Lens Effect with Photonic Crystals

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Lens Effect with Photonic Crystals

Student “#3”

ECEN 5616 Final Project Presentation

12.07.2010

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Overview


Introduction


Negative Refractive Index


Photonic Crystal


Superlens


Methods


Results

2

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Introduction

3

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Negative Refractive Index


V. G.
Veslago

(1968)


Negative permittivity and negative permeability


Real index of refraction


Electric resonance in material


Strong magnetic resonance in material


Metals exhibit negative permittivity below

characteristic plasma frequency


Requires electric resonance and

strong magnetic resonance


No negative refractive index

material in nature


4

n<0

n>0

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Photonic Crystal


Periodic optical nanostructures




Analogous to semiconductor crystal


The feature sizes are comparable to the
wavelength

5









r r R
r r R
 
 
 
 
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Waves in Periodic Media

6



















0
0
H r i r E r
E r i r H r
H r
r E r



 
  
 
 
 
 

Maxwell’s Equations:






Bloch Function


due to translational periodicity









2 2
0
E r E r r E r

 
   
 






2
0
1
H r H r
r


 
  
 
 




i k R
k k
E r R E r e

 
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Lattice Structure

7


Brillouin

zones

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Photonic Band Structure

8

x
k
y
k
Negative effective index region

c
a
Self
-
collimation

Self
-
collimation

Bandgap

Effective medium

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Superlens

9


Perfect, real

image


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Method & Results

10

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Finite Difference Time Domain
(FDTD): MEEP


Numerical method in time domain


Calculates E field and H field in every point of the
computational domain as they evolve in time


Can specify materials


Wide range of frequencies can be

explored at once



11

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Results

12

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Results

13

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Results

14

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Current Research

15

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Thank you