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Ray Optics &
EM Wave Optics
3.46 Fall 2008Photonic Materials & Devices
How can we make an object invisible?
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Resources
Fundamentals of Photonics E. A. Saleh and M. C. Teich
Ch. 1, 2, and 5: ray optics and EM wave optics
Appendix B: linear systems and K-K relation Waves and Fields in Optoelectronics
H. A. Haus
Ch. 1 and 2
Transfer matrix calculation code http://scripts.mit.edu/~sunxc/work/sim/rtfit.html
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Models of light
Propagation models
Free space optics
Ray optics:
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Ray optics: a visual tool (
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Reflection & refraction on curved surfaces
Incident and reflection/refraction angles are taken with
respect to the surface normal
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Optical force: radiation pressure
Wave-particle duality of light
Photons have momentum: p = h /
Force needs to be applied to change the propagation
direction of a photon: p = -Ft
Incident ray Reflected ray
Incident ray
Reflected ray
p
F: radiation pressure
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Radiation pressure in science fictions: solar sail
Count Dookus solar sailer:
Star Wars Episode II: Attack
of the Clones
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Particle movement along waveguide
light
S. Gaugiran et al., "Optical manipulation of microparticles and cells on silicon
nitride waveguides," Opt. Express 13, 6956-6963 (2005)
http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6956
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Optical tweezers & MOEMS
Move particles, live cells, microspheres
More aboutMOEMS (Micro-Opto-Electro-MechanicalSystems):
A. Ashkin et al., Opt. Lett. 11, 288 (1986). M. Eichenfield et al., Nat. Photonics 1, 416 (2007).
M. MacDonald et al., Nature 426, 421 (2003). M. Notomi et al., PRL 97, 023903 (2006).
D. McGloin, Phil. Trans. R. Soc. A 364, 3521 (2006).
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EM wave optics
Maxwell equations
Constitutive relations (linear media)
Wave equations
Boundary conditions
m/s
EED r 0III !! HHB r 0QQQ !! r
c
cn I~0!
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Plane wave solution
Monochromatic plane wave solution
Wave vectork
A measure of spatial periodicity
where
Poynting vector
rn I~)exp()( tirEE [!
)exp( tirkiAE [!
)exp()exp( zikyikxiktiEzyx !
nc
knk !!T2
0
2222
0
22 ||||zyx kkkknk !!
E
B
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Kramers-Kronig (K-K) relation
nr(refractive index) and K (absorption) are
interdepedent !
g
!0
'
'
)'(21)(
T
dK
CPV
c
nr CPV: Cauchy principle value
Absorption peak Variation of refractive index
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Refractive index (real part) enhancement
via quantum coherence High refractive index material is attractive for a number
of applications, e.g. high NA immersion photolithography
Is refractive index enhancement always accompanied by
absorption increase?
Theoretical proposal: M. Scully, Enhancement of index of refraction via quantum
coherence, Phys. Rev Lett. 67, 1855 (1991).
Experimental realization: N. Proite et al., Refractive Index Enhancement with Vanishing
Absorption in an Atomic Vapor (2008). http://arxiv.org/abs/0807.2584v1
(K) (n)
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Transmission through dielectric interfaces
Boundary conditions of fields The conditions have to be satisfied everywhere and at all
times on the boundary
Derivation of Snells law
Phase matching: continuity of
E-field across the boundaries)exp()exp( zikxiktiAE
zx !
)exp()exp()exp( ,22,33,11 xikExikExikE xxx !
|||||| 22
131
kn
nkk !! Usin|| ! kkx
1
2
2
1
sin
sin
n
n!
U
USnells law
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TE/TM wave optical reflection
TE (transverse electric) polarization
Electric field parallel to substrate surface
TM (transverse magnetic) polarization
Magnetic field parallel to substrate surface
low index high index high index low index
TETM
TETM
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Refractive index of gold
n ~ 0.37 @ 1 eV
Experimentalvalue: R > 90%
%21|37.01
37.01| 2 !
!R
Why isthat ???Imaginary part of index n (extinction
coefficient) contributes to reflection
as well!
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Transfer matrix method
n1 n2
d1 d2
n3
d3
ni-1
di-1
ni
diIncident light
Reflected light Refracted light? ?
Interface
E1
E2
E4
E3)()(
4
3
12
2
1
E
ED
E
E!
Transmission matrices
Boundary
conditions
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Transfer matrix method
n1 n2
d1 d2
n3
d3
ni-1
di-1
ni
diIncident light
Reflected light Refracted light? ?
Transfer matrix
)0
()(t
r
iE
ME
E!
Ei is known
Erand Et can be calculated !
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Anti-reflection (AR) coatings
Quarter wave film
Elimination of reflection on surfaces:
Solar cells
Photodetectors
Photolithography
More general treatment:
Hauss Book, Chapter 1
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Optical cloaking for invisibility:
Plasmonics and metamaterials
W. Cai et al., Optical cloaking with meta-
material, Nat. Photonics 1, 224 (2007).
G. Abajo et al., Tunneling mechanism of
light transmission through metallic films,
Phys. Rev. Lett. 95, 067403 (2005).
T. Ebbesen et al., Nature 391, 667 (1998).
G. Gay et al., Phys. Rev. Lett. 96,
213901 (2006).
W. Barnes et al., Phys. Rev. Lett. 92,
107401 (2004).A. Alu & N. Engheta, Phys. Rev. E 72,
016623 (2005).
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Phase vs. group velocity
Carrier: rapidly varying terms
Propagates at vp Envelope: slowly varying envelope -- information
Propagates at vg
Carries information (digital or analog)
Dispersion: distorts the envelope
http://en.wikipedia.org/wiki/Phase_velocity
http://en.wikipedia.org/wiki/Group_velocity
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