Chapter 0 Ray Opticsccf.ee.ntu.edu.tw/~ypchiou/Intro_EO/Ch0_RayOptics.pdf · Ray Optics...

課程編號：901 37500 科目名稱：光電導論授課教師：邱奕鵬

Ray OpticsRay Optics

Quantum optics

E-M wave optics

Ray optics

Wave optics

2


Fundamentals of PhotonicsFundamentals of Photonics

B. E. A. B. E. A. SalehSaleh and and M. C. M. C. TeichTeichWileyWiley--InterscienceInterscience19911991歐亞代理歐亞代理

Chapter 1Chapter 1

3


Fundamentals of PhotonicsFundamentals of Photonics

B. E. A. B. E. A. SalehSaleh and and M. C. M. C. TeichTeichWileyWiley--InterscienceInterscience2007(2nd ed.)2007(2nd ed.)歐亞代理歐亞代理

Chapter 1Chapter 1

4


FermatFermat’’s Principles PrincipleSimple componentsSimple componentsABCD matrixABCD matrix

5


Ray OpticsRay Optics

從透鏡說起

Positive lens

Negative lens

Biconvex Plano-convex Concavo-convex(positive meniscus lens)

Biconcave Plano-concave Convexo-concave(negative meniscus lens)

6


Ray OpticsRay Optics透鏡對球面波或平面波的影響

改變 Amplitude and Phase

由 A 到 B 的變化，可由 Fresnel integral formula (wave optics) 很精確算出，但是太複雜當λ

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8


9


FermatFermat’’s Principles Principle

∫=B

Adsrn )(Optical Path length A

Bds

Fermat’s PrincipleOptical rays traveling between two points A and B, follow a path such that the time of travel (or the optical path length) between the two points is an extremum relative to neighboring paths.

Light ray travels along the path of least time.

0)( =∫B

Adsrnδ

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11


SnellSnell’’s Laws Law1122 sinsin θθ nn = (1.1-1)

12


MirrorsMirrors

Law of Reflection: - The reflected ray lies in the plane of incidence; - The angle of reflection equals the angle of incidence.

paraxialapproximation

13


Spherical MirrorsSpherical Mirrors

Ry

−≈+−

212 θθ (1.2-1)

Rzz −≈+

211

21

(1.2-2)

2Rf −≡ (1.2-3)

Focal length of a spherical mirror

fzz111

21

=+ (1.2-4)

Image Equation for paraxial rays

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15


Spherical MirrorsSpherical Mirrors

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Refraction at Plane BoundariesRefraction at Plane Boundaries

17


Total Internal RefractionTotal Internal Refraction

1

21sinnn

c−=θ (1.2-5)Critical Angle

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PrismsPrisms)cossinsin(sinsin 221 αθθααθθ ⋅−−⋅+−= − nd (1.2-6)

Deviation Angle

αθ ⋅−≈ )1(nd (1.2-7)Thin Prism

19


Beam Splitters &Beam Splitters &Beam CombinersBeam Combiners

20


Refraction at Spherical BoundariesRefraction at Spherical Boundaries

yRnnn

nn

2

121

2

12

−−≈ θθ

Rnn

zn

zn 12

2

2

1

1 −≈+

11

2

2

12 yz

znny =

(1.2-8)

(1.2-9)

(1.2-10)

21


φ

φ

22


ImagingImaging

23


Thin LensesThin Lenses

fy

−= 12 θθ

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

21

11)1(1RR

nf

fzz111

21

=+

(1.2-11)

(1.2-12)

(1.2-13)

11

22 yz

zy −=

(1.2-14)

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Thin LensesThin Lenses

yRnnn

nn

2

121

2

12

−−≈ θθ (1.2-8)

fy

−= 12 θθ

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

21

11)1(1RR

nf

fzz111

21

=+

(1.2-11)

(1.2-12)

(1.2-13)

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Thick Lens (NonThick Lens (Non--paraxial rays)paraxial rays)

- Cannot assume same y when the ray enters and leaves the lens

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Light GuidesLight Guides

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Numerical Aperture of an Optical FiberNumerical Aperture of an Optical Fiber

22

21sin nnNA a −== θ (1.2-15)

28

課程編號：901 37500 科目名稱：光電導論授課教師：邱奕鵬It is difficult for light originating inside a medium of large refractive index to be extracted in to air. (e.g. LED etc.)

TrappingTrappingof lightof light

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30


Matrix OpticsMatrix Optics

112 θBAyy +=

112 θθ DCy +=

(1.4-1)

(1.4-2)

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Ray Matrix (ABCD Matrix)Ray Matrix (ABCD Matrix)

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

1

1

2

2

θθy

DCBAy

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Ray Matrices of Simple Optical ComponentsRay Matrices of Simple Optical ComponentsFree-Space Propagation

⎥⎦

⎤⎢⎣

⎡=

101 d

M (1.4-3)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

2

1001

nnM

Refracting at a planar boundary

(1.4-4)

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Ray Matrices of Simple Optical ComponentsRay Matrices of Simple Optical Components

Refracting at a spherical boundary

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−

−=2

1

2

12 )(01

nn

RnnnM (1.4-5)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−= 11

01

fM

Transmission through a thin lens

(1.4-6)

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Ray Matrices of Simple Optical ComponentsRay Matrices of Simple Optical Components

Reflection from a planar mirror

⎥⎦

⎤⎢⎣

⎡=

1001

M (1.4-7)

⎥⎥⎦

⎤

⎢⎢⎣

⎡= 12

01

RM

Reflection from a spherical mirror

(1.4-8)

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Matrices of Cascaded Optical ComponentsMatrices of Cascaded Optical Components

M1 M2 M3 MN...

123 MMMMM N= (1.4-9)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡= ∑=

10

11

N

i i

i

nd

M (1.4-10)

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Matrices of Cascaded Optical ComponentsMatrices of Cascaded Optical Components

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−−=

fd

f

dM 11

1(1.4-11)

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Imaging with a Thick LensImaging with a Thick Lens

221

21

111 fssorfzz

==+ (1.4-12)

fzshdzfzshdz

−=+=−=+=

22

22

11

11

nRfdnh )1( −=

⎥⎦⎤

⎢⎣⎡ −−

−=

Rd

nn

Rn

f12)1(1

where

(1.4-16)

(1.4-15)

(1.4-14)

(1.4-13)

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Periodic Optical SystemsPeriodic Optical Systems

BAyy mm

m−

= +1θ⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

0

0

θθy

DCBAy m

m

m

BAyy mm

m12

1++

+−

=θ

mmm yFbyy2

12 2 −= ++ 2DAb += [ ]MBCADF det2 =−=

mm hyy 0= 02 22 =+− Fbhh 22 bFjbh −±= F

b1cos−=ϕ

)sin( 0max ϕϕ += mFyym

m

)sin( 0max ϕϕ += myym1=FIf

39


Periodic Optical SystemsPeriodic Optical Systems

12

1 ≤+

≤DA

orbStable Condition

40


Equally Spaced Identical LensesEqually Spaced Identical Lenses

fd 40 ≤≤

)sin( 0max ϕϕ += myym

⎟⎟⎠

⎞⎜⎜⎝

⎛−= −

fd

21cos 1ϕ

fd 2=

fd =

Case 1

Case 2

41


Equally Spaced Identical LensesEqually Spaced Identical Lenses

12

12

1011

≤⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−≤

fd

fd (1.4-33)

42


Optical ResonatorOptical Resonator

43


Optical SystemsOptical Systems

Projector

44


LCD LCD 投投影影機機原原理理: : 穿透式穿透式

資料來源：PC Magazine, 資策會MIC 1999年5月*PBS:Polarizing Beam Splitter

Light source

鏡片陣列

PBS陣列

分色鏡

LCD Panel

合光稜鏡

Projectror Lens

screen

45


Optical SystemsOptical SystemsMicroscope

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Optical SystemsOptical SystemsTelescope

Chapter 0 Ray Opticsccf.ee.ntu.edu.tw/~ypchiou/Intro_EO/Ch0_RayOptics.pdf · Ray Optics...

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Transcript of Chapter 0 Ray Opticsccf.ee.ntu.edu.tw/~ypchiou/Intro_EO/Ch0_RayOptics.pdf · Ray Optics...