Electromagnetic Fields in Complex Mediums

Electromagnetic Fields in Complex Mediums

Akhlesh Lakhtakia

Department of Engineering Science and Mechanics

The Pennsylvania State University

February 27, 2006Department of Electronics EngineeringInstitute of Technology, BHUVaranasi, India

What is a Medium?

A spacetime manifold allowing signals to propagate

Free Space (Reference Medium)

Vacuum (Gravitation? Quantum?)

Materials

What is Complex?

That which is not SIMPLE!

What is SIMPLE?

Textbook stuff!

From the Microscopic to the Macroscopic

Microscopic Fields:

Discrete (point) Charges:


Maxwell Postulates (microscopic):

Homogeneous

Homogeneous

Nonhomogeneous

Nonhomogeneous


Maxwell Postulates (macroscopic):

Homogeneous

Homogeneous

Nonhomogeneous

Nonhomogeneous

spatial averaging


Free sources (impressed) Bound sources (matter)


Induction fields:



Homogeneous

Homogeneous

Nonhomogeneous

Nonhomogeneous

Free sources Bound sources (induction fields)



Homogeneous

Homogeneous

Nonhomogeneous

Nonhomogeneous

Constitutive Relations(always macroscopic)

Primitive fields:

Induction fields:

D and H as functions of E and B


D and H as functions of E and B

Simplest medium: Free space

Simple medium: Linear, Homogeneous, Isotropic, DielectricDelayAbsorption

Complex medium: Everything elseDelayAbsorptionAnisotropyChiralityNonhomogeneityNonlinearity

Macroscopic Maxwell Postulates (Time-Harmonic)

Temporal FourierTransformation:


1. Free space

2. Linear, isotropic dielectric


3. Linear, anisotropic dielectric


4. Linear bianisotropic:


4. Linear bianisotropic:

Structural constraint (Post):

Reciprocity:

Crystallographic symmetries: ….


5. Nonlinear bianisotropic:

My CME Research(2001-2005)

• Sculptured Thin Films• Homogenization of Composite Materials• Negative-Phase-Velocity Propagation• Related Topics in Nanotechnology

– Carbon nanotubes– Broadband ultraviolet lithography– Photonic bandgap structures

• Fundamental CME Issues

Sculptured Thin Films


Conceived by Lakhtakia & Messier (1992-1995)

Nanoengineered Materials (1-3 nm clusters)

Assemblies of Parallel Curved Nanowires/Submicronwires

Controllable Nanowire Shape

2-D - nematic3-D - helicoidalcombination morphologiesvertical sectioning

Controllable Porosity (10-90 %)

Physical Vapor Deposition (Columnar Thin Films)

Physical Vapor Deposition (Sculptured Thin Films)

Rotate abouty axis fornematicmorphology

Rotate aboutz axis forhelicoidalmorphology

Mix and matchrotations forcomplexmorphologies


Optical Devices: Polarization FiltersBragg FiltersUltranarrowband FiltersFluid Concentration SensorsBacterial Sensors

Biomedical Applications: Tissue ScaffoldsDrug/Gene DeliveryBone RepairVirus Traps

Other Applications

Chiral STF as CP Filter

Spectral Hole Filter

Fluid Concentration Sensor

Tissue Scaffolds

Optical Modeling of STFs

Optical Modeling of STFs

Homogenize a collectionofparallel ellipsoidsto get

STFs with Transverse Architecture

1.5 um x 1.5 um photoresist pattern fabricated using a lithographic stepper

Chiral SiO2 thin films grown using e-beam evaporation

Different periods achieved by changing deposition conditions

100 KX

2 KX 17 KX

40 KX

Homogenization of Composite Materials

Metamaterials

Rodger Walser

Particulate Composite Material with ellipsoidal inclusions


VWP VWP

NPV


GVE


NLE

NLE

NLE

Negative-Phase-VelocityPropagation

Refraction of Light

Incident beam

Reflected beam

Refracted beam

Negative-Phase-Velocity Propagation

Refractive Index

n = refractive index


Law of Refraction


Negative refraction?


Speculation by Victor Veselago (1968)


Schultz & Smith’s Experiment(2000)

Sheldon Schultz David Smith


Material with n<0

Adapted fromDavid Smith’swebsite


Another material with n<0

Courtesy:Claudio Parazzoli& Boeing Aerospace


Two Important Quantities

• Phase velocity vector

• Time-averaged Poynting vector

= direction of energy flow & attenuation


NPV in Simple Mediums


NPV in Bianisotropic Mediums


• Nihility: D = 0, B = 0

• Perfect Lens eqvt. to Nihility

• Goos-Hänchen shifts

• Chiral and Bianisotropic NPV Materials


NPV and Special Relativity

Observer 1 is holdinga material block

Observer 2 is movingat a uniform velocitywith respect to Observer 1

Observer 1 thinks the materialis isotropic

Observer 2 thinks the materialIs bianisotropic


Question 1:

Can an isotropic PPV medium for Observer 1 show NPV behavior for Observer 2?

Question 2:

Can an isotropic NPV medium for Observer 1 show PPV behavior for Observer 2?


PPV for Observer 1r = 3 + i0.5r = 2 + i0.5


NPV for Observer 1r = -3 + i0.5r = -2 + i0.5


Question 1:

Can an isotropic PPV medium for Observer 1 show NPV behavior for Observer 2?

Question 2:

Can an isotropic NPV medium for Observer 1 show PPV behavior for Observer 2?


Everyday Impact ofGeneral Relativity

• Satellite clock - Earth clock = 39000 ns/day

• Special Relativity = -7000 ns/day

• General Relativity = 46000 ns/day


Mediates the relation between space and time

solution of

Einstein equations

NPV and General Relativity

Define:


Constitutive Relations of Gravitationally Affected Vacuum


Properties:

1. Spatiotemporally nonhomogeneous

2. Spatiotemporally local

3. Bianisotropic

Partitioning of spacetime

uniformnonuniform


Piecewise Uniformity Approximation

Keep just

Planewave Solution


• spherical symmetry• time-independent• m = 0 “apparent singularity”

NPV in deSitter/anti-deSitter Spacetime

Conclusions:

(i)anti-de Sitter spacetime does not support NPV

(ii)de Sitter spacetime supports NPV in the neighborhood of r

if > 3 (c/r)2



NPV Experiment

could help

Determine the Sign of theCosmological Constant

NPV in the Ergosphere of a Rotating Black Hole

Geometric mass

Angular velocity parameter

NPV in the Ergosphere of a Rotating Black Hole

Conclusions:

(i)NPV not possible outside the ergosphere

(ii)Rotation essential for NPV

(iii)No NPV along axis of rotation

(iv)Concentration of NPV in equatorial plane

(v)Higher angular velocity promotes NPV

Electromagnetic Fields in Complex Mediums

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