electro-optic devices - ray tracing
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ELECTRO-
OPTIC DEVICES- RAY TRACING
LECTURE 1
Dr. Ty OlmsteadRty.olmstead@gmail.com
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Outline of Semester
Introduction
Ray Optics
Wave Optics
Beam Optics
Electro-Magnetics
Resonators
Photons and Atoms Polarization and
Crystal Optics
Semiconductor PhotonSources
Semiconductor Photon
Detectors Non Linear Optics
Acousto Optics
Photonic Switchingand Computing
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Postulates of Ray OpticsSimple Components
Mirrors
Planar Boundaries
Spherical BoundariesMatrix Optics
Ray Transfer Matrices
Matrices for Simple Components
Matrices of CascadesPeriodic Systems
Ray Optics
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Ray Optics: Postulates
Light Travels in Rays
Optical Media is characterized by a quantity,
n, referred to as the index of refraction. Thisquantity is greater than or equal to 1.
The index is used to scale the speed of light in aparticular media.
The time it takes light to travel a distance, d, in
media would be=
(Optical Path
Length)
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Index of refraction
= - Relative magnetic permeability ( = ) - Relative Electric Permittivity ( = )
For most optically transmissive material and
positive real numbers, thus n is real
and positive
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Ray Optics: Postulates
In an inhomogeneous media, the refractive indexn(r) is a function of (x,y,z). The optical pathlength along a direction can then be defined by:
=
Here, ds is the differential length along the path.The time taken by light to transverse the path fromA to B is proportional to the optical path length.
A
B
ds
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Ray Optics: Postulates
Fermats Principle: Optical Rayspropagating between two points follow apath such that the optical path length is anextrema relative to neighboring paths. i.e.
= 0
This means that light travels between to pointssuch that it takes the least amount of time.
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Propagation in Homogeneous Media
Fermats Principle inhomogenous media:
Light takes the
shortest path.
LENS.ZMXConfiguration 1 of 1
3D Layout
/8/2012
X
Y
Z
Rays propagate in straight lines
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Propagation in Homogeneous Media
Reflections Proof: According toFermats Principle thedistance mustbe a minima distance. If is a mirror of ,then must alsobe minimize to meetsFermats Principle. This
only happens when is a straightline. i.e. B coincides withB and q coincides with q
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Propagation in Homogeneous Media
Snells Law: The angle of the refracted ray in a plane inmedia n2 is related to the angle of the ray in media n1by the relation:
sin() = 2sin(2)
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Propagation in Homogeneous Media
Fermats Principle: 2 must beminimized in the time it takes to get from A
to C. (n1 < n2)()
() = minima
tan 2tan(
)= d
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Propagation in Homogeneous Media
= +
+
= 0
= 0 =
2
+
2
+
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Propagation in Homogeneous Media
= 0 =
2
+
2
+
= 0 = + +
sin() = +
sin() = +
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Propagation in Homogeneous Media
= 0 =
()
()
This solves to Snells Law
sin() = 2sin()
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Simple Optical Components
Planar Mirror
3D Layout
0/2012
Z
Mirror
+
Optical Axis
Parabolic Mirror
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Simple Optical Components
Parabolic Mirror Definitions
is the focal length, f, ofthe parabola.
The blocked rays are saidto be obscured from thesystem.
3D Layout
0/2012
Z
f
F P
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Simple Optical Components
No Obscuration Obscuration
LENS.ZMXConfiguration 1 of 1
3D Layout
/10/2012
X
Y
Z
LENS.ZMXConfiguration 1 of 1
3D Layout
/10/2012
X
Y
Z
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Simple Optical Components
No Obscuration Obscuration
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
LENS.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 24.93 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
LENS.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 24.93 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
Remember nothing is free
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Simple Optical Components
Elliptical Reflector Diffracted limited spot
Elliptical reflector 320 degree light cone .zmxConfiguration 1 of 1
Layout
bject radiating a 320 degree cone/10/2012
otal Axial Length: 800.00000 mm
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
Elliptical reflector 320 degree light cone .zmxConfiguration 1 of 1
Polychromatic FFT PSF
Object radiating a 320 degree cone1/10/20120.5500 to 0.5500 m at 0.0000 (deg).Side is 3.23 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
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Simple Optical Components
Why Elliptical Cavity MirrorsFlash Lamp Pumping
Architectures
Lasers
Depending on service lifeflash lamps can be cheaperto operate than laserdiodes.
http://en.wikipedia.org/wiki/Laser_pumping
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Simple Optical Components
Spherical Mirror Spot looks like
Parabola at 0 degrees.ZMXConfiguration 1 of 1
3D Layout
/10/2012
X
Y
Z 0.0000
0.0036
0.0072
0.0107
0.0143
0.0179
0.0215
0.0251
0.0286
0.0322
0.0358
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 35.24 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
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Simple Optical Components
Spherical Reflector Parabolic Reflector
0.0000
0.0036
0.0072
0.0107
0.0143
0.0179
0.0215
0.0251
0.0286
0.0322
0.0358
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 35.24 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 35.51 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
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Paraxial Optics
Paraxial Optics i.e. rays on very near on axis
Spot approaches parabolicfocal spot
Parabola at 0 degrees.ZMXConfiguration 1 of 1
3D Layout
/10/2012
X
Y
Z 0.0000
0.0899
0.1798
0.2698
0.3597
0.4496
0.5395
0.6295
0.7194
0.8093
0.8992
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 17.31 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
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Paraxial Optics
Spherical Optic Parabolic Optic
0.0000
0.0899
0.1798
0.2698
0.3597
0.4496
0.5395
0.6295
0.7194
0.8093
0.8992
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 17.31 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
Parabola at 0 degrees.ZMXConfiguration 1 of 1
Polychromatic FFT PSF
1/10/20120.5500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 17.34 m.Surface: ImageReference Coordinates: 0.00000E+000, 0.00000E+000
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Paraxial Optics:
= 2= 2 =2 2 =2
=2
=
2
f=2
=
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Refraction at a Plane
Two Type of Refraction: External Refraction
(n1 < n2 ) When a rays are incident from a medium with a smaller indexthan the medium that the has higher index, the rays will refract into thenew medium such that the angle of the incident ray from the surfacenormal is greater than the angle of the refracted beam from the surface
normal.
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Refraction at a Plane
Two Type of Refraction: Internal Refraction (n1 > n2 ) When a rays are incident from a medium with a greater
index to a medium that the has lesser index, if the rays refract, therays will refract into the new medium such that the angle of theincident ray from the surface normal is less than the angle of therefracted beam from the surface normal.
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Critical Angle: Total Internal Reflection
Recall Snells Law
sin = 2 sin 2
sin 2is maximum when is 90.
Result:
= 2Rays should totaling internally reflect
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Glass
Glass Name Index Abbe
F2 1.62004 36.37
F5 1.60342 38.03
LAFN7 1.74950 34.95
N-BAK2 1.53996 59.71
N-BK10 1.49782 66.95
N-BK7 1.51680 64.17 N-F2 1.62005 36.43
N-LAF21 1.78800 47.49
N-LAF7 1.74950 34.82
N-LASF31A 1.88300 40.76
N-SF1 1.71736 29.62
N-SF11 1.78472 25.68
N-SK11 1.56384 60.80
P-LASF50 1.80860 40.46
SF56A 1.78470 26.08
LITHOSIL-Q 1.45844 67.83
N-LASF46 1.90138 31.64
F8 1.59551 39.18
SF54 1.74080 28.09http://micro.magnet.fsu.edu/optics/timeline/p
eople/abbe.html
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Refraction: Prism
Surface: IMA
200.
00
OBJ: 0.0000, 0.0000 (deg)
IMA: 0.000, 3.972 mm
0.4500
0.4750
0.5000
0.5250
0.5500
Prism using tilted surface.zmxConfiguration 1 of 1
Spot Diagram
Prism example1/11/2012 Units are m.Field : 1RMS radius : 50.913GEO radius : 95.651Scale bar : 200 Reference : Chief Ray
X
Y
Z
Prism using tilted surface.zmxConfiguration 1 of 1
Wireframe
rism example/11/2012
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Refraction: Prism
X
Y
Z
Prism using tilted surface.zmxConfiguration 1 of 1
Wireframe
rism example/11/2012
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
Prism using tilted surface.zmxConfiguration 1 of 1
Polychromatic FFT PSF
Prism example1/11/20120.4500 to 0.5500 m at 0.0000, 0.0000 (deg).Side is 393.43 m.Surface: ImageReference Coordinates: 0.00000E+000, 3.97217E+000
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Metal Metals (negative index of refraction)
= most optically
transparent media n>1
> 1> 1 =
It is possible for
< 1< 1 In this case =
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Refraction: Prism
= 2 2 /2 sin cos()Using the paraxial approximation this can be simplified to
= 1
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Refraction: Prisms
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Refraction: Prisms
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Refraction: Prisms
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Refraction: Prisms
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Refraction: Prisms
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Ray Optics: Beam Splitter
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Ray Optics: Refraction
At the boundary, applySnells Law:
n1Sin(q1) = n2Sin(q2)
Assume Paraxial conditionn1 (q1) = n2 (q2)
Substitute for angles
n1 (a-j) = n2 (a-j)
Approximating angle by theretangents
= 2
n1>n2
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Ray Optics: Refraction
Rearranging using thesame sign convention
as before:
=
= Power of the
refracting surface
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Types of Lenses
Convergent Lenses
Divergent Lenses
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Ray Optics: Simple Imaging
First, Image throughfirst refracting surface.
Treat the image from
the first surface as avirtual object for the
second refractingsurface. Find its image
relative to the 2nd
refracting surface.
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Ray Optics: Thin Lens
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Surface 1 Surface 2
Recall, the object for surface 2 is virtual:
2= If t ->0
s2= -s1Substituting
222=2 22
2=
2
22
22
2=
22
2=
2
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