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MNT-301

UNIT-2

Introduction to Photonic bandgap Crystals

Materials and Fabrication techniques of Photonic bandgap Crystals:

Semiconductors,

Amorphous,

Polymers,

Fabrication of photonic crystal structure (1D, 2D, 3D),

Optics in nano sized quantum wells and wires (periodicnanostructures),

Negative refractive index

Microwave induced transport.

Nano-scale photonic devices:

couplers, waveguides

liquid crystals and their applications at the nanoscale

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Technical road map showing the requirement to reduce the

size of photonic devices for shorterdistance

optical fiber communication systems.

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Introduction to nanophotonic

Nanophotonics orNano-optics is the study of the behavior of light on the nanometer scale.

It is considered as a branch of optical engineering which deals with optics, or the interaction of

light with particles or substances at deeply subwavelength length scales.

AIM: The study of nanophotonics involves two broad themes

1) studying the novel properties of light at the nanometer scale

2) enabling highly power efficient devices for engineering applications.

Appplications: The study has the potential to revolutionize the telecommunications industry

by providing low power, high speed, interference-free devices such as electrooptic and all-

optical switches on a chip.

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Explanation:

As we know that the wavelength of ultraviolet, visible and near IR light of approximately 300 to

1200 nanometers.

The interaction of light with these nanoscale features leads to confinement of

the electromagnetic field to the surface or tip of the nanostructure resulting in a region referred

to as the optical near field.

This effect is similar to the lightning rod, where the field concentrates at the tip.

In this region, the field may need to adjust to the topography of the nanostructure (by the

boundary conditions of Maxwells equations). This means that the electromagnetic field will be

dependent on the size and shape of the nanostructure that the light is interacting with.

Why Nanophotonic:

Technologies in the field of nano-optics include near-field scanning optical microscopy (NSOM),

photoassisted scanning tunnelling microscopy and surface plasmon optics.

Traditional microscopy makes use of diffractive elements to focus light tightly in order to

increase resolution. But because of the diffraction limit, propagating light may be focused to a

spot with a minimum diameter of roughly half the wavelength of the light.

Thus, even with diffraction-limited confocal microscopy, the maximum resolution obtainable is

on the order of a couple of hundred nanometers.

The scientific and industrial communities are becoming more interested in the characterization

of materials and phenomena on the scale of a few nanometers, so alternative techniques must

be utilized.

Scanning Probe Microscopy (SPM) makes use of a probe, (usually either a tiny aperture or

super-sharp tip), which either locally excites a sample or transmits local information from a

sample to be collected and analyzed.

The ability to fabricate devices in nanoscale that has been developed recently provided the

catalyst for this area of study.

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Introduction to Nanophotonics

To go beyond the diffraction limit, we neednonpropagating nanometer-sized light to induce

primary excitation in a nanometer-sized material (called nanophotonic crystal) in such a

manner that the phase of excitation is independent of that of the incident light.

One promising technology to decrease the size of light is nanophotonics, which was

proposed in 1993.

If a nanometer sized particle is illuminated by propagating light, it generates scattered

light, which propagates to the far field and exhibits diffraction.

However, also generated at the surface of the particle is anoptical near-field, which is non-

propagating light whose energy is localized at the particle surface. (also calledvirtual cloud of

photons)

Novel or nanometer-sized materials called photonic crystal that may be used for future

advanced photonic devices.

This also applies to improvements in the resolution of optical fabrication and for increasing the

storage density of optical disk memories.

The use of optical near fields has been proposed as a way to transcend the diffraction limit.

This proposal holds that an optical near field can be generated on a sub-wavelength-sized

aperture by irradiating the propagating light.

the optical near-f ield energy depends not on the wavelength of the incident light, but on the

aperture size.

An optical near field is generated by the electronic dipoles induced in a nanometric particle

(i.e., a sub-wavelength-sized zerodimensional topographical material).

opt ical near fields have been applied to real ize diffraction-free, high-resolution opticalmicroscopy.

How to generate Optical near field:

an optical near field is generated by the electronic dipoles induced in a nanometric particle

(i.e., a sub-wavelength-sized topographical material).

Their alignment of a particle is independent of the phase of the incident light because the

particles are much smaller than the wavelength of the incident light. But, it depends on the

size, and structure of the particle.

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optical near fields: The use of optical near fields has been proposed as a way to transcend

the diffraction limit.

This proposal holds that an optical near field can be generated on a sub-wavelength-sizedaperture by irradiating the propagating light.

length of the optical near-field energy

depend not on the wavelength of the

light, but on the size, conformation,

and structure of the particle.

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Principle:

dressed photon, not

the free photon, thatcarries the material

excitation energy.

Therefore, the

energy of the

dressed photon,

hvdp , is larger than

that of the free

photon, hv , due to

contribution of the

material excitation

energy.Transfer of energy

Photonic CrystalThis is a study of a photonic crystal waveguide.

Photonic crystal devices are periodic structures of alternating layers of materials with

different refractive indices.

Waveguides that are confined inside of a photonic crystal can have very sharp low-loss

bends, which may enable an increase in integration density of several orders of

magnitude.

The crystal features a grid of GaAs pillars. Depending on the distance between the pillars

(If the photonic Crystal in 2D), waves within a certain frequency range will be reflected

instead of propagated through the crystal.

This frequency range is called the photonic band gap. If some of the GaAs pil lars in the

crystal structure are removed, a guide for the frequencies within the band gap is created.

Light can then propagate along the outlined guide geometry.

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Photonic crystals are periodic optical nanostructures that are designed to affect the motion

of photons.

A photonic crystal consists of a lattice of dielectric particles with separations on the order of the

wavelength of visible light.

photonic crystals contain regularly repeating internal regions of high and low dielectric constant.

Photons (behaving as waves) propagate through this structure - or not it depending on their

wavelength.

Wavelengths of light that are allowed to travel are known as modes, and groups of allowed

modes formbands.

Disallowedbands of wavelengths are called photonicband gaps.

Since the basic physical phenomenon is based on diffraction, the periodicity of the photonic crystal

structure has to be of the same length-scale as half the wavelength of the EM waves i.e. ~200 nm

(blue) to 350 nm (red) for photonic crystals operating in the visible part of the spectrum - the

repeating regions of high and low dielectric constants have to be of this dimension.

This makes the fabrication of optical photonic crystals complex.

Photonic band gape

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In the nearly free-electron model of metals the valence or conduction electrons are treated as

noninteracting free electrons moving in a periodic potential arising from the positively charged

ion cores.

The energy is proportional to the square of the wavevector, except near the band edge wherek=/a

The important result is that there is an energy gap of widthEg

meaning that there are certain wavelengths or wavevectors that will not propagate in the

lattice.

Consider a plot of the energy versus the

wavevector for a one dimensional lattice of

identical ions.

The reflection of waves of electrons in ordinary metallic crystal lattices.

The wavefunction of an electron in a metal can be written in the free-electron approximation as

Consider Bragg reflection

Consider a series of parallel planes in a lat tice separated by a distance dcontaining the

atoms of the lattice.

The path difference between two waves reflected from adjacent planes is 2dsin, where is

the angle of incidence of the wavevector to the planes.

If the path difference 2d sin is a half-wavelength, the reflected waves will destructively

interfere, and cannot propagate in the lattice, so there is an energy gap.

This is a result of the lattice periodicity and the wave nature of the electrons.

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Defects in Photonic Crystals: Localization of Light:

A linear defect, in which the field propagates along the direction of the defect and decays exponentiallyin the

transverse direction, can serve as an on-chip optical waveguide with some exceptional properties.

More-typically-fabricated on-chip optical waveguides confine optical modes through differential indices of

refraction and can display radiation lossesfor example, at the bends of curved waveguides.

Appropriately designed photonic crystal waveguides are prohibited from radiating into the surrounding bulk

material, even for a 90 bend in the waveguide

In 1987Yablonovitch andJohn proposed the idea of building a lattice with separations such that light could

undergo Bragg reflections in the lattice.

For visible light this requires a lattice dimension ofabout 0.5 pm or500 nm.

Such crystals have to be arti ficially fabricated by methods such as electron-beam lithography or X-ray

lithography.

Essentially aphotonic crystal is aperiodic array ofdielectric particles havingseparations on the order of

500nm

Current research on photonic crystals truly embodies the concepts of nanophotonics, with spatial index

modulat ion (etched holes or sol id rods) at the 100 nanometer (nm) scale, that al lows compact, highly

integrable waveguides, filters, resonators, and high-efficiency lasers.

The first experimental demonstration was carried out for a photonic crystal comprising

alumina rods with a lattice constant of 1.27 mm, evidencing 80 percent transmission around

a 90 bend (Faraon et al., 2007; Lin et al., 1998; Scherer et al., 2005).

Various photonic crystal waveguides have since been fabricated with much smaller lattice

constants (

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One-dimensional photonic crystals can be either isotropic or

anisotropic, with the latter having potential use as an optical

switch.

Recently, a graphene-based one-dimensional photonic crystal

has been fabricated and demonstrated its competence for

excitation of surface electromagnetic waves in the periodic

structure using prism coupling technique.

Design of photonic crystals:

1 D photonic crystal:

In a one-dimensional photonic crystal, layers of different dielectric constant may be deposited or adhered

together to form a band gap in a single direction.

Two-dimensional photonic crystals

Two dimensional photonic crystal made of dielectric rods arranged in a square lattice.

Triangular and square lattices of holes have been successfully employed.

The photonic crystal fiber can be made by taking cylindrical rods of glass in hexagonal lattice,

and then heating and stretching them, the triangle-like airgaps between the glass rods become

the holes that confine the modes.

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Three-dimensional photonic crystals

There are several structure types that have been constructed: Spheres in a diamond lattice

Yablonovite The Woodpile Structure "rods" are repeatedly etched using beam lithography,filled in and new material is then deposited thereon, and the process is repeated on the next

layer with etched channels that are perpendicular to the layer below, and parallel to and out of

phase with the channels two layers below.

The process is repeated until the structure is of the desired height.

The fill-in material is then dissolved using an agent that can dissolve the fil l in material but not

the deposition material. It is generally hard to introduce defects into this structure.

Inverse opals or Inverse Colloidal Crystals-Spheres (such as polystyrene) can be allowed to

deposit into a cubic close packed lattice suspended in a solvent.

Then a hardener is introduced which makes a transparent solid out of the volume occupied by

the solvent.

The spheres are then dissolved using an acid such as Hydrochloric acid.

A stack of two-dimensional crystals - This is a more general class of photonic crystals than

Yablonovite, but the original implementation of Yablonovite was created using this method.

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Applications of photonics crystal:

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 colour 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.

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Fabrication techniques of Photonic Band gape (PBC)

materials

2D PBG materials can confine light in two spat ial dimensions, 3D PBG materials faci litate

complete localization of light and can facilitate complete inhibition of spontaneous emission of

light from atoms, molecules, and other excitations.

If the transition frequency from such an atom lies within a 3D PBG, the photon that would

normally be emitted and escape from the atom forms a bound state to the atom.

Such feedback effects have important consequences on laser action from a collection of

atoms.

Indeed lasing may occur near a photonic band edge even without the need for mirrors as in a

conventional laser cavity.

There are two methods can be used to fabricatePBG:

1. Layer-by-layer structures

2. Self-organizing structures

Layer-by-layer structures:

The woodpile structure represents a three-dimensional PBG material that lends itself to layer-

by-layer fabrication.

It resembles (see Figure 9) a criss-crossed stack of wooden logs, where in each layer the logs

are in parallel orientation to each other.

To fabricate one layer of the stack, a SiO2 layer is grown on a substrate wafer, then patterned

and etched.

Next, the resulting trenches are filled with a high-index material such as silicon or GaAs and the

surface of the wafer is polished in order to allow the next SiO2 layer to be grown.

The logs of second nearest layers are displaced midway between the logs of the original layer.

As a consequence, 4 layers are necessary to obtain one unit cell in the stackingdirection.

In a final step, the SiO2 is removed through a selective etching process leaving behind the high-

index logs.

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Recent works report about the successful fabrication of such a layer-by-layer PBG materialmade from silicon with a PBG around 1.5 m. However, this structure consisted of only 5layers in the stacking direction. Instead of depositing successively more layers, wafer-bondingtechnology may be applied to single-layer substrates. Bonding together two single-layersubstrates and subsequent removal of the upper substrate results in a double-layer structure.The ensuing technique is multiplicative but tedious and expensive. To date, this type ofcomplex micro-lithography has lead to the successful fabrication of an 8 layer structure (2 unitcells) in the stacking direction.

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2. Self-organizing structures: In three dimensions a number of large-scale self-assembling periodic

structures already exist.

These include colloidal systems and artificial opals.

Unfortunately, these readily available materials do not satisfy the necessary criteria of high

index contrast and correct network topology to produce a complete PBG.

Theoretical studies, however, indicate the possibil ity of a complete PBG in closely related

structures.

Face centered cubic lattices consisting of low dielectric inclusions in a connected high dielectric

network (henceforth called inverse structures) can exhibit small PBGs.

The recipe of producing inverse structures from artif icial opals is to infiltrate them with a high

dielectric material such as si licon and to subsequently etch out the SiO2 spheres, leaving

behind a connected network of high dielectric material with fi ll ing ratios of about 26% by

volume.

Such a "Swiss cheese structures" with air voids in a si licon backbone is displayed in Figure.

This large-scale inverse opal PBG material exhibits a complete 5% PBG relative to its center

frequency at 1.5 m. The etching out of the SiO2 provides the necessary dielectric contrast for the

emergence of a complete 3D PBG.

Moreover, the presence of air voids rather than sol id SiO2 may allow the injection of atomic

vapors with which quantum optical experiments can be carried out. I t also faci litates the

infiltration of optically anisotropic materials such as nematic liquid crystals for the realization

of electro-optic tuning effects and enables the infiltration of active materials such as

conjugated polymers and dyes for laser applications.

The structure has been obtained

through an infiltration of an artificial

opal with silicon (light shaded

regions) and subsequent removal of

the SiO2 spheres of the opal. The air

sphere diameter is 870 nanometers.

Clearly visible is the incomplete

inf iltrat ion (diamond shaped voids

between spheres) and the effect of

sintering the artificial opal prior to

infiltration (small holes connecting

adjacent spheres).

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Quantum confined materials(optics in nano sized quantum wells and wires)

Quantum confinement produces a number of important manifestations in the optical properties

of semiconductors.

The optical properties discussed in this subsection are summarized in Table 4.2

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Size Dependence of Optical Propert ies:

Quantum confinement produces a blue shift in the bandgap as well as appearance of discrete

subbands corresponding to quantization along the direction of confinement.

As the dimensions of confinement increase, the bandgap decreases; hence the interband

transitions shift to longer wavelengths, finally approaching the bulk value for a large width.

Increase of Osci l lator Strength .

Quantum confinement produces a major modification in the density of states both for valence

and conduction bands.

Instead of a continuous, smooth distribution of the density of states, the energy states are

squeezed in a narrow energy range. This packing of energy states near the bandgap becomes

more pronounced as the dimensions of confinement increase from quantum well, to quantum

wire, to quantum dots.

New Intraband Transit ion s.

In quantum-confined structures such as a quantum well, there are sub-bands characterized by

the different quantum numbers (n = 1, 2, . . .) corresponding to quantization along the direction

of confinement (growth).

I n c r ea s e d Ex c i t o n B i n d i n g . Quantum confinement of electrons and holes also leads to

enhanced binding between them and thereby produces increased exciton binding energy

compared to the exciton binding energy for the bulk sample.

I n c r ea s e o f Tr a n s i t i o n P r o b ab i l i t y i n In d i r e c t G a p Se m i c o n d u c t o r .

As we discussed in Chapter 2, an opt ical transition for an indirect bandgap semiconductor

requires a change of quasi-momentum and thus involves the participation of phonons. Silicon

is an example of an indirect gap semiconductor.

Example:

A quantum rod represents an intermediate form between a zero-dimensional quantum dot

(0DEG) and a one-dimensional quantum wire (1DEG) and offers, in some way, a combination

of properties exhibited by a quantum dot and a quantum wire.

Thus, their bandgaps can be tuned by precise control of both the length and the diameter of

the rod.

Alivisatos and co-workers have produced CdSe quantum rods of various diameters (3.56.5

nm) and lengths (7.540 nm) (Li et al., 2001). They have reported that the photoluminescence

emission maximum shifts to lower energy (longer wavelength) with an increase either in the

width or the length.

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Metamaterials with negative refractive index

A medium with simultaneously Re() < 0 and Re() < 0 can be

characterized by a negative index of refraction. These considerations can

be extended to anisotropic structures as well when Re() < 0 and Re()