Nano Photonic s

7/27/2019 Nano Photonic s

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Nanome

chanics

Nano-opto-electronics

Nanophysics:

Main trends


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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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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 (Particles with dimensions much less than ):

Insulators: Rayleigh Scattering (blue sky)

Semiconductors: Resonant absorption at EGAP (size dependent

fluorescence)

Metals: Resonant absorption at surface plasmon frequency.

Micr

oparticles (Particles with dimensions on the order of or bigger ):

Enhanced forward scattering, Intuitive ray-picture useful,

Rainbows due to dispersion H20,

Applications: resonators, lasers, etc

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Scattered light

Molecules: Scattering by a harmonic oscillator

Radiation field

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The blue sky

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Semiconductor nanopartilces

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Important application: Tagging biomaterials with semiconductor nanocrystals

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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 electrondensity, 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 9Nanophotonics


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Simple model the quasi-static Rayleigh theory

Relative to the medium dielectric function,

leads to polarizability

The scattering and absorption cross-section are then

with

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

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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 beinvalid 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.

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Microspheres:

The picture is well described by

geometric optics;

Microsphere can act as a resonator

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Photonic crystals

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 m, while

(right) the diameter of the holes is 4

m

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.


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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.

Conventional silica fiber, n~0.01, photonic crystal structure, n ~ 1New conceptual framework in optics

Band structure concepts.

Coupled mode theory approach for photon transport.

Photonic crystal: semiconductors for light.

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Band structure

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Mapping on quantum mechanics

f


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Bloch theorem for electromagnetism

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

has to satisfy the following relations:

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

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Consequences:

Band structure similarities to

semiconductor physics

(slowing down and stopping

light, etc.)

O i l i f l l l i


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Optical properties of metals: Plasmons, polaritons, etc

Optical properties of free electrons: Plasma oscillations

Equation of motion

(no damping)Polarization

Search solution as

Electron concentration

Plasma frequency

(Gaussian units)


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Optical properties of free electrons: Plasma waves (Plasmons)

From Maxwell equations:

Plasma frequencies:

Metals - p 10 eV;Semiconductors - p < 0.5 eV

(depending on dopant conc.)

Dispersion relation

Solutions lie above the light line


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Optical properties of free electrons: Surface-Plasmon Polaritons (SPPs)

We need to solve Maxwells equations with boundary conditions

Search solutions inthe form:

Maxwells equations:

Boundary conditions:


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Dispersion law:

Solution lies below the light line

Dispersion relation

plasma modes and SPP


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Nanophotonics with Plasmonics: A logical next step?

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SPP = Surface Plasmonic Polaritons


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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 commercialapplications. The first commercial products involving two-dimensionally periodic

photonic crystals are already available in the form ofphotonic-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.

Summary

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and many other books

Very important new research

area

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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 morecomplicated 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 laserwith diagonal transition also showing

the moduli squared of the wave functions.

Schematic representation of the dispersion of

the n = 1; 2 and 3 states parallel to the layers; k

is the corresponding wave vector. The wavy lines

represent the laser transition; the straight

arrows identify the inter-subband scatteringprocess by optical phonons.

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Schematic energy diagram of a portion of the Ga0.47In0.53AsAl0.48In0.52Asquantum 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-subband

scattering 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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