Recent breakthroughs:

•The use of strong index contrast, and the developments of nanofabrication technologies, which leads to entirely new sets of phenomena.

•New conceptual framework in opticsBand structure concepts.Coupled mode theory approach for photon transport.

•Photonic crystal: semiconductors for light.

48Nanophotonics

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• Photonic crystals are attractive optical materials for controlling and manipulating the flow of light.

• One-dimensional photonic crystals are already in widespread use in the form of thin-film optics with applications ranging from low and high reflection coatings on lenses and mirrors to color changing paints and inks.

• Higher dimensional photonic crystals are of great interest for both fundamental and applied research, and the two-dimensional ones are beginning to find commercial applications. The first commercial products involving two-dimensionally periodic photonic crystals are already available in the form of photonic-crystal fibers, which use a microscale structure to confine light with radically different characteristics compared to conventional optical fiber for applications in nonlinear devices and guiding exotic wavelengths.

• The three-dimensional counterparts are still far from commercialization but offer additional features possibly leading to new device concepts (e.g. optical computers), when some technological aspects such as manufacturability and principal difficulties such as disorder are under control.

49Nanophotonics

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Band structure

50Nanophotonics

Mapping on quantum mechanics

16. Describe mathematical similarities between electromagnetism and semiconductor physics, electromagnetism and quantum

mechanics. What does Bloch theorem for electromagnetism state? Does it lead to band structure? Can, as a result of the band

structure, light be slowed down and stopped?

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Bloch theorem for electromagnetism

In a periodic dielectric media, i.e. ε(r+a)=ε(r), the solution H(r) to

has to satisfy the following relations:

where uk(r) = uk(r+a) is a periodic function.

51Nanophotonics

Consequences:Band structure – similarities to

semiconductor physics (slowing down and stopping

light, etc.)

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A topological quantum optics interfaceSabyasachi Barik, Aziz Karasahin, Christopher Flower, Tao Cai, Hirokazu Miyake, Wade DeGottardi,

Mohammad Hafezi, Edo Waks

52Nanophotonics

Science 359, 666–668, 9 February 2018

‘We demonstrate a strong interface between single quantum emitters and topologicalphotonic states. Our approach creates robust counterpropagating edge states at theboundary of two distinct topological photonic crystals. We demonstrate the chiralemission of a quantum emitter into these modes and establish their robustnessagainst sharp bends. This approach may enable the development of quantum opticsdevices with built-in protection, with potential applications in quantum simulationand sensing.’

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A topological quantum optics interface

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Transmission characteristics of the topological waveguide. (A) A schematic of the excitation schemeidentifying the three relevant regions (L, left grating; R, right grating; M, middle of the waveguide).(B) Simulated band structure of transverse electromagnetic modes of a straight topologicalwaveguide. The gray region corresponds to bulk modes of the individual topological photoniccrystals, and red lines represent modes within the bandgap corresponding to topological edge states.The adjacent panel shows the measured spectrum at the transmitted end of the waveguide. The redshaded region identifies the topological edge band. kx, reciprocal wave vector; a, lattice constant. (C)Transmission spectrum at point L as a function of the excitation laser position.

Science 359, 666–668, 9 February 2018

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A topological quantum optics interface

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Chirality in a straight topological waveguide. (A) Schematic of quantum dot–level structure inthe presence of a magnetic field and radiative transitions with opposite circular polarizations. (B)Emission spectrum collected from the excitation region as a function of magnetic field (B). (C andD) Transmission spectra to left and right gratings, respectively

Science 359, 666–668, 9 February 2018

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A topological quantum optics interface

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Science 359, 666–668, 9 February 2018

Robust transport in two dimensions along a bend. (A) Schematic of a modified topologicalwaveguide with a bend. (B and C) Photoluminescence collected from points L and R, respectively,showing only one branch of the quantum dot.

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Nanophotonics with Plasmonics: A logical next step?

56Nanophotonics

Wavelength-division multiplexing (WDM) is a method of combining multiple signals on laser beams at various infrared for transmission along media. Each laser is modulated by an independent set of signals. Wavelength-sensitive filters, the IR analogue of visible-light colour filters, are used at the receiving end.

https://en.wikipedia.org/wiki/Wavelength-division_multiplexing

Dense wavelength-division multiplexing

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57Nanophotonics

17. What are principal limitations for bit-rate of signals in electronics and photonics? What are advantages of plasmonics? Describe

bulk and surface plasmon excitations. What is their dispersion relation? Why surface plasmons are often referred to as “X-rays” with

optical frequencies?

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Nanophotonics 59

Bulk plasmons

If one displaces by a tiny amount all of the electrons with respect to the ions, the Coulomb force pulls back, acting as a restoring force.

The charge density oscillates at the plasma frequency (SI units).

Surface plasmonsElectron density wave propagating along a metal –dielectric interface. The charge density oscillations

and associated electromagnetic fields are called surface plasmon-polariton waves. These waves can be excited very efficiently with light in the visible range of the electromagnetic spectrum.

Solution with proper boundary conditions gives the dispersion relation

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Nanophotonics 60

Surface plasmons can have very low wavelengths at optical frequencies.

They are as “X-rays” with optical frequencies

Particle plasmons with tunable resonances

Movie 4

0

0

m

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and many other books

Very important new research area …

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Movie 5

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Quantum cascade laser

A quantum-cascade laser is a sliver of semiconductor material about the size of a tick.Inside, electrons are constrained within layers of gallium and aluminum compounds,called quantum wells. They are nanometers thick - much smaller than the thickness of ahair.

Adapted from the Bell Labs web-site

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18. Describe principle of work of the quantum cascade laser. Draw an energy diagram of it. What could be the role of inter-sub-band

transitions and optical phonons there? How to provide a well-defined wavelength in a distributed-feedback quantum cascade laser?

Page 64: Nanophysics: Main trends - uio.no

Inter-band transitions in conventional semiconductor lasers emit a single photon.

In quantum cascade structures, electrons undergo inter-subband transitions and photons are emitted. The electrons tunnel to the next period of the structure and the process repeats.

This diagram is oversimplified. To optimize lasing one has to invent much more complicated design of the active region

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The scattering rate between two subbands is heavily dependent upon the overlap of the wave functions and energy spacing between the subbands.

Energy diagram of a quantum cascade laser with diagonal transition also showingthe moduli squared of the wave functions.

Schematic representation of the dispersion of the n = 1; 2 and 3 states parallel to the layers; kis the corresponding wave vector. The wavy lines represent the laser transition; the straight arrows identify the inter-subband scattering process by optical phonons.

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Schematic energy diagram of a portion of the Ga0.47In0.53As–Al0.48In0.52Asquantum cascade laser with vertical transition.

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“The quantum cascade (QC) laser is an excellent example of how quantum engineering can be used to design new laser materials and related light emitters in the mid-IR.

The population inversion occurs between excited subbands of coupled quantum wells and is designed by tailoring the electron inter-subbandscattering times.

This tailoring adds an important dimension to the quantum engineering of heterostructures.

The pumping mechanism is provided by injecting electrons into the upper state of the laser transition by resonant tunneling through a potential barrier.”

From Sirtori et al., 1998

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