Microsoft PowerPoint - Chapter 0 Ray Optics

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1 Ray Optics Quantum optics E-M wave optics Wave optics Ray optics

2 Fundamentals of Photonics B. E. A. Saleh and M. C. Teich Wiley-Interscience 99 歐亞代理 Chapter

3 Fundamentals of Photonics B. E. A. Saleh and M. C. Teich Wiley-Interscience 007(nd ed.) 歐亞代理 Chapter 3

4 Fermat s Principle Simple components ABCD matrix 4

5 Ray Optics 從透鏡說起 Positive lens Biconvex Plano-convex Concavo-convex (positive meniscus lens) Negative lens Biconcave Plano-concave Convexo-concave (negative meniscus lens) 5

6 Ray Optics 透鏡對球面波或平面波的影響改變 Amplitude and Phase λ D A B 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<< D 可以 Fermat s principle 導出簡化的 Ray propagation equation 求得近似解 6

7 Fermat s Principle Simple components ABCD matrix 7

8 8

9 Fermat s Principle Optical Path length Fermat s Principle = B A n ( r ) ds Optical 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. A ds B δ B A n( r ) ds = 0 Light ray travels along the path of least time. 9

10 Fermat s Principle Simple components ABCD matrix 0

11 Snell s Law n = θ (.-) sinθ n sin

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

13 Spherical Mirrors y θ + θ R (.-) + z z R (.-) Focal length of a spherical mirror z R f (.-3) Image Equation for paraxial rays + = (.-4) z f 3

14 4

15 Spherical Mirrors 5

16 Refraction at Plane Boundaries 6

17 Total Internal Refraction Critical Angle n θ c = sin (.-5) n 7

18 Deviation Angle Prisms θ d = θ α + sin (sinα n sin θ sinθ cosα) (.-6) Thin Prism θd (n ) α (.-7) 8

19 Beam Splitters & Beam Combiners 9

20 Refraction at Spherical Boundaries θ n n n n θ n R n n n n + z z R y = n z y n z y (.-8) (.-9) (.-0) 0

21 φ φ

22 Imaging

23 Thin Lenses θ θ = y f (.-) f z = + ( n z ) = f R R (.-3) (.-) y z = y z (.-4) 3

24 4 Thin Lenses y R n n n n n θ θ (.-8) f y = θ θ = ) ( R R n f f z z = + (.-) (.-) (.-3)

25 Thick Lens (Non-paraxial rays) - Cannot assume same y when the ray enters and leaves the lens 5

26 Light Guides 6

27 Numerical Aperture of an Optical Fiber NA = sinθ a = n n (.-5) 7

$large refractive index$ to be extracted in to

28 It is difficult for light originating inside a medium of large refractive index to be extracted in to air. (e.g. LED etc.) Trapping of light 8

29 Fermat s Principle Simple components ABCD matrix 9

30 Matrix Optics y = Ay + θ B θ = Cy + D θ (.4-) (.4-) 30

31 Ray Matrix (ABCD Matrix) y θ = A C B y D θ 3

$4-3) 0 Refracting at a planar$

32 Ray Matrices of Simple Optical Components Free-Space Propagation d M = (.4-3) 0 Refracting at a planar boundary M = 0 0 n n (.4-4) 3

33 33 Ray Matrices of Simple Optical Components Refracting at a spherical boundary = ) ( 0 n n R n n n M (.4-5) = 0 f M Transmission through a thin lens (.4-6)

34 Ray Matrices of Simple Optical Components Reflection from a planar mirror 0 M = (.4-7) 0 Reflection from a spherical mirror M = R 0 (.4-8) 34

35 Matrices of Cascaded Optical Components M M M 3... M N M = M M (.4-9) N 3M M N d i M = i= n (.4-0) i 0 35

36 Matrices of Cascaded Optical Components M = f d d f (.4-) 36

37 37 Imaging with a Thick Lens f s s or f z z = = + (.4-) f z s h d z f z s h d z = + = = + = nr fd n h ( ) = = R d n n R n f ) ( where (.4-6) (.4-5) (.4-4) (.4-3)

38 Periodic Optical Systems ym θ m y A = C B D m+ = bym+ m F y0 θ 0 y m θ θ m m+ b y m Aym = + B y m+ Ay = B A + D m+ = F = AD BC = det [ M ] m y m= y0h h bh + F = 0 y m m = y F sin( mϕ + ϕ ) 0 max h = b ± j F b ϕ = cos b F If F = y m = y sin( mϕ + ϕ ) 0 max 38

39 Periodic Optical Systems Stable Condition b A + D or 39

40 Equally Spaced Identical Lenses 0 d 4 f y m ϕ = y sin( mϕ + ϕ0) max cos = d f Case Case d = f d = f 40

41 Equally Spaced Identical Lenses 0 d f d f (.4-33) 4

42 Optical Resonator 4

43 Optical Systems Projector 43

44 LCD 投影機原理 : 穿透式 Light source 鏡片陣列 PBS 陣列分色鏡 LCD Panel 合光稜鏡 Projectror Lens 資料來源 :PC Magazine, 資策會 MIC 999 年 5 月 *PBS:Polarizing Beam Splitter screen 44

45 Microscope Optical Systems 45

46 Optical Systems Telescope 46

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untitled 01 1.. 380~780nm 3. 4. 5. (Long-cone cell) (Red-cone cell) (Medium-cone cell) (Green-cone cell) (Short-cone cell) (Blue-cone cell) 6. 7. 8. 1 9. 10. c= f λ hc E = hf = λ c n = v (Snell s law) n1(sin θ1)