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Discrete optics v.s. Integrated optics

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Presentation on theme: "Discrete optics v.s. Integrated optics"— Presentation transcript:

1 Discrete optics v.s. Integrated optics
Mirrors, lens, mechanical mounts bulky labor intensive alignment ray optics environment sensitive Waveguide Bendable, portable Free-of-alignment wave optics robust more functionalities

2 Discrete optics v.s. Integrated optics
Applications of Integrated optics: Transmitters and receivers, transceivers All optical signal processing Ultra-high speed communications (100Gbit/s), optical packet switching RF spectrum analyzer Smart sensors OEIC, bio/sensor Optical transceivers

3 Optical waveguides 2-D Optical waveguide x Core, refractive index n1 Cladding, n2 z y n2 < n1 d 1 n2 n1 n0 = 1 0 90º-1 n0*sin(0) = n1*sin(1) Numerical aperture (NA) Critical angle n1*sin(90º-1)=n2*sin(90º) cos(1)=n2/n1

4 : total acceptance angle
Optical waveguides 2-D Optical waveguide : total acceptance angle

5 Optical waveguides Example 2: Calculate the acceptance angle of a core layer with index of n1= 1.468, and cladding layer of n0 = for wavelength of 1.3m and 1.55 m. Solution: acceptance angle: Wavelength independent:

6 Reflections at the interface
Fresnel equations n2 < n1 x z E1s E3s y z 1 1 y 1 1 n1 n1 2 n2 2 E2s n2 s-polarized beam (senkrecht: perpendicular) p-polarized beam (parallel) Trans-electric beam (TE) Trans-magnetic beam (TM)

7 Reflections at the interface
Fresnel equations n2 < n1 x z E1s E3s y z 1 1 y 1 1 n1 n1 2 n2 2 E2s n2 Poynting vector, energy flow rate

8 Reflections at the interface
Phase shift of reflection n2 < n1 x E1s E3s z y 1 1 n1 n2 2 E2s when i.e. because In this case, is a real number The reflection is not associated with phase shift, or phase shift is 0

9 Reflections at the interface
Phase shift of reflection n2 < n1 E1s x E3s z 1 1 y n1 n2 2 E2s when i.e. c 1

10 Reflections at the interface
Evanescent wave n2 < n1 x E1s E3s z y 1 1 n1 Momentum conservation n2 2 E2s Attenuated wave, penetration depth: d

11 Ray optics approach Optical modes C A 1 1 1 2 d 1 B k*n1*AC – k*n1*AB = 2m AC = AB*cos(21) AB = d/sin(1)

12 Ray optics approach Optical modes C A 1 1 1 2 d 1 B Propagation constant Effective index:

13 Ray optics approach Optical modes, considering phase shift at reflection C A 1 1 1 2 d 1 B k*n1*AC – k*n1*AB + 2* = 2m AC = AB*cos(21) AB = d/sin(1)

14 V number, normalized thickness, or normalized frequency
Ray optics approach Optical modes C A 1 1 1 2 d 1 B V number, normalized thickness, or normalized frequency Cut-off wavelength :

15 Example: estimate the number of modes
Ray optics approach Optical modes Example: estimate the number of modes waveguide thickness 100m, free-space wavelength 1m, 49 modes

16 Normalized waveguide equation:
Ray optics approach Normalized waveguide equation: b: normalized propagation constant

17 Ray optics approach Discussion: Attenuated wave, penetration depth: D

18 mode numbers v.s. index difference and wavelength
Ray optics approach Discussions: mode numbers v.s. index difference and wavelength effective index difference of higher and lower order modes mode profiles dependence on index difference and wavelength Example 1: Calculate the thickness of a core layer with index of n1= 1.468, and cladding layer of n0 = 1.447 for wavelength of 1.3m. Solution: For single mode:

19 Normalized waveguide equation:
Ray optics approach Normalized waveguide equation: V = 3.3 b

20 Ray optics approach Asymmetric waveguide n2 n1 n0 = 1 n3

21 Wave optics approach Maxwell equations: Dielectric materials Maxwell equations in dielectric materials: phasor

22 Wave optics approach Helmholtz Equation: Free-space solutions 2-D Optical waveguide x Core, refractive index n1 Cladding, n2 z y n2 < n1 d TM mode: TE mode:

23 Wave optics approach Core, refractive index n1 Cladding, n2 z y n2 < n1 d III n2 x d x y I n1 II n2

24 Wave optics approach III n2 x d x y I n1 II n2

25 Wave optics approach III n2 x d x y I n1 II n2

26 Wave optics approach III n2 x d x y I n1 II n2

27 Wave optics approach III n2 x d x y I n1 II n2

28 Wave optics approach III n2 x d x y I n1 II n2

29 Wave optics approach Graphic solution

30 Dispersion Dispersion Time delay

31 Example --- material dispersion
Calculate the material dispersion effect for LED with line width of 100nm and a laser with a line width of 2nm for a fiber with dispersion coefficient of Dm = 22pskm-1nm-1 at 1310nm. Solution: for the LED for the Laser

32 Example --- waveguide dispersion
n2 = 1.48, and delta n = 0.2 percent. Calculate Dw at 1310nm. Solution: for V between 1.5 – 2.5.

33 Waveguide mode dispersion
Higher order mode, Lower order mode,

34 chromatic dispersion (material plus waveduide dispersion)
material dispersion is determined by the material composition of a fiber. waveguide dispersion is determined by the waveguide index profile of a fiber

35 Dispersion induced limitations
For RZ bit With no intersymbol interference For NRZ bit With no intersymbol interference

36 Dispersion induced limitations
Optical and Electrical Bandwidth Bandwidth length product

37 Dispersion induced limitations
Example --- bit rate and bandwidth Calculate the bandwidth and length product for an optical fiber with chromatic dispersion coefficient 8pskm-1nm-1 and optical bandwidth for 10km of this kind of fiber and linewidth of 2nm. Solution: Fiber limiting factor absorption or dispersion?


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