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![Page 1: Electromagnetic Fields in Complex Mediums Akhlesh Lakhtakia Department of Engineering Science and Mechanics The Pennsylvania State University February.](https://reader036.fdocuments.net/reader036/viewer/2022070412/56649cff5503460f949d0ecd/html5/thumbnails/1.jpg)
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
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What is a Medium?
A spacetime manifold allowing signals to propagate
Free Space (Reference Medium)
Vacuum (Gravitation? Quantum?)
Materials
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What is Complex?
That which is not SIMPLE!
What is SIMPLE?
Textbook stuff!
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From the Microscopic to the Macroscopic
Microscopic Fields:
Discrete (point) Charges:
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From the Microscopic to the Macroscopic
Maxwell Postulates (microscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
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From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
spatial averaging
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From the Microscopic to the Macroscopic
Free sources (impressed) Bound sources (matter)
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From the Microscopic to the Macroscopic
Induction fields:
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From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
Free sources Bound sources (induction fields)
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From the Microscopic to the Macroscopic
Maxwell Postulates (macroscopic):
Homogeneous
Homogeneous
Nonhomogeneous
Nonhomogeneous
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Constitutive Relations(always macroscopic)
Primitive fields:
Induction fields:
D and H as functions of E and B
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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
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Macroscopic Maxwell Postulates (Time-Harmonic)
Temporal FourierTransformation:
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Constitutive Relations(always macroscopic)
1. Free space
2. Linear, isotropic dielectric
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Constitutive Relations(always macroscopic)
3. Linear, anisotropic dielectric
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Constitutive Relations(always macroscopic)
4. Linear bianisotropic:
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Constitutive Relations(always macroscopic)
4. Linear bianisotropic:
Structural constraint (Post):
Reciprocity:
Crystallographic symmetries: ….
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Constitutive Relations(always macroscopic)
5. Nonlinear bianisotropic:
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Constitutive Relations(always macroscopic)
5. Nonlinear bianisotropic:
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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
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Sculptured Thin Films
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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 %)
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Physical Vapor Deposition (Columnar Thin Films)
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Physical Vapor Deposition (Sculptured Thin Films)
Rotate abouty axis fornematicmorphology
Rotate aboutz axis forhelicoidalmorphology
Mix and matchrotations forcomplexmorphologies
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Sculptured Thin Films
Optical Devices: Polarization FiltersBragg FiltersUltranarrowband FiltersFluid Concentration SensorsBacterial Sensors
Biomedical Applications: Tissue ScaffoldsDrug/Gene DeliveryBone RepairVirus Traps
Other Applications
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Chiral STF as CP Filter
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Spectral Hole Filter
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Fluid Concentration Sensor
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Tissue Scaffolds
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Optical Modeling of STFs
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Optical Modeling of STFs
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Optical Modeling of STFs
Homogenize a collectionofparallel ellipsoidsto get
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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
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Homogenization of Composite Materials
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Metamaterials
Rodger Walser
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Particulate Composite Material with ellipsoidal inclusions
Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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VWP VWP
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Homogenization of Composite Materials
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NPV
Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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GVE
Homogenization of Composite Materials
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Homogenization of Composite Materials
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Homogenization of Composite Materials
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NLE
NLE
NLE
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Negative-Phase-VelocityPropagation
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Refraction of Light
Incident beam
Reflected beam
Refracted beam
Negative-Phase-Velocity Propagation
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Refractive Index
n = refractive index
Negative-Phase-Velocity Propagation
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Law of Refraction
Negative-Phase-Velocity Propagation
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Negative refraction?
Negative-Phase-Velocity Propagation
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Speculation by Victor Veselago (1968)
Negative-Phase-Velocity Propagation
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Schultz & Smith’s Experiment(2000)
Sheldon Schultz David Smith
Negative-Phase-Velocity Propagation
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Material with n<0
Adapted fromDavid Smith’swebsite
Negative-Phase-Velocity Propagation
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Another material with n<0
Courtesy:Claudio Parazzoli& Boeing Aerospace
Negative-Phase-Velocity Propagation
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Two Important Quantities
• Phase velocity vector
• Time-averaged Poynting vector
= direction of energy flow & attenuation
Negative-Phase-Velocity Propagation
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NPV in Simple Mediums
Negative-Phase-Velocity Propagation
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NPV in Bianisotropic Mediums
Negative-Phase-Velocity Propagation
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• Nihility: D = 0, B = 0
• Perfect Lens eqvt. to Nihility
• Goos-Hänchen shifts
• Chiral and Bianisotropic NPV Materials
Negative-Phase-Velocity Propagation
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NPV and Special Relativity
Observer 1 is holdinga material block
Observer 2 is movingat a uniform velocitywith respect to Observer 1
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Observer 1 thinks the materialis isotropic
Observer 2 thinks the materialIs bianisotropic
NPV and Special Relativity
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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
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PPV for Observer 1r = 3 + i0.5r = 2 + i0.5
NPV and Special Relativity
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NPV for Observer 1r = -3 + i0.5r = -2 + i0.5
NPV and Special Relativity
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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
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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
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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
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Mediates the relation between space and time
solution of
Einstein equations
NPV and General Relativity
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Define:
NPV and General Relativity
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Constitutive Relations of Gravitationally Affected Vacuum
NPV and General Relativity
Properties:
1. Spatiotemporally nonhomogeneous
2. Spatiotemporally local
3. Bianisotropic
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Partitioning of spacetime
uniformnonuniform
NPV and General Relativity
Piecewise Uniformity Approximation
Keep just
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Planewave Solution
NPV and General Relativity
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• spherical symmetry• time-independent• m = 0 “apparent singularity”
NPV in deSitter/anti-deSitter Spacetime
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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
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NPV in deSitter/anti-deSitter Spacetime
NPV Experiment
could help
Determine the Sign of theCosmological Constant
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NPV in the Ergosphere of a Rotating Black Hole
Geometric mass
Angular velocity parameter
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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
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Related Topics in Nanotechnology
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Related Topics in Nanotechnology
1. Carbon nanotubes
2. Photonic bandgap structures
3. Ultraviolet broadband lithography
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Fundamental CME Issues
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1. Voigt wave propagation
2. Beltrami fields
3. Conjugation symmetry
4. Post constraint
5. Onsager relations
6. Fractional electromagnetism
Fundamental CME Issues
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