electromagnetic fields in complex mediums akhlesh lakhtakia department of engineering science and...
TRANSCRIPT
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:
From the Microscopic to the Macroscopic
Maxwell Postulates (microscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
spatial averaging
From the Microscopic to the Macroscopic
Free sources (impressed) Bound sources (matter)
From the Microscopic to the Macroscopic
Induction fields:
From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
Free sources Bound sources (induction fields)
From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
Constitutive Relations(always macroscopic)
Primitive fields:
Induction fields:
D and H as functions of E and B
Constitutive Relations(always macroscopic)
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:
Constitutive Relations(always macroscopic)
1. Free space
2. Linear, isotropic dielectric
Constitutive Relations(always macroscopic)
3. Linear, anisotropic dielectric
Constitutive Relations(always macroscopic)
4. Linear bianisotropic:
Constitutive Relations(always macroscopic)
4. Linear bianisotropic:
Structural constraint (Post):
Reciprocity:
Crystallographic symmetries: ….
Constitutive Relations(always macroscopic)
5. Nonlinear bianisotropic:
Constitutive Relations(always macroscopic)
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
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
Sculptured Thin Films
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
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
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
VWP VWP
Homogenization of Composite Materials
NPV
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
GVE
Homogenization of Composite Materials
Homogenization of Composite Materials
Homogenization of Composite Materials
NLE
NLE
NLE
Negative-Phase-VelocityPropagation
Refraction of Light
Incident beam
Reflected beam
Refracted beam
Negative-Phase-Velocity Propagation
Refractive Index
n = refractive index
Negative-Phase-Velocity Propagation
Law of Refraction
Negative-Phase-Velocity Propagation
Negative refraction?
Negative-Phase-Velocity Propagation
Speculation by Victor Veselago (1968)
Negative-Phase-Velocity Propagation
Schultz & Smith’s Experiment(2000)
Sheldon Schultz David Smith
Negative-Phase-Velocity Propagation
Material with n<0
Adapted fromDavid Smith’swebsite
Negative-Phase-Velocity Propagation
Another material with n<0
Courtesy:Claudio Parazzoli& Boeing Aerospace
Negative-Phase-Velocity Propagation
Two Important Quantities
• Phase velocity vector
• Time-averaged Poynting vector
= direction of energy flow & attenuation
Negative-Phase-Velocity Propagation
NPV in Simple Mediums
Negative-Phase-Velocity Propagation
NPV in Bianisotropic Mediums
Negative-Phase-Velocity Propagation
• Nihility: D = 0, B = 0
• Perfect Lens eqvt. to Nihility
• Goos-Hänchen shifts
• Chiral and Bianisotropic NPV Materials
Negative-Phase-Velocity Propagation
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
NPV and Special Relativity
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?
NPV and Special Relativity
PPV for Observer 1r = 3 + i0.5r = 2 + i0.5
NPV and Special Relativity
NPV for Observer 1r = -3 + i0.5r = -2 + i0.5
NPV and Special Relativity
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?
NPV and Special Relativity
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?
NPV and Special Relativity
Everyday Impact ofGeneral Relativity
• Satellite clock - Earth clock = 39000 ns/day
• Special Relativity = -7000 ns/day
• General Relativity = 46000 ns/day
Negative-Phase-Velocity Propagation
Mediates the relation between space and time
solution of
Einstein equations
NPV and General Relativity
Define:
NPV and General Relativity
Constitutive Relations of Gravitationally Affected Vacuum
NPV and General Relativity
Properties:
1. Spatiotemporally nonhomogeneous
2. Spatiotemporally local
3. Bianisotropic
Partitioning of spacetime
uniformnonuniform
NPV and General Relativity
Piecewise Uniformity Approximation
Keep just
Planewave Solution
NPV and General Relativity
• 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 in deSitter/anti-deSitter Spacetime
NPV in deSitter/anti-deSitter Spacetime
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
Related Topics in Nanotechnology
Related Topics in Nanotechnology
1. Carbon nanotubes
2. Photonic bandgap structures
3. Ultraviolet broadband lithography
Fundamental CME Issues
1. Voigt wave propagation
2. Beltrami fields
3. Conjugation symmetry
4. Post constraint
5. Onsager relations
6. Fractional electromagnetism
Fundamental CME Issues