Transcript Electromagnetic Fields in Complex Mediums

Electromagnetic Fields in
Complex Mediums
Akhlesh Lakhtakia
Department of Engineering Science and Mechanics
The Pennsylvania State University
February 27, 2006
Department of Electronics Engineering
Institute of Technology, BHU
Varanasi, 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):
Nonhomogeneous
Nonhomogeneous
Homogeneous
Homogeneous
From the Microscopic to the
Macroscopic
Maxwell Postulates (macroscopic):
spatial averaging
Nonhomogeneous
Nonhomogeneous
Homogeneous
Homogeneous
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):
Nonhomogeneous
Nonhomogeneous
Homogeneous
Homogeneous
Free sources
Bound sources (induction fields)
From the Microscopic to the
Macroscopic
Maxwell Postulates (macroscopic):
Nonhomogeneous
Nonhomogeneous
Homogeneous
Homogeneous
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, Dielectric
Delay
Absorption
Complex medium: Everything else
Delay
Absorption
Anisotropy
Chirality
Nonhomogeneity
Nonlinearity
Macroscopic Maxwell Postulates
(Time-Harmonic)
Temporal Fourier
Transformation:
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 - nematic
3-D - helicoidal
combination morphologies
vertical sectioning
Controllable Porosity (10-90 %)
Physical Vapor Deposition
(Columnar Thin Films)
Physical Vapor Deposition
(Sculptured Thin Films)
Rotate about
y axis for
nematic
morphology
Rotate about
z axis for
helicoidal
morphology
Mix and match
rotations for
complex
morphologies
Sculptured Thin Films
Optical Devices:
Polarization Filters
Bragg Filters
Ultranarrowband Filters
Fluid Concentration Sensors
Bacterial Sensors
Biomedical Applications:
Tissue Scaffolds
Drug/Gene Delivery
Bone Repair
Virus 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
collection
of
parallel ellipsoids
to get
STFs with Transverse Architecture
1.5 um x 1.5 um
photoresist pattern
fabricated using a
lithographic stepper
2 KX
17 KX
Chiral SiO2 thin films grown
using e-beam evaporation
Different periods achieved
by changing deposition
conditions
40 KX
100 KX
Homogenization of
Composite Materials
Metamaterials
Rodger Walser
Homogenization of Composite Materials
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
VWP
VWP
Homogenization of Composite Materials
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
NLE
NLE
NLE
Negative-Phase-Velocity
Propagation
Negative-Phase-Velocity Propagation
Refraction of Light
Reflected beam
Incident 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 from
David Smith’s
website
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
NPV and Special Relativity
Observer 1 is holding
a material block
Observer 2 is moving
at a uniform velocity
with respect to Observer 1
NPV and Special Relativity
Observer 1 thinks the material
is isotropic
Observer 2 thinks the material
Is 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 1
r = 3 + i0.5
mr = 2 + i0.5
NPV and Special Relativity
NPV for Observer 1
r = -3 + i0.5
mr = -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?
Negative-Phase-Velocity Propagation
Everyday Impact of
General Relativity
• Satellite clock - Earth clock = 39000 ns/day
• Special Relativity = -7000 ns/day
• General Relativity = 46000 ns/day
NPV and General Relativity
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
Properties:
1. Spatiotemporally nonhomogeneous
2. Spatiotemporally local
3. Bianisotropic
NPV and General Relativity
Partitioning of spacetime
uniform
Piecewise Uniformity Approximation
Keep just
nonuniform
NPV and General Relativity
Planewave Solution
NPV in deSitter/anti-deSitter Spacetime
• 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 L > 3 (c/r)2
NPV in deSitter/anti-deSitter Spacetime
NPV Experiment
could help
Determine the Sign of the
Cosmological 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
Fundamental CME Issues
1. Voigt wave propagation
2. Beltrami fields
3. Conjugation symmetry
4. Post constraint
5. Onsager relations
6. Fractional electromagnetism