Electro-optic Devices - Ray Tracing

7/25/2019 Electro-optic Devices - Ray Tracing

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ELECTRO-

OPTIC DEVICES- RAY TRACING

LECTURE 1

Dr. Ty [email protected]


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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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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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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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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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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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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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= +

+

= 0

= 0 =

2

+

2

+


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= 0 =

2

+

2

+

= 0 = + +

sin() = +

sin() = +


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= 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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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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No Obscuration Obscuration


3D Layout

/10/2012

X

Y

Z


3D Layout

/10/2012

X

Y

Z


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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


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




Remember nothing is free


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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


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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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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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





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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




0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000





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Paraxial Optics

Paraxial Optics i.e. rays on very near on axis

Spot approaches parabolicfocal spot


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





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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




0.0000

0.1000

0.2000

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0.4000

0.5000

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0.9000

1.0000





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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


Wireframe

rism example/11/2012


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Refraction: Prism

X

Y

Z


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 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

Electro-optic Devices - Ray Tracing

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