Plasmonic Lasers and Spasers Analysis

Nanotechnology

• Nanotechnology is the creation of materials with dimensions measured in nanometers, an intermediate size between isolated molecules and bulk materials.
• This unique size range changes the physical and chemical properties compared to atoms, molecules, and bulk materials.

Physical Properties of Nanoparticles

• Optical Properties: Nanoparticles exhibit properties related to absorption, emission, and band gap.
• Electric Properties: Conductivity and resistivity are significantly affected by size.
• Magnetic Properties: Properties like magnetic field, magnetic intensity, susceptibility, retentivity, and coercivity are modified.
• Thermal Properties: Thermal conductivity, melting point, and heat capacity are affected.
• Mechanical Properties: Hardness, yield strength, tensile strength, ductility, and toughness are often altered.

Classification of Nanostructures

• The classification of nanostructures depends on the number of dimensions falling within the nanometer range.
• Bulk: Three-dimensional structures.
• Quantum Well: Two-dimensional structures, confined in one direction.
• Quantum Wire: One-dimensional structures, confined in two directions.
• Quantum Dot: Zero-dimensional structures, confined in three directions.

Physical Properties of Nanomaterials

• Size, shape (spheres, rods, platelets, etc.), composition, crystal structure (FCC, BCC, etc.), surface ligands/capping agents, and dispersion medium all influence the physical properties of nanoparticles.

Size (Nanoparticles)

• Nanoparticles exhibit unique properties due to a high surface area to volume ratio.
• A 100nm spherical particle has a calculated volume of 5.24 x 10⁻²² m³ and a surface area of 3.141 x 10⁻¹⁴ m².
• As the surface area to volume ratio increases, the percentage of atoms at the surface increases, and surface forces become more dominant, changing material properties compared to bulk.

Surface Area to Volume Ratio

• A higher surface area to volume ratio in nanoparticles leads to a greater amount of substance contacting the surrounding material.
• This effect enhances catalytic activity, as a larger proportion of the material is exposed for potential reactions.
• This ratio increases significantly below a 100nm particle diameter (as shown in the provided graph).

Surface Area : Volume Ratio

• Nanoparticles have a significantly larger surface area to volume ratio than macroscopic particles ( >10⁷:1).
• As the ratio increases, the percentage of surface atoms and surface forces become more substantial, altering material properties from those exhibited by bulk material.

Melting Point as a Function of Particle Size (Nanoparticles)

• Nanoparticles generally have a lower melting point compared to their bulk counterparts.
• This decrease in melting point is strongly correlated with particle size, affecting gold nanoparticles in the nanoscale region (as demonstrated by the graph).

Melting Point versus Shape

• Nanoparticles can sinter (join together) at lower temperatures than expected.
• Rod-shaped nanoparticles can melt and form spherical droplets if heated above a certain temperature.
• Thin films are particularly susceptible to pinhole formation and de-wetting/island formation with increasing temperature.

Unique Characteristics of Nanomaterials

• A substantial surface to volume ratio;
• High percentage of atoms/molecules on the surface;
• Surface forces are crucial;
• Metal nanoparticles exhibit unique light-scattering properties and plasmon resonance;
• Semiconductor nanoparticles may display confined energy states within their structure (quantum dots);
• Unique chemical & physical properties; and- size similarity to many biological structures.

Optical Properties

• Reduced material dimensions lead to pronounced effects on optical properties, often categorized into groups:
  • Increased energy level spacing in confined systems (semiconductors)
  • Surface plasmon resonance in metals.

Energy Gap of Materials

• The energy gap in semiconductor materials separates the conduction and valence bands, defining their conductivity type (conductor, semiconductor, insulator).
• The gap size is influenced by material properties.

Confinement Length

• In semiconductors, confinement occurs if any dimension (a) is smaller than the Bohr radius.
• In metals, if a dimension (a) is less than the electron's mean free path. Confinement length relates to specific dimensions of materials and their behavior.

Type of Confinement

• Strong: a < a_B
• Intermediate: a ~ a_B
• Weak: a > a_B

Metal Nanoparticles

• Different shapes and sizes of metal nanoparticles (e.g., 20nm, 100nm, 500nm) are shown in the images.

Surface Plasmon Absorption

• The interaction of light with a metal nanoparticle's free electrons causes surface plasmon oscillations with a specific frequency.
• These oscillations influence the optical properties of metal nanoparticles.

Optical Properties (Surface Plasmons)

• Plasmons are the coherent excitation of free electrons in a metal.
• The resonance frequency depends on particle size, shape, and material type, related to plasmon energy by Planck's constant.
• Optical properties of metal nanoparticles are primarily driven by surface plasmon interaction with incident photons.
• Gold and silver nanoparticles show plasmon frequencies within the visible range; thus, light wavelengths matching this frequency get absorbed.

Rayleigh and Mie Scattering

• Rayleigh scattering: Dominant for particles much smaller than the wavelengths of light, associated with the scattering of blue light in the sky.
• Mie scattering: Important when particles are comparable in size to the wavelengths, involved in scattering phenomena like haze.

Elastic Scattering

• Elastic scattering: No energy change during scattering; three types of elastic scattering exist: Rayleigh scattering, Mie scattering, and nonselective scattering.

Scattering

• Radiation scattering from a particle depends on size, shape, index of refraction, wavelength of radiation, and view geometry.

Rayleigh Scattering (Further Detail)

• Rayleigh scattering, the scattering coefficient (σλ), which is influenced by the number of particles per square centimeter (N), the volume (V), refractive indices of the particles (μ) and medium (μ₀), and the wavelength (λ) of the radiation, is significant in remote sensing.

Mie Scattering (Further Detail)

• Mie scattering, the scattering coefficient (σλ), depends on the number of particles within intervals of radius (a) and da, the scattering coefficient K(α, μ) as a function of radius and refractive index, influences multispectral imagery under hazy conditions.

Scattering Types

• Rayleigh scattering: Particles much smaller than the wavelength; scattering is uniformly in all directions, and is wavelength dependent; commonly associated with the sky appearing blue.
• Mie scattering: Particles comparable in size to the wavelength; scattering is nonuniform, dependent on the size of the particle.

Electromagnetic Modes

• Transverse mode: electromagnetic field pattern perpendicular to the propagation direction, with the electric and magnetic fields oscillating perpendicular to the direction
• Longitudinal mode: electromagnetic field pattern parallel to the propagation direction.

Mie Theory

• Gustav Mie developed the mathematical description of spectral dependence for scattering by a spherical nanoparticle.
• The theory accounts for the interaction of electromagnetic waves with a homogeneous medium differing in refractive index from the surrounding medium.
• It is the foundation for determining particle sizes by scattering electromagnetic radiation.

Mie Theory (Further Detail)

• Mie theory describes scattering and absorption of electromagnetic radiation by a sphere to understand colors of colloidal gold.
• The approach expands the internal and scattered fields into vector harmonics to solve the wave equation, matching boundary conditions at the particle interface.

Size and Shape Dependence of Surface Plasmon Absorption

• Size and shape significantly influence surface plasmon absorption. Graphs illustrate spectral locations, strengths (of the absorption), and numbers of plasmon resonances.

Semiconductor Nanoparticles

• This section focuses on the theoretical calculations of energy levels in semiconductor conduction and valence bands.

Confinement Length (Semiconductors)

• The equation for the Bohr radius is given.

Type of Confinement (Semiconductors)

• Strong: a < a_B; Intermediate: a ~ a_B; Weak: a > a_B

Effect of Nanometer Scale

• Confinement length directly affects energy systems and structures, changing physical and chemical properties.

Density of States

• The density of states is described in relation to the model of a free-electron gas, in 3D, 2D, and 1D systems.

Two-Dimensional Systems (Quantum Wells)

• The quantum well equation describing electron states is presented.

One-Dimensional Systems (Quantum Wires)

• Equations for the density of states for quantum wires are shown.

Zero-Dimensional Systems (Quantum Dots)

• The expressions for energy levels (E_e,h) are featured.
• Quantum dots equations are featured in the presented information.

Energy Levels of a Semiconductor Quantum Dot

• The equation for the energy levels (E_e,h) of a semiconductor quantum dot in relation to its size is presented in the provided text.

Optical Properties of Quantum Dots

• The optical properties are size-tunable in nanostructures.

Effect of Quantum Confinement

• The energy gap increases due to the reduction in nanoparticle size

QD's (Quantum Dots)

• Quantum yield. Photoluminescence is influenced by size.

Core-Shell Nanoparticles

• Different shaped core-shell nanoparticles are shown: spherical, hexagonal, multiple small core materials, nano matryushka, and movable core within hollow shell.
• Properties are size and shape-dependent, influencing catalytic activity, selectivity, electrical/optical properties, SERS sensitivity, and plasmon resonance and melting point.
• Descriptions of various types of core-shell nanoparticles (inorganic/inorganic, lanthanide-core) exist.
• Types of core-shell nanoparticles (I and II) exist, with differing potential properties and photoluminescence behavior.

CdTe/CdSe core shell

• Synthesis methods for CdTe/CdSe core shell are described.

Inorganic/Inorganic Lanthanide Core/Shell Nanoparticles

• These nanoparticles exhibit upconversion and are promising for bio-sensing.
• Equations for energy level calculations are included.

Upconversion Architecture

• The advantages of back-reflectors in increasing device efficiency by at least a factor of two were mentioned.

Quiz

• Questions related to schematics of synthesis and properties of various types of nanomaterials (e.g., core/shell, metal-based, polymer-based) are described.

Thermal Properties of Nanomaterials

• A section on the influence of size and shape on the thermal properties of nanomaterials exists, including thermal conductivity. The influence of grain size/boundaries on thermal conduction is highlighted.

Physical Properties Change: Melting Point of a Substance

• The definition of the melting point as the temperature when atoms/ions/molecules overcome intermolecular forces is shown.
• Surface atoms require less energy due to contact with fewer atoms, impacting melting phenomena.

Melting Points

• Lower melting points for nanostructures smaller than 100nm are noted.
• Surface energy increase with decreasing size.

Melting Point Property

• Melting-point depression is the decrease in melting point as material size decreases.

Physical Properties Example: Melting Point

• The discussion contrasts the atomic arrangements at macroscopic and nanoscale levels to show their impact on the melting point effect.

Mechanical Properties of Nanomaterials

• Stress and strain are fundamental descriptors to understand how materials respond under mechanical loading.
• Concepts of strength, elasticity, plasticity, strain, stress, and material loading are discussed in relation to nanomaterials.

Strength

• Strength is the ability of a material to withstand destruction from external loads.
• Ultimate strength refers to the maximum stress a material can withstand before it breaks.

Elasticity

• Elasticity describes the tendency of a material to return to its original shape after deformation when the cause of the deformation (stress or load) is removed.

Plasticity

• Plasticity is the ability of a material to undergo permanent deformation without fracture.
• Plastic deformation is only possible above the elastic limit..

Ductility

• Ductility is the ability of a material to deform plastically (stretch) before fracturing.
• Properties like percent elongation and reduction in area are used to measure ductility.

Hardness

• Hardness measures a material's resistance to scratching, abrasion, cutting, indentation, or penetration.

Nanomaterials

• Nanocrystalline materials exhibit properties related to grain size (nanoscale), impacting mechanical properties like hardness, yield strength, elastic modulus, and toughness. The properties of nanomaterials are dependent on their size and shape.

Nanocomposite

• Nanocomposites are materials composed of two or more components with at least one component at the nanometer scale (1-100 nm). They contain inorganic/organic, inorganic/inorganic, and organic/organic phases.

Features of Nanocomposites

• Physical sensitivity: Size effect and quantum confinement have major impacts.
• Chemical reactivity: Increased gas absorption and non-stoichiometric compound formation are relevant.
• Regrowth: Materials recrystallize more easily.
• Rotation and Orientation: Crystallographic modifications from processing are notable.
• Assembly: Easy aggregation in liquid/gaseous media results from their nanoscale size.

Classification of Nanocomposites

• Ceramic matrix nanocomposites (CMC) have unique properties like high thermal resistance, chemical inertness, wear resistance, and corrosion resistance.
• Metals and polymers also form nanocomposites with distinctive properties.

Processing Methods for Ceramic Nanocomposites

• The descriptions of common methods of processing nanocomposites, including powder processing, polymer precursor processing, and sol-gel processing, are present in the provided information.

Applications of CMC's

• Applications such as cutting tools, aerospace, jet engines, turbine blades, and hot fluid channels are cited.

Processing Methods for Metal-Based Nanocomposites

• Several methods exist for producing metal-based nanocomposites, which often involve the melting of the related components and the manipulation of their consolidation or bonding procedures. These approaches are described in the provided text information.

Advantages and Limitations of Processing Methods of Metal Based Nanocomposites

• The advantages and limitations of spray pyrolysis, liquid infiltration, rapid solidification processing, high energy ball milling, and chemical vapor deposition are separately presented in the data.

Processing Methods for Polymer-Based Nanocomposites

• Intercalation Methods from Solution, In-situ Polymerization, Melt Intercalation, Template Synthesis, and Chemical Processes (Sol-Gel/Colloidal) are part of this section.