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?